Designing High Performance Devices in Silicon Using Subwavelength

In recent years many research efforts have been devoted to the study and exploitation of nonlinear optical phenomena in silicon photonic integrated circuits (PICs) at infrared (IR) frequencies (1,2) for applications in all-optical signal processing, (3) spectroscopy (4) and quantum optics. (5,6) In this context, second-order nonlinear optics is essential for many classical and quantum applications, from high-speed optical modulation via the Pockels effect (7) to f–2f frequency-comb self-referencing, (8) and even to direct frequency-comb generation by cascaded SHG events that can mimic third-order nonlinear effects. (9) Bulk Si and Ge are compatible with PIC foundry processes, (10,11) however, they feature vanishing second-order susceptibility χ⁽²⁾ due to their centrosymmetric unit cell. Several approaches have then been proposed to achieve second-order nonlinearities in silicon PICs: Electric field bias can induce nonlinearity in periodically poled silicon-on-insulator (SOI) waveguides, however, with a rather small χ⁽²⁾ = 0.64 pm/V; (12) SHG has been observed in Si₃N₄ waveguides on SiO_x featuring χ⁽²⁾ = 2.5 pm/V, (13) and more recently in microresonators. (14) The transparency range of both SOI and Si₃N₄ waveguides is, however, limited to wavelengths λ < 4 μm as a result of the strong phonon absorption of SiO_x. (15−17) Proposed unconventional approaches to generate optical nonlinearity in bulk Si include nanostructures with strain gradients, (18) which are difficult to realize in a controlled manner, multiphoton absorption by impurities in Si, (19−21) which is, however, limited to the far-IR, and nonlinear free-electron plasma oscillations in heavily doped Si or Ge, (22) which are accompanied by high ohmic losses. A different solution for second-order nonlinearity in Si PICs is here provided by asymmetric-coupled quantum wells (ACQWs) made of SiGe epitaxial layers grown on Si substrates (Figure 1a). ACQWs are a type of semiconductor heterostructure based on two quantum wells of different thicknesses and/or compositions, separated by a thin tunneling barrier (Figure 1b). Electrons or holes confined into the ACQW planes (the epitaxial growth direction being normal to those planes) populate quantized levels arranged in discrete subbands, that is, "copies" of either the valence or the conduction band separated by the differences in quantization energy E _i (Figure 1c). In ACQWs, either holes or electrons provide the dipole strength for the nonlinear interaction of the material with the laser pump through their intersubband transitions (ISBTs). (23,24) The ACQW subband structure can be specifically designed for resonant enhancement of certain nonlinear effects (here, SHG) and they can behave as artificial nonlinear materials with high efficiency. (25−27) It is important to notice that the ACQW second-order nonlinearity is purely based on the electron wave functions being asymmetrically delocalized in the two coupled wells and not on the crystal lattice asymmetry, as in natural nonlinear materials. Then, the Miller's rule, a phenomenological argument for estimating nonlinear susceptibilities based on the value of the crystal lattice parameter does not hold for ACQWs, (23,24) releasing the physical limit setting the value of χ⁽²⁾ in the range of 10 pm/V for all existing natural nonlinear crystals. (5) One can then quantum-design the ACQW wave functions and obtain a giant χ⁽²⁾ for SHG up to 10⁵ pm/V, (25−28) exploiting the key fact that, in an ideal ISBT, the joint optical density of states is a Dirac delta function, because all initial and final subband states have exactly the same energy distance, unlike in a conventional interband transition. The design criterion for SHG in ACQWs is that the ISBT energies hν₁₂ and hν₂₃ (where hν_ij is the energy of the ISBT between i and j, hereafter indicated as i → j) should both be in resonance with the pump photon energy hν_pump or hν₁₂ ≅ hν ₂₃ ≅ hν _pump. Setting the z axis parallel to the carrier confinement direction (i.e., orthogonal to the QW growth plane), the χ_zzz ⁽²⁾ (2v) element of the second-order susceptibility tensor can be conveniently approximated, assuming parabolic subband dispersion, by the following expression: (23) (1) where N _i is the 3D population density of subband i, z _ij is the vertically oriented dipole moments of i → j, and g is the intrinsic line width assumed identical for all ISBTs. N _i is calculated as the 2D free carrier density divided by the total ACQW heterostructure period. In symmetric systems where parity is a good quantum number, z ₃₁ = 0 because z is an odd operator, and therefore, SHG is forbidden according to eq 1. This selection rule is broken for asymmetric systems like ACQWs. (23,24) In the ideal case of parabolic subband dispersion, ν_ij does not depend on the in-plane crystal momentum k _∥ and the SHG doubly resonant condition is obtained at the same ν_pump for all electrons (or holes) populating the involved subbands, while in real cases one has to integrate over k _∥ in the entire 2D Brillouin zone and the SHG resonance spectrum can broaden considerably. (28) Not only the ACQW structure breaks the inversion symmetry as required for SHG, but it also provides the freedom of wave function design to achieve doubly resonant second-order electromagnetic interaction. (24) In addition, the doping level sets the strength of the nonlinearity. The doping can be introduced by chemical substitution (in this work B for Ge and Si) or it can be modulated at the picosecond time scale with a near-IR optical pump. (29)

Figure 1. (a) Schematic of sample A showing the different epitaxial block thickness and composition: buffer, virtual substrate, and ACQW stack repeated 20 times. (b) Valence band-edge profiles of sample A forming the main and secondary wells (thick lines, HH: heavy holes; LH: light holes; SO: split-off band) and the subband wave functions (thin lines; for holes, wells correspond to band-edge potential maxima and transitions are downward in energy). (c) In-plane dispersion of the hole states in the first Brillouin zone around the Γ point as a function of the in-plane wavevector k _||. (d) Calculated second-order nonlinear susceptibility χ⁽²⁾ _zzz for one single heterostructure period as a function of the pump photon energy and frequency. Impurity transitions are not included in our model.

SHG has been systematically observed in the mid-IR from ACQWs (23,25,26) made of III–V compound semiconductor materials and, in a pioneering work, also from Si-rich SiGe ACQWs. (30) Attempts to reach PIC-standard wavelengths in the near-IR with intersubband transitions have been done using high band offset semiconductor pairs (31) and metal–dielectric heterostructures. (32) Recently, SHG efficiency enhancements of 3 orders of magnitude have been reported in III–V compound ACQWs using plasmonic nanoantennas (26,33) and diffraction grating couplers (27) for electric field enhancement; however, the integration of ACQW nonlinearity into silicon PICs has never been targeted before. In this work, we demonstrate SHG in Ge-rich SiGe ACQWs grown on Si substrates (as shown in Figure 1a) using silicon-foundry-compatible processes. The epitaxial deposition of Ge-rich SiGe heterostructures on silicon has undergone an impressive development in the past decade driven by the envisioned applications in telecom and datacom. Optical modulators based on Ge/SiGe multiple quantum wells have been reported (34−36) and Ge/SiGe quantum cascade lasers are under investigation. (37,38) In the case of nonlinear PICs, the use of Ge-rich heterostructures will be necessary to realize integrated rib or ridge waveguides, which is a requirement to obtain long interaction regions for efficient SHG in PICs without having to use very high pump power densities. Indeed, Ge/SiGe epitaxial layers forming the ACQWs (refractive index n close to 4.0) can be etched to form the waveguide core on top of the Si substrate (n = 3.4), operating as the waveguide cladding together with the air or the dielectric environment, an ideal configuration for on-chip mid-IR spectroscopy applications. (39−42)

The interband transition edge of Ge in the near-IR at 0.66 eV together with its high transparency region extending to λ < 15 μm, make it the ideal material for mid-IR PICs, whereas intrinsic absorption losses limit waveguiding in pure Si to λ < 8 μm. (43−45) Here, we aimed at demonstrating the nonlinear Ge/SiGe ACQW operation in a broad mid-IR wavelength range: laser pump wavelengths were selected in the 12 to 9.2 μm range (SHG wavelengths from 6.0 down to 4.6 μm). We leverage on hole-doped rather than electron-doped structures in order to exploit the larger valence band offsets up to 0.5 eV. It is worth noticing that ISBTs in hole-doped materials, at odds with more common electron-doped ACQWs, also feature nonvanishing in-plane components of the optical transition dipoles connecting the heavy hole (HH), light hole (LH), and split-off (SO) valence bands. Consequently, one could achieve also large off-diagonal tensor components χ_xzl ⁽²⁾ (2v) with l = x, y, or z thus opening interesting opportunities to realize polarization mixing in nonlinear phenomena. (46,28) In this work, however, we have designed and investigated samples with an epitaxial structure specifically optimized for SHG featuring three energy levels E ₁, E ₂, and E ₃ belonging to the HH band (well/barrier thickness 2.4/1.0/2.7/3.9 nm, and Ge content x _Ge = 0.76/0.67/0.93/0.52, see Figure 1). The levels are equally spaced: hν₁₂ = hν₂₃. Sample design parameters are reported in Table 1: if compared to the ideal case of sample A, sample B has half the doping level, sample C has its E ₃ purposely offset from double SHG resonance (hν₁₂ ≠ hν₂₃), which was obtained by varying the main well width only, and sample D is undoped. Samples B–D are used for comparison to define the performance of the ideal sample A, whose predicted χ_zzz ⁽²⁾ (2v) is reported in Figure 1d (other tensor components χ_zjk ⁽²⁾ (2v) are reported in Supporting Information, a).

Table 1. Summary of Design and Measured Parameters of the Four Samples

Experimental Results

The samples have been grown by low-energy plasma-enhanced chemical vapor deposition (LEPE-CVD) (47) on Si(001) wafers, a standard for PICs (see Supporting Information, b). The superlattice consists of 20 periods of the ACQW stack shown in Figure 1a. Such low number of ACQW repetitions has been chosen to optimize the linear dichroism effect of ISBTs in IR transmission spectroscopy, (38) but it should be pointed out that the growth procedure can be straightforwardly extended to deposit hundreds of ACQW periods (48) required to fill the ridge height >2 μm of a mid-IR integrated waveguide (43)

A Si-rich buffer layer is deposited at the interface with the Si substrate to reduce the lattice mismatch (hence, the threading dislocation formation at the initial stage of the relaxation). (49) A Ge-rich layer is then deposited to serve as a virtual substrate for the growth of ACQWs. High resolution X-ray diffraction (HR-XRD) has been used to measure the Ge content, the strain and the in-plane lattice parameters for all samples. A clear superlattice period is observed indicating regular periodicity of the ACQW structure (Figure 2a,b, see Methods). The scanning transmission electron microscopy (STEM) image in Figure 2c,e shows ACQWs with sharp interfaces arranged in identical subsequent periods along the growth direction z. The corresponding energy-dispersive X-ray emission spectroscopy (EDS) data (red marks in Figure 2f) confirm the different Ge content in the two wells obtained by fitting the HR-XRD data (blue curve in Figure 2f), which is crucial to break the inversion symmetry for SHG.

Figure 2. (a, b) HR-XRD reciprocal space maps of sample A with respect to the (224) and (004) Si reflections. (c) STEM images of a different piece of sample A. (d) ω–2θ scan of the Si(004) reflection (red) together with Darwin model simulations (blue) performed to extract the Ge composition of each layer and the intermixing depth. (e) High-resolution STEM, greyscale intensity is proportional to local Ge content. (f) Ge content profile of sample A retrieved from HR-XRD measurements (blue curve) and by EDS measurements (red dots).

Ge/SiGe heterostructures with narrow wells, abrupt interfaces and high compositional mismatches between adjacent layers pose significant challenges in terms of epitaxial deposition. To this aim, one has to consider that, unlike III–V semiconductors, Si and Ge are completely miscible over the entire compositional range. As a consequence, the realization of atomically sharp interfaces is hindered by entropic intermixing of Si into pure Ge layers and Ge into SiGe layers. Therefore, the pure Ge/SiGe heterostructures proposed in ref (28) could not be grown, because the actual compositional profile is smoothed out by intermixing and, in the case of the main well, also by the presence of residual SiH₄ gas in the CVD reactor. The resulting ACQW potential profile of sample A shown in Figure 1b represents the best possible compromise, with hν₁₂ = hν₂₃ = 105 meV and a doubly resonant giant χ_zzz ⁽²⁾ up to 3 × 10⁴ pm/V, as seen in the calculation of Figure 1d, in which the subband energy separation dependence on k _∥ has been taken into account in order to compute χ_zzz ⁽²⁾ (2v) by integrating over the crystal momentum in the entire 2D Brillouin zone. Although the pure Ge/SiGe heterostructure design proposed in ref (28) had hν₁₂ = hν₂₃ = 120 meV and χ_zzz ⁽²⁾ up to 1 × 10⁵ pm/V, (28) the presently expected values of χ_zzz ⁽²⁾ are still 3 orders of magnitude higher than those of typical nonlinear crystals; however, the total SHG emitted power can be comparable because the interaction length in bulk crystals can be generally made longer than it is in heterostructures and absorption losses are generally much lower.

The linear absorption by ISBTs in the doped samples A, B, and C was measured by Fourier Transform Infrared spectroscopy (FTIR) in linear dichroism mode to filter out the substrate contributions, with the samples prepared in the prism-shaped slab-waveguide configuration, as sketched in Figure 3a, where the TM polarization senses the ISBTs with a dipole along z and the TE polarization is used for an internal reference. In the dichroic absorption spectra of Figure 3b,d, one can observe that all samples display two ISBT peaks of similar intensity: the low frequency peak around 32 THz is naturally assigned to 1 → 2, and the high frequency peak (58 THz in samples A and B and 53 THz in C) to 1 → 3. Note that sample C was intentionally detuned by design from the double resonance condition, but also in samples A and B the perfect double resonance condition hν₁₃ = 2hν ₁₂ is only approximately realized. The best-fit Lorentzian frequencies ν_ij, oscillator strengths f _ij, and half-line widths γ_ij of the absorption peaks are reported in Supporting Information, c.

Figure 3. Linear dichroic absorption spectroscopy of the doped ACQW samples A, B, and C. (a) Sketch of the surface-plasmon waveguide structure with prism-shaped slab geometry. The electric field polarization in the illuminated ACQW region is mostly vertical (TM-mode transmitted intensity I _TM), while the TE-mode transmitted intensity I _TE serves as spectral reference. (b) Dichroic absorption −ln(I _TM/I _TE) from the theoretical model of sample A (magenta curve, the main ISBT transitions are marked) and from the experiments at T = 10 K. (c, d) Enlarged view of the curves in panel b at T = 10 K (thick lines). Data at T = 300 K are also reported (thin lines). Note that the horizontal scale of panels c,d is exactly double of that of panel b to highlight SHG resonance in samples A and B. The vertical dashed gray line marks the QCL pump frequency of 29.3 THz in panels c and d and its double (58.6 THz) in panel b. The QCL pump photon energy is 120 meV to compare with Figure 1d.

The main effect of heating the samples to 300 K is the notable broadening of the ISBT line widths, as shown in Figure 3d. At room temperature, due to thermal excitation, carriers are spread in the k space around the Γ point, hence, the nonparabolicity of the subbands produces a nontrivial dependence of the ν_ij values on k _∥, which is the main factor contributing to the broadening of the line widths. This effect is also responsible for the temperature-induced redshift of the 1 → 3 absorption peak. In fact, the population of the fundamental subband at larger k _∥ due to thermal excitation activates different 1 → 3 transitions featuring lower photon energies, as it can be argued from the nonparabolicity of the band structure shown in Figure 1c. Intrinsic line broadening effects at finite-T are expected to constitute the main limitation to the SHG power that can be obtained from doubly resonant ACQWs.

In Figure 3b,d, the experimental spectra are plotted on two different horizontal scales to highlight SHG resonances, with an indication of the selected pump photon frequency for the experiments described below employing a quantum cascade laser (QCL) pump (samples cooled to 10 K).One can identify by comparing Figure 3b and d, the perfect resonance of 2ν_QCL = 58.6 THz with ν₁₃ of samples A and B. Lastly, we compare in Figure 3c,d the theoretical and experimental dichroic absorption spectra for sample A. The overall spectral shape and the absorption intensities are very well reproduced by our calculations at both T values. The dip at 40 THz is a signature of the TE-polarized ISBT 1 → LH₂, in good agreement with the energy difference of 175 meV observed in Figure 1b. The rigid frequency offset of approximately 7 THz for the two TM-polarized peaks 1 → 2 and 1 → 3 can instead be attributed to the many-body depolarization effect, not included in our calculations (see Methods), which induces a blueshift of the TM-polarized absorption frequencies if compared to the bare bandstructure energy differences in Figure 1b. Note that the values to be inserted in eq 1 are the actual absorption frequencies, not the bare energy differences.

The demonstration of the doubly resonant nonlinearity in Ge/SiGe ACQWs is here provided by experimental comparison of samples A and C at 10 K with different ν₁₃ but otherwise identical relevant parameters: ν₁₂, doping, and number of periods. We used ν_QCL = 29.3 THz ≈ ν₁₃/2 for sample A; however, there is a slight detuning Δ = ν₁₂ – ν_QCL that reduces the pump intensity depletion while traveling through the waveguide: this choice of ν_QCL maximizes the SHG efficiency difference between samples A and C and also the total SHG intensity, as we shall see below.

The experimental setup is sketched in Figure 4a (the waveguide length crossed by the pump radiation beam is approximately 400 μm long, see Methods for details). Using a calculated spot size of 1.3 × 10^–3 cm^–2, we estimate a peak power density at focus for the nonattenuated pump I _QCL,max = 23 W/cm² (see Supporting Information, d). The resulting emitted SHG power P _SHG is plotted in Figure 4b as a function of I _QCL: a square-law relation is fitted to the integrated power data set P _SHG = K ₂ P _QCL ² (see Supporting Information, e). The value of K ₂ in W^1– reported in Table 1 is a measure of the SHG generation efficiency, because it is proportional to the square of χ_zzz ⁽²⁾(v) calculated at ν_pump = 29.3 THz. The resonance of 2ν_pump with 1 → 3 of sample A then explains its highest K ₂. Sample B is also resonant at 1 → 3, but its doping level is almost half of that of sample A, and therefore, its K ₂ is approximately 4× lower than that of sample A. Finally, sample C, in spite of the same doping level as sample A, has the lowest K ₂, apparently because it is not doubly resonant. This interpretation is supported by calculations based on eq 1 (see Supporting Information, d). We note that a maximum dimensionless conversion efficiency P _SHG/P _QCL = 1.5 × 10^–4 at I _QCL,max = 23 W/cm² in sample A is comparable to that found in recent experiments performed with a similar QCL pump on InGaAs/AlInAs ACQWs with comparable number of periods. (26,27)

Figure 4. (a) Scheme of the nonlinear experiment for absolute characterization of SHG efficiency. In the TM mode, the radiation electric field is oriented along the ISBT dipoles of the resonant HH transitions. (b) Measured SHG power vs squared pump power density at focus for samples A, B, and C. Sample D was used as reference to subtract the linear background. Also, the SHG emission disappeared when the sample was shifted by ±1 mm (twice the estimated depth of focus) because the electric field value dropped quickly when the ACQWs were out of focus. This technique was used to subtract the contribution of the residual pump photons to the detector signal. (c) Simplified sketch of the SHG process in the HH valence band. E _F: Fermi level. Note that hole ISBTs 1 → 2 and 2 → 3 are represented by downward arrows.

In order to clearly demonstrate nonlinear emission at room temperature, we pumped the samples with very high peak-power pulses from a nonlinear optical parametric amplifier (NOPA) driving a difference-frequency generation (DFG) setup in Figure 5a. (50) The maximum power density at focus inside the sample I _DFG = 9 × 10⁷ W/cm² is more than 6 orders of magnitude higher than that of the QCL pump. The tunability and the high power of this optical pump permit the investigation of SHG efficiency in the entire frequency range, where eq 1 provides significant values and not only at the peak value, as for the QCL pump. In particular, we used the three DFG pulses in Figure 5b,c with center frequency ν_DFG,1 = 25 THz (ν_pump slightly off resonance), ν_DFG,2 = 29 THz (2ν_pump at resonance with ν₁₃), and ν_DFG,3 = 32 THz (ν_pump at resonance with ν₁₂).

Figure 5. SHG performance with high-intensity ultrashort pulses. (a) Experimental setup based on difference-frequency generation (DFG) and spectrally resolved detection with a mercury–cadmium telluride (MCT) diode. (b, c) Field-time profiles obtained by electro-optic sampling and corresponding FT spectrum of MIR pump pulses employed in the experiment. (d) SHG spectra measured with sample A at different pump frequency and intensity. (e) SHG efficiency of different samples at optimal pumping conditions (i.e., ν_DFG,2 and highest pulse power).

In waveguides containing ACQWs, when pumping at resonance with ν₁₂, the pump intensity is rapidly depleted, ending up in an interaction region shorter than the waveguide length. Therefore, in ACQWs it is generally convenient to pump in exact resonance with ν₁₃/2, instead. This scenario is approximately confirmed by the SHG spectra for sample A: the red dashed line in Figure 5d represents the χ_zzz ⁽²⁾ calculation based on eq 1 (not accounting for pump depletion) using the data of Figure 3 (see Supporting Information, c). This calculation predicts approximately equal SHG efficiencies for ν_DFG,1 and ν_DFG,3, however, the SHG efficiency observed in Figure 5d with the pump tuned at ν_DFG,3 is 3× lower than at ν_DFG,1.

The shaded gray Lorentzian curve represents the effect of the 1 → 2 ISBT in depleting the pump beam, which is obviously stronger at ν_DFG,3; one can also see that even at ν_DFG,2 the ideal SHG efficiency is not reached due to pump depletion. We note that, at these very high pump intensities, 1 → 2 absorption saturation and free carrier heating (i.e., high-k _∥ states occupied by holes in the subband 1, leading to broader effective transition line widths) can also play a role in decreasing the observed SHG efficiency from the ideal value.

Finally, in Figure 5e, the relative efficiency of samples A, B, and C when pumping at ν_DFG,2 ≈ ν_QCL compares very well with that of Figure 4b: sample B is less efficient than sample A, due to lower doping levels, and sample C because it is not doubly resonant. No SHG emission was observed from the undoped sample D.

Discussion

In Figure 6 we plot, for sample A, the emitted SHG peak power versus the peak pump power for both QCL and DFG pumps, in a log–log scale. It can be seen that the slope of the QCL data, corresponding to a quadratic dependence on the input pump power density, is not maintained in the DFG pump power range. An almost linear dependence is observed instead, a fact that we relate to a concurring two-photon absorption (TPA) effect that, at very high pump intensities, becomes a non-negligible competitor of the SHG process. (5) Indeed the presence of the 1 → 3 ISBT at twice the pump frequency makes the TPA effect non-negligible at high pump intensities. In quantum well systems displaying ISBTs, the radiative decay of the excited states (photoluminescence) is negligible if compared to the nonradiative decay; therefore, the emission spectrum only shows SHG. The competition between TPA and SHG sets an ultimate high pump-power limit to SHG efficiency in SiGe ACQWs. The expected transition between a quadratic regime at low pump power to a linear regime at high pump power can be inferred by plotting in Figure 6 a line parallel to the 300 K best-fit line considering the SHG efficiency improvement at 10 K shown in Figure 1d.

Figure 6. Log–log plot of SHG emission power vs pump power density for all QCL and DFG pump experiments performed on sample A. A quadratic slope has been superimposed to the QCL data, and a linear slope to the DFG data. Note that the two experiments have been performed at different sample temperatures. The theoretical DFG line at 10 K is drawn parallel to the 300 K derived from the efficiency improvement, with cooling predicted in Figure 1d.

The experimental value of χ⁽²⁾ to be compared with calculations should then be extracted from the QCL pump experiment using the definition of χ⁽²⁾ = F _2w/ F _w ², with F being the electric field intensity at focus. Using K ₂ of sample A from Table 1 we find χ^(2),exp = 5 × 10⁴ pm/V for one single heterostructure period (see Supporting Information, d). This value compares well with the predicted peak value at 10 K of χ^(2),theo = 3 × 10⁴ pm/V (see Figure 1d), the disagreement being probably related to uncertainty in the detector calibration. Notice that in ACQWs the giant χ⁽²⁾ is counterbalanced by high propagation losses due to strong absorption of both the pump and the SHG signal by the resonant ISBTs. (23−25)

A final consideration is worth phase matching. In nonlinear crystals, the difference in the phase velocity c/n(ν) between pump and second-harmonic defines a maximum length along the waveguide over which the SHG power adds up coherently to that generated in previous positions along the waveguide, thereby imposing an upper limit to the SHG efficiency. In III–V compound semiconductor ACQWs at mid-IR frequencies, the dispersion due to the strong polar optical phonon absorption at around 10 THz limits SHG phase coherence. Instead, in SiGe ACQWs, which feature a nonpolar crystal lattice, the dispersion due to phonons is totally absent. In integrated waveguides, the modes will still have a dispersion due to the varying ratio between λ and the (fixed) geometrical parameters of the waveguides, but in the presently employed slab waveguide, this source of dispersion is negligible. There also exists a residual dispersion generated by the ISBT absorption resonances themselves, but this phenomenon can be neglected in the case of detuning from exact resonances, as for example when pumping the sample A at 25 and 29 THz. Therefore, in most of the present experiments, homogeneous phase matching conditions apply, without having to include specific dispersion–compensation structures. This also indicates that there is considerable room for improvement of the observed SHG power levels by pumping through properly fabricated SiGe ridge waveguides with millimeter-scale lengths.

Conclusion

We have designed, grown, and optically analyzed hole-doped Ge/SiGe asymmetric-coupled quantum wells optimized for second harmonic generation in silicon photonic chips. A giant second-order nonlinearity, 4 orders of magnitude higher than that of any natural nonlinear material, is observed with laser pump wavelengths in the 9.2 to 12 μm range (second harmonic in the 4.6 to 6 μm range), well within the even broader transparency range of existing Ge-rich integrated waveguides that have been developed for on-chip spectroscopic sensing applications. The giant nonlinearity is attributed to the double-resonance effect of the laser pump photon energy and the SHG photon energy with the intersubband transitions among three confined energy levels equally spaced in energy. The absolute nonlinear susceptibility has been determined at low temperatures and found to be in good agreement with wave function calculations. Room-temperature operation with ultrashort pulses has shown that the optimal SHG efficiency is obtained for small red-detuning of the pump photon energy from the double resonance. The material growth technology and the infrared wavelength range employed here are compatible with the standard silicon photonics foundry processes, opening the way to the on-chip integration of second-order optical nonlinearities, to be exploited in future molecular sensing and free-space telecommunication devices.

Methods

Theoretical Calculations

The valence band structure has been calculated relying on a semiempirical tight-binding Hamiltonian model in the first neighbor approximation. (51,52) The adopted basis set includes sp ³ d ⁵σ* orbitals in both spin configurations. Self and hopping energies together with scaling exponents used to account for the strain-induced lattice distortion are reported in refs (53) and (54) for Si and Ge, respectively. In order to properly describe nonparabolicity effects, the linear absorption and second harmonic susceptivity spectra have been calculated performing a 3D sampling of the BZ zone in a neighbor of the G point. Dipole matrix elements have been estimated following the procedure given in ref (51). χ_lmn ⁽²⁾ (2v) has been calculated assuming that holes populate the fundamental subband only following eq 1 of ref (28), which describes both resonant and nonresonant contributions. A Lorentzian line shape with a HWHM of 5 meV has been used to phenomenologically describe the line broadening of the ISBTs.

Sample Growth and Characterization

Samples A–D were grown by low energy plasma-enhanced chemical vapor deposition (LEPECVD) (47) on a 100 mm intrinsic Si(001) substrates with a resistivity >6000 Ω·cm. Before heteroepitaxy, the native oxide was removed by dipping the substrate in aqueous HF solution (HF:H₂O 1:10) for 30 s. The first part of the structure consists of a 1 μm thick Si_0.8Ge_0.2 layer deposited at a rate of 5 nm/s at a temperature of 600 °C. The deposition was followed by an in situ thermal annealing at 700 °C for 30 min in order to promote the full relaxation of the layer. The second part of the structure consists of a 1 μm thick Si_0.3Ge_0.7 deposited at 5 nm/s at 500 °C forming a fully relaxed virtual substrate for the ACQW stack. The ACQW structure has been grown at a rate ∼0.1 nm/s at a temperature of 350 °C to minimize the intermixing, and it consists of 20 repetitions of the following sequence: Si_0.1Ge_0.9 main well/Si_0.4Ge_0.6 tunneling barrier/Si_0.25Ge_0.75 secondary well/Si_0.4Ge_0.6 main barrier. The main well has been p-doped in situ by adding B₂H₆ during the growth. The thickness of the main barrier has been designed to obtain a mean Ge concentration in the ACQW stack equal to the one of the VS. In this way the compressive strain of the wells is compensated by the tensile strain in the barriers, thus, obtaining a strain-symmetrized structure.

A XRD apparatus was used to record the (224) and (004) reciprocal space maps of sample A are shown in Figure 2a and b, respectively. Figure 2c shows the (004) ω–2θ scan of Sample A, together with multibeam dynamical Darwin model simulations, (55,56) as implemented in the software "xrayutilities". (57) This software has been used to retrieve the compositional profile of Figure 2f. A different piece of sample A has been further characterized by STEM and EDS. A JEOL Monochromated ARM200F TEM equipped with a monochromator, probe and image aberration correctors, and double silicon drift detector (SDD) EDS detectors was operated at 200 kV for STEM annular dark field (ADF) imaging and EDS analysis. The beam convergence semiangle used for STEM and EDS analysis was ∼27 mrad. The inner collection semiangle for ADF imaging was set to ∼55 mrad. The electron beam size was estimated to ∼1 Å in diameter. The STEM image (Figure 2c) shows ACQWs with sharp interfaces arranged in identical subsequent periods along the growth direction z.

IR Spectroscopy

A research-grade FTIR spectrometer (Bruker Vertex 70v) was used to collect the TM and TE transmission spectra, equipped with a wideband beamsplitter, a high linearity range MCT detector, a liquid-He flow optical cryostat (Janis Research co.) and a wire-grid lithographic KRS5 polarizer (Specac). The transmitted spectral intensity is measured for both TM and TE polarizations (electric field parallel and orthogonal to z, respectively). The dichroic absorption is calculated as A = −ln(TM/TE), therefore, peaks correspond to z-dipole ISBTs and dip to xy-dipole ISBTs (one dip can be glimpsed at 42 THz in Figure 3c). The narrow γ₁₂ < 4 THz obtained at T = 10 K for all samples confirms the high quality of the heterostructures. At T = 10 K, only the fundamental subband 1 is populated, so the integrated spectral weight Σ_I f _1i provides an estimate of the total hole sheet-density (38) in reasonable agreement with the nominal doping values (one has N ₁ ≈ N _a see Table 1). The spectral weight ratios f ₁₃/f ₁₂ = 0.96 and 0.82 for samples A and B, respectively, are reasonably close to unity, which represents the optimal value for SHG in ACQWs, as explained in ref (58), while we get f ₁₃/f ₁₂ = 1.33 for the purposely detuned sample C.

For the first SHG experiment at 10 K, a monochromatic distributed feedback grating QCL (by Alpes Laser) emitting at λ = 10.3 μm, or ν_QCL = 29.3 THz ≈ ν₁₃/2 was used to pump the SHG emission at T = 10 K, where ISBT line widths are narrowest. ZnSe lenses and wire-grid KRS5 polarizers were employed, together with the same optical cryostat of the FTIR setup. A MCT detector with a bandgap at λ = 8 μm was used to intrinsically reject the signal due to the pump photons, but thermal excitation of the detector by the pump beam could not be avoided. The resulting linear background was subtracted by offsetting the sample position along the optical axis (z-scan technique). The MCT detector and subsequent lock-in amplification chain was calibrated with a second QCL emitting at λ = 5.7 μm. The pump electric field was vertically polarized (TM), so only the tensor component χ⁽²⁾ _zzz was probed. The pump power was progressively attenuated from its maximum peak power P _QCL = 30 mW without varying the polarization direction, using the cross-polarizer technique shown in Figure 4a (see Supporting Information, e). The collimated QCL beam was focused into the cryostat precisely at the center of the slab waveguide so as to maximize F _z in the ACQW layer.

For the second SHG experiment at 300 K, strong multicycle pump pulses were generated as described in, (50) centered at ν_DFG,1 = 25 THz, ν_DFG,2 = 29 THz or ν_DFG,3 = 32 THz, and featuring a Fourier-transform-limited bandwidth Δν _DFG ≈ 2 THz. The radiation exiting the waveguide was spectrally resolved with a mid-IR grating spectrometer in the range of 50–75 THz. Because Δν _DFG values are narrower than the ISBT line widths at T = 300 K, they define the output SHG spectrum bandwidths equal to 2Δν _DFG. Due to the high peak power density at focus up to 9 × 10⁷ W/cm², the carrier temperature T _holes after optical pump absorption is expected to surpass the lattice temperature at 300 K, hence, making cryogenic cooling unessential.

All power values are estimated inside a generic sample, taking into account the reflection losses of 0.31 at the 20° Si-prism facet and, for the QCL experiment, the reflections at the KRS5 cryostat windows and polarizers.

Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.1c01162.

Additional theoretical calculations, experimental details, fitting results, and electron microscopy images of the samples (PDF)

ph1c01162_si_001.pdf (1.68 MB)

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Author Information

- Michele Virgilio - Dipartimento di Fisica "E. Fermi", Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy; Email: [email protected]
- Jacopo Frigerio - L-NESS, Dipartimento di Fisica, Politecnico di Milano, Polo di Como, Via Anzani 42, I-22100 Como, Italy
- Chiara Ciano - Dipartimento di Scienze, Università di Roma Tre, Viale Marconi 446, I-00146 Rome, Italy
- Joel Kuttruff - Department of Physics and Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany
- Andrea Mancini - Nanoinstitute Munich, Königinstrasse 10, Ludwig-Maximilians-Universität, D-80539 Munich, Germany; Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Rome, Italy; https://orcid.org/0000-0001-5927-9032
- Andrea Ballabio - L-NESS, Dipartimento di Fisica, Politecnico di Milano, Polo di Como, Via Anzani 42, I-22100 Como, Italy; https://orcid.org/0000-0002-2957-8717
- Daniel Chrastina - L-NESS, Dipartimento di Fisica, Politecnico di Milano, Polo di Como, Via Anzani 42, I-22100 Como, Italy
- Virginia Falcone - L-NESS, Dipartimento di Fisica, Politecnico di Milano, Polo di Como, Via Anzani 42, I-22100 Como, Italy
- Leonetta Baldassarre - Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Rome, Italy; https://orcid.org/0000-0003-2217-0564
- Jonas Allerbeck - Department of Physics and Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany; Faculté des Sciences, de la Technologie et de la Communication, Université de Luxembourg, Luxembourg L-1511, Luxembourg
- Daniele Brida - Faculté des Sciences, de la Technologie et de la Communication, Université de Luxembourg, Luxembourg L-1511, Luxembourg
- Lunjie Zeng - Department of Physics, Chalmers University of Technology, Fysikgränd 3, 412 96 Gothenburg, Sweden; https://orcid.org/0000-0002-4564-7217
- Eva Olsson - Department of Physics, Chalmers University of Technology, Fysikgränd 3, 412 96 Gothenburg, Sweden; https://orcid.org/0000-0002-3791-9569
These authors contributed equally to this work. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.
The research leading to these results has received funding from the Italian Ministry of Education, University, and Research (MIUR), PRIN Project ID 2017Z8TS5B. This project has received funding from the European Union's Horizon 2020 Research and Innovation Program under Grant Agreement Nos. 823717-ESTEEM3 and 766955-microSPIRE. This work has been supported by Fondazione Cariplo, Grant No. 2020–4427, by the LazioInnova project "TeraLaser", Grant No. A0375-2020-36579 and by Sapienza University of Rome, Grant No. PH11715C7E435F41.
The authors declare no competing financial interest.

ABBREVIATIONS

PIC	photonic integrated circuit
ACQW	asymmetric coupled quantum wells
SHG	second harmonic generation
ISBT	intersub-band transition
QCL	quantum cascade laser
DFG	difference frequency generation
FTIR	Fourier-transform IR spectroscopy
MCT	mercury–cadmium–telluride alloy
TM/TE	transverse magnetic/transverse electric

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The mid-infrared spectral range (λ~2-20 μm) is of particular importance as many molecules exhibit strong vibrational fingerprints in this region. Optical frequency combs--broadband optical sources consisting of equally spaced and mutually coherent sharp lines--are creating new opportunities for advanced spectroscopy. Here we demonstrate a novel approach to create mid-infrared optical frequency combs via four-wave mixing in a continuous-wave pumped ultra-high Q crystalline microresonator made of magnesium fluoride. Careful choice of the resonator material and design made it possible to generate a broadband, low-phase noise Kerr comb at λ=2.5 μm spanning 200 nm (≈10 THz) with a line spacing of 100 GHz. With its distinguishing features of compactness, efficient conversion, large mode spacing and high power per comb line, this novel frequency comb source holds promise for new approaches to molecular spectroscopy and is suitable to be extended further into the mid-infrared.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC3s3nvVWjtg%253D%253D&md5=00d588795f3beb9ffe9208130cb8303b
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Gaeta, A. L. ; Lipson, M. ; Kippenberg, T. J. Photonic-chip-based frequency combs. Nat. Photonics 2019, 13 , 158– 169, DOI: 10.1038/s41566-019-0358-x

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17

Photonic-chip-based frequency combs

Gaeta, Alexander L.; Lipson, Michal; Kippenberg, Tobias J.

Nature Photonics (2019), 13 (3), 158-169CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)

A Review. Recent developments in chip-based nonlinear photonics offer the tantalizing prospect of realizing many applications that can use optical frequency comb devices that have form factors smaller than 1 cm3 and that require less than 1 W of power. A key feature that enables such technol. is the tight confinement of light due to the high refractive index contrast between the core and the cladding. This simultaneously produces high optical nonlinearities and allows for dispersion engineering to realize and phase match parametric nonlinear processes with laser-pointer powers across large spectral bandwidths. In this Review, we summarize the developments, applications and underlying physics of optical frequency comb generation in photonic-chip waveguides via supercontinuum generation and in microresonators via Kerr-comb generation that enable comb technol. from the near-UV to the mid-IR regime.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXnsleqtLs%253D&md5=ef5542fcca8e02024357b2f4f3fd7c53
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Makarov, S. V. ; Petrov, M. I. ; Zywietz, U. ; Milichko, V. ; Zuev, D. ; Lopanitsyna, N. ; Kuksin, A. ; Mukhin, I. ; Zograf, G. ; Ubyivovk, E. ; Smirnova, D. A. ; Starikov, S. ; Chichkov, B. N. ; Kivshar, Y. S. Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles. Nano Lett. 2017, 17 , 3047– 3053, DOI: 10.1021/acs.nanolett.7b00392

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Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles

Makarov, Sergey V.; Petrov, Mihail I.; Zywietz, Urs; Milichko, Valentin; Zuev, Dmitry; Lopanitsyna, Natalia; Kuksin, Alexey; Mukhin, Ivan; Zograf, George; Ubyivovk, Evgeniy; Smirnova, Daria A.; Starikov, Sergey; Chichkov, Boris N.; Kivshar, Yuri S.

Nano Letters (2017), 17 (5), 3047-3053CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)

Exptl. and theor., resonantly excited nanocryst. Si nanoparticles fabricated by an optimized laser printing technique can exhibit strong 2nd-harmonic generation (SHG) effects was demonstrated. An unexpectedly high yield of the nonlinear conversion is attributed to a nanocryst. structure of nanoparticles supporting the Mie resonances. The demonstrated efficient SHG at green light from a single Si nanoparticle is 2 orders of magnitude higher than that from unstructured Si films. This efficiency is significantly higher than that of many plasmonic nanostructures and small Si nanoparticles in the visible range, and it can be useful for a design of nonlinear nanoantennas and Si-based integrated light sources.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXmtFCksr4%253D&md5=0a66e56fddf545bfed041be31ccacf08
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van Loon, M. A. W. ; Stavrias, N. ; Le, N. H. ; Litvinenko, K. L. ; Greenland, P. T. ; Pidgeon, C. R. ; Saeedi, K. ; Redlich, B. ; Aeppli, G. ; Murdin, B. N. Giant multiphoton absorption for THz resonances in silicon hydrogenic donors. Nat. Photonics 2018, 12 , 179, DOI: 10.1038/s41566-018-0111-x

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Giant multiphoton absorption for THz resonances in silicon hydrogenic donors

van Loon, M. A. W.; Stavrias, N.; Le, Nguyen H.; Litvinenko, K. L.; Greenland, P. T.; Pidgeon, C. R.; Saeedi, K.; Redlich, B.; Aeppli, G.; Murdin, B. N.

Nature Photonics (2018), 12 (3), 179-184CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)

The absorption of multiple photons when there is no resonant intermediate state is a well-known nonlinear process in at. vapors, dyes and semiconductors. The N-photon absorption (NPA) rate for donors in semiconductors scales proportionally from hydrogenic atoms in vacuum with the dielec. const. and inversely with the effective mass, factors that carry exponents 6N and 4N, resp., suggesting that extremely large enhancements are possible. We obsd. 1PA, 2PA and 3PA in Si:P with a terahertz free-electron laser. The 2PA coeff. for 1s-2s at 4.25 THz was 400,000,000 GM (=4 × 10-42 cm4 s), many orders of magnitude larger than is available in other systems. Such high cross-sections allow us to enter a regime where the NPA cross-section exceeds that of 1PA-i.e., when the intensity approaches the binding energy per Bohr radius squared divided by the uncertainty time (only 3.84 MW cm-2 in silicon)-and will enable new kinds of terahertz quantum control.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjsFWls7w%253D&md5=ef8500321bc20370a753d819447e19bb
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Le, N. H. ; Lanskii, G. V. ; Aeppli, G. ; Murdin, B. N. Giant non-linear susceptibility of hydrogenic donors in silicon and germanium. Light: Sci. Appl. 2019, 8 , 64, DOI: 10.1038/s41377-019-0174-6

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Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Le Nguyen H; Murdin Benedict N; Lanskii Grigory V; Aeppli Gabriel; Aeppli Gabriel; Aeppli Gabriel

Light, science & applications (2019), 8 (), 64 ISSN:.

Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals. Here, we derive the equivalent technique for hydrogenic impurities in multi-valley semiconductors. While the absorption has useful applications, it is primarily a loss process; conversely, the non-linear susceptibility is a crucial parameter for active photonic devices. For Si:P, we predict the hyperpolarizability ranges from χ((3))/n3D = 2.9 to 580 × 10(-38) m(5)/V(2) depending on the frequency, even while avoiding resonance. Using samples of a reasonable density, n3D, and thickness, L, to produce third-harmonic generation at 9 THz, a frequency that is difficult to produce with existing solid-state sources, we predict that χ((3)) should exceed that of bulk InSb and χ((3))L should exceed that of graphene and resonantly enhanced quantum wells.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3MjhtVyrtQ%253D%253D&md5=f25d5330650c955a2ec130e64cae9252
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Meng, F. ; Thomson, M. D. ; ul-Islam, Q. ; Klug, B. ; Pashkin, A. ; Schneider, H. ; Roskos, H. G. Intracavity third-harmonic generation in Si:B pumped by intense terahertz pulses. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 102 , 075205, DOI: 10.1103/PhysRevB.102.075205
22

Fischer, M. ; Riede, A. ; Gallacher, K. ; Frigerio, J. ; Pellegrini, G. ; Ortolani, M. ; Paul, D. J. ; Isella, G. ; Leitenstorfer, A. ; Biagioni, P. ; Brida, D. Plasmonic mid-infrared third harmonic generation in germanium nanoantennas. Light: Sci. Appl. 2018, 7 , 106, DOI: 10.1038/s41377-018-0108-8

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22

Plasmonic mid-infrared third harmonic generation in germanium nanoantennas

Fischer, Marco P.; Riede, Aaron; Gallacher, Kevin; Frigerio, Jacopo; Pellegrini, Giovanni; Ortolani, Michele; Paul, Douglas J.; Isella, Giovanni; Leitenstorfer, Alfred; Biagioni, Paolo; Brida, Daniele

Light: Science & Applications (2018), 7 (1), 106CODEN: LSAIAZ; ISSN:2047-7538. (Nature Research)

We demonstrate third harmonic generation in plasmonic antennas consisting of highly doped germanium grown on silicon substrates and designed to be resonant in the mid-IR frequency range that is inaccessible with conventional nonlinear plasmonic materials. Owing to the near-field enhancement, the result is an ultrafast, subdiffraction, coherent light source with a wavelength tunable between 3 and 5μm, and ideally overlapping with the fingerprint region of mol. vibrations. To observe the nonlinearity in this challenging spectral window, a high-power femtosecond laser system equipped with parametric frequency conversion in combination with an all-reflective confocal microscope setup is employed. We demonstrate spatially resolved maps of the linear scattering cross section and the nonlinear emission of single isolated antenna structures. A clear third-order power dependence as well as mid-IR emission spectra prove the nonlinear nature of the light emission. Simulations support the obsd. resonance length of the double-rod antenna and demonstrate that the field enhancement inside the antenna material is responsible for the nonlinear frequency mixing.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVygsbbE&md5=5861ae5b57080c73a387d849163cd4f6
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Rosencher, E. ; Fiore, A. ; Vinter, B. ; Berger, V. ; Bois, Ph ; Nagle, J. Quantum engineering of optical nonlinearities. Science 1996, 271 , 168– 173, DOI: 10.1126/science.271.5246.168

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Quantum engineering of optical nonlinearities

Rosencher, E.; Fiore, A.; Vinter, B.; Berger, V.; Bois, Ph.; Nagle, J.

Science (Washington, D. C.) (1996), 271 (5246), 168-73CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)

Second-order optical nonlinearities in materials are of paramount importance for optical wavelength conversion techniques, which are the basis of new high-resoln. spectroscopic tools. Semiconductor technol. now makes it possible to design and fabricate artificially asym. quantum structure sin which optical nonlinearities can be calcd. and optimized from 1st principles. Extremely large 2nd-order susceptibilities can be obtained in these asym. quantum wells. Also, properties such as double resonance enhancement or elec. field control will open the way to new devices, such as fully solid-state optical parametric oscillators. A review with 40 refs.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XktFOlsA%253D%253D&md5=b9ebdc095bd0dd07625beb01c0fe2d41
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Sirtori, C.; Capasso, F.; Sivco, D. L.; Cho, A. Y. Nonlinear optics in coupled-quantum-well quasi-molecules. Semiconductors and Semimetals; Elsevier, 1999; Vol 66, Ch. 2, pp 85– 125.
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Vodopyanov, K. L. ; O'Neill, K. ; Serapiglia, G. B. ; Phillips, C. C. ; Hopkinson, M. ; Vurgaftman, I. ; Meyer, J. R. Phase-matched second harmonic generation in asymmetric double quantum wells. Appl. Phys. Lett. 1998, 72 , 2654– 2656, DOI: 10.1063/1.121088

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25

Phase-matched second harmonic generation in asymmetric double quantum wells

Vodopyanov, K. L.; O'Neill, K.; Serapiglia, G. B.; Phillips, C. C.; Hopkinson, M.; Vurgaftman, I.; Meyer, J. R.

Applied Physics Letters (1998), 72 (21), 2654-2656CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)

Efficient (∼1%) second harmonic generation, resonantly enhanced near λ=8.6 μm, has been obsd. in asym. double multi-quantum well structures. We used (i) edge-emitting waveguide geometry where the phase matching was achieved by incorporating a sep. multiple quantum well region which modifies (via the Kramers-Kronig relation) the dispersion of light and (ii) 45° wedge multi-bounce geometry where the phases of second harmonic waves generated at sequential bounces were synchronized by changing the angle of incidence.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXjtV2rtL8%253D&md5=c20fb22cda5be2a0d4fc0cfa066f98c3
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Lee, J. ; Tymchenko, M. ; Argyropoulos, C. ; Chen, P.-Y. ; Lu, F. ; Demmerle, F. ; Boehm, G. ; Amann, M.-C. ; Alu, A. ; Belkin, M. A. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature 2014, 511 , 65– 69, DOI: 10.1038/nature13455

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Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions

Lee, Jongwon; Tymchenko, Mykhailo; Argyropoulos, Christos; Chen, Pai-Yen; Lu, Feng; Demmerle, Frederic; Boehm, Gerhard; Amann, Markus-Christian; Alu, Andrea; Belkin, Mikhail A.

Nature (London, United Kingdom) (2014), 511 (7507), 65-69CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)

Intersubband transitions in n-doped multi-quantum-well semiconductor heterostructures make it possible to engineer one of the largest known nonlinear optical responses in condensed matter systems-but this nonlinear response is limited to light with elec. field polarized normal to the semiconductor layers. In a different context, plasmonic metasurfaces (thin conductor-dielec. composite materials) have been proposed as a way of strongly enhancing light-matter interaction and realizing ultrathin planarized devices with exotic wave properties. Here we propose and exptl. realize metasurfaces with a record-high nonlinear response based on the coupling of electromagnetic modes in plasmonic metasurfaces with quantum-engineered electronic intersubband transitions in semiconductor heterostructures. We show that it is possible to engineer almost any element of the nonlinear susceptibility tensor of these structures, and we exptl. verify this concept by realizing a 400-nm-thick metasurface with nonlinear susceptibility of greater than 5 × 104 picometres per V for second harmonic generation at a wavelength of about 8 μm under normal incidence. This susceptibility is many orders of magnitude larger than any second-order nonlinear response in optical metasurfaces measured so far. The proposed structures can act as ultrathin highly nonlinear optical elements that enable efficient frequency mixing with relaxed phase-matching conditions, ideal for realizing broadband frequency up- and down-conversions, phase conjugation and all-optical control and tunability over a surface.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtV2qtbzN&md5=ace2af147e377ebd7a001e5694c45632
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Sarma, R. ; De Ceglia, D. ; Nookala, N. ; Vincenti, M. A. ; Campione, S. ; Wolf, O. ; Scalora, M. ; Sinclair, M. B. ; Belkin, A. ; Brener, I. Broadband and efficient second-harmonic generation from a hybrid dielectric metasurface/semiconductor quantum-well structure. ACS Photonics 2019, 6 , 1458– 1465, DOI: 10.1021/acsphotonics.9b00114

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Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure

Sarma, Raktim; de Ceglia, Domenico; Nookala, Nishant; Vincenti, Maria A.; Campione, Salvatore; Wolf, Omri; Scalora, Michael; Sinclair, Michael B.; Belkin, Mikhail A.; Brener, Igal

ACS Photonics (2019), 6 (6), 1458-1465CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)

A prominent nonlinear optical phenomenon that is extensively studied using nanostructured materials is 2nd-harmonic generation (SHG) as it has applications in various fields. Achieving efficient SHG from a nanostructure requires a large 2nd-order nonlinear susceptibility of the material system and large electromagnetic fields. For practical applications, the nanostructures should also have low losses, high damage thresholds, large bandwidths, wavelength scalability, dual mode operation in transmission and reflection, monolithic integrability, and ease of fabrication. While various approaches demonstrated efficient SHG, to the best of the authors' knowledge, none demonstrated all these desired qualities simultaneously. Here, the authors present a hybrid approach for realizing efficient SHG in an ultrathin dielec.-semiconductor nonlinear device with all the above-mentioned desired properties. The authors' approach uses high quality factor leaky mode resonances in dielec. metasurfaces that are coupled to intersubband transitions of semiconductor quantum wells. Using the authors' device, the authors demonstrate SHG at pump wavelengths ranging from 8.5 to 11 μm, with a max. 2nd-harmonic nonlinear conversion factor of 1.1 mW/W2 and max. 2nd-harmonic conversion efficiency of 2.5 × 10-5 at modest pump intensities of 10 kW/cm2. The authors' results open a new direction for designing low loss, broadband, and efficient ultrathin nonlinear optical devices.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtVagsrvP&md5=2588c9c7087a0da93b934ee06ba31be6
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Frigerio, J. ; Ballabio, A. ; Ortolani, M. ; Virgilio, M. Modeling of second harmonic generation in hole-doped silicon-germanium quantum wells for mid-infrared sensing. Opt. Express 2018, 26 , 31861– 31872, DOI: 10.1364/OE.26.031861

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Modeling of second harmonic generation in hole-doped silicon-germanium quantum wells for mid-infrared sensing

Frigerio, Jacopo; Ballabio, Andrea; Ortolani, Michele; Virgilio, Michele

Optics Express (2018), 26 (24), 31861-31872CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)

The development of Ge and SiGe chem. vapor deposition techniques on silicon wafers has enabled the integration of multi-quantum well structures in silicon photonics chips for nonlinear optics with potential applications to integrated nonlinear optics, however research has focused up to now on undoped quantum wells and interband optical excitations. In this work, we present model calcns. for the giant nonlinear coeffs. provided by intersubband transitions in hole-doped Ge/SiGe and Si/SiGe multi-quantum wells. We employ a valence band-structure model for Si1-xGex to calc. the confined hole states of asym.-coupled quantum wells for second-harmonic generation in the mid-IR. We calc. the nonlinear emission spectra from the second-order susceptibility tensor, including the particular vertical emission spectra of valence-band quantum wells. Two possible nonlinear mid-IR sensor architectures, one based on waveguides and another based on metasurfaces, are described as perspective application.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXnt1Ohtbg%253D&md5=7e427b01b8f30148f0cce0558dad33ec
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Fischer, M. P. ; Schmidt, C. ; Sakat, E. ; Stock, E. ; Samarelli, A. ; Frigerio, J. ; Ortolani, M. ; Paul, D. J. ; Isella, G. ; Leitenstorfer, A. ; Biagioni, P. ; Brida, D. Optical activation of germanium plasmonic antennas in the mid-infrared. Phys. Rev. Lett. 2016, 117 , 047401, DOI: 10.1103/PhysRevLett.117.047401

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Optical activation of germanium plasmonic antennas in the mid-infrared

Fischer, Marco P.; Schmidt, Christian; Sakat, Emilie; Stock, Johannes; Samarelli, Antonio; Frigerio, Jacopo; Ortolani, Michele; Paul, Douglas J.; Isella, Giovanni; Leitenstorfer, Alfred; Biagioni, Paolo; Brida, Daniele

Physical Review Letters (2016), 117 (4), 047401/1-047401/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

Impulsive interband excitation with femtosecond near-IR pulses establishes a plasma response in intrinsic germanium structures fabricated on a silicon substrate. This direct approach activates the plasmonic resonance of the Ge structures and enables their use as optical antennas up to the mid-IR spectral range. The optical switching lasts for hundreds of picoseconds until charge recombination red shifts the plasma frequency. The full behavior of the structures is modeled by the electrodynamic response established by an electron-hole plasma in a regular array of antennas.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitFaktr7M&md5=c6efa09472efefbad89d18e569c8f3a5
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Seto, M. ; Helm, M. ; Moussa, Z. ; Boucaud, P. ; Julien, F. H. ; Lourtioz, J.-M. ; Nützel, J. F. ; Abstreiter, G. Second-harmonic generation in asymmetric Si/SiGe quantum wells. Appl. Phys. Lett. 1994, 65 , 2969– 2971, DOI: 10.1063/1.113028

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30

Second-harmonic generation in asymmetric Si/SiGe quantum wells

Seto, M.; Helm, M.; Moussa, Z.; Boucaud, P.; Julien, F. H.; Lourtioz, J.-M.; Nutzel, J. F.; Abstreiter, G.

Applied Physics Letters (1994), 65 (23), 2969-71CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)

The observation of IR 2nd-harmonic generation in asym. Si/SiGe p-doped quantum wells is reported. The generated signal stems entirely from valence intersubband transitions, since bulk Si, with an inversion sym. crystal structure, has a zero 2nd-order susceptibility. The expts. were performed using a Q-switched CO2 laser operating at 10.56 μm and give a nonlinear susceptibility of 5 × 10-8 m/V.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXitlOmtLc%253D&md5=00e872e1a7a84e132c9e8be1971aba92
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Grimm, C. V.-B. ; Priegnitz, M. ; Winnerl, S. ; Schneider, H. ; Helm, M. ; Biermann, K. ; Künzel, H. Intersubband relaxation dynamics in single and double quantum wells based on strained InGaAs/AlAs/AlAsSb. Appl. Phys. Lett. 2007, 91 , 191121, DOI: 10.1063/1.2809409

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Intersubband relaxation dynamics in single and double quantum wells based on strained InGaAs/AlAs/AlAsSb

Grimm, C. V.-B.; Priegnitz, M.; Winnerl, S.; Schneider, H.; Helm, M.; Biermann, K.; Kuenzel, H.

Applied Physics Letters (2007), 91 (19), 191121/1-191121/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)

Intersubband relaxation dynamics in single and coupled double quantum well (QW) structures based on strained InGaAs/AlAs/AlAsSb were studied by femtosecond pump probe spectroscopy at wavelengths around 2 μm. For single QWs, the transient transmission was obsd. to decay exponentially with a time const. of 2 ps, showing that side valleys have negligible influence on the intersubband relaxation dynamics for strained InGaAs QWs. For double QWs, the pump-probe signal at the intersubband energy involving the two electronic levels located at the wider QW exhibits an induced absorption component attributed to the population of the 2nd subband (assocd. with the narrow QW) by hot electrons.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhtlGgtL3N&md5=c395cfb1968f6c8c331218a287582602
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Qian, H. ; Li, S. ; Chen, C. F. ; Hsu, S. W. ; Bopp, S. E. ; Ma, Q. ; Tao, A. R. ; Liu, Z. Large optical nonlinearity enabled by coupled metallic quantum wells. Light: Sci. Appl. 2019, 8 , 13, DOI: 10.1038/s41377-019-0123-4

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Large optical nonlinearity enabled by coupled metallic quantum wells

Qian Haoliang; Li Shilong; Chen Ching-Fu; Ma Qian; Liu Zhaowei; Hsu Su-Wen; Tao Andrea R; Bopp Steven Edward; Tao Andrea R; Liu Zhaowei; Liu Zhaowei

Light, science & applications (2019), 8 (), 13 ISSN:.

New materials that exhibit strong second-order optical nonlinearities at a desired operational frequency are of paramount importance for nonlinear optics. Giant second-order susceptibility χ((2)) has been obtained in semiconductor quantum wells (QWs). Unfortunately, the limited confining potential in semiconductor QWs causes formidable challenges in scaling such a scheme to the visible/near-infrared (NIR) frequencies for more vital nonlinear-optic applications. Here, we introduce a metal/dielectric heterostructured platform, i.e., TiN/Al2O3 epitaxial multilayers, to overcome that limitation. This platform has an extremely high χ((2)) of approximately 1500 pm/V at NIR frequencies. By combining the aforementioned heterostructure with the large electric field enhancement afforded by a nanostructured metasurface, the power efficiency of second harmonic generation (SHG) achieved 10(-4) at an incident pulse intensity of 10 GW/cm(2), which is an improvement of several orders of magnitude compared to that of previous demonstrations from nonlinear surfaces at similar frequencies. The proposed quantum-engineered heterostructures enable efficient wave mixing at visible/NIR frequencies into ultracompact nonlinear optical devices.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3cjntFyrug%253D%253D&md5=fb35bea448c5af9d5220c8b70752f90a
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Wolf, O. ; Campione, S. ; Benz, A. ; Ravikumar, A. P. ; Liu, S. ; Luk, T. S. ; Kadlec, E. A. ; Shaner, E. A. ; Klem, J. F. ; Sinclair, M. B. ; Brener, I. Phased-array sources based on nonlinear metamaterial nanocavities. Nat. Commun. 2015, 6 , 7667, DOI: 10.1038/ncomms8667

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Phased-array sources based on nonlinear metamaterial nanocavities

Wolf Omri; Campione Salvatore; Benz Alexander; Liu Sheng; Luk Ting S; Brener Igal; Wolf Omri; Campione Salvatore; Benz Alexander; Liu Sheng; Luk Ting S; Kadlec Emil A; Shaner Eric A; Klem John F; Sinclair Michael B; Brener Igal; Ravikumar Arvind P

Nature communications (2015), 6 (), 7667 ISSN:.

Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization. As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (∼5 μm): a beam splitter and a polarizing beam splitter. Proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC2MbovVOitA%253D%253D&md5=6cf3963648ba86ae0de04ed6b818f60d
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Chaisakul, P. ; Marris-Morini, D. ; Frigerio, J. ; Chrastina, D. ; Rouifed, M.-S. ; Cecchi, S. ; Crozat, P. ; Isella, G. ; Vivien, L. Integrated germanium optical interconnects on silicon substrates. Nat. Photonics 2014, 8 , 482– 488, DOI: 10.1038/nphoton.2014.73

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Integrated germanium optical interconnects on silicon substrates

Chaisakul, Papichaya; Marris-Morini, Delphine; Frigerio, Jacopo; Chrastina, Daniel; Rouifed, Mohamed-Said; Cecchi, Stefano; Crozat, Paul; Isella, Giovanni; Vivien, Laurent

Nature Photonics (2014), 8 (6), 482-488CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)

Monolithic integration of optoelectronics with electronics is a much-desired functionality. Here, we demonstrate that it is possible to realize low-loss Ge quantum-well photonic interconnects on Si wafers. We show that Ge-rich Si1-xGex virtual substrates can act as a passive, high-quality optical waveguide on which low-temp., epitaxial growth of Ge quantum-well devices can be realized. As a proof of concept, the photonic integration of a passive Si0.16Ge0.84 waveguide and two Ge/SiGe multi-quantum-well active devices, an optical modulator and a photodetector was realized to form a photonic interconnect using a single epitaxial growth step. This demonstration confirms that Ge quantum-well interconnects are feasible for low-voltage, broadband optical links integrated on Si chips. Our approach can be extended to any kind of Ge-based optoelectronic device working within telecommunication wavelengths as long as a suitable Ge concn. is selected for the Ge-rich virtual substrate.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXnslGltLs%253D&md5=f189eadbda980ace621d585bc29402a3
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Kuo, Y.-H. ; Lee, Y. K. ; Ge, Y. ; Ren, S. ; Roth, J. E. ; Kamins, T. I. ; Miller, D. A. B. ; Harris, J. S. Strong quantum confined Stark effect in germanium quantum-well structures on silicon. Nature 2005, 437 , 1334– 1336, DOI: 10.1038/nature04204

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35

Strong quantum-confined Stark effect in germanium quantum-well structures on silicon

Kuo, Yu-Hsuan; Lee, Yong Kyu; Ge, Yangsi; Ren, Shen; Roth, Jonathan E.; Kamins, Theodore I.; Miller, David A. B.; Harris, James S.

Nature (London, United Kingdom) (2005), 437 (7063), 1334-1336CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)

Silicon is the dominant semiconductor for electronics, but there is now a growing need to integrate such components with optoelectronics for telecommunications and computer interconnections. Silicon-based optical modulators have recently been successfully demonstrated; but because the light modulation mechanisms in silicon are relatively weak, long (for example, several millimetres) devices or sophisticated high-quality-factor resonators have been necessary. Thin quantum-well structures made from III-V semiconductors such as GaAs, InP and their alloys exhibit the much stronger quantum-confined Stark effect (QCSE) mechanism, which allows modulator structures with only micrometres of optical path length. Such III-V materials are unfortunately difficult to integrate with silicon electronic devices. Germanium is routinely integrated with silicon in electronics, but previous silicon-germanium structures have also not shown strong modulation effects. Here we report the discovery of the QCSE, at room temp., in thin germanium quantum-well structures grown on silicon. The QCSE here has strengths comparable to that in III-V materials. Its clarity and strength are particularly surprising because germanium is an indirect gap semiconductor; such semiconductors often display much weaker optical effects than direct gap materials (such as the III-V materials typically used for optoelectronics). This discovery is very promising for small, high-speed, low-power optical output devices fully compatible with silicon electronics manuf.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtFCrur3J&md5=30aaf6962cd3709202c390cb15b777e2
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Lever, L. ; Hu, Y. ; Myronov, M. ; Liu, X. ; Owens, N. ; Gardes, F. Y. ; Marko, S. J. ; Sweeney, S. J. ; Ikonic, Z. ; Leadley, D. R. ; Reed, G. T. ; Kelsall, R. W. Modulation of the absorption coefficient at 1.3 mm in Ge/SiGe multiple quantum well heterostructures on silicon. Opt. Lett. 2011, 36 , 4158– 4160, DOI: 10.1364/OL.36.004158

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36

Modulation of the absorption coefficient at 1.3μm in Ge/SiGe multiple quantum well heterostructures on silicon

Lever, L.; Hu, Y.; Myronov, M.; Liu, X.; Owens, N.; Gardes, F. Y.; Marko, I. P.; Sweeney, S. J.; Ikonic, Z.; Leadley, D. R.; Reed, G. T.; Kelsall, R. W.

Optics Letters (2011), 36 (21), 4158-4160CODEN: OPLEDP; ISSN:0146-9592. (Optical Society of America)

We report modulation of the absorption coeff. at 1.3 μm in Ge/SiGe multiple quantum well heterostructures on silicon via the quantum-confined Stark effect. Strain engineering was exploited to increase the direct optical band-gap in the Ge quantum wells. We grew 9nm-thick Ge quantum wells on a relaxed Si0.22Ge0.78 buffer and a contrast in the absorption coeff. of a factor of greater than 3.2 was achieved in the spectral range 1290-1315nm.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xht1yitro%253D&md5=55f445aa09081f3671bf592146b5a064
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Grange, T. ; Stark, D. ; Scalari, G. ; Faist, J. ; Persichetti, L. ; Di Gaspare, L. ; De Seta, M. ; Ortolani, M. ; Paul, D. J. ; Capellini, G. ; Birner, S. ; Virgilio, M. Room temperature operation of n-type Ge/SiGe terahertz quantum cascade lasers predicted by non-equilibrium Green's functions. Appl. Phys. Lett. 2019, 114 , 111102, DOI: 10.1063/1.5082172

[Crossref], [CAS], Google Scholar

37

Room temperature operation of n-type Ge/SiGe terahertz quantum cascade lasers predicted by non-equilibrium Green's functions

Grange, Thomas; Stark, David; Scalari, Giacomo; Faist, Jerome; Persichetti, Luca; Di Gaspare, Luciana; De Seta, Monica; Ortolani, Michele; Paul, Douglas J.; Capellini, Giovanni; Birner, Stefan; Virgilio, Michele

Applied Physics Letters (2019), 114 (11), 111102/1-111102/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)

N-type Ge/SiGe terahertz quantum cascade lasers are investigated using non-equil. Green's functions calcns. We compare the temp. dependence of the terahertz gain properties with an equiv. GaAs/AlGaAs quantum cascade laser design. In the Ge/SiGe case, the gain is found to be much more robust to temp. increase, enabling operation up to room temp. The better temp. robustness with respect to III-V is attributed to the much weaker interaction with optical phonons. The effect of lower interface quality is investigated and can be partly overcome by engineering smoother quantum confinement. (c) 2019 American Institute of Physics.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXls1ehu7Y%253D&md5=e2a0c365c284a3e6b0e4219721f389f8
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Ciano, C. ; Virgilio, M. ; Montanari, M. ; Persichetti, L. ; Di Gaspare, L. ; Ortolani, M. ; Baldassarre, L. ; Zoellner, M.H. ; Skibitzki, O. ; Scalari, G. ; Faist, J. ; Paul, D.J. ; Scuderi, M. ; Nicotra, G. ; Grange, T. ; Birner, S. ; Capellini, G. ; De Seta, M. Control of electron-state coupling in asymmetric Ge/Si–Ge quantum wells. Phys. Rev. Appl. 2019, 11 , 014003, DOI: 10.1103/PhysRevApplied.11.014003

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38

Control of Electron-State Coupling in Asymmetric Ge/Si-Ge Quantum Wells

Ciano, C.; Virgilio, M.; Montanari, M.; Persichetti, L.; Di Gaspare, L.; Ortolani, M.; Baldassarre, L.; Zoellner, M. H.; Skibitzki, O.; Scalari, G.; Faist, J.; Paul, D. J.; Scuderi, M.; Nicotra, G.; Grange, T.; Birner, S.; Capellini, G.; De Seta, M.

Physical Review Applied (2019), 11 (1), 014003CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)

Theor. predictions indicate that the n-type Ge/Si-Ge multi-quantum-well system is the most promising material for the realization of a Si-compatible THz quantum cascade laser operating at room temp. To advance in this direction, we study, both exptl. and theor., asym. coupled multi-quantum-well samples based on this material system, that can be considered as the basic building block of a cascade architecture. Extensive structural characterization shows the high material quality of strain-symmetrized structures grown by chem. vapor deposition, down to the ultrathin barrier limit. Moreover, THz absorption spectroscopy measurements supported by theor. modeling unambiguously demonstrate inter-well coupling and wavefunction tunneling. The agreement between exptl. data and simulations allows us to characterize the tunneling barrier parameters and, in turn, achieve highly controlled engineering of the electronic structure in forthcoming unipolar cascade systems based on n-type Ge/Si-Ge multi-quantum-wells.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXnslWqsLY%253D&md5=d161e33f6a6753ce1c4ed68f1a71ba78
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Chang, Y.-C. ; Paeder, V. ; Hvozdara, L. ; Hartmann, J.-M. ; Herzig, H. P. Low-loss germanium strip waveguides on silicon for the mid-infrared. Opt. Lett. 2012, 37 , 2883– 2885, DOI: 10.1364/OL.37.002883

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Low-loss germanium strip waveguides on silicon for the mid-infrared

Chang, Yu-Chi; Paeder, Vincent; Hvozdara, Lubos; Hartmann, Jean-Michel; Herzig, Hans Peter

Optics Letters (2012), 37 (14), 2883-2885CODEN: OPLEDP; ISSN:0146-9592. (Optical Society of America)

Mid-IR photonics in silicon needs low-loss integrated waveguides. While monocryst. germanium waveguides on silicon have been proposed, exptl. realization has not been reported. Here we demonstrate a germanium strip waveguide on a silicon substrate. It is designed for single mode transmission of light in transverse magnetic (TM) polarization generated from quantum cascade lasers at a wavelength of 5.8 μm. The propagation losses were measured with the Fabry-Perot resonance method. The lowest achieved propagation loss is 2.5 dB/cm, while the bending loss is measured to be 0.12 dB for a 90° bend with a radius of 115 μm.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsVSnu7rN&md5=e6525c3743bd867cf3b0f7eee33d3b26
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Brun, M. ; Labeye, P. ; Grand, G. ; Hartmann, J.-M. ; Boulila, F. ; Carras, M. ; Nicoletti, S. Low loss SiGe graded index waveguides for mid-IR applications. Opt. Express 2014, 22 , 508– 518, DOI: 10.1364/OE.22.000508

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40

Low loss SiGe graded index waveguides for mid-IR applications

Brun, Mickael; Labeye, Pierre; Grand, Gilles; Hartmann, Jean-Michel; Boulila, Fahem; Carras, Mathieu; Nicoletti, Sergio

Optics Express (2014), 22 (1), 508-518, 11 pp.CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)

In the last few years Mid IR (MIR) photonics has received renewed interest for a variety of com., scientific and military applications. This paper reports the design, the fabrication and the characterization of SiGe/Si based graded index waveguides and photonics integrated devices. The thickness and the Ge concn. of the core layer were optimized to cover the full [3 - 8 μm] band. The developed SiGe/Si stack has been used to fabricate straight waveguides and basic optical functions such as Y-junction, crossings and couplers. Straight waveguides showed losses as low as 1 dB/cm at λ = 4.5 μm and 2 dB/cm at 7.4 μm. Likewise straight waveguides, basic functions exhibit nearly theor. behavior with losses compatible with the implementation of more complex functions in integrated photonics circuits. To the best of our knowledge, the performances of those Mid-IR waveguides significantly exceed the state of the art, confirming the feasibility of using graded SiGe/Si devices in a wide range of wavelengths. These results represent a capital breakthrough to develop a photonic platform working in the Mid-IR range.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXptVKqs7c%253D&md5=8ac6441b6f8767bd46b35b99cb7a24b1
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Nedeljkovic, M. ; Penades, J. S. ; Mittal, V. ; Murugan, S. M. ; Khokhar, A. Z. ; Littlejohns, C. ; Carpenter, L. G. ; Gawith, C. B. E. ; Wilkinson, J. S. ; Mashanovich, G. Z. Germanium-on-silicon waveguides operating at mid-infrared wavelengths up to 8.5 μm. Opt. Express 2017, 25 , 27431– 27441, DOI: 10.1364/OE.25.027431

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41

Germanium-on-silicon waveguides operating at mid-infrared wavelengths up to 8.5 μm

Nedeljkovic, Milos; Penades, Jordi Soler; Mittal, Vinita; Senthil Murugan, Ganapathy; Khokhar, Ali Z.; Littlejohns, Callum; Carpenter, Lewis G.; Gawith, Corin B. E.; Wilkinson, James S.; Mashanovich, Goran Z.

Optics Express (2017), 25 (22), 27431-27441CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)

We report transmission measurements of germanium on silicon waveguides in the 7.5-8.5 μm wavelength range, with a min. propagation loss of 2.5 dB/cm at 7.575 μm. However, we find an unexpected strongly increasing loss at higher wavelengths, potential causes of which we discuss in detail. We also demonstrate the first germanium on silicon multimode interferometers operating in this range, as well as grating couplers optimized for measurement using a long wavelength IR camera. Finally, we use an implementation of the "cut-back" method for loss measurements that allows simultaneous transmission measurement through multiple waveguides of different lengths, and we use dicing in the ductile regime for fast and reproducible high quality optical waveguide end-facet prepn.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXnsVyktLg%253D&md5=18b400d359ce8c9e0b9c12d78c852540
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Ramirez, J. M. ; Liu, Q. ; Vakarin, V. ; Frigerio, J. ; Ballabio, A. ; Le Roux, X. ; Bouville, D. ; Vivien, L. ; Isella, G. ; Marris-Morini, D. Graded SiGe waveguides with broadband low-loss propagation in the mid infrared. Opt. Express 2018, 26 , 870– 877, DOI: 10.1364/OE.26.000870

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42

Graded SiGe waveguides with broadband low-loss propagation in the mid infrared

Ramirez, J. M.; Liu, Q.; Vakarin, V.; Frigerio, J.; Ballabio, A.; Le Roux, X.; Bouville, D.; Vivien, L.; Isella, G.; Marris-Morini, D.

Optics Express (2018), 26 (2), 870-877CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)

Mid-IR (mid-IR) silicon photonics is expected to lead key advances in different areas including spectroscopy, remote sensing, nonlinear optics or free-space communications, among others. Still, the inherent limitations of the silicon-on-insulator (SOI) technol., namely the early mid-IR absorption of silicon oxide and silicon at λ∼3.6 μm and at λ ∼8.5 μm resp., remain the main stumbling blocks that prevent this platform to fully exploit the mid-IR spectrum (λ ∼2-20 μm). Here, we propose using a compact Ge-rich graded-index Si1-xGex platform to overcome this constraint. A flat propagation loss characteristic as low as 2-3 dB/cm over a wavelength span from λ = 5.5 μm to 8.5 μm is demonstrated in Ge-rich Si1-xGex waveguides of only 6 μm thick. The comparison of three different waveguides design with different vertical index profiles demonstrates the benefit of reducing the fraction of the guided mode that overlaps with the Si substrate to obtain such flat low loss behavior. Such Ge-rich Si1-xGex platforms may open the route towards the implementation of mid-IR photonic integrated circuits with low-loss beyond the Si multi-phonon absorption band onset, hence truly exploiting the full Ge transparency window up to λ ∼15 μm.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXit12qt7bM&md5=2d9fa4e497609ab82d433b2c62402369
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Gallacher, K. ; Millar, R. W. ; Griškevičiu̅te, U. ; Baldassarre, L. ; Sorel, M. ; Ortolani, M. ; Paul, D. J. Low loss Ge-on-Si waveguides operating in the 8–14 μm atmospheric transmission window. Opt. Express 2018, 26 , 25667– 25675, DOI: 10.1364/OE.26.025667

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43

Low loss Ge-on-Si waveguides operating in the 8-14 um atmospheric transmission window

Gallacher, K.; Millar, R. W.; Griskeviciute, U.; Baldassarre, L.; Sorel, M.; Ortolani, M.; Paul, D. J.

Optics Express (2018), 26 (20), 25667-25675CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)

Germanium-on-silicon waveguides were modeled, fabricated and characterized at wavelengths ranging from 7.5 to 11μm. Measured waveguide losses are below 5 dB/cm for both TE and TM polarization and reach values of ∼ 1 dB/cm for ≥ 10μm wavelengths for the TE polarization. This work demonstrates exptl. for the first time that Ge-on-Si is a viable waveguide platform for sensing in the mol. fingerprint spectral region. Detailed modeling and anal. is presented to identify the various loss contributions, showing that with practical techniques losses below 1 dB/cm could be achieved across the full measurement range.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVGktLrE&md5=326d37757fba57760ca1ea4c9851438c
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Gallacher, K. ; Millar, R. W. ; Paul, D. J. ; Frigerio, J. ; Ballabio, A. ; Isella, G. ; Rusconi, F. ; Biagioni, P. ; Giliberti, V. ; Sorgi, A. ; Baldassarre, L. ; Ortolani, M. Characterization of integrated waveguides by atomic-force-microscopy-assisted mid-infrared imaging and spectroscopy. Opt. Express 2020, 28 , 22186– 22199, DOI: 10.1364/OE.393748

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44

Characterization of integrated waveguides by atomic-force-microscopy-assisted mid-infrared imaging and spectroscopy

Gallacher, Kevin; Millar, Ross W.; Paul, Douglas J.; Frigerio, Jacopo; Ballabio, Andrea; Isella, Giovanni; Rusconi, Francesco; Biagioni, Paolo; Giliberti, Valeria; Sorgi, Alessia; Baldassarre, Leonetta; Ortolani, Michele

Optics Express (2020), 28 (15), 22186-22199CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)

A novel spectroscopy technique to enable the rapid characterization of discrete mid-IR integrated photonic waveguides is demonstrated. The technique utilizes lithog. patterned polymer blocks that absorb light strongly within the mol. fingerprint region. These act as integrated waveguide detectors when combined with an at. force microscope that measures the photothermal expansion when IR light is guided to the block. As a proof of concept, the technique is used to exptl. characterize propagation loss and grating coupler response of Ge-on-Si waveguides at wavelengths from 6 to 10μm. In addn., when the microscope is operated in scanning mode at fixed wavelength, the guided mode exiting the output facet is imaged with a lateral resoln. better than 500 nm i.e. below the diffraction limit. The characterization technique can be applied to any mid-IR waveguide platform and can provide non-destructive in-situ testing of discrete waveguide components.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitlSqtLrL&md5=477278931f2a3e4817a9ee5754b77ff6
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Gallacher, K. ; Millar, R. W. ; Griškevičiu̅te, U. ; Sinclair, M. ; Sorel, M. ; Baldassarre, L. ; Ortolani, M. ; Soref, R. ; Paul, D. J. Ultra-broadband mid-infrared Ge-on-Si waveguide polarization rotator. APL Photonics 2020, 5 , 026102, DOI: 10.1063/1.5134973

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45

Ultra-broadband mid-infrared Ge-on-Si waveguide polarization rotator

Gallacher, Kevin; Millar, Ross W.; Griskeviciute, Ugne; Sinclair, Martin; Sorel, Marc; Baldassarre, Leonetta; Ortolani, Michele; Soref, Richard; Paul, Douglas J.

APL Photonics (2020), 5 (2), 026102CODEN: APPHD2; ISSN:2378-0967. (American Institute of Physics)

The design, modeling, micro-fabrication, and characterization of an ultra-broadband Ge-on-Si waveguide polarization rotator are presented. The polarization rotator is based on the mode evolution approach where adiabatic sym. and anti-sym. tapers are utilized to convert from the fundamental transverse magnetic to elec. mode. The device is shown to be extremely fabrication tolerant and simple to fabricate. The fabricated devices demonstrate a polarization extinction ratio of ≥15 dB over a 2μm bandwidth (9-11μm wavelength) with an av. insertion loss of <1 dB, which is an order of magnitude improvement compared to previously demonstrated devices. This device will provide polarization flexibility when integrating quantum cascade lasers on-chip for mid-IR waveguide mol. spectroscopy. (c) 2020 American Institute of Physics.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXnsVSgs74%253D&md5=191e0057673891b3837a1d288172c802
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Li, S. ; Khurgin, J. Second-order nonlinear optical susceptibility in p-doped asymmetric quantum wells. Appl. Phys. Lett. 1993, 62 , 1727– 1729, DOI: 10.1063/1.109587

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46

Second-order nonlinear optical susceptibility in p-doped asymmetric quantum wells

Li, Shaozhong; Khurgin, J.

Applied Physics Letters (1993), 62 (15), 1727-9CODEN: APPLAB; ISSN:0003-6951.

The possibility of the surface-emitting second-harmonic generation (SHG) based on intersubband transitions in multiple quantum-well (QW) structures is examd. theor. The crit. role of valence band mixing is demonstrated. The off-diagonal SHG coeffs., necessary for the surface-emitting SHG, are evaluated for the transitions between the valence subbands in GaAs/AlAs QW structures, and are found to be comparable in magnitude to the diagonal SHG coeffs. reported in the literature.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3sXisVCjt7o%253D&md5=ceda55e6bc465b225cd477f1a2cdd5a9
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Isella, G. ; Chrastina, D. ; Rossner, B. ; Hackbarth, T. ; Herzog, H. J. ; Konig, U. ; Von Kanel, H. Low-energy plasma-enhanced chemical vapor deposition for strained Si and Ge heterostructures and devices. Solid-State Electron. 2004, 48 , 1317– 1323, DOI: 10.1016/j.sse.2004.01.013

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47

Low-energy plasma-enhanced chemical vapor deposition for strained Si and Ge heterostructures and devices

Isella, G.; Chrastina, D.; Rossner, B.; Hackbarth, T.; Herzog, H.-J.; Konig, U.; von Kanel, H.

Solid-State Electronics (2004), 48 (8), 1317-1323CODEN: SSELA5; ISSN:0038-1101. (Elsevier Science Ltd.)

A review on the potential of low-energy plasma-enhanced chem. vapor deposition (LEPECVD) for the fabrication of strained Si and Ge heterostructures and devices. The technique is shown to be equally applicable to the formation of relaxed SiGe buffer layers, and to entire heterostructures including strained modulation doped channels. Pure Ge channels on Ge-rich linearly graded buffers are shown to exhibit low-temp. hole mobilities up to 120,000 cm2 V-1 s-1, limited by remote impurity and background impurity scattering rather than interface roughness scattering. Strained-Si modulation-doped field-effect transistors (n-MODFETs) with excellent frequency response have been fabricated by combining LEPECVD and MBE for buffer layer and active layer growth, resp. Maximum oscillation frequencies of n-MODFETs above 140 GHz have been achieved for active layer stacks both on buffers linearly graded to a Ge fraction of 40% at a rate of 10% per μ, and on const. compn. buffers which are 10 times thinner. The use of a thin buffer results in significantly less device self-heating.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjs1anu78%253D&md5=520153eec18dd29134b9d8a7c8b64abe
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Bashir, A. ; Gallacher, K. ; Millar, R. W. ; Paul, D. J. ; Ballabio, A. ; Frigerio, J. ; Isella, G. ; Kriegner, D. ; Ortolani, M. ; Barthel, J. ; MacLaren, I. Interfacial sharpness and intermixing in a Ge-SiGe multiple quantum well structure. J. Appl. Phys. 2018, 123 , 035703, DOI: 10.1063/1.5001158

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48

Interfacial sharpness and intermixing in a Ge-SiGe multiple quantum well structure

Bashir, A.; Gallacher, K.; Millar, R. W.; Paul, D. J.; Ballabio, A.; Frigerio, J.; Isella, G.; Kriegner, D.; Ortolani, M.; Barthel, J.; MacLaren, I.

Journal of Applied Physics (Melville, NY, United States) (2018), 123 (3), 035703/1-035703/11CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)

A Ge-SiGe multiple quantum well structure created by low energy plasma enhanced CVD, with nominal well thickness of 5.4 nm sepd. by 3.6 nm SiGe spacers, is analyzed quant. using scanning TEM. Both high angle annular dark field imaging and EELS show that the interfaces are not completely sharp, suggesting that there is some intermixing of Si and Ge at each interface. Two methods are compared for the quantification of the spectroscopy datasets: a self-consistent approach that calcs. binary substitutional trends without requiring exptl. or computational k-factors from elsewhere and a stds.-based cross sectional calcn. While the cross section approach is ultimately more reliable, the self-consistent approach provides surprisingly good results. The Ge quantum wells are actually ∼95% Ge and the spacers, while apparently peaking at ∼35% Si, contain significant interdiffused Ge at each side. This result is not just an artifact of electron beam spreading in the sample, but mostly arising from a real chem. interdiffusion resulting from the growth. Similar results are found using x-ray diffraction from a similar area of the sample. Putting the results together suggests a real interdiffusion with a std. deviation of ∼0.87 nm, or put another way-a true width defined from 10%-90% of the compositional gradient of ∼2.9 nm. This suggests an intrinsic limit on how sharp such interfaces can be grown by this method and, while 95% Ge quantum wells (QWs) still behave well enough to have good properties, any attempt to grow thinner QWs would require modifications to the growth procedure to reduce this interdiffusion, to maintain a compn. of ≥95% Ge. (c) 2018 American Institute of Physics.

https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtlOmtbo%253D&md5=4b1295a2e1414e5f0affd086dedae6bd
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Cecchi, S. ; Gatti, E. ; Chrastina, D. ; Frigerio, J. ; Mueller-Gubler, E. ; Paul, D. J. ; Guzzi, M. ; Isella, G. Thin SiGe virtual substrates for Ge heterostructures integration on silicon. J. Appl. Phys. 2014, 115 , 093502, DOI: 10.1063/1.4867368

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49

Thin SiGe virtual substrates for Ge heterostructures integration on silicon

Cecchi, S.; Gatti, E.; Chrastina, D.; Frigerio, J.; Muller Gubler, E.; Paul, D. J.; Guzzi, M.; Isella, G.

Journal of Applied Physics (Melville, NY, United States) (2014), 115 (9), 093502/1-093502/6CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)

The possibility to reduce the thickness of the SiGe virtual substrate, required for the integration of Ge heterostructures on Si, without heavily affecting the crystal quality is becoming fundamental in several applications. The authors present 1 μm thick Si1-Ge buffers (with x > 0.7) having different designs which could be suitable for applications requiring a thin virtual substrate. The rationale is to reduce the lattice mismatch at the interface with the Si substrate by introducing compn. steps and/or partial grading. The relatively low growth temp. (475°) makes this approach appealing for complementary metal-oxide-semiconductor integration. For all the studied designs, a redn. of the threading dislocation d. compared to const. compn. Si1-Ge layers was obsd. The best buffer in terms of defects redn. was used as a virtual substrate for the deposition of a Ge/SiGe multiple quantum well structure. Room temp. optical absorption and photoluminescence anal. performed on nominally identical quantum wells grown on both a thick graded virtual substrate and the selected thin buffer demonstrates a comparable optical quality, confirming the effectiveness of the proposed approach. (c) 2014 American Institute of Physics.

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Journal of Applied Physics (2006), 100 (9), 093506/1-093506/6CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)

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The surface properties of topol. insulators are strongly correlated with their structural properties, requiring high-resoln. techniques capable of probing both surface and bulk structures at once. In this work, the high flux of a synchrotron source, a set of recursive equations for fast X-ray dynamical diffraction simulation and a genetic algorithm for data fitting are combined to reveal the detailed structure of bismuth telluride epitaxial films with thicknesses ranging from 8 to 168 nm. This includes stacking sequences, thickness and compn. of layers in model structures, interface coherence, surface termination, and morphol. The results are in agreement with the surface morphol. detd. by at. force microscopy. Moreover, by using X-ray data from a zero-noise area detector to construct three-dimensional reciprocal-space maps, insights into the nanostructure of the domains and stacking faults in Bi2Te3 films are given.

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General algorithms to convert scattering data of linear and area detectors recorded in various scattering geometries to reciprocal space coordinates are presented. These algorithms work for any goniometer configuration including popular four-circle, six-circle and kappa goniometers. The use of commonly employed approxns. is avoided and therefore the algorithms work also for large detectors at small sample-detector distances. A recipe for detg. the necessary detector parameters including mostly ignored misalignments is given. The algorithms are implemented in a freely available open-source package.

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Optimized second-harmonic generation in asymmetric double quantum wells

Vurgaftman, Igor; Meyer, Jerry R.; Ram-Mohan, L. Randas

IEEE Journal of Quantum Electronics (1996), 32 (8), 1334-1346CODEN: IEJQA7; ISSN:0018-9197. (Institute of Electrical and Electronics Engineers)

The authors present a theor. anal. of surface-incidence and waveguide-mode 2nd harmonic generation with detuned intersubband transitions in GaAs-AlGaAs, InGaAs-InAlAs and GaSb-InGaSb-AlGaSb asym. double quantum wells. The anal. includes the effects of absorption, satn., pump depletion, optical carrier heating, mode confinement and competition, and the loss of phase coherence due to waveguide, bulk and resonant intersubband contributions to the refractive index mismatch. Optimal structure were detd. for each material system in both surface-incidence and waveguide-mode geometries. A scheme for maintaining phase matching by incorporation of a sep. region with an intersubband transition tuned midway between the 1st and 2nd harmonic frequencies is analyzed. At 10.6 μm, the max. conversion efficiency for the optimized InGaAs-InAlAs waveguide-mode device is ≈ 16% at a pump-beam intensity of 40 MW/cm2. Also, the same device can be modulated to vanishing 2nd harmonic output power when an elec. field of -32 kV/cm is applied.

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Abstract

Figure 1

Figure 1. (a) Schematic of sample A showing the different epitaxial block thickness and composition: buffer, virtual substrate, and ACQW stack repeated 20 times. (b) Valence band-edge profiles of sample A forming the main and secondary wells (thick lines, HH: heavy holes; LH: light holes; SO: split-off band) and the subband wave functions (thin lines; for holes, wells correspond to band-edge potential maxima and transitions are downward in energy). (c) In-plane dispersion of the hole states in the first Brillouin zone around the Γ point as a function of the in-plane wavevector k _||. (d) Calculated second-order nonlinear susceptibility χ⁽²⁾ _zzz for one single heterostructure period as a function of the pump photon energy and frequency. Impurity transitions are not included in our model.

Figure 2

Figure 2. (a, b) HR-XRD reciprocal space maps of sample A with respect to the (224) and (004) Si reflections. (c) STEM images of a different piece of sample A. (d) ω–2θ scan of the Si(004) reflection (red) together with Darwin model simulations (blue) performed to extract the Ge composition of each layer and the intermixing depth. (e) High-resolution STEM, greyscale intensity is proportional to local Ge content. (f) Ge content profile of sample A retrieved from HR-XRD measurements (blue curve) and by EDS measurements (red dots).

Figure 3

Figure 3. Linear dichroic absorption spectroscopy of the doped ACQW samples A, B, and C. (a) Sketch of the surface-plasmon waveguide structure with prism-shaped slab geometry. The electric field polarization in the illuminated ACQW region is mostly vertical (TM-mode transmitted intensity I _TM), while the TE-mode transmitted intensity I _TE serves as spectral reference. (b) Dichroic absorption −ln(I _TM/I _TE) from the theoretical model of sample A (magenta curve, the main ISBT transitions are marked) and from the experiments at T = 10 K. (c, d) Enlarged view of the curves in panel b at T = 10 K (thick lines). Data at T = 300 K are also reported (thin lines). Note that the horizontal scale of panels c,d is exactly double of that of panel b to highlight SHG resonance in samples A and B. The vertical dashed gray line marks the QCL pump frequency of 29.3 THz in panels c and d and its double (58.6 THz) in panel b. The QCL pump photon energy is 120 meV to compare with Figure 1d.

Figure 4

Figure 4. (a) Scheme of the nonlinear experiment for absolute characterization of SHG efficiency. In the TM mode, the radiation electric field is oriented along the ISBT dipoles of the resonant HH transitions. (b) Measured SHG power vs squared pump power density at focus for samples A, B, and C. Sample D was used as reference to subtract the linear background. Also, the SHG emission disappeared when the sample was shifted by ±1 mm (twice the estimated depth of focus) because the electric field value dropped quickly when the ACQWs were out of focus. This technique was used to subtract the contribution of the residual pump photons to the detector signal. (c) Simplified sketch of the SHG process in the HH valence band. E _F: Fermi level. Note that hole ISBTs 1 → 2 and 2 → 3 are represented by downward arrows.

Figure 5

Figure 5. SHG performance with high-intensity ultrashort pulses. (a) Experimental setup based on difference-frequency generation (DFG) and spectrally resolved detection with a mercury–cadmium telluride (MCT) diode. (b, c) Field-time profiles obtained by electro-optic sampling and corresponding FT spectrum of MIR pump pulses employed in the experiment. (d) SHG spectra measured with sample A at different pump frequency and intensity. (e) SHG efficiency of different samples at optimal pumping conditions (i.e., ν_DFG,2 and highest pulse power).

Figure 6

Figure 6. Log–log plot of SHG emission power vs pump power density for all QCL and DFG pump experiments performed on sample A. A quadratic slope has been superimposed to the QCL data, and a linear slope to the DFG data. Note that the two experiments have been performed at different sample temperatures. The theoretical DFG line at 10 K is drawn parallel to the 300 K derived from the efficiency improvement, with cooling predicted in Figure 1d.
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  Jones, D. J. ; Diddams, S. A. ; Ranka, J. K. ; Stentz, A. ; Windeler, R. S. ; Hall, J. L. ; Cundiff, S. T. Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science 2000, 288 , 635– 639, DOI: 10.1126/science.288.5466.635
  
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  Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis
  
  Jones, David J.; Diddams, Scott A.; Ranka, Jinendra K.; Stentz, Andrew; Windeler, Robert S.; Hall, John L.; Cundiff, Steven T.
  
  Science (Washington, D. C.) (2000), 288 (5466), 635-639CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  
  We stabilized the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools of frequency-domain laser stabilization. We confirmed control of the pulse-to-pulse carrier-envelope phase using temporal cross correlation. This phase stabilization locks the abs. frequencies emitted by the laser, which we used to perform abs. optical frequency measurements that were directly referenced to a stable microwave clock.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXivFCitbk%253D&md5=cf68c37dea54770fdd005c2302939c61
9. 9
  
  Mosca, S. ; Ricciardi, I. ; Parisi, M. ; Maddaloni, P. ; Santamaria, L. ; De Natale, P. ; De Rosa, M. Direct generation of optical frequency combs in χ⁽²⁾ nonlinear cavities. Nanophotonics 2016, 5 , 316– 331, DOI: 10.1515/nanoph-2016-0023
  
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  Direct generation of optical frequency combs in χ(2) nonlinear cavities
  
  Mosca, Simona; Ricciardi, Iolanda; Parisi, Maria; Maddaloni, Pasquale; Santamaria, Luigi; De Natale, Paolo; De Rosa, Maurizio
  
  Nanophotonics (2016), 5 (2), 316-331CODEN: NANOLP; ISSN:2192-8614. (Walter de Gruyter GmbH)
  
  Quadratic nonlinear processes are currently exploited for frequency comb transfer and extension from the visible and near IR regions to other spectral ranges where direct comb generation cannot be accomplished. However, frequency comb generation has been directly obsd. in continuously pumped quadratic nonlinear crystals placed inside an optical cavity. At the same time, an introductory theor. description of the phenomenon has been provided, showing a remarkable analogy with the dynamics of third-order Kerr microresonators. Here, we give an overview of our recent work on χ(2) frequency comb generation. Furthermore, we generalize the preliminary three-wave spectral model to a many-mode comb and present a stability anal. of different cavity field regimes. Although our work is a very early stage, it lays the groundwork for a novel class of highly efficient and versatile frequency comb synthesizers based on second-order nonlinear materials.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhtVWlsr7K&md5=d5af90735d49fc20757eb3fea674340b
10. 10
  
  Absil, P. P. ; Verheyen, P. ; De Heyn, P. ; Pantouvaki, M. ; Lepage, G. ; De Coster, J. ; Van Campenhout, J. Silicon photonics integrated circuits: a manufacturing platform for high density; low power optical I/O's. Opt. Express 2015, 23 , 9369, DOI: 10.1364/OE.23.009369
  
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  Silicon photonics integrated circuits: a manufacturing platform for high density, low power optical I/O's
  
  Absil, Philippe P.; Verheyen, Peter; De Heyn, Peter; Pantouvaki, Marianna; Lepage, Guy; De Coster, Jeroen; Van Campenhout, Joris
  
  Optics Express (2015), 23 (7), 9369-9378CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
  
  Silicon photonics integrated circuits are considered to enable future computing systems with optical input-outputs co-packaged with CMOS chips to circumvent the limitations of elec. interfaces. In this paper we present the recent progress made to enable dense multiplexing by exploiting the integration advantage of silicon photonics integrated circuits. We also discuss the manufacturability of such circuits, a key factor for a wide adoption of this technol.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXksFWitr4%253D&md5=d72e13d7e52ce2b4f6a2f6b64f4952fb
11. 11
  
  Lim, A. E-J. ; Song, J. ; Fang, Q. ; Li, C. ; Tu, X. ; Duan, N. ; Chen, K. K. ; Tern, R. P.-C. ; Liow, T. Y. Review of silicon photonics foundry efforts. IEEE J. Sel. Top. Quantum Electron. 2014, 20 , 405– 416, DOI: 10.1109/JSTQE.2013.2293274
12. 12
  
  Franchi, R. ; Castellan, C. ; Ghulinyan, M. ; Pavesi, L. Second-harmonic generation in periodically poled silicon waveguides with lateral p-i-n junctions. Opt. Lett. 2020, 45 , 3188– 3191, DOI: 10.1364/OL.391988
  
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  12
  
  Second-harmonic generation in periodically poled silicon waveguides with lateral p-i-n junctions
  
  Franchi Riccardo; Castellan Claudio; Ghulinyan Mher; Pavesi Lorenzo
  
  Optics letters (2020), 45 (12), 3188-3191 ISSN:.
  
  Electric-field-induced second-harmonic generation is demonstrated in silicon waveguides with reverse biased lateral p-i-n junctions. Phase matching is achieved by periodically poling the applied electric field. Two different poling configurations are compared: in the first, the p- and n-type doped regions of the junctions are on different sides of the waveguide (simple configuration), while in the second, they are alternated periodically across the waveguide sides (interdigitated configuration). Both simulations and experiments show that the generation efficiency is increased by 10 times comparing the interdigitated and simple configurations. The effective second-order susceptibility modulation obtained at a reverse bias voltage of 3.5 V is Δχeff,S(2)≃0.14pm/V for the simple configuration and Δχeff,I(2)≃0.64pm/V for the interdigitated one.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB38rpvFCrtQ%253D%253D&md5=89c62f5aa46456f80605a4ef476af5bb
13. 13
  
  Ning, T. ; Pietarinen, H. ; Hyvarinen, O. ; Simonen, J. ; Genty, G. ; Kauranen, M. Strong second-harmonic generation in silicon nitride films. Appl. Phys. Lett. 2012, 100 , 161902, DOI: 10.1063/1.4704159
  
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  Strong second-harmonic generation in silicon nitride films
  
  Ning, Tingyin; Pietarinen, Henna; Hyvaerinen, Outi; Simonen, Janne; Genty, Goery; Kauranen, Martti
  
  Applied Physics Letters (2012), 100 (16), 161902/1-161902/4CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  
  The authors observe strong 2nd-harmonic generation from Si nitride films prepd. on fused SiO2 substrates by plasma enhanced CVD. The components of the 2nd-order nonlinear optical susceptibility tensor of the films are calibrated against quartz crystal. The dominant component has the magnitude of 2.5 pm/V, almost 2 orders of magnitude larger than reported for Si3N4, and ∼3 times larger than for the traditional nonlinear crystal of K dihydrogen phosphate. Si nitride has great potential for 2nd-order nonlinear optical devices, esp. in on-chip nanophotonics. (c) 2012 American Institute of Physics.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xls1WnsbY%253D&md5=95f2cdee0ddc16c1cfe6cbc02c586778
14. 14
  
  Lu, X. ; Moille, G. ; Rao, A. ; Westly, D. A. ; Srinivasan, K. Efficient photoinduced second-harmonic generation in silicon nitride photonics. Nat. Photonics 2021, 15 , 131– 136, DOI: 10.1038/s41566-020-00708-4
  
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  Efficient photoinduced second-harmonic generation in silicon nitride photonics
  
  Lu, Xiyuan; Moille, Gregory; Rao, Ashutosh; Westly, Daron A.; Srinivasan, Kartik
  
  Nature Photonics (2021), 15 (2), 131-136CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
  
  Silicon photonics lacks a second-order nonlinear optical (χ(2)) response in general, because the typical constituent materials are centrosym. and lack inversion symmetry, which prohibits χ(2) nonlinear processes such as second-harmonic generation (SHG). Here, we realize high SHG efficiency in silicon photonics by combining a photoinduced effective χ(2) nonlinearity with resonant enhancement and perfect phase matching. We show a conversion efficiency of (2,500 ± 100)% W-1 that is two to four orders of magnitude larger than previous field-induced SHG works. In particular, our devices realize milliwatt-level SHG output powers with up to (22 ± 1)% power conversion efficiency. This demonstration is a breakthrough in realizing efficient χ(2) processes in silicon photonics, and paves the way for further integration of self-referenced frequency combs and optical frequency refs.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXit1ChsrzI&md5=0697f94255016ac401c6767962fd73fc
15. 15
  
  Moss, D. J. ; Morandotti, R. ; Gaeta, A. L. ; Lipson, M. New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics. Nat. Photonics 2013, 7 , 597– 607, DOI: 10.1038/nphoton.2013.183
  
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  New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics
  
  Moss, David J.; Morandotti, Roberto; Gaeta, Alexander L.; Lipson, Michal
  
  Nature Photonics (2013), 7 (8), 597-607CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
  
  A review. Nonlinear photonic chips can generate and process signals all-optically with far superior performance to that possible electronically - particularly with respect to speed. Although silicon-on-insulator has been the leading platform for nonlinear optics, its high two-photon absorption at telecommunication wavelengths poses a fundamental limitation. We review recent progress in non-silicon CMOS-compatible platforms for nonlinear optics, with a focus on Si3N4 and Hydex. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation and ultrafast optical pulse generation and measurement. We highlight their potential future impact as well as the challenges to achieving practical solns. for many key applications.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhtFygsL3I&md5=8ae9a6349bb720567c630158bd3a9a5d
16. 16
  
  Wang, C. Y. ; Herr, T. ; Del'Haye, P. ; Schliesser, A. ; Hofer, J. ; Holzwarth, R. ; Hansch, T. W. ; Picque, N. ; Kippenberg, T. J. Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators. Nat. Commun. 2013, 4 , 1345, DOI: 10.1038/ncomms2335
  
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  Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators
  
  Wang C Y; Herr T; Del'Haye P; Schliesser A; Hofer J; Holzwarth R; Hansch T W; Picque N; Kippenberg T J
  
  Nature communications (2013), 4 (), 1345 ISSN:.
  
  The mid-infrared spectral range (λ~2-20 μm) is of particular importance as many molecules exhibit strong vibrational fingerprints in this region. Optical frequency combs--broadband optical sources consisting of equally spaced and mutually coherent sharp lines--are creating new opportunities for advanced spectroscopy. Here we demonstrate a novel approach to create mid-infrared optical frequency combs via four-wave mixing in a continuous-wave pumped ultra-high Q crystalline microresonator made of magnesium fluoride. Careful choice of the resonator material and design made it possible to generate a broadband, low-phase noise Kerr comb at λ=2.5 μm spanning 200 nm (≈10 THz) with a line spacing of 100 GHz. With its distinguishing features of compactness, efficient conversion, large mode spacing and high power per comb line, this novel frequency comb source holds promise for new approaches to molecular spectroscopy and is suitable to be extended further into the mid-infrared.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC3s3nvVWjtg%253D%253D&md5=00d588795f3beb9ffe9208130cb8303b
17. 17
  
  Gaeta, A. L. ; Lipson, M. ; Kippenberg, T. J. Photonic-chip-based frequency combs. Nat. Photonics 2019, 13 , 158– 169, DOI: 10.1038/s41566-019-0358-x
  
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  Photonic-chip-based frequency combs
  
  Gaeta, Alexander L.; Lipson, Michal; Kippenberg, Tobias J.
  
  Nature Photonics (2019), 13 (3), 158-169CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
  
  A Review. Recent developments in chip-based nonlinear photonics offer the tantalizing prospect of realizing many applications that can use optical frequency comb devices that have form factors smaller than 1 cm3 and that require less than 1 W of power. A key feature that enables such technol. is the tight confinement of light due to the high refractive index contrast between the core and the cladding. This simultaneously produces high optical nonlinearities and allows for dispersion engineering to realize and phase match parametric nonlinear processes with laser-pointer powers across large spectral bandwidths. In this Review, we summarize the developments, applications and underlying physics of optical frequency comb generation in photonic-chip waveguides via supercontinuum generation and in microresonators via Kerr-comb generation that enable comb technol. from the near-UV to the mid-IR regime.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXnsleqtLs%253D&md5=ef5542fcca8e02024357b2f4f3fd7c53
18. 18
  
  Makarov, S. V. ; Petrov, M. I. ; Zywietz, U. ; Milichko, V. ; Zuev, D. ; Lopanitsyna, N. ; Kuksin, A. ; Mukhin, I. ; Zograf, G. ; Ubyivovk, E. ; Smirnova, D. A. ; Starikov, S. ; Chichkov, B. N. ; Kivshar, Y. S. Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles. Nano Lett. 2017, 17 , 3047– 3053, DOI: 10.1021/acs.nanolett.7b00392
  
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  18
  
  Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles
  
  Makarov, Sergey V.; Petrov, Mihail I.; Zywietz, Urs; Milichko, Valentin; Zuev, Dmitry; Lopanitsyna, Natalia; Kuksin, Alexey; Mukhin, Ivan; Zograf, George; Ubyivovk, Evgeniy; Smirnova, Daria A.; Starikov, Sergey; Chichkov, Boris N.; Kivshar, Yuri S.
  
  Nano Letters (2017), 17 (5), 3047-3053CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  
  Exptl. and theor., resonantly excited nanocryst. Si nanoparticles fabricated by an optimized laser printing technique can exhibit strong 2nd-harmonic generation (SHG) effects was demonstrated. An unexpectedly high yield of the nonlinear conversion is attributed to a nanocryst. structure of nanoparticles supporting the Mie resonances. The demonstrated efficient SHG at green light from a single Si nanoparticle is 2 orders of magnitude higher than that from unstructured Si films. This efficiency is significantly higher than that of many plasmonic nanostructures and small Si nanoparticles in the visible range, and it can be useful for a design of nonlinear nanoantennas and Si-based integrated light sources.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXmtFCksr4%253D&md5=0a66e56fddf545bfed041be31ccacf08
19. 19
  
  van Loon, M. A. W. ; Stavrias, N. ; Le, N. H. ; Litvinenko, K. L. ; Greenland, P. T. ; Pidgeon, C. R. ; Saeedi, K. ; Redlich, B. ; Aeppli, G. ; Murdin, B. N. Giant multiphoton absorption for THz resonances in silicon hydrogenic donors. Nat. Photonics 2018, 12 , 179, DOI: 10.1038/s41566-018-0111-x
  
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  Giant multiphoton absorption for THz resonances in silicon hydrogenic donors
  
  van Loon, M. A. W.; Stavrias, N.; Le, Nguyen H.; Litvinenko, K. L.; Greenland, P. T.; Pidgeon, C. R.; Saeedi, K.; Redlich, B.; Aeppli, G.; Murdin, B. N.
  
  Nature Photonics (2018), 12 (3), 179-184CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
  
  The absorption of multiple photons when there is no resonant intermediate state is a well-known nonlinear process in at. vapors, dyes and semiconductors. The N-photon absorption (NPA) rate for donors in semiconductors scales proportionally from hydrogenic atoms in vacuum with the dielec. const. and inversely with the effective mass, factors that carry exponents 6N and 4N, resp., suggesting that extremely large enhancements are possible. We obsd. 1PA, 2PA and 3PA in Si:P with a terahertz free-electron laser. The 2PA coeff. for 1s-2s at 4.25 THz was 400,000,000 GM (=4 × 10-42 cm4 s), many orders of magnitude larger than is available in other systems. Such high cross-sections allow us to enter a regime where the NPA cross-section exceeds that of 1PA-i.e., when the intensity approaches the binding energy per Bohr radius squared divided by the uncertainty time (only 3.84 MW cm-2 in silicon)-and will enable new kinds of terahertz quantum control.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjsFWls7w%253D&md5=ef8500321bc20370a753d819447e19bb
20. 20
  
  Le, N. H. ; Lanskii, G. V. ; Aeppli, G. ; Murdin, B. N. Giant non-linear susceptibility of hydrogenic donors in silicon and germanium. Light: Sci. Appl. 2019, 8 , 64, DOI: 10.1038/s41377-019-0174-6
  
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  20
  
  Giant non-linear susceptibility of hydrogenic donors in silicon and germanium
  
  Le Nguyen H; Murdin Benedict N; Lanskii Grigory V; Aeppli Gabriel; Aeppli Gabriel; Aeppli Gabriel
  
  Light, science & applications (2019), 8 (), 64 ISSN:.
  
  Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals. Here, we derive the equivalent technique for hydrogenic impurities in multi-valley semiconductors. While the absorption has useful applications, it is primarily a loss process; conversely, the non-linear susceptibility is a crucial parameter for active photonic devices. For Si:P, we predict the hyperpolarizability ranges from χ((3))/n3D = 2.9 to 580 × 10(-38) m(5)/V(2) depending on the frequency, even while avoiding resonance. Using samples of a reasonable density, n3D, and thickness, L, to produce third-harmonic generation at 9 THz, a frequency that is difficult to produce with existing solid-state sources, we predict that χ((3)) should exceed that of bulk InSb and χ((3))L should exceed that of graphene and resonantly enhanced quantum wells.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3MjhtVyrtQ%253D%253D&md5=f25d5330650c955a2ec130e64cae9252
21. 21
  
  Meng, F. ; Thomson, M. D. ; ul-Islam, Q. ; Klug, B. ; Pashkin, A. ; Schneider, H. ; Roskos, H. G. Intracavity third-harmonic generation in Si:B pumped by intense terahertz pulses. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 102 , 075205, DOI: 10.1103/PhysRevB.102.075205
22. 22
  
  Fischer, M. ; Riede, A. ; Gallacher, K. ; Frigerio, J. ; Pellegrini, G. ; Ortolani, M. ; Paul, D. J. ; Isella, G. ; Leitenstorfer, A. ; Biagioni, P. ; Brida, D. Plasmonic mid-infrared third harmonic generation in germanium nanoantennas. Light: Sci. Appl. 2018, 7 , 106, DOI: 10.1038/s41377-018-0108-8
  
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  22
  
  Plasmonic mid-infrared third harmonic generation in germanium nanoantennas
  
  Fischer, Marco P.; Riede, Aaron; Gallacher, Kevin; Frigerio, Jacopo; Pellegrini, Giovanni; Ortolani, Michele; Paul, Douglas J.; Isella, Giovanni; Leitenstorfer, Alfred; Biagioni, Paolo; Brida, Daniele
  
  Light: Science & Applications (2018), 7 (1), 106CODEN: LSAIAZ; ISSN:2047-7538. (Nature Research)
  
  We demonstrate third harmonic generation in plasmonic antennas consisting of highly doped germanium grown on silicon substrates and designed to be resonant in the mid-IR frequency range that is inaccessible with conventional nonlinear plasmonic materials. Owing to the near-field enhancement, the result is an ultrafast, subdiffraction, coherent light source with a wavelength tunable between 3 and 5μm, and ideally overlapping with the fingerprint region of mol. vibrations. To observe the nonlinearity in this challenging spectral window, a high-power femtosecond laser system equipped with parametric frequency conversion in combination with an all-reflective confocal microscope setup is employed. We demonstrate spatially resolved maps of the linear scattering cross section and the nonlinear emission of single isolated antenna structures. A clear third-order power dependence as well as mid-IR emission spectra prove the nonlinear nature of the light emission. Simulations support the obsd. resonance length of the double-rod antenna and demonstrate that the field enhancement inside the antenna material is responsible for the nonlinear frequency mixing.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVygsbbE&md5=5861ae5b57080c73a387d849163cd4f6
23. 23
  
  Rosencher, E. ; Fiore, A. ; Vinter, B. ; Berger, V. ; Bois, Ph ; Nagle, J. Quantum engineering of optical nonlinearities. Science 1996, 271 , 168– 173, DOI: 10.1126/science.271.5246.168
  
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  Quantum engineering of optical nonlinearities
  
  Rosencher, E.; Fiore, A.; Vinter, B.; Berger, V.; Bois, Ph.; Nagle, J.
  
  Science (Washington, D. C.) (1996), 271 (5246), 168-73CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  
  Second-order optical nonlinearities in materials are of paramount importance for optical wavelength conversion techniques, which are the basis of new high-resoln. spectroscopic tools. Semiconductor technol. now makes it possible to design and fabricate artificially asym. quantum structure sin which optical nonlinearities can be calcd. and optimized from 1st principles. Extremely large 2nd-order susceptibilities can be obtained in these asym. quantum wells. Also, properties such as double resonance enhancement or elec. field control will open the way to new devices, such as fully solid-state optical parametric oscillators. A review with 40 refs.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XktFOlsA%253D%253D&md5=b9ebdc095bd0dd07625beb01c0fe2d41
24. 24
  
  Sirtori, C.; Capasso, F.; Sivco, D. L.; Cho, A. Y. Nonlinear optics in coupled-quantum-well quasi-molecules. Semiconductors and Semimetals; Elsevier, 1999; Vol 66, Ch. 2, pp 85– 125.
25. 25
  
  Vodopyanov, K. L. ; O'Neill, K. ; Serapiglia, G. B. ; Phillips, C. C. ; Hopkinson, M. ; Vurgaftman, I. ; Meyer, J. R. Phase-matched second harmonic generation in asymmetric double quantum wells. Appl. Phys. Lett. 1998, 72 , 2654– 2656, DOI: 10.1063/1.121088
  
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  Phase-matched second harmonic generation in asymmetric double quantum wells
  
  Vodopyanov, K. L.; O'Neill, K.; Serapiglia, G. B.; Phillips, C. C.; Hopkinson, M.; Vurgaftman, I.; Meyer, J. R.
  
  Applied Physics Letters (1998), 72 (21), 2654-2656CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  
  Efficient (∼1%) second harmonic generation, resonantly enhanced near λ=8.6 μm, has been obsd. in asym. double multi-quantum well structures. We used (i) edge-emitting waveguide geometry where the phase matching was achieved by incorporating a sep. multiple quantum well region which modifies (via the Kramers-Kronig relation) the dispersion of light and (ii) 45° wedge multi-bounce geometry where the phases of second harmonic waves generated at sequential bounces were synchronized by changing the angle of incidence.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXjtV2rtL8%253D&md5=c20fb22cda5be2a0d4fc0cfa066f98c3
26. 26
  
  Lee, J. ; Tymchenko, M. ; Argyropoulos, C. ; Chen, P.-Y. ; Lu, F. ; Demmerle, F. ; Boehm, G. ; Amann, M.-C. ; Alu, A. ; Belkin, M. A. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature 2014, 511 , 65– 69, DOI: 10.1038/nature13455
  
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  Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions
  
  Lee, Jongwon; Tymchenko, Mykhailo; Argyropoulos, Christos; Chen, Pai-Yen; Lu, Feng; Demmerle, Frederic; Boehm, Gerhard; Amann, Markus-Christian; Alu, Andrea; Belkin, Mikhail A.
  
  Nature (London, United Kingdom) (2014), 511 (7507), 65-69CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  
  Intersubband transitions in n-doped multi-quantum-well semiconductor heterostructures make it possible to engineer one of the largest known nonlinear optical responses in condensed matter systems-but this nonlinear response is limited to light with elec. field polarized normal to the semiconductor layers. In a different context, plasmonic metasurfaces (thin conductor-dielec. composite materials) have been proposed as a way of strongly enhancing light-matter interaction and realizing ultrathin planarized devices with exotic wave properties. Here we propose and exptl. realize metasurfaces with a record-high nonlinear response based on the coupling of electromagnetic modes in plasmonic metasurfaces with quantum-engineered electronic intersubband transitions in semiconductor heterostructures. We show that it is possible to engineer almost any element of the nonlinear susceptibility tensor of these structures, and we exptl. verify this concept by realizing a 400-nm-thick metasurface with nonlinear susceptibility of greater than 5 × 104 picometres per V for second harmonic generation at a wavelength of about 8 μm under normal incidence. This susceptibility is many orders of magnitude larger than any second-order nonlinear response in optical metasurfaces measured so far. The proposed structures can act as ultrathin highly nonlinear optical elements that enable efficient frequency mixing with relaxed phase-matching conditions, ideal for realizing broadband frequency up- and down-conversions, phase conjugation and all-optical control and tunability over a surface.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtV2qtbzN&md5=ace2af147e377ebd7a001e5694c45632
27. 27
  
  Sarma, R. ; De Ceglia, D. ; Nookala, N. ; Vincenti, M. A. ; Campione, S. ; Wolf, O. ; Scalora, M. ; Sinclair, M. B. ; Belkin, A. ; Brener, I. Broadband and efficient second-harmonic generation from a hybrid dielectric metasurface/semiconductor quantum-well structure. ACS Photonics 2019, 6 , 1458– 1465, DOI: 10.1021/acsphotonics.9b00114
  
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  27
  
  Broadband and Efficient Second-Harmonic Generation from a Hybrid Dielectric Metasurface/Semiconductor Quantum-Well Structure
  
  Sarma, Raktim; de Ceglia, Domenico; Nookala, Nishant; Vincenti, Maria A.; Campione, Salvatore; Wolf, Omri; Scalora, Michael; Sinclair, Michael B.; Belkin, Mikhail A.; Brener, Igal
  
  ACS Photonics (2019), 6 (6), 1458-1465CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
  
  A prominent nonlinear optical phenomenon that is extensively studied using nanostructured materials is 2nd-harmonic generation (SHG) as it has applications in various fields. Achieving efficient SHG from a nanostructure requires a large 2nd-order nonlinear susceptibility of the material system and large electromagnetic fields. For practical applications, the nanostructures should also have low losses, high damage thresholds, large bandwidths, wavelength scalability, dual mode operation in transmission and reflection, monolithic integrability, and ease of fabrication. While various approaches demonstrated efficient SHG, to the best of the authors' knowledge, none demonstrated all these desired qualities simultaneously. Here, the authors present a hybrid approach for realizing efficient SHG in an ultrathin dielec.-semiconductor nonlinear device with all the above-mentioned desired properties. The authors' approach uses high quality factor leaky mode resonances in dielec. metasurfaces that are coupled to intersubband transitions of semiconductor quantum wells. Using the authors' device, the authors demonstrate SHG at pump wavelengths ranging from 8.5 to 11 μm, with a max. 2nd-harmonic nonlinear conversion factor of 1.1 mW/W2 and max. 2nd-harmonic conversion efficiency of 2.5 × 10-5 at modest pump intensities of 10 kW/cm2. The authors' results open a new direction for designing low loss, broadband, and efficient ultrathin nonlinear optical devices.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtVagsrvP&md5=2588c9c7087a0da93b934ee06ba31be6
28. 28
  
  Frigerio, J. ; Ballabio, A. ; Ortolani, M. ; Virgilio, M. Modeling of second harmonic generation in hole-doped silicon-germanium quantum wells for mid-infrared sensing. Opt. Express 2018, 26 , 31861– 31872, DOI: 10.1364/OE.26.031861
  
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  28
  
  Modeling of second harmonic generation in hole-doped silicon-germanium quantum wells for mid-infrared sensing
  
  Frigerio, Jacopo; Ballabio, Andrea; Ortolani, Michele; Virgilio, Michele
  
  Optics Express (2018), 26 (24), 31861-31872CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
  
  The development of Ge and SiGe chem. vapor deposition techniques on silicon wafers has enabled the integration of multi-quantum well structures in silicon photonics chips for nonlinear optics with potential applications to integrated nonlinear optics, however research has focused up to now on undoped quantum wells and interband optical excitations. In this work, we present model calcns. for the giant nonlinear coeffs. provided by intersubband transitions in hole-doped Ge/SiGe and Si/SiGe multi-quantum wells. We employ a valence band-structure model for Si1-xGex to calc. the confined hole states of asym.-coupled quantum wells for second-harmonic generation in the mid-IR. We calc. the nonlinear emission spectra from the second-order susceptibility tensor, including the particular vertical emission spectra of valence-band quantum wells. Two possible nonlinear mid-IR sensor architectures, one based on waveguides and another based on metasurfaces, are described as perspective application.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXnt1Ohtbg%253D&md5=7e427b01b8f30148f0cce0558dad33ec
29. 29
  
  Fischer, M. P. ; Schmidt, C. ; Sakat, E. ; Stock, E. ; Samarelli, A. ; Frigerio, J. ; Ortolani, M. ; Paul, D. J. ; Isella, G. ; Leitenstorfer, A. ; Biagioni, P. ; Brida, D. Optical activation of germanium plasmonic antennas in the mid-infrared. Phys. Rev. Lett. 2016, 117 , 047401, DOI: 10.1103/PhysRevLett.117.047401
  
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  29
  
  Optical activation of germanium plasmonic antennas in the mid-infrared
  
  Fischer, Marco P.; Schmidt, Christian; Sakat, Emilie; Stock, Johannes; Samarelli, Antonio; Frigerio, Jacopo; Ortolani, Michele; Paul, Douglas J.; Isella, Giovanni; Leitenstorfer, Alfred; Biagioni, Paolo; Brida, Daniele
  
  Physical Review Letters (2016), 117 (4), 047401/1-047401/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  
  Impulsive interband excitation with femtosecond near-IR pulses establishes a plasma response in intrinsic germanium structures fabricated on a silicon substrate. This direct approach activates the plasmonic resonance of the Ge structures and enables their use as optical antennas up to the mid-IR spectral range. The optical switching lasts for hundreds of picoseconds until charge recombination red shifts the plasma frequency. The full behavior of the structures is modeled by the electrodynamic response established by an electron-hole plasma in a regular array of antennas.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XitFaktr7M&md5=c6efa09472efefbad89d18e569c8f3a5
30. 30
  
  Seto, M. ; Helm, M. ; Moussa, Z. ; Boucaud, P. ; Julien, F. H. ; Lourtioz, J.-M. ; Nützel, J. F. ; Abstreiter, G. Second-harmonic generation in asymmetric Si/SiGe quantum wells. Appl. Phys. Lett. 1994, 65 , 2969– 2971, DOI: 10.1063/1.113028
  
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  Second-harmonic generation in asymmetric Si/SiGe quantum wells
  
  Seto, M.; Helm, M.; Moussa, Z.; Boucaud, P.; Julien, F. H.; Lourtioz, J.-M.; Nutzel, J. F.; Abstreiter, G.
  
  Applied Physics Letters (1994), 65 (23), 2969-71CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  
  The observation of IR 2nd-harmonic generation in asym. Si/SiGe p-doped quantum wells is reported. The generated signal stems entirely from valence intersubband transitions, since bulk Si, with an inversion sym. crystal structure, has a zero 2nd-order susceptibility. The expts. were performed using a Q-switched CO2 laser operating at 10.56 μm and give a nonlinear susceptibility of 5 × 10-8 m/V.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXitlOmtLc%253D&md5=00e872e1a7a84e132c9e8be1971aba92
31. 31
  
  Grimm, C. V.-B. ; Priegnitz, M. ; Winnerl, S. ; Schneider, H. ; Helm, M. ; Biermann, K. ; Künzel, H. Intersubband relaxation dynamics in single and double quantum wells based on strained InGaAs/AlAs/AlAsSb. Appl. Phys. Lett. 2007, 91 , 191121, DOI: 10.1063/1.2809409
  
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  Intersubband relaxation dynamics in single and double quantum wells based on strained InGaAs/AlAs/AlAsSb
  
  Grimm, C. V.-B.; Priegnitz, M.; Winnerl, S.; Schneider, H.; Helm, M.; Biermann, K.; Kuenzel, H.
  
  Applied Physics Letters (2007), 91 (19), 191121/1-191121/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  
  Intersubband relaxation dynamics in single and coupled double quantum well (QW) structures based on strained InGaAs/AlAs/AlAsSb were studied by femtosecond pump probe spectroscopy at wavelengths around 2 μm. For single QWs, the transient transmission was obsd. to decay exponentially with a time const. of 2 ps, showing that side valleys have negligible influence on the intersubband relaxation dynamics for strained InGaAs QWs. For double QWs, the pump-probe signal at the intersubband energy involving the two electronic levels located at the wider QW exhibits an induced absorption component attributed to the population of the 2nd subband (assocd. with the narrow QW) by hot electrons.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhtlGgtL3N&md5=c395cfb1968f6c8c331218a287582602
32. 32
  
  Qian, H. ; Li, S. ; Chen, C. F. ; Hsu, S. W. ; Bopp, S. E. ; Ma, Q. ; Tao, A. R. ; Liu, Z. Large optical nonlinearity enabled by coupled metallic quantum wells. Light: Sci. Appl. 2019, 8 , 13, DOI: 10.1038/s41377-019-0123-4
  
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  Large optical nonlinearity enabled by coupled metallic quantum wells
  
  Qian Haoliang; Li Shilong; Chen Ching-Fu; Ma Qian; Liu Zhaowei; Hsu Su-Wen; Tao Andrea R; Bopp Steven Edward; Tao Andrea R; Liu Zhaowei; Liu Zhaowei
  
  Light, science & applications (2019), 8 (), 13 ISSN:.
  
  New materials that exhibit strong second-order optical nonlinearities at a desired operational frequency are of paramount importance for nonlinear optics. Giant second-order susceptibility χ((2)) has been obtained in semiconductor quantum wells (QWs). Unfortunately, the limited confining potential in semiconductor QWs causes formidable challenges in scaling such a scheme to the visible/near-infrared (NIR) frequencies for more vital nonlinear-optic applications. Here, we introduce a metal/dielectric heterostructured platform, i.e., TiN/Al2O3 epitaxial multilayers, to overcome that limitation. This platform has an extremely high χ((2)) of approximately 1500 pm/V at NIR frequencies. By combining the aforementioned heterostructure with the large electric field enhancement afforded by a nanostructured metasurface, the power efficiency of second harmonic generation (SHG) achieved 10(-4) at an incident pulse intensity of 10 GW/cm(2), which is an improvement of several orders of magnitude compared to that of previous demonstrations from nonlinear surfaces at similar frequencies. The proposed quantum-engineered heterostructures enable efficient wave mixing at visible/NIR frequencies into ultracompact nonlinear optical devices.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3cjntFyrug%253D%253D&md5=fb35bea448c5af9d5220c8b70752f90a
33. 33
  
  Wolf, O. ; Campione, S. ; Benz, A. ; Ravikumar, A. P. ; Liu, S. ; Luk, T. S. ; Kadlec, E. A. ; Shaner, E. A. ; Klem, J. F. ; Sinclair, M. B. ; Brener, I. Phased-array sources based on nonlinear metamaterial nanocavities. Nat. Commun. 2015, 6 , 7667, DOI: 10.1038/ncomms8667
  
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  Phased-array sources based on nonlinear metamaterial nanocavities
  
  Wolf Omri; Campione Salvatore; Benz Alexander; Liu Sheng; Luk Ting S; Brener Igal; Wolf Omri; Campione Salvatore; Benz Alexander; Liu Sheng; Luk Ting S; Kadlec Emil A; Shaner Eric A; Klem John F; Sinclair Michael B; Brener Igal; Ravikumar Arvind P
  
  Nature communications (2015), 6 (), 7667 ISSN:.
  
  Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization. As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (∼5 μm): a beam splitter and a polarizing beam splitter. Proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC2MbovVOitA%253D%253D&md5=6cf3963648ba86ae0de04ed6b818f60d
34. 34
  
  Chaisakul, P. ; Marris-Morini, D. ; Frigerio, J. ; Chrastina, D. ; Rouifed, M.-S. ; Cecchi, S. ; Crozat, P. ; Isella, G. ; Vivien, L. Integrated germanium optical interconnects on silicon substrates. Nat. Photonics 2014, 8 , 482– 488, DOI: 10.1038/nphoton.2014.73
  
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  Integrated germanium optical interconnects on silicon substrates
  
  Chaisakul, Papichaya; Marris-Morini, Delphine; Frigerio, Jacopo; Chrastina, Daniel; Rouifed, Mohamed-Said; Cecchi, Stefano; Crozat, Paul; Isella, Giovanni; Vivien, Laurent
  
  Nature Photonics (2014), 8 (6), 482-488CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
  
  Monolithic integration of optoelectronics with electronics is a much-desired functionality. Here, we demonstrate that it is possible to realize low-loss Ge quantum-well photonic interconnects on Si wafers. We show that Ge-rich Si1-xGex virtual substrates can act as a passive, high-quality optical waveguide on which low-temp., epitaxial growth of Ge quantum-well devices can be realized. As a proof of concept, the photonic integration of a passive Si0.16Ge0.84 waveguide and two Ge/SiGe multi-quantum-well active devices, an optical modulator and a photodetector was realized to form a photonic interconnect using a single epitaxial growth step. This demonstration confirms that Ge quantum-well interconnects are feasible for low-voltage, broadband optical links integrated on Si chips. Our approach can be extended to any kind of Ge-based optoelectronic device working within telecommunication wavelengths as long as a suitable Ge concn. is selected for the Ge-rich virtual substrate.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXnslGltLs%253D&md5=f189eadbda980ace621d585bc29402a3
35. 35
  
  Kuo, Y.-H. ; Lee, Y. K. ; Ge, Y. ; Ren, S. ; Roth, J. E. ; Kamins, T. I. ; Miller, D. A. B. ; Harris, J. S. Strong quantum confined Stark effect in germanium quantum-well structures on silicon. Nature 2005, 437 , 1334– 1336, DOI: 10.1038/nature04204
  
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  Strong quantum-confined Stark effect in germanium quantum-well structures on silicon
  
  Kuo, Yu-Hsuan; Lee, Yong Kyu; Ge, Yangsi; Ren, Shen; Roth, Jonathan E.; Kamins, Theodore I.; Miller, David A. B.; Harris, James S.
  
  Nature (London, United Kingdom) (2005), 437 (7063), 1334-1336CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  
  Silicon is the dominant semiconductor for electronics, but there is now a growing need to integrate such components with optoelectronics for telecommunications and computer interconnections. Silicon-based optical modulators have recently been successfully demonstrated; but because the light modulation mechanisms in silicon are relatively weak, long (for example, several millimetres) devices or sophisticated high-quality-factor resonators have been necessary. Thin quantum-well structures made from III-V semiconductors such as GaAs, InP and their alloys exhibit the much stronger quantum-confined Stark effect (QCSE) mechanism, which allows modulator structures with only micrometres of optical path length. Such III-V materials are unfortunately difficult to integrate with silicon electronic devices. Germanium is routinely integrated with silicon in electronics, but previous silicon-germanium structures have also not shown strong modulation effects. Here we report the discovery of the QCSE, at room temp., in thin germanium quantum-well structures grown on silicon. The QCSE here has strengths comparable to that in III-V materials. Its clarity and strength are particularly surprising because germanium is an indirect gap semiconductor; such semiconductors often display much weaker optical effects than direct gap materials (such as the III-V materials typically used for optoelectronics). This discovery is very promising for small, high-speed, low-power optical output devices fully compatible with silicon electronics manuf.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtFCrur3J&md5=30aaf6962cd3709202c390cb15b777e2
36. 36
  
  Lever, L. ; Hu, Y. ; Myronov, M. ; Liu, X. ; Owens, N. ; Gardes, F. Y. ; Marko, S. J. ; Sweeney, S. J. ; Ikonic, Z. ; Leadley, D. R. ; Reed, G. T. ; Kelsall, R. W. Modulation of the absorption coefficient at 1.3 mm in Ge/SiGe multiple quantum well heterostructures on silicon. Opt. Lett. 2011, 36 , 4158– 4160, DOI: 10.1364/OL.36.004158
  
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  Modulation of the absorption coefficient at 1.3μm in Ge/SiGe multiple quantum well heterostructures on silicon
  
  Lever, L.; Hu, Y.; Myronov, M.; Liu, X.; Owens, N.; Gardes, F. Y.; Marko, I. P.; Sweeney, S. J.; Ikonic, Z.; Leadley, D. R.; Reed, G. T.; Kelsall, R. W.
  
  Optics Letters (2011), 36 (21), 4158-4160CODEN: OPLEDP; ISSN:0146-9592. (Optical Society of America)
  
  We report modulation of the absorption coeff. at 1.3 μm in Ge/SiGe multiple quantum well heterostructures on silicon via the quantum-confined Stark effect. Strain engineering was exploited to increase the direct optical band-gap in the Ge quantum wells. We grew 9nm-thick Ge quantum wells on a relaxed Si0.22Ge0.78 buffer and a contrast in the absorption coeff. of a factor of greater than 3.2 was achieved in the spectral range 1290-1315nm.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xht1yitro%253D&md5=55f445aa09081f3671bf592146b5a064
37. 37
  
  Grange, T. ; Stark, D. ; Scalari, G. ; Faist, J. ; Persichetti, L. ; Di Gaspare, L. ; De Seta, M. ; Ortolani, M. ; Paul, D. J. ; Capellini, G. ; Birner, S. ; Virgilio, M. Room temperature operation of n-type Ge/SiGe terahertz quantum cascade lasers predicted by non-equilibrium Green's functions. Appl. Phys. Lett. 2019, 114 , 111102, DOI: 10.1063/1.5082172
  
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  Room temperature operation of n-type Ge/SiGe terahertz quantum cascade lasers predicted by non-equilibrium Green's functions
  
  Grange, Thomas; Stark, David; Scalari, Giacomo; Faist, Jerome; Persichetti, Luca; Di Gaspare, Luciana; De Seta, Monica; Ortolani, Michele; Paul, Douglas J.; Capellini, Giovanni; Birner, Stefan; Virgilio, Michele
  
  Applied Physics Letters (2019), 114 (11), 111102/1-111102/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  
  N-type Ge/SiGe terahertz quantum cascade lasers are investigated using non-equil. Green's functions calcns. We compare the temp. dependence of the terahertz gain properties with an equiv. GaAs/AlGaAs quantum cascade laser design. In the Ge/SiGe case, the gain is found to be much more robust to temp. increase, enabling operation up to room temp. The better temp. robustness with respect to III-V is attributed to the much weaker interaction with optical phonons. The effect of lower interface quality is investigated and can be partly overcome by engineering smoother quantum confinement. (c) 2019 American Institute of Physics.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXls1ehu7Y%253D&md5=e2a0c365c284a3e6b0e4219721f389f8
38. 38
  
  Ciano, C. ; Virgilio, M. ; Montanari, M. ; Persichetti, L. ; Di Gaspare, L. ; Ortolani, M. ; Baldassarre, L. ; Zoellner, M.H. ; Skibitzki, O. ; Scalari, G. ; Faist, J. ; Paul, D.J. ; Scuderi, M. ; Nicotra, G. ; Grange, T. ; Birner, S. ; Capellini, G. ; De Seta, M. Control of electron-state coupling in asymmetric Ge/Si–Ge quantum wells. Phys. Rev. Appl. 2019, 11 , 014003, DOI: 10.1103/PhysRevApplied.11.014003
  
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  Control of Electron-State Coupling in Asymmetric Ge/Si-Ge Quantum Wells
  
  Ciano, C.; Virgilio, M.; Montanari, M.; Persichetti, L.; Di Gaspare, L.; Ortolani, M.; Baldassarre, L.; Zoellner, M. H.; Skibitzki, O.; Scalari, G.; Faist, J.; Paul, D. J.; Scuderi, M.; Nicotra, G.; Grange, T.; Birner, S.; Capellini, G.; De Seta, M.
  
  Physical Review Applied (2019), 11 (1), 014003CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)
  
  Theor. predictions indicate that the n-type Ge/Si-Ge multi-quantum-well system is the most promising material for the realization of a Si-compatible THz quantum cascade laser operating at room temp. To advance in this direction, we study, both exptl. and theor., asym. coupled multi-quantum-well samples based on this material system, that can be considered as the basic building block of a cascade architecture. Extensive structural characterization shows the high material quality of strain-symmetrized structures grown by chem. vapor deposition, down to the ultrathin barrier limit. Moreover, THz absorption spectroscopy measurements supported by theor. modeling unambiguously demonstrate inter-well coupling and wavefunction tunneling. The agreement between exptl. data and simulations allows us to characterize the tunneling barrier parameters and, in turn, achieve highly controlled engineering of the electronic structure in forthcoming unipolar cascade systems based on n-type Ge/Si-Ge multi-quantum-wells.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXnslWqsLY%253D&md5=d161e33f6a6753ce1c4ed68f1a71ba78
39. 39
  
  Chang, Y.-C. ; Paeder, V. ; Hvozdara, L. ; Hartmann, J.-M. ; Herzig, H. P. Low-loss germanium strip waveguides on silicon for the mid-infrared. Opt. Lett. 2012, 37 , 2883– 2885, DOI: 10.1364/OL.37.002883
  
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  39
  
  Low-loss germanium strip waveguides on silicon for the mid-infrared
  
  Chang, Yu-Chi; Paeder, Vincent; Hvozdara, Lubos; Hartmann, Jean-Michel; Herzig, Hans Peter
  
  Optics Letters (2012), 37 (14), 2883-2885CODEN: OPLEDP; ISSN:0146-9592. (Optical Society of America)
  
  Mid-IR photonics in silicon needs low-loss integrated waveguides. While monocryst. germanium waveguides on silicon have been proposed, exptl. realization has not been reported. Here we demonstrate a germanium strip waveguide on a silicon substrate. It is designed for single mode transmission of light in transverse magnetic (TM) polarization generated from quantum cascade lasers at a wavelength of 5.8 μm. The propagation losses were measured with the Fabry-Perot resonance method. The lowest achieved propagation loss is 2.5 dB/cm, while the bending loss is measured to be 0.12 dB for a 90° bend with a radius of 115 μm.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsVSnu7rN&md5=e6525c3743bd867cf3b0f7eee33d3b26
40. 40
  
  Brun, M. ; Labeye, P. ; Grand, G. ; Hartmann, J.-M. ; Boulila, F. ; Carras, M. ; Nicoletti, S. Low loss SiGe graded index waveguides for mid-IR applications. Opt. Express 2014, 22 , 508– 518, DOI: 10.1364/OE.22.000508
  
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  40
  
  Low loss SiGe graded index waveguides for mid-IR applications
  
  Brun, Mickael; Labeye, Pierre; Grand, Gilles; Hartmann, Jean-Michel; Boulila, Fahem; Carras, Mathieu; Nicoletti, Sergio
  
  Optics Express (2014), 22 (1), 508-518, 11 pp.CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
  
  In the last few years Mid IR (MIR) photonics has received renewed interest for a variety of com., scientific and military applications. This paper reports the design, the fabrication and the characterization of SiGe/Si based graded index waveguides and photonics integrated devices. The thickness and the Ge concn. of the core layer were optimized to cover the full [3 - 8 μm] band. The developed SiGe/Si stack has been used to fabricate straight waveguides and basic optical functions such as Y-junction, crossings and couplers. Straight waveguides showed losses as low as 1 dB/cm at λ = 4.5 μm and 2 dB/cm at 7.4 μm. Likewise straight waveguides, basic functions exhibit nearly theor. behavior with losses compatible with the implementation of more complex functions in integrated photonics circuits. To the best of our knowledge, the performances of those Mid-IR waveguides significantly exceed the state of the art, confirming the feasibility of using graded SiGe/Si devices in a wide range of wavelengths. These results represent a capital breakthrough to develop a photonic platform working in the Mid-IR range.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXptVKqs7c%253D&md5=8ac6441b6f8767bd46b35b99cb7a24b1
41. 41
  
  Nedeljkovic, M. ; Penades, J. S. ; Mittal, V. ; Murugan, S. M. ; Khokhar, A. Z. ; Littlejohns, C. ; Carpenter, L. G. ; Gawith, C. B. E. ; Wilkinson, J. S. ; Mashanovich, G. Z. Germanium-on-silicon waveguides operating at mid-infrared wavelengths up to 8.5 μm. Opt. Express 2017, 25 , 27431– 27441, DOI: 10.1364/OE.25.027431
  
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  41
  
  Germanium-on-silicon waveguides operating at mid-infrared wavelengths up to 8.5 μm
  
  Nedeljkovic, Milos; Penades, Jordi Soler; Mittal, Vinita; Senthil Murugan, Ganapathy; Khokhar, Ali Z.; Littlejohns, Callum; Carpenter, Lewis G.; Gawith, Corin B. E.; Wilkinson, James S.; Mashanovich, Goran Z.
  
  Optics Express (2017), 25 (22), 27431-27441CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
  
  We report transmission measurements of germanium on silicon waveguides in the 7.5-8.5 μm wavelength range, with a min. propagation loss of 2.5 dB/cm at 7.575 μm. However, we find an unexpected strongly increasing loss at higher wavelengths, potential causes of which we discuss in detail. We also demonstrate the first germanium on silicon multimode interferometers operating in this range, as well as grating couplers optimized for measurement using a long wavelength IR camera. Finally, we use an implementation of the "cut-back" method for loss measurements that allows simultaneous transmission measurement through multiple waveguides of different lengths, and we use dicing in the ductile regime for fast and reproducible high quality optical waveguide end-facet prepn.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXnsVyktLg%253D&md5=18b400d359ce8c9e0b9c12d78c852540
42. 42
  
  Ramirez, J. M. ; Liu, Q. ; Vakarin, V. ; Frigerio, J. ; Ballabio, A. ; Le Roux, X. ; Bouville, D. ; Vivien, L. ; Isella, G. ; Marris-Morini, D. Graded SiGe waveguides with broadband low-loss propagation in the mid infrared. Opt. Express 2018, 26 , 870– 877, DOI: 10.1364/OE.26.000870
  
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  Graded SiGe waveguides with broadband low-loss propagation in the mid infrared
  
  Ramirez, J. M.; Liu, Q.; Vakarin, V.; Frigerio, J.; Ballabio, A.; Le Roux, X.; Bouville, D.; Vivien, L.; Isella, G.; Marris-Morini, D.
  
  Optics Express (2018), 26 (2), 870-877CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
  
  Mid-IR (mid-IR) silicon photonics is expected to lead key advances in different areas including spectroscopy, remote sensing, nonlinear optics or free-space communications, among others. Still, the inherent limitations of the silicon-on-insulator (SOI) technol., namely the early mid-IR absorption of silicon oxide and silicon at λ∼3.6 μm and at λ ∼8.5 μm resp., remain the main stumbling blocks that prevent this platform to fully exploit the mid-IR spectrum (λ ∼2-20 μm). Here, we propose using a compact Ge-rich graded-index Si1-xGex platform to overcome this constraint. A flat propagation loss characteristic as low as 2-3 dB/cm over a wavelength span from λ = 5.5 μm to 8.5 μm is demonstrated in Ge-rich Si1-xGex waveguides of only 6 μm thick. The comparison of three different waveguides design with different vertical index profiles demonstrates the benefit of reducing the fraction of the guided mode that overlaps with the Si substrate to obtain such flat low loss behavior. Such Ge-rich Si1-xGex platforms may open the route towards the implementation of mid-IR photonic integrated circuits with low-loss beyond the Si multi-phonon absorption band onset, hence truly exploiting the full Ge transparency window up to λ ∼15 μm.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXit12qt7bM&md5=2d9fa4e497609ab82d433b2c62402369
43. 43
  
  Gallacher, K. ; Millar, R. W. ; Griškevičiu̅te, U. ; Baldassarre, L. ; Sorel, M. ; Ortolani, M. ; Paul, D. J. Low loss Ge-on-Si waveguides operating in the 8–14 μm atmospheric transmission window. Opt. Express 2018, 26 , 25667– 25675, DOI: 10.1364/OE.26.025667
  
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  Low loss Ge-on-Si waveguides operating in the 8-14 um atmospheric transmission window
  
  Gallacher, K.; Millar, R. W.; Griskeviciute, U.; Baldassarre, L.; Sorel, M.; Ortolani, M.; Paul, D. J.
  
  Optics Express (2018), 26 (20), 25667-25675CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
  
  Germanium-on-silicon waveguides were modeled, fabricated and characterized at wavelengths ranging from 7.5 to 11μm. Measured waveguide losses are below 5 dB/cm for both TE and TM polarization and reach values of ∼ 1 dB/cm for ≥ 10μm wavelengths for the TE polarization. This work demonstrates exptl. for the first time that Ge-on-Si is a viable waveguide platform for sensing in the mol. fingerprint spectral region. Detailed modeling and anal. is presented to identify the various loss contributions, showing that with practical techniques losses below 1 dB/cm could be achieved across the full measurement range.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVGktLrE&md5=326d37757fba57760ca1ea4c9851438c
44. 44
  
  Gallacher, K. ; Millar, R. W. ; Paul, D. J. ; Frigerio, J. ; Ballabio, A. ; Isella, G. ; Rusconi, F. ; Biagioni, P. ; Giliberti, V. ; Sorgi, A. ; Baldassarre, L. ; Ortolani, M. Characterization of integrated waveguides by atomic-force-microscopy-assisted mid-infrared imaging and spectroscopy. Opt. Express 2020, 28 , 22186– 22199, DOI: 10.1364/OE.393748
  
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  Characterization of integrated waveguides by atomic-force-microscopy-assisted mid-infrared imaging and spectroscopy
  
  Gallacher, Kevin; Millar, Ross W.; Paul, Douglas J.; Frigerio, Jacopo; Ballabio, Andrea; Isella, Giovanni; Rusconi, Francesco; Biagioni, Paolo; Giliberti, Valeria; Sorgi, Alessia; Baldassarre, Leonetta; Ortolani, Michele
  
  Optics Express (2020), 28 (15), 22186-22199CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
  
  A novel spectroscopy technique to enable the rapid characterization of discrete mid-IR integrated photonic waveguides is demonstrated. The technique utilizes lithog. patterned polymer blocks that absorb light strongly within the mol. fingerprint region. These act as integrated waveguide detectors when combined with an at. force microscope that measures the photothermal expansion when IR light is guided to the block. As a proof of concept, the technique is used to exptl. characterize propagation loss and grating coupler response of Ge-on-Si waveguides at wavelengths from 6 to 10μm. In addn., when the microscope is operated in scanning mode at fixed wavelength, the guided mode exiting the output facet is imaged with a lateral resoln. better than 500 nm i.e. below the diffraction limit. The characterization technique can be applied to any mid-IR waveguide platform and can provide non-destructive in-situ testing of discrete waveguide components.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitlSqtLrL&md5=477278931f2a3e4817a9ee5754b77ff6
45. 45
  
  Gallacher, K. ; Millar, R. W. ; Griškevičiu̅te, U. ; Sinclair, M. ; Sorel, M. ; Baldassarre, L. ; Ortolani, M. ; Soref, R. ; Paul, D. J. Ultra-broadband mid-infrared Ge-on-Si waveguide polarization rotator. APL Photonics 2020, 5 , 026102, DOI: 10.1063/1.5134973
  
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  Ultra-broadband mid-infrared Ge-on-Si waveguide polarization rotator
  
  Gallacher, Kevin; Millar, Ross W.; Griskeviciute, Ugne; Sinclair, Martin; Sorel, Marc; Baldassarre, Leonetta; Ortolani, Michele; Soref, Richard; Paul, Douglas J.
  
  APL Photonics (2020), 5 (2), 026102CODEN: APPHD2; ISSN:2378-0967. (American Institute of Physics)
  
  The design, modeling, micro-fabrication, and characterization of an ultra-broadband Ge-on-Si waveguide polarization rotator are presented. The polarization rotator is based on the mode evolution approach where adiabatic sym. and anti-sym. tapers are utilized to convert from the fundamental transverse magnetic to elec. mode. The device is shown to be extremely fabrication tolerant and simple to fabricate. The fabricated devices demonstrate a polarization extinction ratio of ≥15 dB over a 2μm bandwidth (9-11μm wavelength) with an av. insertion loss of <1 dB, which is an order of magnitude improvement compared to previously demonstrated devices. This device will provide polarization flexibility when integrating quantum cascade lasers on-chip for mid-IR waveguide mol. spectroscopy. (c) 2020 American Institute of Physics.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXnsVSgs74%253D&md5=191e0057673891b3837a1d288172c802
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  The possibility of the surface-emitting second-harmonic generation (SHG) based on intersubband transitions in multiple quantum-well (QW) structures is examd. theor. The crit. role of valence band mixing is demonstrated. The off-diagonal SHG coeffs., necessary for the surface-emitting SHG, are evaluated for the transitions between the valence subbands in GaAs/AlAs QW structures, and are found to be comparable in magnitude to the diagonal SHG coeffs. reported in the literature.
  
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  Isella, G. ; Chrastina, D. ; Rossner, B. ; Hackbarth, T. ; Herzog, H. J. ; Konig, U. ; Von Kanel, H. Low-energy plasma-enhanced chemical vapor deposition for strained Si and Ge heterostructures and devices. Solid-State Electron. 2004, 48 , 1317– 1323, DOI: 10.1016/j.sse.2004.01.013
  
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  Solid-State Electronics (2004), 48 (8), 1317-1323CODEN: SSELA5; ISSN:0038-1101. (Elsevier Science Ltd.)
  
  A review on the potential of low-energy plasma-enhanced chem. vapor deposition (LEPECVD) for the fabrication of strained Si and Ge heterostructures and devices. The technique is shown to be equally applicable to the formation of relaxed SiGe buffer layers, and to entire heterostructures including strained modulation doped channels. Pure Ge channels on Ge-rich linearly graded buffers are shown to exhibit low-temp. hole mobilities up to 120,000 cm2 V-1 s-1, limited by remote impurity and background impurity scattering rather than interface roughness scattering. Strained-Si modulation-doped field-effect transistors (n-MODFETs) with excellent frequency response have been fabricated by combining LEPECVD and MBE for buffer layer and active layer growth, resp. Maximum oscillation frequencies of n-MODFETs above 140 GHz have been achieved for active layer stacks both on buffers linearly graded to a Ge fraction of 40% at a rate of 10% per μ, and on const. compn. buffers which are 10 times thinner. The use of a thin buffer results in significantly less device self-heating.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjs1anu78%253D&md5=520153eec18dd29134b9d8a7c8b64abe
48. 48
  
  Bashir, A. ; Gallacher, K. ; Millar, R. W. ; Paul, D. J. ; Ballabio, A. ; Frigerio, J. ; Isella, G. ; Kriegner, D. ; Ortolani, M. ; Barthel, J. ; MacLaren, I. Interfacial sharpness and intermixing in a Ge-SiGe multiple quantum well structure. J. Appl. Phys. 2018, 123 , 035703, DOI: 10.1063/1.5001158
  
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  Journal of Applied Physics (Melville, NY, United States) (2018), 123 (3), 035703/1-035703/11CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
  
  A Ge-SiGe multiple quantum well structure created by low energy plasma enhanced CVD, with nominal well thickness of 5.4 nm sepd. by 3.6 nm SiGe spacers, is analyzed quant. using scanning TEM. Both high angle annular dark field imaging and EELS show that the interfaces are not completely sharp, suggesting that there is some intermixing of Si and Ge at each interface. Two methods are compared for the quantification of the spectroscopy datasets: a self-consistent approach that calcs. binary substitutional trends without requiring exptl. or computational k-factors from elsewhere and a stds.-based cross sectional calcn. While the cross section approach is ultimately more reliable, the self-consistent approach provides surprisingly good results. The Ge quantum wells are actually ∼95% Ge and the spacers, while apparently peaking at ∼35% Si, contain significant interdiffused Ge at each side. This result is not just an artifact of electron beam spreading in the sample, but mostly arising from a real chem. interdiffusion resulting from the growth. Similar results are found using x-ray diffraction from a similar area of the sample. Putting the results together suggests a real interdiffusion with a std. deviation of ∼0.87 nm, or put another way-a true width defined from 10%-90% of the compositional gradient of ∼2.9 nm. This suggests an intrinsic limit on how sharp such interfaces can be grown by this method and, while 95% Ge quantum wells (QWs) still behave well enough to have good properties, any attempt to grow thinner QWs would require modifications to the growth procedure to reduce this interdiffusion, to maintain a compn. of ≥95% Ge. (c) 2018 American Institute of Physics.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtlOmtbo%253D&md5=4b1295a2e1414e5f0affd086dedae6bd
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  Cecchi, S. ; Gatti, E. ; Chrastina, D. ; Frigerio, J. ; Mueller-Gubler, E. ; Paul, D. J. ; Guzzi, M. ; Isella, G. Thin SiGe virtual substrates for Ge heterostructures integration on silicon. J. Appl. Phys. 2014, 115 , 093502, DOI: 10.1063/1.4867368
  
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  Thin SiGe virtual substrates for Ge heterostructures integration on silicon
  
  Cecchi, S.; Gatti, E.; Chrastina, D.; Frigerio, J.; Muller Gubler, E.; Paul, D. J.; Guzzi, M.; Isella, G.
  
  Journal of Applied Physics (Melville, NY, United States) (2014), 115 (9), 093502/1-093502/6CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
  
  The possibility to reduce the thickness of the SiGe virtual substrate, required for the integration of Ge heterostructures on Si, without heavily affecting the crystal quality is becoming fundamental in several applications. The authors present 1 μm thick Si1-Ge buffers (with x > 0.7) having different designs which could be suitable for applications requiring a thin virtual substrate. The rationale is to reduce the lattice mismatch at the interface with the Si substrate by introducing compn. steps and/or partial grading. The relatively low growth temp. (475°) makes this approach appealing for complementary metal-oxide-semiconductor integration. For all the studied designs, a redn. of the threading dislocation d. compared to const. compn. Si1-Ge layers was obsd. The best buffer in terms of defects redn. was used as a virtual substrate for the deposition of a Ge/SiGe multiple quantum well structure. Room temp. optical absorption and photoluminescence anal. performed on nominally identical quantum wells grown on both a thick graded virtual substrate and the selected thin buffer demonstrates a comparable optical quality, confirming the effectiveness of the proposed approach. (c) 2014 American Institute of Physics.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXjvV2iurw%253D&md5=4f07e6ec7b7466438ec7651c6e1aa192
50. 50
  
  Grupp, A. ; Budweg, A. ; Fischer, M. P. ; Allerbeck, J. ; Soavi, G. ; Leitenstorfer, A. ; Brida, D. Broadly tunable ultrafast pump-probe system operating at multi-kHz repetition rate. J. Opt. 2018, 20 , 014005, DOI: 10.1088/2040-8986/aa9b07
  
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  Journal of Optics (Bristol, United Kingdom) (2018), 20 (1), 014005/1-014005/11CODEN: JOOPCA; ISSN:2040-8978. (IOP Publishing Ltd.)
  
  Femtosecond systems based on ytterbium as active medium are ideal for driving ultrafast optical parametric amplifiers in a broad frequency range. The excellent stability of the source and the repetition rate tunable to up to hundreds of kHz allow for the implementation of an advanced two-color pump probe setup with the capability to achieve excellent signal-to-noise performances with sub-10 fs temporal resoln.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitlWrsLvJ&md5=f9029172a6a136f1fd043facad06d137
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  Virgilio, M. ; Grosso, G. Valence and conduction intersubband transitions in SiGe; Ge-rich; quantum wells on [001] Si0.5Ge0.5 substrates: A tight-binding approach. J. Appl. Phys. 2006, 100 , 093506, DOI: 10.1063/1.2360144
  
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  Valence and conduction intersubband transitions in SiGe, Ge-rich, quantum wells on [001] Si0.5Ge0.5 substrates: A tight-binding approach
  
  Virgilio, Michele; Grosso, Giuseppe
  
  Journal of Applied Physics (2006), 100 (9), 093506/1-093506/6CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
  
  Electronic and optical properties of germanium-rich Si/SiGe quantum wells grown on Si0.5Ge0.5 substrates are investigated by a nearest neighbor tight-binding Hamiltonian. The basis set includes spds* orbitals with both spin states. Appropriate scaling laws account for strain effects. We present full electronic band structure calcns. both for valence and conduction bands. Confinement effects on the electronic states are considered in detail. Optical spectra related to hole and electron intersubband transitions are derived. Our results for optical absorption due to valence intersubband transitions show excellent agreement with exptl. spectra and previous k·p calcns. For the same quantum well samples, spectra due to conduction intersubband absorption are provided here.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xht1ajt7jM&md5=357686c9ef7c4b971aa3503f17284fae
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  Virgilio, M. ; Grosso, G. Valley splitting and optical intersubband transitions at parallel and normal incidence in [001]-Ge/SiGe quantum wells. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79 , 165310, DOI: 10.1103/PhysRevB.79.165310
  
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  Virgilio, Michele; Grosso, Giuseppe
  
  Physical Review B: Condensed Matter and Materials Physics (2009), 79 (16), 165310/1-165310/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  
  We investigate intervalley splitting in the conduction band of strained [001]-Ge quantum well (QW) systems with finite SiGe alloy barriers by means of a sp3d5s* tight-binding Hamiltonian. We find that interaction between germanium bulk L min. splits each confined subband into a doublet. We first characterize this splitting as a function of the well width and of the strength of a uniform elec. field superimposed along the growth direction. Varying the well width, an oscillating behavior of the splitting magnitude similar to that predicted for Si QW systems is obsd. and explained. Then we focus on the optical intersubband transitions occurring between states belonging to the fundamental and the first-excited doublets. Selection rules for intersubband transitions at normal and parallel incidence are discussed exploiting the parity character of the involved doublet states. Numerical results for IR-absorption spectra, evaluated for both sym. and biased Ge QWs, support our findings.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXlsVagtr0%253D&md5=13823d5b0a3bf085fd9d4eede4074505
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  Physical Review B: Condensed Matter and Materials Physics (1998), 57 (11), 6493-6507CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  
  An empirical tight-binding method for tetrahedrally coordinated cubic materials is presented and applied to group-IV and III-V semiconductors. The present spds* method extends existing calcns. by the inclusion of all 5 d orbitals per atom in the basis set. On-site energies and 2-center integrals between nearest neighbors in the Hamiltonian are fitted to measured energies, pseudopotential results, and the free-electron band structure. The authors demonstrate excellent agreement with pseudopotential calcns. up to ∼6 eV above the valence-band max. even without inclusion of interactions with more distant atoms and 3-center integrals. The symmetry character of the Bloch functions at the X point is considerably improved by the inclusion of d orbitals. D. of states, reduced masses, and deformation potentials are correctly reproduced.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXhvVartbg%253D&md5=fe009ebb7abe66ef86346ee83ae5c1e3
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  The deformation potentials of cubic semiconductors are reexamd. from the point of view of the extended-basis sp3d5s* tight-binding model. Previous parametrizations had failed to account properly for trigonal deformations, even leading to incorrect sign of the acoustic component of the shear deformation potential d. The strain-induced shifts and splittings of the on-site energies of the p and d orbitals play a prominent role in obtaining satisfactory values of deformation potentials both at the zone center and zone extrema. The present approach results in excellent agreement with available exptl. data and recent ab initio calcns.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhtFeqtLnP&md5=6aa5ea6bb381107763b484de6ca0973e
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  The surface properties of topol. insulators are strongly correlated with their structural properties, requiring high-resoln. techniques capable of probing both surface and bulk structures at once. In this work, the high flux of a synchrotron source, a set of recursive equations for fast X-ray dynamical diffraction simulation and a genetic algorithm for data fitting are combined to reveal the detailed structure of bismuth telluride epitaxial films with thicknesses ranging from 8 to 168 nm. This includes stacking sequences, thickness and compn. of layers in model structures, interface coherence, surface termination, and morphol. The results are in agreement with the surface morphol. detd. by at. force microscopy. Moreover, by using X-ray data from a zero-noise area detector to construct three-dimensional reciprocal-space maps, insights into the nanostructure of the domains and stacking faults in Bi2Te3 films are given.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXls1Srsbs%253D&md5=d74ec04ac8c1cda4b1e24cb0a7a423b5
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  Using a theory exactly analogous to that of light, the intensity of reflection of X-rays may be found for both monochromatic and for heterogeneous radiation. The theory indicates the existence of a refractive index for both cryst. and amorphous substances. A calcn. of the effect of the several electrons in an atom accounts for the phenomenon of "excess radiation" observed in the scattering of X-rays by amorphous substances. Comparing the results from the theory with the experimental results of Moseley and Darwin upon rocksalt (C. A., 7, 3710), too great reflection is obtained, indicating that the wave scattered by one atom disturbs the vibrations of the others.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaC2cXhtFCnsw%253D%253D&md5=618fcf13d719a2eee5249bc7d6f0f071
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  xrayutilities: a versatile tool for reciprocal space conversion of scattering data recorded with linear and area detectors
  
  Kriegner, Dominik; Wintersberger, Eugen; Stangl, Julian
  
  Journal of Applied Crystallography (2013), 46 (4), 1162-1170CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
  
  General algorithms to convert scattering data of linear and area detectors recorded in various scattering geometries to reciprocal space coordinates are presented. These algorithms work for any goniometer configuration including popular four-circle, six-circle and kappa goniometers. The use of commonly employed approxns. is avoided and therefore the algorithms work also for large detectors at small sample-detector distances. A recipe for detg. the necessary detector parameters including mostly ignored misalignments is given. The algorithms are implemented in a freely available open-source package.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhtFChsbvJ&md5=248f2c8b07637ebd2d78a24176e83483
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  Optimized second-harmonic generation in asymmetric double quantum wells
  
  Vurgaftman, Igor; Meyer, Jerry R.; Ram-Mohan, L. Randas
  
  IEEE Journal of Quantum Electronics (1996), 32 (8), 1334-1346CODEN: IEJQA7; ISSN:0018-9197. (Institute of Electrical and Electronics Engineers)
  
  The authors present a theor. anal. of surface-incidence and waveguide-mode 2nd harmonic generation with detuned intersubband transitions in GaAs-AlGaAs, InGaAs-InAlAs and GaSb-InGaSb-AlGaSb asym. double quantum wells. The anal. includes the effects of absorption, satn., pump depletion, optical carrier heating, mode confinement and competition, and the loss of phase coherence due to waveguide, bulk and resonant intersubband contributions to the refractive index mismatch. Optimal structure were detd. for each material system in both surface-incidence and waveguide-mode geometries. A scheme for maintaining phase matching by incorporation of a sep. region with an intersubband transition tuned midway between the 1st and 2nd harmonic frequencies is analyzed. At 10.6 μm, the max. conversion efficiency for the optimized InGaAs-InAlAs waveguide-mode device is ≈ 16% at a pump-beam intensity of 40 MW/cm2. Also, the same device can be modulated to vanishing 2nd harmonic output power when an elec. field of -32 kV/cm is applied.
  
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XkvVCjt7w%253D&md5=36628f32cb2015468450235fba2be9fa
Supporting Information
Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.1c01162.
- Additional theoretical calculations, experimental details, fitting results, and electron microscopy images of the samples (PDF)
- ph1c01162_si_001.pdf (1.68 MB)
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Designing High Performance Devices in Silicon Using Subwavelength

Source: https://pubs.acs.org/doi/10.1021/acsphotonics.1c01162

Designing High Performance Devices in Silicon Using Subwavelength

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Experimental Results

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Discussion

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Conclusion

Methods

Theoretical Calculations

Sample Growth and Characterization

IR Spectroscopy

Supporting Information

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ABBREVIATIONS

Cited By

Abstract

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Supporting Information

Supporting Information

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