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We present a theoretical investigation of guided second harmonic generation at THz frequencies in SiGe waveguides embedding n-type Ge/SiGe asymmetric coupled quantum wells to engineer a giant second order nonlinear susceptibility. A characteristic of the chosen material system is the existence of large off-diagonal elements in the χ 2 tensor, coupling optical modes with different polarization. To account for this effect, we generalize the coupled-mode theory, proposing a theoretical model suitable for concurrently resolving every second harmonic generation interaction among guide-sustained modes, regardless of which χ 2 tensor elements it originates from. Furthermore, we exploit the presence of off-diagonal χ 2 elements and the peculiarity of the SiGe material system to develop a simple and novel approach to achieve perfect phase matching without requiring any fabrication process. For a realistic design of the quantum heterostructure we estimate second order nonlinear susceptibility peak values of ∼7 and ∼1.4 × 105 pm/V for diagonal and off diagonal χ 2 elements, respectively. Embedding such heterostructure in Ge-rich SiGe waveguides of thicknesses of the order of 10–15 μm leads to second harmonic generation efficiencies comprised between 0.2 and 2 %, depending on the choice of device parameters. As a case study, we focus on the technologically relevant frequency of 7.1 THz, yet the results we report may be extended to the whole 5–20 THz range.

A parabolic potential that confines charge carriers along the growth direction of quantum wells semiconductor systems is characterized by a single resonance frequency, associated to intersubband transitions. Motivated by fascinating quantum optics applications leveraging on this property, we use the technologically relevant SiGe material system to design, grow, and characterize n-type doped parabolic quantum wells realized by continuously grading Ge-rich Si1−x Gex alloys, deposited on silicon wafers. An extensive structural analysis highlights the capability of the ultra-high-vacuum chemical vapor deposition technique here used to precisely control the quadratic confining potential and the target doping profile. The absorption spectrum, measured by means of Fourier transform infrared spectroscopy, revealed a single peak with a full width at half maximum at low and room temperature of about 2 and 5 meV, respectively, associated to degenerate intersubband transitions. The energy of the absorption resonance scales with the inverse of the well width, covering the 2.5–5 THz spectral range, and is almost independent of temperature and doping, as predicted for a parabolic confining potential. On the basis of these results, we discuss the perspective observation of THz strong light–matter coupling in this silicon compatible material system, leveraging on intersubband transitions embedded in all-semiconductor microcavities.