Asymmetric-coupled Ge/SiGe quantum wells for second harmonic generation at 7.1 THz in integrated waveguides: a theoretical study

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.