Modelling second harmonic generation at mid-infrared frequencies in waveguide integrated Ge/SiGe quantum wells

A promising alternative to bulk materials for the nonlinear coupling of optical fields is provided by photonic integrated circuits based on heterostructures made of asymmetric-coupled quantum wells. These devices achieve a huge nonlinear susceptivity but are affected by strong absorption. Here, driven by the technological relevance of the SiGe material system, we focus on Second-Harmonic Generation in the mid-infrared spectral region, realized by means of Ge-rich waveguides hosting p-type Ge/SiGe asymmetric coupled quantum wells. We present a theoretical investigation of the generation efficiency in terms of phase mismatch effects and trade-off between nonlinear coupling and absorption. To maximize the SHG efficiency at feasible propagation distances, we also individuate the optimal density of quantum wells. Our results indicate that conversion efficiencies of ≈ 0.6%/W can be achieved in WGs featuring lengths of few hundreds µm only.