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

The development of Ge and SiGe chemical 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 calculations for the giant nonlinear coefficients provided by intersubband transitions in hole-doped Ge/SiGe and Si/SiGe multi-quantum wells. We employ a valence band-structure model for Si_1-xGe_x to calculate the confined hole states of asymmetric-coupled quantum wells for second-harmonic generation in the mid-infrared. We calculate 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-infrared sensor architectures, one based on waveguides and another based on metasurfaces, are described as perspective application.