Analysis of difference frequency generation and cascaded second-harmonic generation and difference frequency generation in lossy quasi-phase-matched semiconductor waveguides

The analytical expressions of converted wave power for difference frequency generation (DFG), cascaded second-harmonic generation and difference frequency generation (cSHG/DFG) processes have been obtained under the non-depletion approximation in lossy waveguides. It is shown that the analytical results and the numerical simulation with depletion agree very well for lossy waveguides. Employing the analytical solutions, the formulas of optimized waveguide lengths in lossy waveguides are obtained for DFG and cSHG/DFG processes. After designing an AlGaAs quasi-phase-matched ridge waveguide, we investigate and compare the characteristics of the second-order nonlinear effects with and without waveguide loss, such as conversion efficiency, conversion bandwidth, pump wavelength tolerance and temperature stability in detail.