Theoretical analysis of phase-matched second-harmonic generation and optical parametric oscillation in birefringent semiconductor waveguides

We analyze the phase-matching conditions for second-harmonic generation (SHG) and optical parametric oscillation (OPO) in birefringent nonlinear semiconductor waveguides and apply these results to the model system of ZnGeP2 on a GaP substrate. The analyses and numerical results show that phase matching can be achieved for OPO and SHG for reasonable guide thicknesses throughout much of the infrared, indicating significant potential applications for nonlinear birefringent waveguides. For the fundamental mode of a relatively thick guide the region of phase matching and the phase-matching angles are similar to those in bulk material. However, the waveguide has the added flexibility that phase-matched coupling can occur between the various modes of the guide. For example, the phase-matching region for SHG can be considerably extended by coupling the pump into the guide in the fundamental, m = 0, mode and phase matching to the m = 2 mode of the second harmonic. Significantly, the results indicate, among other things, that ZnGeP2 waveguides with harmonic output in the m = 2 mode can be used for efficient SHG from input radiation in the 9.6-10.6-microm region where bulk efficiencies in this wavelength range are too small to be useful.