Wavelength Conversion Efficiency Enhancement in Modal Phase Matched $\chi^{(2)}$ Nonlinear Waveguides

Modal phase matching (MPM) is a widely used phase matching technique in Al$_x$Ga$_{1-x}$As and other $\chi^{(2)}$ nonlinear waveguides for efficient wavelength conversions. The use of a non-fundamental spatial mode compensates the material dispersion but also reduces the spatial overlap of the three interacting waves and therefore limits the conversion efficiency. In this work, we develop a technique to increase the nonlinear overlap by modifying the material nonlinearity, instead of the traditional method of optimizing the modal field profiles. This could eliminate the limiting factor of low spatial overlap inherent to MPM and significantly enhance the conversion efficiency. Among the design examples provided, this technique could increase the conversion efficiency by a factor of up to $\sim$290 in an Al$_x$Ga$_{1-x}$As waveguide. We further show that this technique is applicable to all $\chi^{(2)}$ material systems that utilize MPM for wavelength conversion.