Analysis and design equations for phase matching using Bragg reflector waveguides

In this paper, we introduce and analyze a novel wave-guide design to provide phase matching for nonlinear optical processes. Phase matching is achieved by designing the structure to guide the fundamental frequency by total internal reflection and the second harmonic (SH) frequency by transverse Bragg reflection. By forcing the SH mode to operate in the middle of the Bragg stopband, we solve for the waveguide dimensions for arbitrary waveguide materials, given the material dispersion between the fundamental and SH frequencies. Using GaAs-AlGaAs as an example, we analytically investigate and quantify properties such as nonlinear coupling efficiency, bandwidth, tunability, and limitations due to dispersion. The technique shows tremendous promise when compared to alternate technologies, where it is particularly attractive as an effective means to obtain ultralow-loss nonlinear optical elements for monolithic integration with coherent light sources and other active devices.