Coupling-length phase matching for nonlinear optical frequency conversion in parallel waveguides

We describe and analyze a quasi-phase-matching scheme for nonlinear optical frequency conversion where the spatial modulation of mode intensity in coupled parallel waveguides provides the required modulation in the generation of the frequency conversion signal, instead of a variation of any material parameter or propagation constant. We analyze this coupling-length phase-matching (CLPM) scheme both for second-order frequency conversion, such as second harmonic generation or difference-frequency generation, as well as for third-order four-wave mixing processes, for which we consider the example of generating a longer wavelength by third-order nonlinear mixing of two shorter wavelength waves. Numerous phase-matching conditions are identified in each case. We show that the maximum photon conversion efficiencies reached after an optimum propagation length are always higher than half those obtained for perfect phase matching in a single waveguide, with nearly 100% photon conversion possible for several of the CLPM conditions we studied.