Phase-matched second-harmonic generation in coupled nonlinear optical waveguides

Phase matching is crucial for effective nonlinear frequency conversion. Recent advances in photonic miniaturization greatly promote implementations of efficient nonlinear frequency conversion in integrated photonic devices. Here, we investigate second-harmonic generation in coupled nonlinear waveguides. We develop a nonlinear optical coupled-mode theory and implement the concept of supermode to analyze the phase-matching condition, which greatly facilitates deep understanding of physics therein and optimization of device design. We have successfully identified six phase-matching conditions for the first time. The dynamic nonlinear optical processes are analytically modeled, which explicitly demonstrates that the phase-matching condition can be realized by extra momentum compensating due to the interwaveguide coupling. The influences of input pump amplitude and relative phase difference are successively investigated. The theoretical model presented here should be readily generalized to other nonlinear optical processes (e.g., difference frequency generations) and will remain valid in asymmetric coupled waveguide structures or even beyond a weakly coupling regime. Our results will be useful for constructing highly efficient integrated nonlinear optical conversion devices with extended functionality.