Perfecting Phase Matching in Nonlinear Resonant Photonic Structures via Green’s Function Integral Formalism

Phase mismatch poses a key challenge in nonlinear photonics, where existing methods generally fail to characterize the localized phase mismatch. Here, we demonstrate the Green’s function integral method (GFIM) as a fundamental analytical framework for microscopic phase engineering, enabling perfect phase matching in χ(2)-based resonant structures. By modeling second-harmonic generation as the integration (or superposition) of subharmonic components generated by microscopic nonlinear sources, GFIM permits precise identification of phase mismatch at the microscopic scale and establishes a quantitative metric for assessing phase-matching efficiency. Our phase analysis reveals that the triple-DBR resonator induces periodic π-phase discontinuities of subharmonic fields, allowing for a refined quasi-phase matching technique that converts destructive-to-constructive interference, thereby achieving unprecedented perfect phase matching. In a 2 μm nonlinear film, this approach yields a calculated 14% harmonic efficiency under 1 MW/cm2 pumping. With its capability to decode complicated phase distributions, GFIM emerges as an essential framework for the microscopic phase analysis and rational optimization of nonlinear photonic devices.