Matrix analysis for optical frequency conversion through quasi-phase-matched media considering multiple reflection

Various quasi-phase-matched (QPM) media including periodic domain-inverted structure, nonlinear hetero-multilayer structure, corrugated nonlinear waveguide structure, and so forth are under intensive research for optical frequency conversion. The QPM structure compensates for phase-matching condition by periodic nonlinearity modulation, which is applicable to not only anisotropic nonlinear media but also isotropic nonlinear media. However, isotropic QPM media have a shortcoming, that is, refractive index matching between neighborhood laminas is more difficult than domain-inverted structure of anisotropic media. Up to now, the analyses of QPM frequency conversion have been achieved by coupled-mode theory, direct non-depletion pump wave approximation, etc., with concern only about the second-order nonlinearity modulation depth. Recently, a method of non-depletion pump wave approximation with propagation loss was proposed. However, Fabry-Perot effect, i.e., multiple reflection from the modulated refractive index has not been taken into account. Multiple reflection as well as frequency conversion occurs when optical waves propagate through the multilayers of nonlinear media in which both linear and nonlinear optical parameters are modulated. The multiple reflection could affect conversion efficiency, since the pump wave and the generated waves are deformed by reflection. Here, we propose a new matrix-method with distributed non-depletion pump wave approximation considering multiple reflection for the precise analysis of QPM optical frequency conversion