Theory of Slow Light Enhanced Four-Wave Mixing in Photonic Crystal Waveguides

TL;DR

This paper develops a detailed theoretical model for four-wave mixing in photonic crystal waveguides, accounting for slow-light effects, mode reshaping, and tensor nonlinearities, predicting significant nonlinear gain enhancements.

Contribution

It introduces an accurate theoretical framework that includes dispersive and tensor effects, providing more precise predictions than simpler models for slow-light enhanced nonlinear interactions.

Findings

Predicted >10 dB gain with 1 W pump in a 1.3 mm GaInP waveguide

Numerical results show substantial differences from simpler models, increasing at lower group velocities

Model accounts for Bloch mode reshaping and tensor nature of third-order polarization

Abstract

The equations for Four-Wave-Mixing in a Photonic Crystal waveguide are derived accurately. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the third order polarization are therefore taken into account. Numerical calculations reveal substantial differences with simpler models, which increase with decreasing group velocity. We predict that the gain for a 1.3 mm long, unoptimized GaInP waveguide will exceed 10 dB if the pump power exceeds 1 W.