Theory of Pulsed Four-Wave-Mixing in One-dimensional Silicon Photonic Crystal Slab Waveguides

TL;DR

This paper provides a comprehensive theoretical and computational analysis of four-wave mixing in one-dimensional silicon photonic crystal waveguides, considering various linear and nonlinear effects, and explores differences between slow- and fast-light regimes.

Contribution

It introduces a general coupled-mode theory framework for FWM in Si-PhCWGs, including all relevant linear and nonlinear effects, and derives explicit formulae for key waveguide coefficients.

Findings

Key differences between slow- and fast-light FWM regimes identified

Derived formulae for dispersion and nonlinear coefficients

Numerical simulations support theoretical predictions

Abstract

We present a comprehensive theoretical analysis and computational study of four-wave mixing (FWM) of optical pulses co-propagating in one-dimensional silicon photonic crystal waveguides (Si-PhCWGs). Our theoretical analysis describes a very general set-up of the interacting optical pulses, namely we consider nondegenerate FWM in a configuration in which at each frequency there exists a superposition of guiding modes. We incorporate in our theoretical model all relevant linear optical effects, including waveguide loss, free-carrier (FC) dispersion and FC absorption, nonlinear optical effects such as self- and cross-phase modulation (SPM, XPM), two-photon absorption (TPA), and cross-absorption modulation (XAM), as well as the coupled dynamics of FCs and optical field. In particular, our theoretical analysis based on the coupled-mode theory provides rigorously derived formulae for linear dispersion coefficients of the guiding modes, linear coupling coefficients between these modes, as well as the nonlinear waveguide coefficients describing SPM, XPM, TPA, XAM, and FWM. In addition, our theoretical analysis and numerical simulations reveal key differences between the characteristics of FWM in the slow- and fast-light regimes, which could potentially have important implications to the design of ultra-compact active photonic devices.