Modulation instability in noninstantaneous Kerr media with walk-off effects and cross-phase modulation for two copropagating beams experiencing anomalous GVD regime

TL;DR

This paper investigates how walk-off and noninstantaneous response effects influence modulation instability in two copropagating beams within anomalous GVD media, revealing distinct gain behaviors and new wave evolution possibilities.

Contribution

It introduces an extended nonlinear Schrödinger model with Debye polarization to analyze modulation instability under noninstantaneous and walk-off effects in anomalous dispersion regimes.

Findings

Two distinct sideband bands with different gain behaviors

Maximum gain and frequency depend differently on delay parameter τ

Distinct evolution patterns compared to normal and mixed dispersion regimes

Abstract

The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous regime of dispersion. To do so, we make use of extensions of the nonlinear Schr\"odinger equation jointly with the Debye model for polarization, which is shown to be effective and simplified when compared to the implementation of other methods for the noninstantaneous nonlinear response. In analyzing the sideband formation, two bands are observed with different behaviors with respect to the way the maximum gain and the respective frequency vary with increasing phase mismatch. Further, we also show that the manner in which the maximum gain as well as its corresponding frequency scale with the delay parameter $\tau$ is substantially different from the cases of both fields experiencing the normal group-velocity dispersion regime and the case of mixed regimes. These facts may give rise to many new possibilities for the evolution of the modulated wave when compared to the nonanomalous cases studied in the literature.