Analytical study of coherence in seeded modulation instability

TL;DR

This paper provides analytical expressions for the coherence in modulation instability onset, validated by numerical simulations, considering various parameters and the impact of higher-order dispersion, relevant for supercontinuum generation from CW pumps.

Contribution

It introduces analytical formulas for coherence in seeded modulation instability, including effects of higher-order dispersion, advancing understanding of supercontinuum coherence.

Findings

Coherence depends on fiber type, pump power, seed SNR, and propagation distance.

Including higher-order dispersion is crucial for mid-IR supercontinuum coherence.

Analytical results agree well with numerical simulations.

Abstract

We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a continuous wave (CW) pump; then, we investigate the effect of adding a deterministic seed to the CW pump, a case of singular interest as it is commonly encountered in parametric amplification schemes. Results for the dependence of coherence on parameters such as fiber type, pump power, propagated distance, seed signal-to-noise ratio are presented. Finally, we show the importance of including higher-order linear and nonlinear dispersion when dealing with generation in longer wavelength regions (mid IR). We believe these results to be of relevance when applied to the analysis of the coherence properties of supercontinua generated from CW pumps.