Peregrine solitons and resonant radiation in cubic and quadratic media

TL;DR

This paper investigates resonant radiation emitted by Peregrine solitons in cubic and quadratic nonlinear media, revealing mechanisms and criteria for radiation emission, supported by analytical and numerical analysis.

Contribution

It provides new analytical criteria for resonant radiation frequencies in Peregrine solitons across different media, including effects of higher-order dispersion and phase-matching mechanisms.

Findings

Resonant radiation in cubic media depends on higher-order dispersion and local wavenumber variation.

In quadratic media, two-color Peregrine rogue waves can radiate dispersive waves without higher-order dispersion.

Analytical criteria match well with numerical simulations for predicting radiated frequencies.

Abstract

We present the fascinating phenomena of resonant radiation emitted by transient rogue waves in cubic and quadratic nonlinear media, particularly those shed from Peregrine solitons, one of the main wavepackets used today to model real-world rogue waves. In cubic media, it turns out that the emission of radiation from a Peregrine soliton can be attributed to the presence of higher-order dispersion, but is affected by the intrinsic local longitudinal variation of the soliton wavenumber. In quadratic media, we reveal that a two-color Peregrine rogue wave can resonantly radiate dispersive waves even in the absence of higher-order dispersion, subjected to a phase-matching mechanism that involves the second harmonic wave, and to a concomitant difference-frequency generation process. In both cubic and quadratic media, we provide simple analytic criteria for calculating the radiated frequencies in terms of material parameters, showing excellent agreement with numerical simulations.