Regular, beating and dilogarithmic breathers in biased photorefractive crystals

TL;DR

This paper models light beam propagation in photorefractive crystals using a generalized nonlinear Schrödinger equation, predicting stable solitons and breathers, including beating and dilogarithmic solutions, confirmed by numerical simulations.

Contribution

It introduces a variational approximation involving the dilogarithm function to predict and analyze stable solitons and breathers in photorefractive crystals, extending previous models.

Findings

Stable solitons and breathers exist in the model.

Beating breathers with long-period modulations are observed.

Numerical simulations confirm the existence and stability of these modes.

Abstract

The propagation of light beams in photovoltaic pyroelectric photorefractive crystals is modelled by a specific generalization of the nonlinear Schr\"odinger equation (GNLSE). We use the variational approximation (VA) to predict the propagation of solitary-wave inputs in the crystal, finding that the VA equations involve the dilogarithm special function. The VA predicts that solitons and breathers exist, and the Vakhitov-Kolokolov criterion predicts that the solitons are stable solutions. Direct simulations of the underlying GNLSE corroborates the existence of such stable modes. The numerical solutions produce both regular breathers and ones featuring beats (long-period modulations of fast oscillations). In the latter case, the Fourier transform of amplitude oscillations reveals a nearly discrete spectrum characterizing the beats dynamics. Numerical solutions of another type demonstrate spontaneous splitting of the input pulse in two or several secondary ones.