Regimes and Transitions of the Nonlinear Temporal Talbot Effect: Underlying Mechanism for A-Type Breathers, Soliton Crystals, and Soliton Gas

TL;DR

This paper develops a theory for the nonlinear temporal Talbot effect in optical fibers, revealing how nonlinear interactions lead to diverse regimes like breathers, soliton crystals, and soliton gas, with implications for nonlinear optics and wave dynamics.

Contribution

It introduces a dispersion relation integrating linear and nonlinear effects, and demonstrates the power-dependent regime transitions in the nonlinear temporal Talbot effect.

Findings

Nonlinear effects modify the linear Talbot self-imaging.

Regime transitions depend on input power levels.

A-type breathers and soliton crystals arise from different FWM processes.

Abstract

A frequency comb generated from a phase-modulated continuous-wave laser is simultaneously subject to the temporal Talbot effect and modulational instability (MI) when propagating through a piece of optical fiber. The temporal Talbot effect refers to the dispersion-driven self-imaging of optical pulses and is, per se, linear in optical field amplitudes. MI is a nonlinear effect. Despite growing interest and a variety of possible applications, a concise theory of the nonlinear temporal Talbot effect that incorporates nonlinear effects is not yet available; the self-imaging of optical patterns under the influence of nonlinearity remains largely unexplored. Here, I derive a dispersion relation for frequency-comb spatial modes. It integrates the contributions of the linear temporal Talbot effect, self-phase modulation, and MI-driven cross-phase modulation and four-wave mixing (FWM) between frequency-comb lines, paving the way to the development of a concise theory of the nonlinear temporal Talbot effect. With the help of Soliton Radiation Beat Analysis, a technique for retrieving the soliton content of optical fields in fibers, I demonstrate that the temporal Talbot effect seeds the spatio-temporal distribution of the field by driving higher-order spatial-mode interference. Nonlinear effects modify this interference, linking Talbot effect to Fermi-Pasta-Ulam-Tsingou recurrence of optical pulses and producing input-power-dependent regime transitions between the linear Talbot effect, A-type breathers, soliton crystals, and soliton gas. I show that A-type breathers arise from regular FWM at lower input powers, whereas soliton crystals emerge from cascaded FWM at higher powers. This study advances the fields of Nonlinear Optics and Wave Theory.