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

Abstract: A frequency comb from a phase-modulated continuous-wave laser is subject to the temporal Talbot effect and modulational instability in an optical fiber or semiconductor. Using Soliton Radiation Beat Analysis and a dispersion relation for comb lines, I identify distinct regimes of the nonlinear Talbot effect of A-type breathers, soliton crystals, and soliton gas that arise from varying hierarchies of self-phase modulation, cross-phase modulation, and the type of four-wave mixing (regular vs. cascaded). The temporal Talbot effect governs the spatio-temporal distribution of linear and nonlinear pulses and is closely related to the Fermi-Pasta-Ulam-Tsingou recurrence phenomenon. The study advances the fields of Nonlinear Optics and Wave Theory.