Temporal Talbot effect: from a quasi-linear Talbot carpet to soliton crystals and Talbot solitons

The temporal Talbot effect refers to the periodic self-imaging of pulse trains in optical fibers. The connection between the linear and nonlinear temporal Talbot effect is still not fully understood. To address this challenge, we use the soliton radiation beat analysis (SRBA) and numerically investigate the evolution of a phase-modulated continuous-wave laser input in a passive single-mode fiber. We identify three input-power-dependent regimes and their Talbot carpets: the quasi-linear regime for low input powers, the intermediate one, and separated Talbot solitons for higher powers. We show that the intermediate regime hosts soliton crystals rather than rogue waves, as reported in the literature. The Talbot soliton beating can be used for pulse repetition-rate multiplication in the nonlinear regime. We also show two types of solitons involved: some encoded in the whole frequency comb, and the individual solitons carried only by particular comb lines.