Abstract:

The temporal Talbot effect refers to the periodic self-imaging of pulse trains in optical fibres. The linear Talbot effect is widely used for pulse repetition-rate multiplication. The nonlinear Talbot effect is reported to give rise to Talbot carpets of rogue waves. The connection between the linear and nonlinear Talbot effect is still not fully understood. Soliton Radiation Beat Analysis is a numerical technique allowing for soliton-content extraction for an arbitrary input injected into an optical fibre in the anomalous-dispersion regime. It quantitatively analyses spatial frequencies of optical-power oscillations arising due to soliton-soliton or soliton-dispersive-wave beating. Using SRBA, we investigate the evolution of a phase-modulated continuous-wave laser input in a single-mode fibre.

We identify four input-power-dependent regimes: the linear (I) and quasi-linear (II) regimes and two nonlinear regimes (III and IV). We show that regime III hosts soliton crystals rather than rogue waves, whereas the carpets of regime IV are composed of separated Talbot solitons. Talbot-solitons beating can be used for pulse repetition-rate multiplication in the nonlinear regime. Further, the input-power values of the regime transitions depend on the group-velocity dispersion (GVD) and the phase-modulation depth. Thus, lower GVD implies lower values of transitional input powers, whereas the latter increase with phase-modulation depth. We also analyse the phases of different regimes. In the soliton-crystal regime (III), we observe a periodic flip of the phase amplitude over the propagation length. Our preliminary studies allow us to conclude that this phase flip might be exploited to generate +/-phase solitons in single-pass systems. In general, our findings advance the topics of the repetition-rate multiplication of bright and dark pulse trains in fibres and semiconductors, allow the creation of Talbot soliton fibre lasers, and enhance the understanding of the dynamics of frequency-multiplex neuromorphic-photonics schemes.