In this work, the problem of propagation of ultrashort optical solitons through a non-linear optical fiber is investigated in
the joint Time-Frequency (TF) domain using optimized representations [i.e. Wigner-Ville (WV) Distribution or WV-Spectrograms
with reduced cross-term interferences]. Based on these optimized representations, complete numerical
simulations for nonlinear propagation of solitons were carried out. In particular we have analyzed the evolution of
second and third order solitons and soliton interaction in optical fibers using joint TF representations.
Temporal Talbot effect is the time domain counterpart of spatial self imaging phenomenon. When a periodic time signal is propagated through a first order dispersive medium, exact replicas of the signal are reproduced at specific distance along the direction of propagation. At other distances, the signal is self imaged with a higher repetition-rate than the original periodic sequence (Fractional Talbot effect).
In this paper, the problem of propagation of an ideal periodic optical pulse sequence through a linear dispersive fiber is investigated in the joint time-frequency domain using an optimized representation [i.e. Wigner Ville-Multiresolution spectrograms providing an optimal resolution in both time and frequency domains with reduced cross-term interferences]. Based on these optimized representations, complete numerical simulations were carried out to analyze the evolution of the time-frequency distribution of a periodic signal propagating through a linear dispersive medium, thus providing a deeper insight into the physics of the temporal Talbot problem.
Moreover, we have used an elegant ray-matrix approach to describe the signal propagation in phase space and we have showed that for the fractional temporal Talbot effect (repetition rate factor M), each newly generated individual temporal pulse has contributions only from every M<sup>th</sup> spectral component of the train's discrete spectrum. This interpretation is in fact in very good agreement with the notion that the fractional temporal Talbot effect can be explained as a result of interference between consecutive, chirped TF patterns. Our numerical simulations have confirmed our heuristic descriptions of the Talbot phenomena.