Spectral analysis of the temporal self-imaging phenomenon in fiber dispersive lines

A spectral analysis of the temporal Talbot or self-imaging effect based on the exact computation of the radio frequency spectrum of the intensity of pulse trains after propagation in media with arbitrary first-order (β₂) and second-order (β₃) dispersion is presented. This allows the investigation of the performance of fiber dispersive lines as Talbot devices, where second-order dispersion is considered as a degradation factor. Conditions for repetition-rate multiplication and pulse compression over trains composed of linearly chirped Gaussian pulses, describing the effect as a filter in the intensity domain, are analyzed. The Talbot filter acts as a multiple bandpass filter that selects intensity harmonics. The filter´s rejection capability depends on the train´s spectral width normalized by the repetition-rate frequency of the output. The intensity fluctuations and pulse distortions of the output train are described from the spectral point of view. The tolerances of the filter under length and timing variations are also considered, and conditions for optimal filter stability are derived.