Temporal self-imaging effects:: Theory and application for multiplying pulse repetition rates

A time-domain equivalent of the spatial Talbot or self-imaging phenomenon appears when a periodic temporal signal propagates through a dispersive medium under first-order dispersion conditions. The effect is of great interest because it can be applied for multiplying the repetition rate of an arbitrary periodic pulse train without distorting the individual pulse features and essentially without loss of energy. In this way, pulse sequences in the terahertz regime can be generated from typical mode-locked pulse streams (with a few gigahertz repetition rates). The Talbot-based repetition-rate-multiplication technique can be implemented by using a linearly chirped fiber grating (LCFG) as the dispersive medium. As compared with other alternatives, an LCFG can be designed to provide the required bandwidth and dispersion characteristics in significantly more compact forms. Here, by using a signal-theory-based approach, we carry out a general theoretical analysis of the temporal self-imaging phenomenon and derive analytical expressions for all cases of interest (integer and fractional self-imaging effects). We also show how to design a LCFG for implementing the repetition-rate-multiplication technique and discuss the impact of nonidealities in the grating's response on the multiplication process. Results of our study are relevant from both a physical and a practical perspective.