Temporal self-imaging effect for chirped laser pulse sequences: Repetition rate and duty cycle tunability

We express parabolic-dispersion-induced transformations of a linearly chirped signal in terms of those suffered by the unchirped version of the same input signal. Specifically, we unveil that any amount of chirping and dispersion produces, aside from a scale factor, the same pulse-distortion effect as a certain parabolic dispersion in the unchirped input. This relevant result allows us to derive, as a particular case, the dispersion condition that leads to the temporal self-imaging phenomenon for laser pulse sequences globally affected by a quadratic-phase modulation. This combined action of chirping and dispersion is proposed as a technique for generating laser pulse sequences with customized repetition rate and duty cycle. Finally, by using the temporal ABCD matrix approach, we extend the theory of the temporal self-imaging effect to the case of a general temporal Gaussian system. We include some numerical simulations that illustrate our theoretical predictions.