Energy-Preserving Arbitrary Repetition-Rate Control of Periodic Pulse Trains Using Temporal Talbot Effects

The temporal Talbot effect comprises a set of self-imaging phenomena in which a pulse train undergoes various coherence revivals after propagation through a dispersive medium. Besides the intrinsic physical interest of the phenomenon itself, the effect has found practical applications in various scientific areas. In optical signal processing, the temporal Talbot effect has been used to multiply the repetition-rate of periodic pulse sequences by integer factors. Because it operates coherently on the frequencies that comprise a pulse train, the temporal Talbot effect has been shown to mitigate noise such as reduction of pulse-to-pulse timing jitter and amplitude variation, as well as real-time optical averaging. Recently, there has been renewed interest in the temporal Talbot effect due to its use in arbitrary repetition rate multiplication and division, not just integer multiplication. Arbitrary repetition-rate control is based on a suitable combination of temporal phase-modulation and spectral-phase filtering using temporal Talbot conditions. By adjusting the phase-modulation profile and group-velocity dispersion, the multiplication and division factors can be tuned to be any desired values- fractional or integer. One of the main advantages of this methodology compared to traditional approaches of repetition rate control is its energy efficiency. Because temporal and spectral phase filtering are lossless processes, pulse trains using Talbot-based repetition rate control only suffer insertion loss from the system. In this article, we first present an overview of the theory behind temporal Talbot effects and then review recent work on its application for realizing arbitrary control of the repetition-rate of periodic optical pulses. This platform enables the creation of simple, versatile optical pulse sources for diverse applications where customized repetition rates are necessary.