Arbitrary Energy‐Preserving Control of Optical Pulse Trains and Frequency Combs through Generalized Talbot Effects

Trains of optical pulses and optical‐frequency combs are periodic waveforms with deep implications for a wide range of scientific disciplines and technological applications. Recently, phase‐only signal‐processing techniques based upon the theory of Talbot self‐imaging have been demonstrated as simple and practical means for user‐defined periodicity control of optical pulse trains and combs. The resulting schemes implement a desired repetition period control without introducing any noise or distortion, while ideally preserving the entire energy content of the signal. Here, recent developments on phase‐only signal‐processing schemes for periodicity control based on temporal and spectral self‐imaging are reviewed. As a central contribution, a comprehensive theory of generalized Talbot self‐imaging, so called phase‐controlled Talbot effect, is presented, comprising all the different approaches proposed to date. In particular, a closed unified mathematical framework for the design of the spectral and temporal phase manipulations that enable full arbitrary control of the period of repetitive signals is developed. The reported numerical studies fully validate the presented theoretical framework and shed light on crucial aspects of the proposed methods, consistently with previously reported experimental results. Important considerations concerning the practical, real‐world implementation of the described schemes, according to the needed specifications for different applications, are also discussed. Recent developments on phase‐only signal processing schemes for energy‐preserving control of the periodicity of optical pulse trains and frequency combs, based on Talbot self‐imaging effects, are reviewed. A comprehensive theory of generalized Talbot self‐imaging, the so‐called phase‐controlled Talbot effect, is presented, providing a closed unified mathematical framework for full arbitrary control of the period of repetitive signals.