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

Abstract

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.

The temporal analogue of diffractive couplers

“…( 1). For short propagation distances, the temporal pattern leads to Talbot-carpet like pattern [15]. However, as the accumulated dispersion, hence propagation length, becomes more significant [19], well-separated temporal replica emerge from this dispersive grating [16].…”

“…This concept has simulated both fundamental research regarding, for example, the Arago spot [9], two waves interferometers [10], and temporal Fresnel diffraction in fiber optics [11]. But also successful applications such as theory of temporal imaging [12], dispersive Fourier transform [13,14], highrepetition rate sources, and related applications of the Talbot effect [15], and so many others.…”

All-fibre phase filters with 1-GHz resolution for high-speed passive optical logic processing

“…In practice, the energy consumption is just limited by the practical insertion loss of the phase-only filter, which can be optimized to be particularly low. This methodology has enabled remarkable improvements in energy efficiency as compared to photonic processing schemes based upon either nonlinear optics or even linear arbitrary (generally, amplitude-dependent) optical filtering 23 , 24 .…”

Practical issues in repetition-rate control of optical pulse trains and frequency combs by Talbot self-imaging

“…More recently, simultaneous repetition-rate control of optical pulses and frequency combs has been achieved based on generalized Talbot self-imaging 11,12 . The technique utilizes phase-only signal processing operations which usually include combinations of temporal phase modulation and spectral phase filtering.…”