Optical computation of discrete Fourier transform utilizing the temporal Talbot effect with input pulse trains of finite duration

Abstract

The temporal Talbot effect (TTE) embodies the phenomenon of discrete Fourier transform (DFT). However, in an ideal temporal Talbot system, an infinitely long pulse train is required as input, which hinders the application of this property in optical computation of DFT. In this paper, we investigate the phenomenon of DFT in the TTE with input pulse trains of finite duration, aiming to apply it to optical computation of DFT. It is found that precise DFT coefficients can be extracted from the output signal of a system with an input pulse train of finite duration, subject to a specific condition on the pulse train’s duration. A significant advantage of the system employing an input pulse train of finite duration is that the resulting output signal becomes band-limited. This crucially implies that an optical receiver with a limited bandwidth can be utilized to obtain a distortionless signal. We provide a concise and rigorous theoretical framework on the TTE-based DFT system, which fully explains the underlying mechanism for perfect DFT calculation and is consistent with simulation results. Furthermore, we have determined that the single-cycle DFT calculation, using an input pulse train of one period, is feasible. The performance of the single-cycle DFT has been systematically evaluated under various non-ideal conditions, such as sampling time jitter and limited detection bandwidth. This research establishes a foundation for future applications of TTE in optical DFT computation, as it removes the requirement of inputting infinitely long pulse trains.