Passive Amplification and Noise Mitigation of Optical Signals Through Talbot Processing

Noise is one of the rare aspects of experimental work that crosses all boundaries. It is present from scientific fields like ultrafast optical signal detection to applied fields such as image processing, or even in our day-to-day lives when we are simply trying to have a conversation in a loud room. In all these cases, incoherent, stochastic noise tends to drown a signal we aim to detect, and various techniques may need to be employed to improve the clarity of the waveform, which is characterized by the signal-to-noise ratio (SNR). Yet, considering the ubiquity of noise in scientific and technology fields, it may be surprising how few methods there exists for denoising a signal. Active amplification techniques alone cannot be employed for weak, noisy signals, since the SNR is inevitably degraded due to fundamental laws of physics, while bandpass filtering schemes necessarily lead to an attenuation of the signal. In this article, we review recent advances on the concept of passive amplification techniques based on the Talbot effect to enhance the noise properties of signals through coherent energy redistribution. We demonstrate the basic framework starting from pulse repetition rate multiplication with the Talbot effect. We then extend this theory to show the principle behind passive amplification of periodic waveforms, and then how this idea can be extended to arbitrary (generally, aperiodic) signals. Methods for passive amplification of both the time-domain and the frequency-domain representations of the signal of interest are reviewed. While here we focus on the application of the technique for optical signals in the standard telecommunication band (near wavelengths of 1550 nm), the proposed denoising scheme relies on widely available wave manipulations, such that it may offer exciting opportunities for any kind of physical wave support, such as acoustics, plasmonics and other regimes of the electromagnetic spectrum, like microwaves or X-rays.