Subnoise Detection and Passive Amplification of Frequency Combs through Customized Coherent Spectral Energy Redistribution

The problem of noise mitigation has been extensively studied in the conventional real domain of representation of waves, e.g., for signals in the time domain or spatial images. However, in many practical cases, the desired information is acquired in the Fourier domain representation of the relevant signal, e.g., the frequency domain for temporal waveforms, and the treatment and control of random noise in this domain remains a significant challenge. In this work, we propose a concept for noiseless amplification of the Fourier spectrum of a given periodic waveform, here demonstrated for the relevant case of a frequency comb. The concept involves a coherent redistribution of the original comb energy into fewer frequency lines, without altering the uncorrelated noise background. This translates into an effective amplification of the comb peak intensity over the noise floor in a completely passive fashion, thus avoiding the external noise contributions that are intrinsic to conventional active-gain processes. This result is achieved through suitable linear phase manipulations of the comb signal, in a process that can be regarded as a generalization of the spectral Talbot effect. We experimentally demonstrate recovery and measurement of frequency combs originally buried completely under random uncorrelated noise, without any prior knowledge of the absolute frequencies of the comb lines.