Bayesian filtering framework for noise characterization of frequency combs

Amplitude and phase noise correlation matrices are of fundamental importance for studying noise properties of frequency combs. They include information about the origin of noise sources as well as the scaling and correlation of the noise across the comb lines. These matrices provide an insight that is essential for obtaining low-noise performance which is important for, e.g., applications in optical communication, low-noise microwave signal generation, and distance measurements. Estimation of amplitude and phase noise correlation matrices requires highly-accurate measurement technique which can distinguishes between noise sources coming from the frequency comb and the measurement system itself. Bayesian filtering provides a theoretically optimum approach for filtering of measurement noise and thereby, the most accurate measurement of phase and amplitude noise. In this paper, a novel Bayesian filtering based framework for joint estimation of amplitude and phase noise of multiple frequency comb lines is proposed, and demonstrated for phase noise characterization. Compared to the conventional approaches, that do not employ any measurement noise filtering, the proposed approach provides significantly more accurate measurements of correlation matrices, operates over a wide range of signal-to-noise-ratios and gives an insight into comb's dynamics at short scales (<10^-8 s).