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).

In fundamental papers from 1962 [1, 2], Heffener and Haus showed that it is not possible to construct a linear noiseless amplifier. The implies that the amplifier intrinsic noise sources induce random perturbations on the phase of the incoming optical signal which translates into spectral broadening. To achieve the minimum (quantum noise limited) induced phase fluctuation, and the corresponding minimum spectral broadening, an optimum phase measurement method is needed. We demonstrate that a measurement method based on the heterodyne detection and the extended Kalman filtering approaches an optimum phase measurement in the presence of amplifier noise. A penalty of 5 dB (numerical) and 15 dB (experimental) compared to the quantum limited spectral broadening is achieved. For comparison, the conventional phase measurement method's penalty exceeds 30 dB for the measurements. Our results reveal new scientific insights by demonstrating that the impact of amplifier noise can be significantly reduced by using the proposed phase measurement method. An impact is envisioned for the phase-based optical sensing system, as optical amplification could increase sensing distance with the minimum impact on the phase.

In the not-too-distant future, advances in machine learning will spur a new, transformative generation of optical communication and measurement systems.

A novel tool, based on Bayesian filtering framework and expectation maximization algorithm, is numerically and experimentally demonstrated for accurate frequency comb noise characterization. The tool is statistically optimum in a mean-square-errorsense, works at wide range of SNRs and offers more accurate noise estimation compared to conventional methods.

Bayesian inference framework, that considers laser-physics, is proposed and demonstrated for joint learning of laser static and dynamic parameters. Proof-of-concept experimental results demonstrating the main concepts are presented as well.