Noise characterization of lasers and frequency combs using machine learning: A PhD Thesis.

Understanding the coherence of lasers and frequency combs is essential for predicting and improving their performance. The coherence of a laser is determined by its phase noise, while for a frequency comb its coherence is also governed by the correlations between the phase noise of its individual spectral lines. This thesis explores the application of advanced statistical methods to improve noise measurements of lasers and frequency combs. Simple analytical models of key photonic components are introduced and used in numerical simulations. Limits on the allowable path length dierences in balanced detectors are derived. These are relevant for the heterodyne coherent detection schemes used to characterize lasers and frequency combs throughout this thesis. Kalman ltering is explored as a method to mitigate the impact of measurement noise. Specically, a lter is constructed to characterize the amplitude noise of lasers, and the uncertainties associated with Kalman lters are investigated.Subspace tracking is introduced as a method for characterizing the correlations between the phase noise of a frequency comb's spectral lines. This method simultaneously detects multiple lines in a heterodyne coherent detection scheme and subsequently identifies the most signicant noise components aecting their correlations. When applied to the resonant electo-optic (EO) comb, subspace tracking reveals that it approximately follows the standard phase noise model of frequency combs, specically showing that the phase noise of the continuous-wave (CW) laser aects the common oset of the comb lines, while noise from the RF generator driving the EO modulator aects their repetition rate. However, a deviation from the standard phase noise model is predicted both analytically and numerically before ultimately being conrmed experimentally. The consequences of this deviation are discussed in relation to potential applications, including a reduction in the noise ltering eect from the comb's resonator.