We present a statistical inference approach to estimate the frequency noise characteristics of ultra-narrow linewidth lasers from delayed self-heterodyne beat note measurements using Bayesian inference. Particular emphasis is on estimation of the intrinsic (Lorentzian) laser linewidth. The approach is based on a statistical model of the measurement process, taking into account the effects of the interferometer as well as the detector noise. Our method therefore yields accurate results even when the intrinsic linewidth plateau is obscured by detector noise. The regression is performed on periodogram data in the frequency domain using a Markov-chain Monte Carlo method. By using explicit knowledge about the statistical distribution of the observed data, the method yields good results already from a single time series and does not rely on averaging over many realizations, since the information in the available data is evaluated very thoroughly. The approach is demonstrated for simulated time series data from a stochastic laser rate equation model with 1/f-type non-Markovian noise.

翻译：我们提出一种统计推断方法，利用贝叶斯推断从延迟自外差拍频测量中估计超窄线宽激光器的频率噪声特性，重点在于本征（洛伦兹型）激光线宽的估计。该方法基于测量过程的统计模型，综合考虑干涉仪效应及探测器噪声的影响，因而即使在本征线宽平台被探测器噪声掩盖时，仍能获得精确结果。回归过程采用马尔可夫链蒙特卡洛方法在频域中对周期图数据进行分析。通过显式利用观测数据的统计分布知识，该方法能够充分挖掘单次时间序列中的信息，无需依赖多次测量平均即可获得良好结果。我们通过包含1/f型非马尔可夫噪声的随机激光速率方程模型生成的模拟时间序列数据，验证了该方法的有效性。