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：我们提出了一种基于贝叶斯推断的统计方法，用于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，重点聚焦于本征（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，综合考虑了干涉仪效应及探测器噪声的影响。因此，即便本征线宽平台被探测器噪声淹没，我们的方法仍能获得精确结果。回归分析在频域周期图数据上执行，采用马尔可夫链蒙特卡洛方法。通过利用观测数据统计分布的显式知识，该方法仅凭单次时间序列即可获得良好结果，无需依赖多次实现的平均处理——因为可用数据中的信息得到了充分评估。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。