WIAS Preprint No. 3014, (2023)

Bayesian estimation of laser linewidth from delayed self-heterodyne measurements


  • Mertenskötter, Lutz
    ORCID: 0000-0001-5074-2721
  • Kantner, Markus
    ORCID: 0000-0003-4576-3135

2020 Mathematics Subject Classification

  • 37N20 60G10 60G35 62M20 82C31


  • Laser linewidth, phase noise, narrow-linewidth semiconductor lasers, self-heterodyne beat note measurement, non-Markovian noise, Langevin equations, stochastic differential equations, Bayesian inference, Markov-chain Monte Carlo method, Metropolis--Hastings algorithm, time series analysis, spectral analysis




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 / textitf-type non-Markovian noise.

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