**Project Heads**

Uwe Bandelow, Markus Kantner, Wilhelm Stannat (since 01/2022), Hans Wenzel

**Project Members**

Lutz Mertenskötter

**Project Duration**

First funding period: 01.01.2021 − 31.12.2021; second funding period: 01.01.2022 − 31.12.2024

**Located at**

WIAS

Narrow-linewidth lasers are key elements of coherent communication systems, optical atomic clocks, matter-wave interferometers, ion-trap quantum computers and gravitational wave detectors. The spectral width of the emitted optical power spectrum of a laser is essentially determined by its frequency noise power spectral density (FN-PSD), that is influenced by numerous stochastic processes. The standard (Markovian) laser linewidth theory (see Wenzel et al. (2021) for a review) is restricted to Gaussian white noise (in particular spontaneous emission of photons into the laser mode), which predicts a spectrally flat FN-PSD that is associated with a Lorentzian lineshape and the so-called intrinsic linewidth. This model is sufficient for most applications, however, a realistic description of ultra-narrow linewidth lasers requires the inclusion of additional non-Markovian noise components to match the experimental observations. These colored noise processes lead to significant line broadening, but as their modeling from first principles (i.e., quantum Langevin equations) is hardly accessible, only few non-Markovian stochastic laser theories exist. In this project, we pursue a data-driven modeling approach to reconstruct a non-Markovian stochastic semiconductor laser model from experimental time series using data assimilation techniques.

We developed two novel techniques to infer the frequency noise characteristics of lasers from data collected by the widely used self delayed self-heterodyne (DSH) method. Here Wiener filters are used to robustly reproduce the frequency noise power density, even in cases where traditional methods would struggle due to comparatively high measurement noise [2]. Furthermore we employed bayesian regression to infer the intrinsic laser linewidth , as well as other model parameters from DSH measurements [3].

The application goal of the project is the theory-based optimization of extended cavity diode lasers for space-based metrology systems. For this, delayed stochastic differential equation models and stochastic partial differential equation models shall be developed in order to facilitate the understanding of performance bottlenecks and in order to support the identification of an optimal laser design and suitable control schemes.

**Related Publications
**

- [1] H. Wenzel, M. Kantner, M. Radziunas and U. Bandelow: Semiconductor Laser Linewidth Theory Revisited,
*Appl. Sci.***11**, 6004 (2021) - [2] M. Kantner and L. Mertenskötter: Accurate evaluation of self-heterodyne laser linewidth measurements using Wiener filters,
*Opt. Express***31**, 15994 (2023) - [3] L. Mertenskötter and M. Kantner:
*Bayesian Estimation of Laser Linewidth From Delayed Self-Heterodyne Measurements*. In: Belhaq, M. (eds) Advances in Nonlinear Dynamics and Control of Mechanical and Physical Systems. Springer Proceedings in Physics**301,**Springer, Singapore (2024) - [4] L. Mertenskötter and M. Kantner: Frequency Noise Characterization of Narrow-Linewidth Semiconductor Lasers: A Bayesian Approach,
*IEEE Photonics Journal***16**, 0601407 (2024)

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