Simulation-based fitting routine for laser linewidth (DSH)

MATLAB routines to extract the laser linewidth from a Delayed Self Heterodyne (DSH) spectrum with a simulation-based fitting algorithm

This toolbox contains the routines and functions to extract the laser linewidth from a spectrum measured by the Delayed Self Heterodyne (DSH) method (see included documentation). The routine uses a simulation-based algorithm to fit the data, by numercially generating frequency noise contributions of higher order: white (constant), flicker and random-walk noise . It then uses a Nelder-Mead simplex optimization to adjust the corresponding amplitudes to the different noise sources. Finally, It extracts the linewidth components related to the different noise contributions, namely Lorentzian, Gaussian and linewidths respectively.

The MATLAB directory contains useful functions structured in 3 sub-folders, plus a documentation folder about DSH:

• documentation_DSH : This contains documentation about laser linewidth, concepts of phase and frequency noise, linewidth measurement with Delayed Self Heterodyne method.

• general_routines: This contains functions that are used by the other scripts in the toolbox. However, these might be useful in general, also for completely unrelated applications.

• conventional_fitting: This contains the necessary tools and an example script to fit the data to the analytic solution that just includes the conventional white noise. The data will not be perfectly fitted. You should view the value that you will get here more as an orientation for the order of magnitude. Both a least square fit and a Nelder-Mead based optimization (fminsearch) are used and compared. Example spectrum:

• simulation_based_fit: This folder and its sub-directories include the code to simulate DSH spectra for various, also higher order noises (currently included: white noise, flicker noise and random walk noise of the laser frequency). Example files and script are included. The example script has a lot of comments included to help you using it. The simulation is used together with a Nelder-Mead-Simplex search (fminsearch) to obtain a "fit" although you have to guess the starting values already quite well. Example spectrum:

• related paper: https://doi.org/10.1364/AO.58.003555
• For more information also see the related thesis: P. Malik, Linewidth-reduced DBR Laser for Raman Sideband Cooling, MSc thesis, University of Bonn (2020). (available in Quanum Technologies Group, Uni Bonn, Master Thesis)

This code is linked to the following paper (see Appendix A): https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.043321

Please include the following citation when using the code:

E. Uruñuela, M. Ammenwerth, P. Malik, L. Ahlheit, H. Pfeifer, W. Alt, and D. Meschede, Raman imaging of atoms inside a high-bandwidth cavity, Phys. Rev. A 105, 043321 (2022).

We also suggest citing the following paper, on which we based our algorithm:

W. Ma, B. Xiong, C. Sun, X. Ke, Z. Hao, L. Wang, J. Wang, Y. Han, H. Li, and Y. Luo, Laser frequency noise characterization by self-heterodyne with both long and short delay, Appl. Opt. 58, 3555 (2019)