Modal reconstruction of transverse mode-locked laser beams
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Modal reconstruction of transverse mode‑locked laser beams Florian Schepers1 · Tim Hellwig1 · Carsten Fallnich1,2 Received: 30 May 2020 / Accepted: 8 September 2020 © The Author(s) 2020
Abstract Transverse mode-locking in an end-pumped solid state laser by amplitude modulation with an acousto-optic modulator was investigated. Using the stochastic parallel gradient descent algorithm the modal power coefficients and the modal phases of the transverse mode-locked (TML) laser beam were reconstructed from the measured spatial and spatio-temporal intensity distributions, respectively. The distribution of the reconstructed modal power coefficients revealed that the average mode order of the transverse mode-locking process could be increased by a factor of about 8 compared to previous works, corresponding to an increase in the normalized oscillation amplitude by a factor of about 3. Furthermore, we found that besides a non-Poissonian modal power distribution, strong aberrations of the modal phases occurred in the experiment, resulting in a deformation of the oscillating spot. Additionally, we demonstrated the generation of up to four spots oscillating simultaneously on parallel traces by operating the TML laser on a higher mode order in the orthogonal direction to the transverse mode-locking process. TML lasers are of interest, e.g., for beam scanning purposes, as they have the potential to enable spot resolving rates in the multi-GHz regime.
1 Introduction The idea of transverse mode-locking was already suggested [1] and demonstrated [2] by Auston in 1968, shortly after the first demonstration of locking longitudinal laser modes in 1964 [3, 4]. Auston showed that by locking the phases of multiple Hermite–Gaussian (HG) modes a fast scanning beam, oscillating in the transverse direction of the optical axis, could be generated. Since this initial demonstration of transverse mode-locking in a He–Ne laser the successful locking of transverse modes was also realized in semiconductor [5] and solid-state lasers [6, 7]. However, in these experiments the transverse mode-locking was only obtained over limited time periods as the lasers were either Q-switched or pumped by a pulsed laser source. Haug et al. [8] demonstrated that by locking two Laguerre–Gaussian Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00340-020-07513-5) contains supplementary material, which is available to authorized users. * Florian Schepers f.schepers@uni‑muenster.de 1
Institute of Applied Physics, Westfälische WilhelmsUniversität, Corrensstraße 2, 48149 Münster, Germany
MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
2
modes instead of Hermite–Gaussian modes a time varying spot size of the laser beam could be achieved. Furthermore, work has been published demonstrating the simultaneous locking of longitudinal and transverse laser modes, either in frequency-degenerated free-space lasers [9–11] or in nonlinear fiber lasers [12]. Transverse mode-locked
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