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.

中文翻译：

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横向锁模激光束的模态重建

研究了通过声光调制器幅度调制在端部泵浦固态激光器中的横向锁模。使用随机平行梯度下降算法，横向锁模 (TML) 激光束的模态功率系数和模态相位分别从测量的空间和时空强度分布中重建。重构模态功率系数的分布表明，横向锁模过程的平均模阶数与之前的工作相比可以增加约 8 倍，对应于归一化振荡幅度增加约 3 倍. 此外，我们发现除了非泊松模态功率分布外，实验中还出现了模态相位的强烈畸变，导致振荡点变形。此外，我们展示了通过在与横向锁模过程正交的方向上以更高的模式阶操作 TML 激光器，在平行轨迹上同时产生多达四个光斑。TML 激光器很受关注，例如用于光束扫描目的，因为它们有可能在多 GHz 范围内实现光斑分辨率。