Modal reconstruction of transverse mode-locked laser beams

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.

Modal conversion of transverse mode-locked laser beams

“…The TML laser setup was similar to the setup described in our previous publication [20]. A plano-concave twomirror laser cavity was chosen, with a 1 mm long, 1 at.% doped Nd:YVO 4 crystal as active gain medium.…”

“…The fundamental mode size in the plane of the CCD-camera was measured to be w x = 296 ± 4 m and w y = 312 ± 3 m in the horizontal and vertical direction, respectively. The timeaveraged as well as spatio-temporal intensity distributions of the unconverted TML beam were measured in a similar fashion directly behind the TML laser; the corresponding setup is described in detail in our previous publication [20].…”

“…This can for instance be seen when directly comparing the calculated time-dependent intensity distribution of an ideal HG TML beam (Animation 1a), with the time-dependent intensity distribution of the measured HG TML beam (Animation 1c). We have recently shown that these variations of the spot size and shape were caused by deviations of the modal power distribution from a Poisson distribution as well as by higher order terms of the modal phases [20]. As the modal power distributions and modal phases of the incident HG TML beams were passed on to the LG TML beams during the conversion process, they had a significant influence on the spatio-temporal dynamics of the converted beams.…”

“…A variety of different schemes have been developed to obtain a modal decomposition of single-frequency multimode laser beams [32][33][34][35][36][37][38]. For TML laser beams, where the modes oscillate at different frequencies, we have recently demonstrated [20] that a numerical reconstruction method based on the SPGD algorithm [35][36][37] can be used to reconstruct the modal power distribution and the modal phases of the beam. We used the same algorithm here to reconstruct the modal power and phase distributions of the unconverted HG TML beams.…”

“…If the modes are phase-locked with each other, a transverse mode-locked (TML) laser with a periodically scanning output beam is realized [18,19]. The scanning frequency of such TML lasers only depends on the transverse mode spacing of the laser and can, therefore, achieve high spot resolving rates in the multi-GHz regime [20]. Since transverse mode locking was suggested [18] and demonstrated [19] for the first time in a He-Ne laser, it has also been realized in semiconductor [21] and solid state lasers [22,23].…”