Mode-locked generation of transverse modes in a neodymium laser with a positive electrooptic feedback

Abstract

We discuss a universal bound on any excitation of heavy fields during inflation: the ratio of the heavy field's energy density to the one driving inflation must be less than the maximally allowed relative amplitude of oscillations in the power-spectrum (ρ h /ρ I 0.01 according to PLANCK). This bound can be traced back to the sudden change of the equation of state parameter across the excitation event.We employ a sudden transition approximation at the perturbed level, which has been used before in different settings; we check its validity by comparison to the full multi-field result in a concrete case study involving a sudden mass change of an inflaton.

Modal reconstruction of transverse mode-locked laser beams

“…In summary, we have demonstrated the successful transverse mode-locking of an end-pumped solid-state laser with an acousto-optic modulator. Compared to previous publications [2,[5][6][7] we provided an advanced analysis of the transverse mode-locked (TML) laser by reconstructing the modal power coefficients and the modal phases of the generated laser beams with the stochastic parallel gradient descent algorithm. Based on these reconstructions, we found that with the presented setup the average mode order n could be freely adjusted up to a value of 31.…”

“…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.…”

“…However, before TML lasers can be adapted for fast scanning applications a better understanding of the parameters affecting their spatio-temporal dynamics is required. Theoretical considerations predict that the modal power distribution as well as the modal phases have a significant influence on the spatio-temporal dynamics of TML lasers [7]. However, while in previous publications the spatio-temporal intensity distributions of TML lasers have been measured, no analysis of the modal power distribution or the modal phases have been performed [2,[5][6][7].…”

“…Theoretical considerations predict that the modal power distribution as well as the modal phases have a significant influence on the spatio-temporal dynamics of TML lasers [7]. However, while in previous publications the spatio-temporal intensity distributions of TML lasers have been measured, no analysis of the modal power distribution or the modal phases have been performed [2,[5][6][7]. In most cases it was estimated, that a number of 2-7 modes had contributed to the mode-locking process, while the highest average mode order claimed was n = 4 [2].…”

Modal conversion of transverse mode-locked laser beams

“…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]. Furthermore, the simultaneous locking of longitudinal and transverse modes has been demonstrated [24][25][26].…”