Collapse dynamics of super-Gaussian Beams

Abstract

We investigate the self-focusing dynamics of super-Gaussian optical beams in a Kerr medium. We find that up to several times the critical power for self-focusing, super-Gaussian beams evolve towards a Townes profile. At higher powers the super-Gaussian beams form rings which break into filaments as a result of noise. Our results are consistent with the observed self-focusing dynamics of femtosecond laser pulses in air [1] in which filaments are formed along a ring about the axis of the initial beam where the initial beam did not form a ring.

Evolution and Collapse of a Lorentz Beam in Kerr Medium

“…For the sake of intuition, the initial powers have been specified not only in terms of P cr , but also in terms of P 0 = πn 0 /(n 2 k 2 ). The simulations show that as the initial power reaches a certain threshold, the intensity at the center part of the beam will dominate [35][36][37][38][39][40][41][42] and the peak intensity increases with distance z. This threshold is lower for asymmetric beam (see Fig.…”

“…The collapse dynamics of elliptical beams have been extensively studied [22,24]. These studies pointed out significant differences between quantitative predictions of the aberrationless approximation and actual results obtained from NLS equation simulations [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. From our numerical calculations, we find a simple empirical expression for the critical power of asymmetrical Lorentz beam by fitting the results of the numerical calculation…”

“…(12) is the upper bound for Lorentz beam. The critical power overestimates the actual threshold power for collapse [35][36][37][38][39][40][41][42].…”

“…When w 0x = w 0y , the critical collapse power is minimum P min cr = 16π 2 n 0 25n 2 k 2 , corresponding to a symmetrical Lorentz beam. The critical collapse power of a symmetrical Lorentz beam only depends on the nonlinear parameter of the medium, and is almost equal to that of the Gaussian beam P GS cr = 2πn 0 n 2 k 2 [38][39][40][41][42]. The ratio of the critical power of a symmetrical Lorentz beam to that of a Gaussian beam is 8π/25.…”

“…We obtain the critical power [32][33][34][35][36][37][38][39][40][41][42] of the Lorentz beam with uniform wavefront, which is required to collapse the beams, as a function of different beam parameters, particularly the waists w 0x and w 0y . Numerical simulations illustrate in more details the nonlinear dynamics of the beams in the Kerr medium.…”