Critical power for self-focusing in bulk media and in hollow waveguides

Abstract

We determine the threshold power for self-focusing collapse both in a bulk medium and in a hollow-core waveguide for various spatial profiles. We find that the threshold power for collapse in the waveguide is always equal to the lower-bound prediction for a bulk medium.

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.…”

“…(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.…”

“…Although this is unrealistic, the approach provides a qualitative picture. In fact, when the initial power becomes too high, other nonlinear effects that give modulation instability like higher order nonlinearity, self steepening and self-phase modulation should be considered, and higher-order processes such as plasma generation halt the collapse [42]. Also, for ultrashort laser pulse, the numerical calculation of the NLS in the Kerr medium must go beyond the paraxial approximation.…”

“…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.…”