Nonlinear Bessel beams

Abstract

The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schrödinger equation. The nonlinearity is shown to primarily affect the central parts of the Bessel beam, giving rise to radial compression or decompression depending on whether the nonlinearity is focusing or defocusing, respectively. The dynamical properties of Gaussiantruncated Bessel beams are also analysed in the presence of a Kerr nonlinearity. It is found that although a condition for width balance in the root-mean-square sense exists, the beam profile becomes strongly deformed during propagation and may exhibit the phenomena of global and partial collapse.

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…”

“…In order to investigate further the effect of Kerr nonlinearity [23][24][25][26][27][28][29][30][31][32][33][34][35][36] on the Lorentz beam, we need to solve the NLS equation numerically. Numerical simulations were done using the parameters of wavelength λ = 0.53 µm, n 0 = 1, n 2 = 0.5 × 10 −4 cm 2 /GW, w 0x = 10 µm and z 0 = kw 2 0x /2 = 0.6 mm, respectively.…”

“…(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].…”

“…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.…”