Variational approach to nonlinear self-focusing of Gaussian laser beams

Abstract

The problem of nonlinear self-focusing of Gaussian laser beams is reformulated in terms of a variational principle. By means of approximating Gaussian functions, expressions are obtained for the equilibrium radii and nonlinear frequency shifts of stationary self-trapped laser beams. The nonsteady propagation is given an illuminating form in terms of a potential function description. The analysis confirms the recent results obtained by moment theory as opposed to those based on paraxial ray approximations.

Evolution and Collapse of a Lorentz Beam in Kerr Medium

“…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.…”

“…We apply the variational approach [27][28][29][30][31] to obtain important information about the nonlinear dynamics on the spatial distributions of the Lorentz beam in the Kerr medium. 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 .…”

{open_quotes}Heavy light bullets{close_quotes} in electron-positron plasma

“…It is also possible to use different kinds of trial functions like the super Gaussian [20], which may fit the equilibrium profile better than the Gaussian. However, for the nonsteady propagation, our approach provides explicit, although approximate, analytical expressions for the beam parameters.…”

Self-focusing of a high-intensity laser pulse by a magnetized plasma lens in sub-relativistic regime

“…To investigate nonlinear interplay instabilities in the laser-plasma interaction it is desirable to obtain differential equations for the evolution of the macroscopic quantities that characterize the laser beam profile [25,26], including the amplitude, spot size, phase, curvature radius, and centroid. There are various methods for attempting to obtain such envelope equations, including the variation method [27], the moment method [28], and the source dependent expansion (SDE) technique [29]. We can use these mentioned techniques to study the nonlinear relativistic self-focusing phenomena with taking into account the relativistic mass corrections.…”