Computer simulation of laser-beam self-focusing in a plasma

Abstract

Laser-beam or soliton propagation is best modelled for fast computation using a split-step Fourier method based on an orthogonal transform technique known as the beam-propagation method. The beam-propagation split-step Fourier-transform technique in one and two dimensions for the propagation of a soliton or laser beam respectively in a nonlinear plasma and a split-step Hankel-transform-based algorithm for cylindrical-beam propagation close to circular cross-sectional symmetry and its computational implementation are discussed. Attention is particularly focused on the verification of the paraxial approximations of the soliton or the laser beam using these techniques, after a brief review of the beam-propagation method.

Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

“…This non-radiative nature of the paraxial field is similar to the Rabbi oscillations in a two-level system [39]. These aspects need further elaboration and investigation in the present theory not only using analysis but also computer simulations of the full equation using beam propagation methods [25].…”

“…is a reasonably good approximate solution even in the case of saturating nonlinearity [25], (a fact that is easier to verify in the special case of self-trapping when variations in the propagation variable Þ are zero and Õ ½ ) so that eq. (2) is a good approximation for the response function.…”

“…In the case of the soliton, the transverse operator is in the planar coordinate Ü, the variable Þ is then the reduced time variable. See refs [24,25] for clarity on symbols and operators in this context. There is an iterative relationship between the field form in eq.…”

Lie-optic matrix algorithm for computer simulation of paraxial self-focusing in a plasma

“…A whole range of Lie-optic methods exists for linear optics [5,6] which have yet to be adopted for self-focusing and this paper attempts to do just that in the paraxial limit. Lie-optic methods have an in-built economy in analysis and computation and have found a natural way into computational algorithms for self-focusing even in the non-paraxial regions that has been dealt by us elsewhere [7].…”

“…Unlike the methodology of this paper and other computational schemes [7] which can deal with saturating nonlinearity, group-theoretical methods usually deal with the cubic or at most quintic nonlinearities [3,4]. An important feature of nonlinearity saturation of the refractive index with beam intensity in the NLSE for self-focusing is that beam intensity cannot shoot to infinite values because of catastrophic focusing at the self-focusing singularity because of the presence of nonlinearity saturation.…”