Optical guiding of laser beam in nonuniform plasma

Abstract

A plasma channel produced by a short ionising laser pulse is axially nonuniform resulting from the self-defocusing. Through such preformed plasma channel, when a delayed pulse propagates, the phenomena of diffraction, refraction and self-phase modulation come into play. We have solved the nonlinear parabolic partial differential equation governing the propagation characteristics for an approximate analytical solution using variational approach. Results are compared with the theoretical model of Liu and Tripathi (Phys. Plasmas 1, 3100 (1994)) based on paraxial ray approximation. Particular emphasis is on both beam width and longitudinal phase delay which are crucial to many applications.

Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity

“…In particular, it models the propagation of intense laser beams in a homogeneous bulk medium with a Kerr nonlinearity. It was suggested that stable high power propagation can be achieved in plasma by sending a preliminary laser beam that creates a channel with a reduced electron density, and thus reduces the nonlinearity inside the channel [5]. Under these conditions, beam propagation can be modeled, in the simplest case, by the following inhomogeneous nonlinear Schödinger equation (INLS-equation in the sequel) of the form…”

Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

“…Since G 2 < 0, a necessary condition for stability is that V (4) (0) be negative! We recall that the NLS 3) is an exception to this 'rule' as it admits blowup solutions yet its waveguides are stable.…”

“…A few years ago, it was suggested that stable high-power propagation can be achieved in plasma by sending a preliminary laser beam that creates a channel with a reduced electron density, and thus reduces the nonlinearity inside the channel [4,8]. Under these conditions, beam propagation can be modeled, in the simplest case, by the inhomogeneous nonlinear Schrödinger equation…”

“…Indeed, when V is monotonic then V (0) > 0. In principle, this term would have given O(ˆ 2 ) contributions to |φ ω | 2 2 , whereas V (4) (0) would only give O(ˆ 4 ) contributions. However, because the O(ˆ 2 ) terms due to V (0) completely balance each other, stability is determined by both V (0) and V (4) …”

Remarks on the inhomogeneous fractional nonlinear Schrödinger equation

“…When γ > 0, it can be thought of as modeling inhomogeneities in the medium. The nonlinearity enters due to the effect of changes in the field intensity on the wave propagation characteristics of the medium and the nonlinear weight can be looked as the proportional to the electron density [18,33,38].…”