Dynamics of self-focusing and self-phase modulation in a parabolic index optical fiber

Abstract

The dynamics that result from the combined effects of spatial diffraction, nonlinearity, and a parabolic graded index for wave propagation in optical fibers are presented. An approximate analytical solution of the nonlinear Schrödinger equation in a graded-index fiber is obtained by using a variational approach. Particular emphasis is put on the variation of both the pulse width and the longitudinal phase delay with the distance of propagation along the fiber.

Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium

“…The phase may be positive or negative depending on the value of Ô. However, the regularized phase, Ö which is defined as [16] and is contrary to the results of Manassah et al [9]. The latter predicted that under certain conditions regularized phase could change sign with distance of propagation.…”

“…Some aspects of this genuinely non-linear process can be investigated by considering numerical or approximate analytical methods. We adopt here the latter approach in this paper, using a powerful variational method that has been used recently in several similar investigations [14][15][16]28,29]. Equation (1) can be reformulated into a variational problem corresponding to a Lagrangian Ä so as to make AEÄ AEÞ ¼ equivalent to eq.…”

Effect of rippled laser beam on excitation of ion acoustic wave

“…Yet another method involving the invariants of nonlinear Schrödinger equation is variational approach used by Anderson et al to describe self-focusing in plasmas [25] and optical fibers [26]. Variational method which though approximately analytical but fairly general in nature, has been used recently in a number of investigations [27][28][29][30][31][32]. Besides that, it has been reported to give correct regularised phase description [27].…”

“…Variational method which though approximately analytical but fairly general in nature, has been used recently in a number of investigations [27][28][29][30][31][32]. Besides that, it has been reported to give correct regularised phase description [27]. Nevertheless, it is of limited scope in investigation of singularity formation and collapse associated with self-focusing phenomenon [33].…”

Gaussian beam evolution in nonlinear inhomogeneous fibres

“…In paraxial approximation assuming that  is small parameter equation (12) reduces to the ordinary differential equation in the form:…”