Propagation of Cylindrically Symmetric Gaussian Beams in a Higher-Order Nonlinear Medium

Abstract

The propagation of a cylindrically symmetric Gaussian beam in a cubic-quintic nonlinear medium is analysed via a variational approach. Explicit conditions for stationary beam propagation are determined and their stability to symmetric perturbation of the spot width is established. Approximate analytical solutions are secured for the spot width modulation with propagation distance. A comparison is made with beams propagating in a medium exhibiting a two-level saturation.

Light bullet formation in a cubic-quintic nonlinear medium

“…From the reduced variational principle, deriving the Euler-Lagrange equation for A…z †; a…z † and b…z †, leads to the following set of coupled equations [13]:…”

“…The type of behaviour exhibited by the spot width will depend crucially on the form of the potential function ¦…y †, which has di erent properties for di erent parameter values ·;¸and ¶ [12,13].…”

“…As in previous work [12,13], we need to consider di erent regimes of the …·;¸; ¶ †-parameter space. Here we shall choose three regimes: (i) · ¡¸ ‡ ¶ˆ0, (ii) · ¡¸ ‡ ¶ > 0, and (iii) · ¡¸ ‡ ¶ < 0.…”

“…Akhmediev and Soto-Crespo [11] showed numerically that a longitudinally modulated beam in a two-level saturable medium spontaneously breaks into a train of light bullets. A cubic-quintic nonlinearity has previously been employed to study optical beam propagation in simple saturable media with one-and two-transverse dimensions [12,13], and conditions for stable beam propagation were determined.…”

Variational analysis of solitary waves in a homogeneous cubic-quintic nonlinear medium

“…Hence, investigations into the properties of solitary waves have normally been performed numerically. However, it is often desirable to have an analytical model describing the dynamics of beam propagation in a nonlinear medium, and this can be obtained using a variational approach [24,25].…”