Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium

Abstract

Propagation of an asymmetric Gaussian beam in a cubic-quintic absorbing medium is analyzed and compared with that of a symmetric beam in both lossless and lossy media. A "collective variable approach" technique, based on trial functions, is used for solution of the general nonlinear Schrödinger equation. Using this variational approach, we investigate the self-focusing and breathing of an intense asymmetric Gaussian beam, taking into account both linear and nonlinear absorption. For a lossless medium, we define regions of oscillatory and diffractive beam propagation, for both symmetric and asymmetric beams. In particular, for an asymmetric beam, we find that there is no sharp boundary between the oscillatory self-focusing and oscillatory diffractive regimes of propagation. In the oscillatory region, we detect an interesting phenomenon-"beats" of the amplitude and perpendicular widths of the beam. For a lossy medium, significant differences between the amplitudes, widths, and phases of the symmetric and asymmetric beams have been predicted.

Breathing dynamics of an asymmetric Gaussian beam propagating in a saturable absorbing medium

“…This is in contrast to the cubic-quintic medium where the beating is always of the same type [12]. The refractive index n can be written as n 2 = n 2 0 + n 0 n 2 |E| 2 1 + n 0 n 2 |E| 2 / n 2 sat − n 2…”

“…However, considerable physical insight can be gained if the GNLSE is solved approximately in a semianalytical fashion [1,2] using the "collective variable approach" (CVA) [10,11] for conservative systems. The CVA technique is based on a trial function, such as a Gaussian function, with a finite number of variables, which is usually a function of the propagation coordinate that evolves subject to the constraints of the system.The CVA technique was recently used to investigate propagation of an asymmetric Gaussian beam in a lossy cubicquintic medium [12], which is characterized by competition between a self-focusing χ (3) Kerr nonlinearity and a selfdefocusing χ (5) nonlinearity. It was shown that there are two main regions of behavior, periodic and non-periodic.…”

Complex geometrical optics and nonlinear absorption/gain effects

“…Taking into account the permittivity profile defined in Eq. (1), one can notice that the wave number in nonlinear dissipative/gain media is complex-valued: [5][6][7]), one can notice that despite the fact that the wave number k defined in Eq. (4) is, in general, a complex-valued quantity, the propagation constant ( 0, )…”

“…Nowadays, there are many papers concerning nonlinear optics discussing the joint influence of linear and nonlinear absorption processes (embracing twophoton absorption phenomenon) on the self-focusing of a Gaussian light beam. For instance, a number of numerical examples describing and discussing this problem are presented in the paper [6]. However, in the author's opinion it is very difficult to capture, in fact, the role of nonlinear absorption in a nonlinear self-focusing medium when linear dissipation dominates over nonlinear, which is demonstrated by the results in paper [6].…”

“…For instance, a number of numerical examples describing and discussing this problem are presented in the paper [6]. However, in the author's opinion it is very difficult to capture, in fact, the role of nonlinear absorption in a nonlinear self-focusing medium when linear dissipation dominates over nonlinear, which is demonstrated by the results in paper [6]. Thus, in the author's opinion the only reasonable way to answer how a nonlinear absorption phenomenon influences selffocusing/self-defocusing effects is to neglect at once the influence of a linear absorption effect, searching for the area on the absorption curve where the linear optical medium is transparent.…”