Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium

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.