Gaussian beam evolution in inhomogeneous nonlinear media with absorption

The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self−fo− cusing in smoothly inhomogeneous and nonlinear Kerr type and saturable fibres. CGO reduces the problem of Gaussian beam evolution in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self−focusing effects as compared to other methods of nonlinear optics such as variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of Gaussian beam propagation in saturable fibres with either focu− sing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front, phenomenon of weak ab− sorption and effect of either transverse and longitudinal inhomogeneity on GB propagation in nonlinear fibres is discussed in this paper.