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-focusing along a curvilinear trajectory in inhomogeneous and nonlinear saturable media. CGO method reduces the problem of Gaussian beam propagation in inhomogeneous and nonlinear media to solving 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 the 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 the evolution of beam cross-section and wave front cross-section along a curvilinear central ray with torsion in weakly absorptive and nonlinear saturable graded-index fibre, where the effect of initial beam ellipticity is included into our description.