Gaussian Beam Diffraction in Inhomogeneous and Nonlinear Saturable Media

The method of complex geometrical optics is presented, which describes Gaussian beam diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. Complex geometrical optics reduces the problem of Gaussian beam diffraction and self-focusing 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 Gaussian beam amplitude, which can be readily solved both analytically and numerically. As a result, complex geometrical optics 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 complex geometrical optics method is presented on the example of Gaussian beam width evolution in saturable fibre with either focusing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front on Gaussian beam evolution in nonlinear saturable medium is discussed in this paper.