Gaussian beam evolution in logarithmically saturable nonlinear media

The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous 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. The power of PCGO method is presented on the example of GB evolution in logarithmically saturable medium with defocusing refractive profile. The solutions obtained by PCGO method are compared with numerical results of Nonlinear Schrodinger Equation by beam propagation method (BPM). Full Text: PDF References Yu.A. Kravtsov, "Complex rays and complex caustics", Radiophys. Quantum Electronics 10, 719 (1967). CrossRef .B. Keller, W. Streifer, "Complex Rays with an Application to Gaussian Beams", J. Opt. Soc. Am. 61, 40 (1971). CrossRef G. A. Deschamps, "Gaussian beam as a bundle of complex rays", Electron. Lett. 7(23), 684 (1971). CrossRef Yu.A. Kravtsov, G.W. Forbes, A.A. Asatryan, Theory and applications of complex rays, in Progress in Optics, edited by E. Wolf, 39, 3 (Elsevier, Amsterdam, 1999). S.J. Chapman, J.M. Lawry, J.R. Ockendon, R.H. Tew, "On the Theory of Complex Rays", SIAM Review 41, 417 (1999). CrossRef Yu.A. Kravtsov, P. Berczynski, "Gaussian beams in inhomogeneous media: A review", Stud. Geophys. Geod. 51(1), 1 (2007). CrossRef Yu.A. Kravtsov N.Y. Zhu. Theory of diffraction: Heuristic Approaches (Alpha Science International, ISBN 1842653725, 2009). P. Berczynski, Yu.A. Kravtsov, "Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics", Phys. Lett. A 331(3-4), 265 (2004). CrossRef P. Berczynski, K.Yu. Bliokh, Yu.A. Kravtsov, A. Stateczny, "Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach", J. Opt. Soc. Am. A, 23(6), 1442 (2006). CrossRef P. Berczynski, Yu. Kravtsov, "Gaussian beam evolution in nonlinear inhomogeneous fibres", Phot. Lett. Poland 4(1), 26 (2012). CrossRef P. Berczynski, Yu. A. Kravtsov, G. Zeglinski, "Gaussian beam diffraction in inhomogeneous media of cylindrical symmetry", Optica Applicata 40(3), 705 (2010). DirectLink A.W. Snyder, J.D. Mitchell, "Mighty morphing spatial solitons and bullets", Optics Letters 22(1), 16 (1997). CrossRef Y.L. Tang, J.G Chen, D.Y Li, J. Kang, Y. Li, "Specific gaussian beams propagating inside logarithmically saturable nonlinear media", J. Modern Optics 46(8), 1177 (1999). CrossRef T. Hansson, D. Anderson, M. Lisak, "Soliton interaction in logarithmically saturable media", Opt. Comm. 283(2), 318 (2010). CrossRef