Gaussian beam evolution in nonlinear inhomogeneous fibres - Berczyński, Paweł; Kravtsov, Yury (Photonics Letters of Poland, 2012)
The paper analyzes the Gaussian beam (GB) evolution in nonlinear fibers in the framework of paraxial complex geometrical optics (PCGO). This method reduces the problem of Gaussian beam diffraction 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, PCGO 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. It is shown that the PCGO method readily supplies the solution of Nonlinear Schrödinger Equation (NLS) for self-focusing fiber with a focusing refractive profile. Full Text: PDF References: Yu. A. Kravtsov, G.W. Forbes, A.A. Asatryan, in Progress in Optics, Ed. E.Wolf, 39, 3 (Amsterdam, Elsevier 1999). S.J. Chapman, J.M. Lawry, J.R. Ockendon, and 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, Geometrical Optics in Engineering Physics (Alpha Science International, UK 2005) P. Berczynski, Yu.A. Kravtsov., "Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics", Physics Letters 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.A. Kravtsov, A.P. Sukhorukov, "Complex geometrical optics of Kerr type nonlinear media", Physica D: Nonlinear Phenomena 239/5, 241 (2010).CrossRef S.A. Akhmanov, R.V. Khokhlov, A.P. Sukhorukov, Laser Handbook, vol. 2 (Elsevier 1972). J.A. Arnaud, Beams and Fiber Optics (New York, Academic Press 1976). G. Agrawal, Nonlinear Fiber Optics (New York, Academic Press, 1989). J.T. Manash, P.L. Baldeck, R.R. Alfano,, "Self-focusing and self-phase modulation in a parabolic graded-index optical fiber", Opt. Lett. 13(7), 589 (1988).CrossRef M. Karlsson, D. Anderson, M. Desaix, "Dynamics of self-focusing and self-phase modulation in a parabolic index optical fiber", Opt. Lett. 17(1), 22 (1992).CrossRef B.A. Malomed, "Chapter 2 Variational methods in nonlinear fiber optics and related fields", Prog. in Opt. 43, 71 (2002).CrossRef S. Longhi, D. Janner, "Self-focusing and nonlinear periodic beams in parabolic index optical fibres", J. Opt. B. 6 S303 (2004).CrossRef