Complex geometrical optics and nonlinear absorption/gain effects

Abstract

The paper presents systematic analysis of the influence of nonlinear absorption/gain phenomena on Gaussian wave field evolution in Kerr type medium with additional consideration of the initial light beam convergence and divergence. To perform efficient analysis of the joint contribution of the initial curvature of the wave front and nonlinear absorption/gain effects on self-focusing/self-defocusing phenomena I propose to apply the method of complex geometrical optics (CGO) which at once reduces Gaussian beam diffraction and self-action effects (including nonlinear absorption/gain) to domain of ordinary differential equations (ODEs), which are base (output) equations. Description in output ODEs causes that CGO possess great superiority over well known analytic methods of nonlinear optics such as: variational method and method of moments which every time demand to solve Nonlinear Schrodinger Equation (NLS) by applying integral variational procedure or virial theory to obtain resulting equations describing evolution of amplitude, beam width and wave front curvature which happen to be identical with those obtained by CGO method. CGO method dealing with output ODEs is time consuming physical approach comparing to the numerical methods of nonlinear and wave optics. CGO with output evolutionary ODEs enables one to apply basic mathematical computer software such as: Matlab/Octave, Mathcad and Mathematica commonly available on every University, Colleague and secondary school nowadays.

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References

1. N. N. Akhmediev and A. Ankiewicz, Solitons. Nonlinear Pulses and Beams. (Chapman and Hall, London 1997).
2. N. N. Akhmediev and A. Ankiewicz ed. Dissipative Solitons. Lecture Notes in Physics, Vol. 661, p. 1-443, ISBN: 978-3-540-23373-2, (Springer Berlin Heidelberg, 2005). CrossRef
3. E. Jaatinen and M. W. Jones, "Theoretical description of low divergence Gaussian fields in self-defocusing photorefractive media", Optics Communications, 281, p. 3201-3207 (2008). CrossRef
4. P. Berczynski, and S. Marczynski. Book Chapter 1: Gaussian Beam Propagation in Inhomogeneous Nonlinear Media. Description in Ordinary Differential Equations by Complex Geometrical Optics , (Edited by: P. W. Hawkes) , Advances in Imaging and Electron Physics, 185, pages 1-111, ISBN 9780128001448, Elsevier New York, (2014).
5. Y. Silberberg, "Solitons and two-photon absorption", Optics Letters, vol. 15, No. 18, p.1005-1007 (1990). CrossRef
6. D. Ianetz, Yu. Kaganovskii, A. D. Wilson-Gordon, and M. Rosenbluh, "Propagation of an asymmetric Gaussian beam in a nonlinear absorbing medium", Phys. Rev. A 81, 53851, pages-1-6 (2010). CrossRef
7. D. Mc Morrow, W. Lotshaw, J. Melinger, S. Buchner, and R. Pease, "Subbandgap laser-induced single event effects: carrier generation via two-photon absorption", IEEE Trans. Nucl. Sci., vol. 49, no. 6, pp. 3002 ? 3008 (2002). CrossRef