Abstract
The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable 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. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.
[1] Yu.A. Kravtsov, Radiophys. Quant. Electr. 10, 719 (1967) http://dx.doi.org/10.1007/BF0103160110.1007/BF01031601Search in Google Scholar
[2] J.B. Keller, W. Streifer, J. Opt. Soc. Am. 61, 40 (1971) http://dx.doi.org/10.1364/JOSA.61.00004010.1364/JOSA.61.000040Search in Google Scholar
[3] G.A. Deschamps, Electron. Lett. 7, 684 (1971) http://dx.doi.org/10.1049/el:1971046710.1049/el:19710467Search in Google Scholar
[4] Yu.A. Kravtsov, G.W. Forbes, A.A. Asatryan, In: Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 1999) Search in Google Scholar
[5] S.J. Chapman, J.M. Lawry, J.R. Ockendon, R.H. Tew, SIAM Review 41, 417 (1999) http://dx.doi.org/10.1137/S003614459935205810.1137/S0036144599352058Search in Google Scholar
[6] Yu.A. Kravtsov, P. Berczynski, Stud. Geophys. Geod. 51, 1 (2007) http://dx.doi.org/10.1007/s11200-007-0002-y10.1007/s11200-007-0002-ySearch in Google Scholar
[7] Yu.A. Kravtsov, Geometrical Optics in Engineering Physics (Alpha Science International, UK, 2005) Search in Google Scholar
[8] P. Berczynski, Yu.A. Kravtsov, Phys. Lett. A 331, 265 (2004) http://dx.doi.org/10.1016/j.physleta.2004.08.05610.1016/j.physleta.2004.08.056Search in Google Scholar
[9] P. Berczynski, K.Yu. Bliokh, Yu.A. Kravtsov, A. Stateczny, J. Opt. Soc. Am. A 23, 1442 (2006) http://dx.doi.org/10.1364/JOSAA.23.00144210.1364/JOSAA.23.001442Search in Google Scholar
[10] P. Berczynski, Yu.A. Kravtsov, G. Zeglinski, Cent. Eur. J. Phys 6, 603 (2008) http://dx.doi.org/10.2478/s11534-008-0094-110.2478/s11534-008-0094-1Search in Google Scholar
[11] P. Berczynski, Yu.A. Kravtsov, A.P. Sukhorukov, Physica D 239, 241 (2010) http://dx.doi.org/10.1016/j.physd.2009.11.00210.1016/j.physd.2009.11.002Search in Google Scholar
[12] P. Berczynski, J. Opt. 13, 035707 (2011) http://dx.doi.org/10.1088/2040-8978/13/3/03570710.1088/2040-8978/13/3/035707Search in Google Scholar
[13] H. Kogelnik, Appl. Opt. 4, 1562, (1965) http://dx.doi.org/10.1364/AO.4.00156210.1364/AO.4.001562Search in Google Scholar
[14] S.A. Akhmanov, R.V. Khokhlov, A.P. Sukhorukov, In: Laser Handbook, F.T. Arecchi, Shulz-Dubois, Eds. (Elsevier, New York, 1972) Search in Google Scholar
[15] I. Bialynicki-Birula, J. Mycielski, Phys. Scr. 20, 539 (1979) http://dx.doi.org/10.1088/0031-8949/20/3-4/03310.1088/0031-8949/20/3-4/033Search in Google Scholar
[16] Y. Chen, Opt. Lett. 16, 4 (1991) http://dx.doi.org/10.1364/OL.16.00000410.1364/OL.16.000004Search in Google Scholar
[17] M. Karlsson, Phys. Rev. A 46, 2726 (1992) http://dx.doi.org/10.1103/PhysRevA.46.272610.1103/PhysRevA.46.2726Search in Google Scholar
[18] S. N. Vlasov, V.I. Talanov, Radiophys. Quant. Electr. 38, 1 (1995) http://dx.doi.org/10.1007/BF0105185310.1007/BF01051853Search in Google Scholar
[19] A.W. Snyder, J.D. Mitchell, Opt. Lett. 22, 16 (1997) http://dx.doi.org/10.1364/OL.22.00001610.1364/OL.22.000016Search in Google Scholar
[20] D.N. Christodoulides, T.H. Coskun, R.I. Joseph, Opt. Lett. 22, 1080 (1997) http://dx.doi.org/10.1364/OL.22.00108010.1364/OL.22.001080Search in Google Scholar
[21] Y.L. Tang, J.G. Chen, D.Y. Li, J. Kang, Y. Li, J. Mod. Opt. 46, 1177, (1999) 10.1080/09500349908231328Search in Google Scholar
[22] H. Buljan, M. Segev, D.N. Christodoulides, Phys. Rev. E 68, 036607 (2003) http://dx.doi.org/10.1103/PhysRevE.68.03660710.1103/PhysRevE.68.036607Search in Google Scholar
[23] A. Biswas, Appl. Math. Comput. 153, 369 (2004) http://dx.doi.org/10.1016/S0096-3003(03)00638-610.1016/S0096-3003(03)00638-6Search in Google Scholar
[24] T. Hansson, D. Anderson, M. Lisak, Piers Online 5 (2009) Search in Google Scholar
[25] T. Hansson, D. Anderson, M. Lisak, Opt. Comm. 283, 318 (2010) http://dx.doi.org/10.1016/j.optcom.2009.09.03410.1016/j.optcom.2009.09.034Search in Google Scholar
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