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2008 | 6 | 3 | 603-611
Tytuł artykułu

Gaussian beam diffraction in inhomogeneous and nonlinear media: analytical and numerical solutions by complex geometrical optics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.
Wydawca

Czasopismo
Rocznik
Tom
6
Numer
3
Strony
603-611
Opis fizyczny
Daty
wydano
2008-09-01
online
2008-07-17
Twórcy
  • Institute of Electronics, Telecommunication and Computer Science, Szczecin University of Technology, 71-126, Szczecin, Poland
Bibliografia
  • [1] Yu.A. Kravtsov, G.W. Forbes, A.A. Asatryan, Theory and applications of complex rays, In: E. Wolf (Ed.), ProgressinOptics 39, (Elsevier, Amsterdam, 1993) 3
  • [2] S.J. Chapman, J.M. Lawry, J.R. Ockendon, R.H. Tew, SIAM Rev. 41, 417 (1999) http://dx.doi.org/10.1137/S0036144599352058[Crossref]
  • [3] Yu.A. Kravtsov, Geometrical Optics in Engineering Physics (Alpha Science International, UK, 2005)
  • [4] Yu.A. Kravtsov, Radiophys. Quantum Electron. 10, 719 (1967) http://dx.doi.org/10.1007/BF01031601[Crossref]
  • [5] J.B. Keller, W. Streifer, J. Opt. Soc. Am. 61, 40 (1971) http://dx.doi.org/10.1364/JOSA.61.000040[Crossref]
  • [6] G.A. Deschamps, Electron. Lett. 7, 684 (1971) http://dx.doi.org/10.1049/el:19710467[Crossref]
  • [7] R.A. Egorchenkov, Yu.A. Kravtsov, Radiophys. Quantum Electron. 43, 512 (2000)
  • [8] R.A. Egorchenkov, Yu.A. Kravtsov, J. Opt. Soc. Am. A 18, 650 (2001) http://dx.doi.org/10.1364/JOSAA.18.000650[Crossref]
  • [9] R.A. Egorchenkov, Physics of Vibrations 8, 122 (2000) [WoS]
  • [10] V.M. Babich, Eigenfunctions, concentrated in the vicinity of closed geodesics, In: Mathematical Problems of Theory of Waves Propagation 9 (Nauka, Leningrad, 1968), 15 (inRussian)
  • [11] V.M. Babic’, V.S. Buldyrev, Asymptotic Methods in Problem of Diffraction of Short Waves (Nauka, Moscow, 1972), English transl.: V.M. Babic’, V.S. Buldyrev, Short-Wavelength Diffraction Theory: Asymptotic Methods (Springer Verlag, Berlin, Heidelberg, 1991)
  • [12] S. Choudhary, L.B. Felsen, IEEE Trans. AP-21, 827 (1973)
  • [13] Y. Chung, N. Dagli, J. Quantum Electron. 26, 1335 (1990) http://dx.doi.org/10.1109/3.59679[Crossref]
  • [14] G.R. Hadley, Opt. Lett. 16, 624 (1991) [PubMed]
  • [15] G.R. Hadley, IEEE J. Quantum Electron. 28, 363 (1992) http://dx.doi.org/10.1109/3.119536[Crossref]
  • [16] M. Yevick, B. Hermansson, J. Quantum Electron. 26, 109 (1990) http://dx.doi.org/10.1109/3.44923[Crossref]
  • [17] R.K. Luneburg, Mathematical Theory of Optics (Lecture notes, Brown University, Providence, Rhode Island, 1944), (University of California Press, Berkeley and Los Angeles), (1964)
  • [18] Yu.A. Kravtsov, P. Berczynski, Waver Motion 40, 23 (2004) http://dx.doi.org/10.1016/j.wavemoti.2003.12.012[Crossref]
  • [19] M. Bornatici, O. Maj, Plasma Phys. Control. Fusion 45, 707 (2003) http://dx.doi.org/10.1088/0741-3335/45/5/313[Crossref]
  • [20] P. Berczynski, Yu.A. Kravtsov, Phys. Lett. A 331, 265 (2004) http://dx.doi.org/10.1016/j.physleta.2004.08.056[Crossref]
  • [21] 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.23.001442[Crossref]
  • [22] Yu.A. Kravtsov, P. Berczynski, Stud. Geophys. Geod. 51, 1 (2007) http://dx.doi.org/10.1007/s11200-007-0002-y[Crossref]
  • [23] E. Heyman, L.B. Felsen, J. Opt. Soc. Am. A 18, 1588 (2001) http://dx.doi.org/10.1364/JOSAA.18.001588[Crossref]
  • [24] S.A. Akhmanov, A.P. Sukhorukov, R.V. Khokhlov, Soviet Phys. Uspekhi 10, 609 (1967) http://dx.doi.org/10.1070/PU1968v010n05ABEH005849[Crossref]
  • [25] F. Cornolti, M. Lucchesi, B. Zambon, Optics Communications 75, 129 (1990) http://dx.doi.org/10.1016/0030-4018(90)90241-K[Crossref]
  • [26] T. Singh, N.S. Saini, S.S. Kaul, Pramana, J. Phys. 55, 423 (2000) http://dx.doi.org/10.1007/s12043-000-0072-7[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-008-0094-1
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