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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 3 — Mar. 1, 2001
  • pp: 650–656

Complex ray-tracing algorithms with application to optical problems

Roman A. Egorchenkov and Yury A. Kravtsov  »View Author Affiliations

JOSA A, Vol. 18, Issue 3, pp. 650-656 (2001)

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We suggest a numerical algorithm for complex ray tracing. Such an algorithm is intended for the computation of a wave field in the framework of complex geometrical optics. The main advantage of the complex method is the possibility to take into account diffraction effects by use of only ordinary differential equations of geometrical optics, thus reducing the calculation time. The efficiency of the suggested algorithm is illustrated by several numerical examples that allow comparison with known analytic solutions: the field of a plane wave behind a caustic in a linear layer, uniform field asymptotics on a caustic in a linear layer, and a Gaussian beam field in a homogeneous medium. It is pointed out that the approach under consideration can be readily applied to a great variety of real wave problems that have an analytical solution: nonplane waves, nonplane-stratified media, and the like. In particular, a numerical solution for Gaussian beam propagation through inhomogeneities of Gaussian form is presented.

© 2001 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(260.1960) Physical optics : Diffraction theory

Original Manuscript: April 11, 2000
Revised Manuscript: October 2, 2000
Manuscript Accepted: October 2, 2000
Published: March 1, 2001

Roman A. Egorchenkov and Yury A. Kravtsov, "Complex ray-tracing algorithms with application to optical problems," J. Opt. Soc. Am. A 18, 650-656 (2001)

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  1. Yu. A. Kravtsov, G. W. Forbes, A. A. Asatryan, “Theory and applications of complex rays,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1999), Vol. XXXIX, pp. 1–62.
  2. Yu. A. Kravtsov, “Complex rays and complex caustics,” Radiophys. Quantum Electron. 10, 719–730 (1967). [CrossRef]
  3. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).
  4. Yu. A. Kravtsov, Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, Berlin, 1990).
  5. Yu. A. Kravtsov, Yu. I. Orlov, Caustics, Catastrophes and Wave Fields. 2nd ed. (Springer-Verlag, Berlin, 1998).
  6. R. A. Egorchenkov, Yu. A. Kravtsov, “Numerical realization of complex geometrical optics method,” Izv. Vyssh. Uchebn. Zaved. Radiodizika 43, 630–637 (2000) [English translation in Radiophys. Quantum Electron. 43, 512–517 (2000)].
  7. E. Poli, G. V. Pereverzev, A. G. Peeters, “Paraxial Gaussian wave beam propagation in an anisotropic inhomogeneous plasma,” Phys. Plasmas 6, 5–11 (1999). [CrossRef]

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