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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 10 — Oct. 1, 1998
  • pp: 2725–2729

Generalized eikonal approximation. 2. Propagation of stationary electromagnetic waves in linear and nonlinear media

S. C. Yap, B. C. Quek, and K. S. Low  »View Author Affiliations


JOSA A, Vol. 15, Issue 10, pp. 2725-2729 (1998)
http://dx.doi.org/10.1364/JOSAA.15.002725


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Abstract

A recent study [J. Opt. Soc. Am. A 15, 2720 (1998)] showed that the eikonal equation can be generalized to include higher-order terms that can describe the dispersion of a pulse in a linear medium. In this companion paper, the formalism of this generalized eikonal approximation is investigated for stationary waves in both linear and nonlinear media. A local refractive index can be defined that includes higher-order terms in the form of the second derivatives of the amplitude of the wave. It is shown that wave phenomena such as diffraction, self-focusing, and self-trapping of a finite beam in linear and nonlinear media can be derived naturally as a result of the differences in the local refractive indices that arise from the spatial variation of the wave amplitude and the nonlinearity of the medium. This formalism can be readily extended to the study of other complex electromagnetic wave-propagation phenomena in both linear and nonlinear media.

© 1998 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(190.0190) Nonlinear optics : Nonlinear optics
(260.1960) Physical optics : Diffraction theory
(260.2030) Physical optics : Dispersion
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: March 12, 1998
Manuscript Accepted: March 18, 1998
Published: October 1, 1998

Citation
S. C. Yap, B. C. Quek, and K. S. Low, "Generalized eikonal approximation. 2. Propagation of stationary electromagnetic waves in linear and nonlinear media," J. Opt. Soc. Am. A 15, 2725-2729 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-10-2725

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