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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. 5 — May. 1, 1998
  • pp: 1394–1400

Approximate solutions to the scalar wave equation: the decomposition method

Vasudevan Lakshminarayanan and Srinivasa Varadharajan  »View Author Affiliations


JOSA A, Vol. 15, Issue 5, pp. 1394-1400 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001394


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Abstract

Exact solutions can be obtained for electromagnetic wave propagation in a medium with a simple uniform refractive-index distribution. For more-complex distributions, approximate or numerical methods have to be utilized. We describe an elegant approximation scheme called the decomposition method for nonlinear differential equations, which was introduced by Adomian [Non-linear Stochastic Systems Theory and Applications to Physics (Kluwer, Dordrecht, The Netherlands, 1989)]. The method is described and applied to waveguide problems (planar waveguides with step and parabolic refractive-index profiles), and the results are compared with those obtained by JWKB and modified Airy function methods.

© 1998 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(060.2310) Fiber optics and optical communications : Fiber optics
(350.7420) Other areas of optics : Waves

History
Original Manuscript: July 7, 1997
Revised Manuscript: December 23, 1997
Manuscript Accepted: January 20, 1998
Published: May 1, 1998

Citation
Vasudevan Lakshminarayanan and Srinivasa Varadharajan, "Approximate solutions to the scalar wave equation: the decomposition method," J. Opt. Soc. Am. A 15, 1394-1400 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1394


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References

  1. For a discussion of variational method see, for example, H. Goldstein, Classical Mechanics, 2nd ed., Addison-Wesley Series in Physics (Addison-Wesley, Reading, Mass., 1980), Chap. 2. For applications to waveguides see A. Sharma, P. Bindal, “Analysis of diffused planar and channel waveguide,” IEEE J. Quantum Electron. 29, 150–153 (1993); “An accurate variational analysis of single mode diffused channel waveguides,” Opt. Quantum Electron. 24, 1359–1371 (1992). [CrossRef]
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  19. All the computations were done with the commercial software Maple V Release 4, is a product of Waterloo Maple, Inc., Waterloo, Ontario, Canada.
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