## Approximate solutions to the scalar wave equation: the decomposition method

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

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- All the computations were done with the commercial software Maple V Release 4, is a product of Waterloo Maple, Inc., Waterloo, Ontario, Canada.
- C. Yu, D. Yevick, “Application of the bidirectional parabolic equations to optical waveguide facets,” J. Opt. Soc. Am. A 14, 1448–1450 (1997). [CrossRef]
- I. R. Bellman, G. Adomian, Partial Differential Equations: New Methods for Their Treatment and Solution (Reidel, Dordrecht, The Netherlands, 1985).

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