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
(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
Vasudevan Lakshminarayanan and Srinivasa Varadharajan, "Approximate solutions to the scalar wave equation: the decomposition method," J. Opt. Soc. Am. A 15, 1394-1400 (1998)