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.
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