APPROXIMATE SOLUTIONS TO THE SCALAR WAVE-EQUATION - THE DECOMPOSITIONMETHOD

Exact solutions can be obtained for electromagnetic wave propagation i n a medium with a simple uniform refractive-index distribution. For mo re-complex distributions, approximate or numerical methods have to be utilized. We describe an elegant approximation scheme called the decom position method for nonlinear differential equations, which was introd uced 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 wave,oxides with step and parabolic refractive-index profiles), and the results re comp ared with those obtained by JWKB and modified Airy function methods. ( C) 1998 Optical Society of America.