Abstract
A method for determining transition matrices for inhomogeneous dielectric shells is presented. The source can be either inside or outside the shell. The method is based upon expansions of the electric and magnetic fields in vector spherical harmonics. The expansion coefficients in the shell satisfy a system of linear ordinary differential equations in the radial direction. The expansion coefficients for the incident and scattered fields are related via transition matrices, defined in the same way as in the T-matrix or null-field method. Numerical examples show excellent agreement with results obtained by the T-matrix method. Numerically the method is particularly strong for the case of a source at the center of large, but thin, inhomogeneous spherical shell.
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