An analysis is presented for calculating the perturbation of a resonant cavity by a homogeneous sphere characterized by arbitrary radius and scalar values of σ, ε, and μ. This method involves the expansion of the cavity fields in spherical vector potential functions. The solutions are subject only to the restrictions that the perturbation be small, and that the sphere be located so that reflection effects in the cavity walls are negligible. The solutions are, in general, series which converge very rapidly for sphere diameters less than λ0/(2π). The first term gives sufficient accuracy in most instances. Other existing approximate solutions are shown to be limiting cases of the solutions presented in this paper. A numerical comparison is presented for the case of a semiconductor sphere at the location of a field maximum.

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