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A rigorous method of calculating the electromagnetic field, the scatteringmatrix, and scattering cross-sections of an arbitrary finite three-dimensionaloptical system described by its permittivity distribution is presented. Themethod is based on the expansion of the Green's function into the resonantstates of the system. These can be calculated by any means, including thepopular finite element and finite-difference time-domain methods. However,using the resonant-state expansion with a spherically-symmetric analyticalbasis, such as that of a homogeneous sphere, allows to determine a complete setof the resonant states of the system within a given frequency range.Furthermore, it enables to take full advantage of the expansion of the fieldoutside the system into vector spherical harmonics, resulting in simpleanalytic expressions. We verify and illustrate the developed approach on anexample of a dielectric sphere in vacuum, which has an exact analytic solutionknown as Mie scattering.

Resonant-state expansion of three-dimensional open optical systems: Light scattering