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We theoretically study electro-optic light modulation based on a quantum model where the linear electro-optic effect and the externally applied microwave field result in the interaction between optical cavity modes. The model assumes that the number of interacting modes is finite, and effects of the mode overlapping coefficient on the strength of the intermode interaction can be taken into account through dependence of the coupling coefficient on the mode characteristics. We show that, under certain conditions, the model is exactly solvable and can be analyzed using the technique of the Jordan mappings for the su(2) Lie algebra. Analytical results are applied to study effects of light modulation on the frequency dependence of the photon counting rate. In contrast to the limiting case of an infinitely large number of interacting modes, when the number of interacting modes is finite, the sideband intensities reveal …