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 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 strongly nonmonotonic behavior supplemented with asymmetry of the intensity distribution provided the pumped mode is not central. We also analyze different regimes of two-modulator transmission and establish the conditions of validity of the semiclassical approximation by applying the methods of polynomially deformed Lie algebras for analysis of the model with quantized microwave field.
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