Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model

We theoretically study electro-optic light modulation based on the 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, in the semiclassical approximation where the microwave field is treated as a classical mode, 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. We also 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.