  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.
