Quantum theory of light propagation I. General theory

We present a particular approach to quantum theory of light propagation in nonlinear medium using space and time dependent modal operators. Spatial and temporal evolutions of this space and time dependent modal operators are given by the Heisenberg-like equation involving the momentum operator and Heisenberg equation, respectively, which can be justified from point of view of quantum electrodynamics. This useful concept can be applied to an arbitrary nonlinear interaction.The author would like to express his sincere thanks to Professor J. Peina for advice, comments and stimulating discussions.This work was partially supported by the grant PV202/1994 of Czech Ministry of Education and by an internal grant of the Palacký University.