Quantum effects associated with parametric generation of light and the theory of squeezed states

The theory of quantum effects in nonstationary nonlinear media is used to describe the parametric generation of the quantized electromagnetic field. Perturbation theory in the small parameter that characterizes the nonlinearity of the medium is used to construct a system of solutions of an integrodifferential equation that follows from Maxwell's equations. The coefficients of the Bogolyubov transformations that diagonalize the Hamiltonian of the quantized field are calculated and used to obtain the number of photons produced by the medium and the degree of squeezing. The region of applicability of the method of effective Hamiltonians developed earlier for the same purposes is established.