Abstract:
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.
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