  Theory of the optical parametric amplification at high-frequency pumping in
crystals with a regular space modulation of the sign of nonlinear coupling
coefficient of interacting waves is developed. By applying the matrix method,
the theory is based on a step-by-step approach. It is shown that, in the case
where the pumping intensity is less than some critical value, the spatial
dynamics of the signal intensity inside a separate layer with the constant
nonlinear coefficient has an oscillatory behavior and the change of the signal
intensity from layer to layer is defined, in general, by the power function.
The same law is valid for the change of variance of signal's quadrature
components. At large number of layers, these dependences can be reduced to the
well-known ones for homogeneous nonlinear optical crystals.
