To the theory of quasi-phase-matched parametric amplification in periodically-poled optical nonlinear crystals
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.