535.3Cascade parametric amplification in a regular domain structure is examined theoretically taking the variations in phase of all the interacting waves in a dissipative medium into account. Analytic expressions are obtained for the conversion efficiency of the laser energy with low-frequency pumping. The dependence of the parametric amplification efficiency on the number of layers is given. Ways of increasing the frequency conversion efficiency are discussed. The presence of a nonzero input intensity at the sum frequency is found to cause a nonlinear increase in the high-frequency signal at the output of the structure. As the losses of the interacting waves increase, both the frequency conversion efficiency and the optimum domain length decrease.Introduction. Parametric frequency conversion has been used to produce coherent radiation throughout the optical range. Frequency tuneable coherent radiation has widespread applications. Parametric frequency converters are used to study the spectroscopy of gases. In particular, parametric frequency converters have been used in lidars for laser probing of the atmosphere. With nonlinear processes for adding of frequencies, it is possible to transform IR radiation into visible radiation, and visible radiation into UV [1][2][3][4].In combination with frequency mixing effects, tuneable parametric sources of coherent radiation have made it possible greatly to extend the range of tuneable laser wavelengths. Thus, for example, using lasing at the sum frequency it is possible to obtain tuneable laser radiation at short wavelengths up to the vacuum ultraviolet [4].Although the possibility of essentially complete conversion of radiation at the fundamental wavelength into a harmonic has been demonstrated theoretically, we know that this can be done only when a whole series of requirements on the parameters of the beams and the nonlinear medium are met. Under the action of a strong pump wave, the spatial buildup of the nonlinear effect proceeds most actively with an optimum phase relationship between the interacting waves.Efficient conversion of the frequency of laser light into optical harmonics and parametric waves can be realized in several ways: frequency conversion processes [5][6][7] inside the cavity of a laser; in an external Fabry-Perot cavity; in a layered structure (where the direction of the spontaneous polarization remains unchanged from layer to layer, but the sign of the phase detuning changes to the opposite); in a regular domain structure (RDS) with periodically polarized domain-layers; and, in layered structures where a combination of parametric gain and lasing at the sum frequency take place.In this paper we examine the last of these methods for frequency conversion, i.e., a proposed five-layer structure in which cascade (stepwise) frequency conversion takes place.Initially, exponential parametric amplification of a signal wave takes place in the first layer. Then a process of nonlinear frequency conversion occurs in the next four layers, which form a regular doma...