The process of frequency conversion in a multilayer structure of different media with quadratic nonlinearity is investigated by using the constant-intensity approximation. The values of complex amplitudes of the fundamental radiation and the second harmonic at the outlet of each layer are the entrance values of the corresponding complex amplitudes of the next layer. Analytical expressions for second-harmonic conversion efficiency for the case of n layers are proposed. The factors restricting the efficiency of the process of frequency conversion are analyzed. In layered media, upon frequency conversion, from one layer to the next the optimum values of the phase mismatch between layers changes. The character of the process of frequency conversion of the fundamental radiation to the second harmonic depends not only on the value of the nonlinear coefficients of waves, the phase mismatch, but also on the signs of these parameters.

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In the process of doubling the frequency of high-power laser radiation in metamaterials, the self- and cross-phase modulations associated with the cubic nonlinearity of the medium are studied in the constant-intensity approximation. It is assumed that the pump wave propagates in a region with negative refraction. It is shown that in the case of a nonlinear-optical process of frequency doubling of an intense light wave in a metamaterial, it is important to take into account the self-action and cross-interaction effects that directly affect the optimal phase relationship between the interacting waves. It is discovered that, as a result of counter interaction of waves, the period of spatial beats changes. According to the analytic expressions obtained in the work, the choice of optimal parameters of the problem makes it possible to realize the regime of effective frequency doubling. By varying the intensity of the pump, it is possible to control and manipulate the intensity of the output coherent radiation from the minimum to the maximum value. A numerical evaluation of the efficiency of the doubling process in a metamaterial is given, and a comparison is made with similar results in LiNbO and KDP crystals. It is demonstrated that the effects of self- and cross-modulation in media with negative refraction can be used as a powerful tool for developing effective frequency doublers in such materials.

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The parametric interaction of optical wave pulses in metamaterials is considered in the first approximation of the theory of dispersion. The interaction between the quasi-monochromatic pump wave and the wave pulse at the total frequency with quadratic phase modulation is assumed. The results of calculation of the shape of the spectrum of an excited signal wave at a difference frequency are presented for low frequency pumping. It is shown that the effects of group mismatch in metamaterials lead to a narrowing of the spectrum of the excited wave. With an increase in the modulation degree of a weak exciting wave, the spectrum of the excited wave broadens.