The combinatorial frequency generation by the periodic stacks of binary layers of anisotropic nonlinear dielectrics is examined. The products of nonlinear scattering are characterised in terms of the three-wave mixing processes. It is shown that the intensity of the scattered waves of combinatorial frequencies is strongly influenced by the constitutive and geometrical parameters of the anisotropic layers, and the frequency ratio and angles of incidence of pump waves. The enhanced efficiency of the frequency conversion at Wolf-Bragg resonances has been demonstrated for the lossless and lossy-layered structures. 1. Introduction A new generation of artificial electromagnetic materials has opened up new opportunities for engineering the media with the specified properties. The latest advancements in this field have prompted a surge of research in the new phenomenology, which could extend a range of functional capabilities and enable the development of innovative devices in the millimeter, terahertz (THz), and optical ranges. Frequency conversion in dielectrics with nonlinearities of the second and third order has been investigated in optics, particularly, in the context of the second (SHG) and third (THG) harmonic generation. The recent studies have indicated that nonlinear photonic crystals (PhCs) and metamaterials (MMs) have significant potential for enhancement of the nonlinear activity associated with the mechanisms of field confinement, dispersion management and resonant intensification of the interacting waves. For example, it has been demonstrated in [1–5] that the PhCs dispersion can be tailored to facilitate the phase synchronism (The phase synchronism between pump wave and its harmonic is a prerequisite for efficient frequency conversion.) between the second harmonic and the pump wave of fundamental frequency. The harmonic generation efficiency can be further increased when the pump wave frequencies are close to the PhC band edges [6–12] where the higher density of states provides favourable phase-matching conditions. The SHG efficiency also grows with the PhC thickness or the number of stacked layers [5]. Combinatorial frequency generation by mixing pump waves of two different frequencies provides alternative means for frequency conversion. The efficiency of mixing process can be dramatically increased in the layered structures, for example, at the higher order Wolf-Bragg resonances of the combinatorial frequencies generated in the anisotropic nonlinear dielectric slabs. As shown in [13], at the specific thickness of the layers illuminated by the
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