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In 2010 at the DIPED International Seminar/Workshop there was presented the theoretical part for the diffraction problem of the plane wave on the 2D periodical infinite lattice located in the free space . The lattice element represented the conducting wire with the resonant properties. In the first part of this paper we consider the theoretical background for the same lattice embedded in the dielectric with finite width layer. As the dielectric also has resonant properties this will amplify the resonant effects of the whole structure. The final idea of this study is the next: based on computer simulation to find out the best parameters of the structure to get necessary properties of the complex materials. We have created program package for the simplified case when the lattice is located in the free area and in the second part of this paper some numerical results are presented.