**SCATTERING AND GUIDING OF WAVES BY A DOUBLY-PERIODIC MAGNETODIELECTRIC LAYER BOUNDED BY TWO UNIFORM MEDIA**

Natalia V. Sidorchuk, Vladimir V. Yachin and Sergey L. Prosvirnin

Department of Calculus Mathematics, Institute of Radio Astronomy

Krasnoznamennaya Street 4, 61002 Kharkov,Ukraine

email:

**Abstract**

The problem of electromagnetic wave propagation in a doubly-periodic magnetodielectric layer bounded by two uniform in_nite media is solved by new method based on the rigorous volume integro-di_erential equations of electromagnetics. The Galerkin method is applied to reduce these equations to a set of second-order di_erential ones with constant coe?cients in _eld functionals. The functionals contain information about geometry of the scattering structure.

This method uni_es the treatment of both perpendicular (TE) and parallel (TM) polarization by replacing e by m , m by e , E-components by H-components, H-components by E-components. The constituents of the magnetodielectric structure can approximate the structure made from perfect metal if the conditions are satis_ed. Applying this approach to the medium behind the doubly-periodic layer we can consider the layer as a microstrip structure having features of a photonic structure.

Waves guided by the doubly-periodic structure a appear to be characteristic solution of the boundary-value problem in the absence of an incident wave and can be found from nontrivial solutions of this problem. The investigations were restricted to the case of a single periodic layer. However, the analysis can be easily extended to the multilayered structures. To illustrate the application of this approach, quantitative results are presented for the scattering and guiding of electromagnetic waves by various magnetodielectric periodic layers.

**References**

[1] V.V.Yachin and N.V.Ryazantseva, Microwave and optical technology letters. 23 ,No.3, 1263 (1999).