The aim of the thesis is the theoretical research of electromagnetic wave propagation and diffraction in heterogeneous and periodic dielectric structures based on the development of effective methods for solving two– and three–dimensional boundary value problems in electrodynamics.

The following general problems are to be solved to achieve these aims:

—	Developing an effective numerical and analytical method of electromagnetic analysis of electromagnetic wave diffraction on periodic dielectric and metallic nanostructures and three–dimensional solids.
—	Researching the diffraction properties of periodic dielectric and metallic nanostructures.
—	Researching the diffraction properties of dielectric three–dimensional solids filled with homogeneous and heterogeneous substances.
—	Discovering the physical regularities in affecting:
	— The diffraction characteristics of forms and sizes of heterogeneous solids. — The coefficient of transmitting the parameters of dielectric arrays. — The dispersion characteristics of the parameters of dielectric structures.

The practical significance of the thesis results is primarily due to the software packages based on the original numerical methods and algorithms of electrodynamic analysis of electromagnetic wave propagation and diffraction on three-dimensional dielectric solids, on multilayer dielectric diffraction arrays with heterogeneities of complicated shape, on nanostructural metallic periodic arrays. These programs compete with both existing expensive programs implementing direct numerical methods and not less expensive and time–consuming experimental processing.

The developed software packages and research results can be directly used in scientific and research organizations and in enterprises engaged in developing and manufacturing microwave components and also radio–engineering, radiolocation, radionavigation units and wireless communication systems. The practical value of the results is increased by the fact that some results are included in lecture courses and special training courses included in the curriculum of the RGI Physics Department.

The main theses and results presented for the defense:

—	The electrodynamic methods of analyzing the electromagnetic wave diffraction on three–dimensional dielectric solids of a finite size based on the numerical and analytical conversion of the singular part of an integral equation – the modified collocation method and the semi–inversion method.
—	The application of the method of three-dimensional integral equations to the problem of electromagnetic wave diffraction on nonlinear dielectric solids; — the modification of the method of partial areas for the express analysis of electromagnetic wave diffraction on periodic multilayer structures.
—	The modification of the method of partial areas for the express analysis of electromagnetic wave diffraction on periodic multilayer structures.
—	The grounds for the possibility of applying the method of approximate boundary conditions to calculating metallic periodic nanostructures.
—	The results of researching the diffraction characteristics of: three–dimensional dielectric solids; multilayer diffraction arrays of a complex shape; metallic periodic nanostructures in the optical band.
—	The results of researching the properties of natural waves in periodic dielectric structures (dispersion curves, existing radio windows and opacity windows, backward waves).