M.V. Davidovich - Dr. Sc. (Phys.-Math.), Professor, Department of Radiotechnique and Electrodynamics, Saratov State University named after N.G. Chernyshevsky. E-mail: davidovichmv@info.sgu.ru

In the first part of the article, the method of integral and integral-differential equations for problems of diffraction and problems on eigenvalues for dielectric (magnetodielectric) structures is considered. In the General case, the total field is presented as the field ex-citation and the field of diffraction. The integral and integral-differential equations describing the oscillations of localized plasmons and dielectric resonators, waves in plasmonic and photonic crystals, as well as methods for the conversion of these equations and algorithms for their solution are given. Equations are written for the region, where the complex dielectric permittivity different from the units and may contain surface integrals over its boundary. Also, the volume integral equation without surface integrals is presented. The methods of decreasing the order of singularity of the kernels of the equations based on vector integral theorems and transfer differential operators from the point of observation on source point is introduces. The field of diffraction is explicit expressed through the solution of the integral (integral-differential) equation. The types of equations written with respect to the electric fields, magnetic fields and vector potentials are given. The methods of conversion of some equations to others are introduces. The appropriate algorithms for problems of diffraction and tasks on eigenvalues based on iteration procedures for equations and functionals based on them have been considered.

 

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