Volumetric integro-differential equations in diffraction and eigenvalue problems (review)

Volumetric integral and integro-differential equations are considered that describe problems of diffraction by three-dimensional bodies with given macroscopic permittivity and magnetic permeability, as well as problems on free vibrations of such bodies. Similar equations are obtained for waveguide structures: hollow shielded waveguides with dielectric filling, dielectric waveguides (optical beamguides), photonic-crystal waveguides. Dominantly stationary linear electromagnetic problems are considered. Non-stationary and nonlinear problems are mentioned casually. Numerical results are given for oscillations $H_{01\delta}$ and $H_{011}$ of a cylindrical dielectric resonator, for waves of a rectangular dielectric waveguide and a plasmonic waveguide, dispersion in a photonic crystal, and diffraction by a rectangular dielectric cylinder.