The nonstationary theory of excitation for open resonators, waveguides and waveguide transformers has been developed. The open structures which are contained dielectric, magnetic and metallic bodies have been considered.
The integral and integrodifferential equations for photonic crystal waveguides (fibers) have been obtained both for finite and infinite dimensions of quasiperiodic dielectric coverings. Previously the equations for two-dimensional periodic photonic crystals with magnetodielectric and metallic periodic inclusions have been considered. The corresponding numerical results are presented.
The integral relations and integral-differential equations that take into account the influence of the magnetic shields (magnetic) inductance have been obtained. The non-linear magnetic materials with hysteresis and without it, and approximation of nonlinear materials and inductors have been considered. It is shown that for hysteresis we should use the nonlinear equation for the magnetization. The establishment of oscillations in a chain with the simplest approximation of a nonlinear inductance are reviewed.