Transmission matrix of the axial symmetric resonator with piece-homogeneous metal dielectric filling

Addition of a grating consisting of perfectly conducting and infinitely thin rings in the axial symmetric resonator stabilises its spectrum characteristics, increases the Q-factor of the oscillations and the gradient of the dependencies of natural frequencies on the material parameters of the filling, and allows one to model the system without mechanical control. The dispersion and amplitude-frequency properties of the axial symmetric resonator with piece-homogeneous filling and the frequent periodic grating of varying radius are analysed in this paper.