Scattering of Electromagnetic Waves by Loss and Gain Systems of Dielectric Resonators

The problem of wave scattering on a system of coupled Dielectric Resonators (DR) made of an active or absorbing dielectric is considered. The solution of the scattering problem is decomposed over the field of natural oscillations of the DR system. The field describing the natural oscillations of the DR system is decomposed by the field of partial resonators, which are made of a dielectric with a complex permittivity. A system of equations is given, the solution of which allows to determine the frequencies and amplitudes of the natural oscillations of the system of active or absorbing resonators. In the work, a new system of linear equations for amplitudes of forced oscillations of resonators was obtained. General solutions for the scattering field on resonators located in a regular transmission line or in a break of a regular line have been found. Several examples of calculation of the frequency dependences of the scattering matrix for different bands to pand band-pass filters, consisting of coupled active or absorbing dielectric resonators are given. The possibilities of the proposed method are demonstrated on the example of optimization of scattering characteristics on band-stop and hand-pass filters made of an active dielectric. It is shown that the use of resonators made of an active dielectric will make it possible to build and optimize the frequency characteristics of a new class of devices that simultaneously perform the functions of filters and amplifiers. The conditions under which it is possible to build filters with the functions of amplifiers are defined. In the future, the proposed devices may find application in optical communication systems.