Whispering gallery mode resonators in microwave physics and technologies

We review the main results of the development of whispering gallery mode (WGM) resonators and their unique applications due to their quasi-optical functionality. Several types of advanced WGM resonators are proposed by the authors. The theoretical results are described for the resonators with an analytical solution of the electromagnetic problems. Special emphasis is given to the interaction of moving charged particles and waves of cylindrical resonators. Important aspects are described concerning the developed sapphire resonators, for which an exact solution can only be found by using specially designed computer program products. A separate section of the paper is devoted to application aspects of the WGM resonators. In particular, it describes advanced solutions for overcoming the problems of measuring the small microwave (MW) surface impedance of unconventional superconductors in the form of large-area thin films and small samples under study. In addition, a demonstration of accurate complex permittivity measurements of small volumes of lossy liquids is provided. Special emphasis is given to highly stable MW signal sources, namely Ka-band transistor-based feedback oscillator and solid-state maser WGM oscillators. Recently obtained results are presented of experimental studies of the auto-oscillatory system developed on the basis of the WGM resonator with relativistic electron beam