Abstract. AWe construct a rigorous three-dimensional electrodynamic model of hybrid electromagnetic oscillations in a “cylindrical to rectangular waveguide” waveguide branch filled with a dielectric is constructed. The eigen types of oscillations are classified: branching eigen resonances at transcendental modes; and resonances of the waveguide-dielectric type. For resonances of the first type, the electromagnetic the field in the communication region of the waveguides is described as the sum of the fields of the damped waves of the partial waveguides,; for resonances of the second type, the sum fields of damped and propagating waves. Oscillations of the first type exist both when the waveguide branching is filled with a dielectric and in empty branching. The second type of resonance exists only in structures with a dielectric constant greater than unity. The structure under study can be used to measure the electrical parameters of dielectric samples. Since the spectral branching characteristics are determined mainlymainly by the size of the central communication area waveguides and electrical parameters of parts of the dielectric that is located there, the measurements are local in nature.
Keywords: Electromagnetic Field, Cylindrical-Rectangular Waveguide, Numerical Analysis, Simulation, Electrodynamic Processes, Information System.