Abstract: This paper presents a detailed study on the solution of the Helmholtz equation for sectorial cylindrical resonators and waveguides. By employing the method of separation of variables, we systematically analyze the resonance and propagation modes of electromagnetic waves within such resonators and waveguides. The electromagnetic field distributions under various boundary conditions are thoroughly investigated. The correctness and practicality of the analysis are verified through theoretical derivations and numerical simulations. This study provides a theoretical foundation for the design and fabrication of sectorial cylindrical resonators and waveguides.

Key words: sectorial cylindrical resonator, Helmholtz equation, cylindrical coordinate system, separation of variables method