Abstract: Helmholtz equation is a kind of elliptic partial differential equation, which is used to characterize the propagation law of electromagnetic wave. When solving Helmholtz equation in cylindrical coordinate system, most textbooks use the method of separating variables to introduce, but most textbooks do not have a detailed classification and discussion of the results of separating variables, nor do they explain its practical application, which makes it difficult for beginners to understand and master physical meanings. In this paper, the Helmholtz equation is solved by the method of separating variables, the form of solution is discussed systematically, and the typical applications of various results are analyzed by means of electromagnetic simulation and numerical calculation. It has a certain reference significance for the teaching and research of electromagnetic field theory.

Key words: Helmholtz equation, cylindrical coordinate system, waveguide, resonator