Abstract
Abstract A set of vector wave functions is defined in the elliptic cylindrical coordinate system. These vector wave functions can not only describe the propagation characteristics of electromagnetic waves in the elliptic cylindrical coordinate system but also meet the requirements of the electromagnetic field equation. By studying the orthogonality of these vector wave functions, the free space magnetic dyadic Green function is derived by the Ohm-Rayleigh method. The free space electric dyadic Green function is derived from the magnetic dyadic Green function. The special electromagnetic field boundary value problem is transformed into a Green function problem by the electric dyadic Green function. The distribution of the electromagnetic field on the boundary can be obtained by solving the Green function, and then the characteristics of the electromagnetic field can be analyzed. The core of this method is to transform the electromagnetic field problem into a Green function problem, thus simplifying the solving process. This method enriches the electromagnetic field theory and provides a new way to solve the practical electromagnetic field problem.
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