Green’s Functions in Electrodynamics

The application of the Green’s functions to solve the problems of excitation, radiation, propagation, and diffraction of electromagnetic waves is shown. The representation of Green’s functions for free space in the Cartesian, cylindrical and spherical coordinate systems is considered. The electromagnetic field is represented as a superposition of electric and magnetic waves in all of the three coordinate systems. Unbounded space is represented in the form of rectangular, cylindrical and radial-spherical waveguides. A modification of Green’s functions for layered inhomogeneous media is shown. A model of equivalent electrical circuits is used to determine the spectral components of the electromagnetic field. Layer and boundary transfer matrices and terminal loads are used to describe the layered structure and to find modal currents and voltages in the equivalent electrical circuits. The application of the Green’s function method to solve the problems of radiation of patch and slot antennas on flat and cylindrical surfaces, as well as the leaky wave antenna comprising a rectangular waveguide with transverse slots is shown. The solution of the Luneburg lens radiation problem is also considered. In addition, the application of Green’s functions to solving diffraction problems of layered, flat and cylindrical structures is shown.