Derivation and Computation of Surface Differential Equations for the Induced Current on Perfectly Electrically Conducting Objects in Electromagnetics

Surface differential equations (SDEs) are derived for the induced current on the outer surface of a perfectly electrically conducting (PEC) object for the first time. The derived equations are wave equations that describe the propagation of surface current waves along a PEC surface. A numerical method based on SDEs is proposed, which is named the eigenmode theory in this article. In this method, SDEs are discretized into a generalized eigenvalue equation, which can be used to obtain a series of modal currents and expand the surface current induced by any excitation. The modal currents are only dependent on the shape and size of the PEC object and are independent of any specific excitation, including frequency, feeding location, and so on. This property results in an eigenmode theory with great potential in many challenging antenna designs. Numerical examples for both scattering and radiation analyses demonstrate the effectiveness and accuracy of eigenmode theory and, thus, give evidence for the correctness of SDEs.