Mathematical proof for the equivalent edge currents for physical optics (POEECs) is given for plane wave incidence and the observer in far zone; the perfect accuracy of POEECs for plane wave incidence as well as the degradation for the dipole source closer to the scatterer is clearly explained for the first time. POEECs for perfectly conducting plates are extended to those for impedance plates.

It is shown from a computer analysis that there exists a resonant mode of a surface wave which propagates along Goubau line, and that the attenuation of such a mode is very low. The approximate formula for obtaining the resonant frequency is also given.

This paper first gives the exact surface integral representation for PO diffracted electromagnetic fields from bounded flat plate through the deformations of the original surface by using field equivalence principle. This exact representation with the surface integral can be approximately reduced to novel line integral along the boundary of the plate by the use of Maggi-Rubinowicz transformation, which keeps a high accuracy even in near zone. Numerical results for the scattering of the electric dipole wave from the square planar plate are presented for demonstrating the accuracy.

Modified Edge Representation (MER) empirically proposed by one of the authors is the line integral representation for computing surface radiation integrals of diffraction. It has remarkable accuracy in surface to line integral reduction even for sources very close to the scatterer. It also overcomes false and true singularities in equivalent edge currents. This paper gives the mathematical derivation of MER by using Stokes' theorem; MER is not only asymptotic but also global approximation. It proves remarkable applicability of MER, that is, to smooth curved surface, closely located sources and arbitrary currents which are irrelevant to Maxwell equations.

The Modified edge representation (MER) is the concept to be used in the line integral approximation for computing the surface radiation integrals of diffraction. The MER as applied to the physical optics (PO-MER), has remarkable accuracy in the surface-to-line integral reduction even for the curved surfaces and for sources very close to the scatterer. In the discussion of the mathematical foundation for this accuracy, the evaluation of the singularities in the integrand of the PO-MER line integration was left for further study.

The exact characteristic equation for the hybrid modes in Goubau line is given. By solving the equation numerically we find the hybrid modes Lnm, defined in this paper. We also examine the propagation and attenuation constants of the hybrid modes. As a result the hybrid K12 mode has the extremely low attenuation at the specific frequency similar to the hybrid K11 mode. The electric field distributions of K11 and L11 modes are plotted.