Calculation method of EM field diffracted from a conductive circular disk for vertically polarized electric dipole incidence

The electromagnetic scattered field by a perfectly conducting circular disk is analyzed by using a technique developed by Y. Nomura and S. Katsura (J. J. Bowman, T. B. A. Senior and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, 1969, pp.557–561), while a vertically polarized electric dipole source is located near the disk (see Fig. 1). A Hertz vector of the scattered field is expanded as follows: equation and Пz^(s) = 0, where equation are expansion coefficients, εn = 2, (n ≠ 0), = 1, (n = 0). Function Smⁿ (ρ, z) is seen in the literature (Y. Nomura and S. Katsura, J. Phys. Soc. of Jap., 10, 1955, pp.285–304). In the case of vertically polarized dipole incidence, i.e. equation from the boundary condition on the disk, the scattered Hertz vector is presented in the form equation on the disk (z = 0, ρ < a), where equation, and U is a scalar function and satisfies a following two dimensional inhomogeneous wave equation: equation Applying the solution of Eq. (3) to Eq. (2), and matching with Eq. (1) on the disk, an infinite set of simultaneous linear equation of the expansion coefficients is obtained. After truncating the infinite equation and considering the edge condition, we can solve the equation, and the coefficients are evaluated numerically.