Two-Dimensional Image Theory for the Conducting Half Plane

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Abstract
The classical electromagnetic field problem of a perfectly conducting half plane and a two-dimensional line source parallel to the edge is formulated in terms of image sources in complex space. It is seen that the image currents can be expressed in terms of simple trigonometric functions in contrast to the more complicated functions characterizing the physical currents on the half plane. Also, in contrast to the nonphysical edge currents applied in the physical diffraction theory, the image currents are exact and do not depend on the point where the field is to be calculated. However, the field can be computed from a single converging image in a half space only, which can be chosen at will. Because of the exponential decay of the image, approximation by a finite source becomes effective. As a validity check of the theory, the diffraction coefficient of GTD is obtained in the high-frequency asymptotic limit, as a normalized value of the image current at a certain point. Also, diffraction patterns computed from the image source are seen to demonstrate the equivalence to the usually applied field integrals. The method is suggested for integral equation formulation of problems involving a conducting half plane and for extending the physical optics edge current method to field points where the physical optics is no longer valid.