Diffraction by a Cylindrical Obstacle

Abstract

The diffraction of a plane electromagnetic wave by an infinitely long, perfectly conducting cylinder has been treated by a variational method (see the two papers by H. Levine and J. Schwinger). The incident field is assumed to be polarized in the direction of the cylinder axis, and thus the entire field is of two‐dimensional nature. This formulation yields an expression for the diffracted cylindrical wave amplitude, at distances from the cylinder large compared to its transverse dimension and the wave‐length, which is stationary relative to small independent variations of the surface currents arising from plane‐wave excitation along a pair of directions in space; furthermore, the stationary form of the diffracted amplitude is independent of the scale of the surface currents. In accordance with a theorem of Levine and Schwinger, the total plane‐wave scattering cross section is simply related to the diffracted cylindrical wave amplitude in the direction of incidence. To examine the high frequency behavior of the cross section, the surface current induced by a plane wave is taken different from zero only on the illuminated part of the cylinder, where its value is derived from the tangential component of the incident magnetic field. The resulting cross section is obtained and is shown to approach 4ɑ when kɑ approaches infinity (k=2π÷wave‐length, a equals the radius of cylinder).