Single Strip Diffraction: Comparison Between Kirchhoff Theory and Keller's Geometrical Theory in the Limit of Small Glancing Angle and Width.

A comparison is made between the approximate theories of Kirchhoff and Keller, and the exact solution of Maxwell's equations for the case of Fraunhofer diffraction of electromagnetic radiation incident upon a long, thin conducting strip with the electric field vector polarized parallel to the strip axis. Strip widths from approximately 0.3lambda to 3lambda are considered with angles of incidence ranging from 4 degrees to 84 degrees . The predieted intensities are compared as a function of angle in the region on the same side of the strip as the incident radiation. It is found that in the limits of small glancing angle or small strip width, where both approximate theories are of questionable validity, Keller's geometrical theory more closely agrees with the exact solution.