Scattering of a plane electromagnetic wave from a semicircular crack in a perfectly conducting ground plane

The scattering of TM and TE plane electromagnetic waves from a semicylindrical crack in a perfectly conducting ground plane is determined using a dual series eigenfunction expansion technique. Orthogonality properties of the sinusoids are used to reduce the solution to the inversion of a truncated infinite matrix. When the radius of the crack is much smaller than the wavelength, small argument approximations for the spherical radial functions are employed to simplify the results and remove the ka-dependence from the necessary numerical matrix inversion. In this small crack limit, closed form results are developed for both polarizations, and for the TM polarization, results are found to be different by only a constant factor from those for TM scattering from a narrow slit in an infinitely thin conducting screen. TE scattering from a small crack is found to differ significantly from TE scattering from a narrow slit, which indicates that the slit approximation is not valid for real situations that more closely resemble physically an indentation, or crack.