Diffraction by a Narrow Slit in the Interface Between Two Different Media

The two-dimensional problem of diffraction of a plane electromagnetic wave by a narrow slit in an infinitely thin, perfectly conducting screen between two different media is studied. The cases of both E and H polarization are considered. In the case of E polarization, a differential-integral equation is obtained for the unknown function in the slit; in the H polarized case, a pure integral equation is obtained for the unknown. These integral equations are solved by a perturbation technique and formal solutions are given in the form of series in powers of the ratio of slit width to wavelength, the coefficients of which depend on the logarithm of this ratio. Expressions are found for the transmission and back-scatter coefficients and some numerical results are given for special values of the parameters. Errors in earlier work (Barakat 1963; Stöckel 1964) are noted.