Travelling waves in a dielectric slab with an abrupt change in thickness

An analytical investigation is presented of the reflection, transmission, and radiation properties of the simplest possible prototype case of travelling waves in a dielectric slab with an abrupt change in thickness. In this case, a transverse magnetic travelling wave, whose length is large compared with slab thickness, encounters such a change in geometry. The field is modelled by a quasi-static solution for points very close to the junction. An outer approximation is obtained, based on the idea of replacing the actual slab by a hypothetical surface of infinitesimal thickness, with appropriate discontinuity conditions. A solution is obtained in the form of an inverse Fourier integral, and explicit results are presented for the reflection and transmission coefficients.