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

Abstract
If a slab (or tube) of dielectric material of uniform thickness is surrounded by a medium of lower dielectric constant it can support travelling waves that propagate without attenuation. If there is an abrupt change in the slab thickness, reflexion and radiation will occur. This paper deals with the simplest prototype case, in which a transverse magnetic travelling wave, whose length is large compared with slab thickness, encounters such a change in geometry. At points very close to the junction the field is modelled by a quasistatic solution. An outer approximation is calculated, based on the idea of replacing the actual slab by a hypothetical surface of infinitesimal thickness, with appropriate discontinuity conditions. A solution is determined in the form of an inverse Fourier integral, and explicit results are given for the reflexion and transmission coefficients.

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