Ray optical analysis of waveguide transformers with dielectric inserts

The behavior of TE (sub mo) mode wave propagation, in dielectric filled parallel-plate waveguides with axial step change in the dielectric constant, is analyzed using laws of geometrical optics. The resulting expressions are the same as those obtained by the mode matching technique. As a result, reflection, transmission and cut-off conditions at the dielectric discontinuity are determined simply from Snell's law and the laws of reflection and refraction of plane waves at dielectric interfaces. The study also includes an extension of the theory of small reflections used in transmission line analysis to apply in the case of a plane wave obliquely incident on a multilayered dielectric slab with parallel interfaces. As an application, the length and permittivity of matching sections of a waveguide transformer with maximally flat pass-band characteristic connecting two guides filled with different dielectrics are determined using geometrical optics and the extended form of the theory of small reflections.