The Lateral Surface Phonon Modes in Bi-layer Dielectrics with Different Values of Permittivity

Surface phonon polaritons were electromagnetic waves that propagated at the surface of dielectrics. These polaritons had many attentions since the frequency can reach in the order of terahertz. Hence, it can be employ in terahertz technology. One of the general method to study polaritons was by solving Maxwell's equations. The results were dispersion relation which showed the characteristic of the polaritons. In this study, we analyze polaritons of a bilayer dielectric which was comprised of two dielectrics which had different permittivities. We set the thickness of each dielectric was smaller than the wavelength so that we could use effective medium method. In this approximation, we can treat a multilayer system as a single effective medium medium. We also assumed that the surface modes propagated across the thickness of each dielectric. It was found that when the resonant frequency of the two dielectrics were considerably wide, then we had two branches of surface polaritons. In this result, each branch represented each dielectric. The interesting results appeared when there was intersection of the the frequencies near resonant frequency of the dielectrics. In this condition, we found only one branch of surface modes.