Phonon polaritons in a bilayer ferroelectrics structure with a polarization coupling at the interface

Abstract

In this paper, we discuss the optical properties of a bilayer ferroelectrics structure comprised of two different types of ferroelectric materials. The interface interaction between these two ferroelectric materials is considered. This interaction requires the entire-cell effective medium treatment where each layer of ferroelectric is sliced into several latticed. Then, by applying Landau-Khalatnikov (LKh) equation of motion in each lattice and solving it simultaneously, the dynamic susceptibility of the bilayer system can be determined. By employing Maxwell equations, we derive the dispersion relation, which can be solved numerically using the root-finding technique. Since here we use two ferroelectric with different resonant frequencies, then the polaritons can also be found around these two frequencies. Hence, there are two leading bulk bands in the dispersion relation. The existence of polarization coupling between two ferroelectrics at the interface generates the narrow additional bulk bands in the dispersion relation. We found that these additional bulk bands are affected by the strength of interface coupling and the number of lattices in each involved layer. We also found that the increase of the thickness of the layers weaken the additional bulk bands.