Coupled acousto-optical phonons in wurtzites: Micro-to-nano-scale bridging

Frequently, in semiconductor physics, acoustic phonons and optical phonons in nanostructures are described using the elastic continuum model and the dielectric continuum model, respectively. In this article, we have used the Lagrangian formalism to develop a set of coupled differential equations for describing coupled acoustic-optical phonon modes for wurtzite crystal structures considering the anisotropy of the crystal. The quantization of phonon displacements is described as well as the mode normalization need to bridge between the micro-scale and the nano-scale.