Resonant three-dimensional photonic crystals

TL;DR

This paper develops a theoretical model for exciton-polariton band structures in resonant three-dimensional photonic crystals, analyzing how excitonic effects influence photonic band gaps and dispersion relations.

Contribution

It introduces a comprehensive theory for exciton-polariton bands in 3D photonic crystals with arbitrary dielectric contrast and exciton mass, including an analytic dispersion description.

Findings

Lower polariton branches depend on exciton effective mass.

Excitonic effects significantly influence photonic band gaps.

Analytic two-wave approximation describes polariton dispersion.

Abstract

We have developed a theory of exciton-polariton band structure of resonant three-dimensional photonic crystals for arbitrary dielectric contrast and effective mass of the exciton that is excited in one of the compositional materials. The calculation has been carried out for a periodic array of spheres embedded in a dielectric matrix. It has been shown that the position of the lower branches of the polariton dispersion curve monotonously depends on the exciton effective mass and is determined by the coupling of light with the first few states of the mechanical exciton quantum confined inside each sphere. Particularly, we have studied the role of excitonic effects on the photonic-crystal band gap along the [001] direction of the Brillouin zone and presented an analytic description of the polariton dispersion in terms of the two-wave approximation.