Quantum Theory of a Resonant Photonic Crystal

TL;DR

This paper develops a quantum model for a 3D lattice of two-level atoms, revealing combined polaritonic and photonic bandgaps, and identifies slow-light modes with potential applications in photonics.

Contribution

It introduces a quantum theoretical framework for resonant photonic crystals, extending Hopfield theory to include combined polaritonic and photonic gaps in 3D lattices.

Findings

Combined polaritonic and photonic gaps of about 25 cm^{-1}

Identification of slow-light modes with near-zero exciton probability

Significant enhancement of gap size compared to detuned gaps

Abstract

We present a quantum model of two-level atoms localized in a 3D lattice, based on the Hopfield theory of exciton polaritons. In addition to a polaritonic gap at the exciton energy, a photonic bandgap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the exciton energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of 25 cm^{-1}, up to 10^5 times the detuned gap size. The dispersion curve contains a branch supporting slow-light modes with vanishing exciton probability density.