Photonic band-gap in a realistic atomic diamond lattice: penetration depth, finite-size and vacancy effects

TL;DR

This study investigates how finite size, shape, and vacancies influence the photonic band gap in a realistic atomic diamond lattice, revealing border and localized states and analyzing electromagnetic penetration depth.

Contribution

It provides a detailed numerical and theoretical analysis of finite-size and vacancy effects on the photonic band gap in atomic diamond lattices.

Findings

Shape-induced border states in the band gap

Vacancy-induced localized states in the gap

Penetration depth comparable to infinite systems

Abstract

We study the effects of finite size and of vacancies on the photonic band gap recently predicted for an atomic diamond lattice. Close to a $J_g=0\to J_e=1$ atomic transition, and for atomic lattices containing up to $N\approx 3\times10^4$ atoms, we show how the density of states can be affected by both the shape of the system and the possible presence of a fraction of unoccupied lattice sites. We numerically predict and theoretically explain the presence of shape-induced border states and of vacancy-induced localized states appearing in the gap. We also investigate the penetration depth of the electromagnetic field which we compare to the case of an infinite system.