Photonic band structure: The face-centered-cubic case

TLDR

The face‑centered‑cubic lattice can produce a photonic band gap in which optical modes, spontaneous emission, and zero‑point fluctuations are absent. The study applies band theory to analyze electromagnetic wave propagation in three‑dimensional face‑centered‑cubic dielectric structures. Most fcc dielectric structures exhibit a semimetallic band structure, but one identified crystal with 86 % empty space shows a photonic band gap when the refractive index contrast exceeds 3:1, a contrast readily achievable in semiconductor materials.

Abstract

We employ the concepts of band theory to describe the behavior of electromagnetic waves in three dimensionally periodic face-centered-cubic (fcc) dielectric structures. This can produce a ``photonic band gap'' in which optical modes, spontaneous emission, and zero-point fluctuations are all absent. In the course of a broad experimental survey, we have found that most fcc dielectric structures have ``semimetallic'' band structure. Nevertheless, we have identified one particular dielectric ``crystal'' which actually has a ``photonic band gap.'' This dielectric structure, consisting of 86% empty space, requires a refractive index contrast greater than 3 to 1, which happens to be readily obtainable in semiconductor materials.