Finite-size scaling of the density of states inside band gaps of ideal and disordered photonic crystals

TL;DR

This study investigates how the density of states inside band gaps of finite-sized ideal and disordered 3D photonic crystals scales with size, revealing that disorder narrows gaps but the scaling behavior persists.

Contribution

It provides a phenomenological explanation for the size scaling of the density of states in finite photonic crystals, including disordered systems.

Findings

DOS decreases inversely with crystal size in ideal crystals

Disorder narrows the band gap and causes fluctuations in DOS near edges

Scaling behavior of DOS persists despite disorder

Abstract

We study the density of states (DOS) in band gaps of ideal and disordered three-dimensional photonic crystals of finite size. The ideal crystal is a diamond lattice of resonant point scatterers (atoms) whereas the disordered one is obtained from it by displacing the scatterers by random distances in random directions. We find that DOS inside a band gap of the ideal crystal decreases as the inverse of the crystal size. Disorder narrows the band gap and DOS exhibits enhanced fluctuations near the new band edges. However, the average DOS still exhibits the same scaling with the crystal size within the remaining band gap. A phenomenological explanation of this scaling suggests that it should hold for one- and two-dimensional photonic crystals as well.