Density of photonic states in aperiodic structures

TL;DR

This study investigates how band gaps in photonic structures can form in both periodic and aperiodic arrangements, challenging the traditional view that strict periodicity is necessary for band gap formation.

Contribution

It introduces a real-space metric to compare periodicity and demonstrates that disordered lattices and quasicrystals can similarly suppress photonic states, providing new insights into band gap mechanisms.

Findings

Disordered lattices and quasicrystals can both exhibit suppressed photonic density of states.

Similar band gap properties can occur in structures with different degrees of periodicity.

Experimental and theoretical results show comparable band gap suppression in different structures.

Abstract

Periodicity is usually assumed to be the necessary and sufficient condition for the formation of band gaps, i.e., energy bands with a suppressed density of states. Here, we check this premise by analyzing the band gap properties of three structures that differ in the degree of periodicity and ordering. We consider a photonic crystal, disordered lattice, and ordered but nonperiodic quasicrystalline structure. A real-space metric allows us to compare the degree of periodicity of these different structures. Using this metric, we reveal that the disordered lattice and the ordered quasicrystal can be attributed to the same group of material structures. We examine the density of their photonic states both theoretically and experimentally. The analysis reveals that despite their dramatically different degrees of periodicity, the photonic crystal and the quasicrystalline structure demonstrate an almost similar suppression of the density of states. Our results give new insight into the physical mechanisms resulting in the formation of band gaps.