Random edge states on a finite lattice

TL;DR

This paper investigates how random sign fluctuations of the Dirac mass in a finite photonic lattice influence edge states, revealing that these states prevent Anderson localization and enable electromagnetic fields to spread throughout the sample.

Contribution

It demonstrates that random Dirac mass sign fluctuations create edge states that counteract Anderson localization in a finite lattice, contrasting with one-band models.

Findings

Edge states significantly affect electromagnetic field distribution.

Random Dirac mass fluctuations prevent Anderson localization.

Field distribution width increases with larger gaps.

Abstract

A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong influence on the electromagnetic field and its polarization inside the sample. The creation of edge states through a randomly fluctuating sign of the Dirac mass defeats Anderson localization and allows the electromagnetic field to distribute over the entire sample. The width of the distribution increases with an increasing gap due to increasing sharpness of the edge states. These results are compared with those of a random one-band Helmholtz equation. In contrast to the Dirac model, the one-band model displays a clear signature of Anderson localization.