The effect of disorder on the wave propagation in one-dimensional periodic optical systems

TL;DR

This paper examines how disorder affects wave transmission in one-dimensional periodic optical systems, revealing different scaling behaviors of the Lyapunov exponent within bands and near edges, supported by numerical simulations.

Contribution

It introduces a canonical transfer matrix approach to analyze the impact of disorder on wave propagation and characterizes the Lyapunov exponent's dependence on disorder and frequency.

Findings

Lyapunov exponent scales as σ^2 within bands

Near band edges, Lyapunov exponent scales as σ^{2/3}

Numerical simulations confirm theoretical predictions

Abstract

The influence of disorder on the transmission through periodic waveguides is studied. Using a canonical form of the transfer matrix we investigate dependence of the Lyapunov exponent $\gamma$ on the frequency $\nu$ and magnitude of the disorder $\sigma$. It is shown that in the bulk of the bands $\gamma \sim \sigma^2$, while near the band edges it has the order $\gamma \sim \sigma^{2/3}$. This dependence is illustrated by numerical simulations.