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

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.

15 pages, 4 figures

References in corpus (2)

• Scattering solutions in a network of thin fibers: small diameter asymptotics
• Frozen light in photonic crystals with degenerate band edge

Cited by in corpus (2)

• Quantifying the robustness of topological slow light
• Lyapunov exponent of the random Schrödinger operator with short-range correlated noise potential