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

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

2011-10-18

arxiv.org/abs/1110.4132v1

Waves in Random and Complex Media, Volume 21, Issue 1, 2011 pages 135-150

Physics

Mathematical Physics

15 pages, 4 figures

Scientific paper

10.1080/17455030.2010.528064

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.

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