Light Transport and Localization in Two-Dimensional Correlated Disorder

Structural correlations in disordered media are known to affect significantly the propagation of waves. In this Letter, we theoretically investigate the transport and localization of light in 2D photonic structures with short-range correlated disorder. The problem is tackled semianalytically using the Baus-Colot model for the structure factor of correlated media and a modified independent scattering approximation. We find that short-range correlations make it possible to easily tune the transport mean free path by more than a factor of 2 and the related localization length over several orders of magnitude. This trend is confirmed by numerical finite-difference time-domain calculations. This study therefore shows that disorder engineering can offer fine control over light transport and localization in planar geometries, which may open new opportunities in both fundamental and applied photonics research.

Figure 1

Structural correlations in 2D disordered media. (a) Disordered photonic structures with filling fraction $f=20\%$ and different degrees of correlation ($p=30\%$, 50%, 70%). (b) Structure factors $S(q{d}_{\min })$ of the correlated patterns, evaluated numerically with Eq. (2) (hollow dots) and semianalytically using the Baus-Colot model (solid lines).

Figure 2

Modified transport due to correlations. (a) Spectral and angular map of the “effective” differential scattering cross section $d{\sigma }^{\star }/d\theta$ for weakly ($p=30\%$) and strongly ($p=70\%$) correlated media. (b) Inverse transport mean free path ${\ell }_t^{-1}$, (c) scattering anisotropy factor $g$, and (d) localization length $\xi$ for different degrees of correlation $p$.

Figure 3

Numerical FDTD simulations. (a) Sketch of the simulated system for the evaluation of the average decay constant of the modes. (b) Normalized integrated energy density $U_n(t)$ versus time at frequency $a/\lambda =0.21$, for different $p$. The straight lines are decaying exponentials, emphasizing the multiexponential decay observed at short times. The decay constant values $\gamma$ were estimated at long times. (c) Numerically estimated decay constants versus frequency as a function of $p$. The inset shows the decay constants evaluated semianalytically from Eq. (6), only for $L/{\ell }_t\ge 6$. (d) Numerically estimated average lifetime ${\gamma }^{-1}$ as a function of $p$ at frequency $a/\lambda =0.21$. The red line represents the prediction according to diffusion theory and the intensity maps are calculated for different $p$.