Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: Effects of correlated disorder

We have investigated the effects of disorder correlations on light propagation and Anderson localization in one-dimensional dispersive metamaterials. We consider and compare the cases where disorder is uncorrelated to situations where it is totally correlated and anticorrelated. The photonic gaps of the corresponding periodic structure are not completely destroyed by the presence of disorder, which leads to minima in the localization length. In the vicinities of a gap, the behavior of the localization length depends crucially on the physical origin of the gap (Bragg or non-Bragg gaps). Within a Bragg gap, the localization length increases as the degree of disorder increases, an anomalous behavior that only occurs for the uncorrelated and completely correlated cases. In these cases, minima of the localization length at the positions of Bragg gaps are shifted by increasing disorder, which does not occur for the anticorrelated case, where the positions of the minima remain unaltered. Minima in the localization length corresponding to non-Bragg gaps are not shifted by increasing disorder, albeit the widths of these minima are changed. We have found that the asymptotic behavior for the localization length $\xi \propto {\lambda }^6$ for disordered metamaterials is not affected by correlations. Finally, we have investigated the role of absorption on the delocalized Brewster modes and argue that it could be mitigated in light of the state-of-the-art of metamaterials research.

Figure 1

Comparison between the localization length (in units of the system size), given by the IM approximation [Eq. (8)] (open red squares) and numerical simulations with $\Delta =24$ mm (open black circles), as a function of normalized frequency for an angle of incidence $\theta =\pi /6$ and TE polarization: (a) uncorrelated, and (b) correlated disorder. The horizontal dashed line marks the transition from Anderson localized to delocalized situations.

Figure 2

Localization length $\xi$ (in units of the system size) as a function of the vacuum wavelength $\lambda$, obtained from numerical simulations, for different values of the disorder strength $\Delta =0.5$, 6, and 12 mm. The case of anticorrelated disorder is also shown ($\Delta =24$ mm). The dashed line corresponds to the asymptotic behavior $\xi \propto {\lambda }^6$. The horizontal dashed line marks the transition from Anderson-localized to delocalized situations.

Figure 3

Localization length $\xi$ (in units of the system size), obtained by numerical simulations, as a function of the normalized frequency for uncorrelated disorder and for different values of the disorder strength $\Delta =0.5$, 6, 12, and 24 mm for both (a) TE and (b) TM polarizations. The incidence angle is $\theta =\pi /6$. The horizontal dashed line marks the transition from Anderson-localized to delocalized situations.

Figure 4

Localization length $\xi$ (in units of the system size), obtained by numerical simulations, as a function of the normalized frequency for correlated disorder and for different values of the disorder strength $\Delta$: (a) TE and (b) TM polarizations; the parameters used are the same as in Fig. 3.

Figure 5

Localization length $\xi$ (in units of the system size), obtained by numerical simulations, as a function of the normalized frequency for anticorrelated disorder and for different values of the disorder strength $\Delta$: (a) TE and (b) TM polarizations; the parameters used are the same as in Fig. 3.

Figure 6

Localization length $\xi$ (in units of the system size), obtained by numerical simulations, as a function of the normalized frequency for uncorrelated disorder, TE polarization, and different values of the absorption coefficient $\gamma /{\omega }_p=$ 0, 0.0001, and 0.001. The horizontal dashed line marks the transition from Anderson-localized to delocalized situations.