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Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum inter-nanostructure distance or by hyperuniformity properties, is particularly beneficial in some applications such as light extraction. We introduce numerical descriptors inspired from topology to provide quantitative measures of disorder whose universal properties make them suitable for both uncorrelated and correlated disorder, where statistical descriptors are less accurate. We prove theoretically and experimentally the accuracy of these topological descriptors of disorder by using them to design plasmonic metasurfaces of controlled disorder, that we correlate to the strength of their surface lattice resonances. These tools can be used for the fast and accurate design of disordered metasurfaces, or to help tuning large-scale fabrication methods., Comment: 6 figures

We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder transition at the microscopic scale. Such quantitative characterisation of a complex, soft matter system has not yet been achieved with any other method. We show that structural heterogeneity can track structural changes in a liquid crystal nanocomposite, reveal the effect of confined geometry on the nematic-isotropic and isotropic-nematic phase transitions, and uncover physical differences between these two processes. The system used in this work is representative of a class of composite nanomaterials, partially ordered and with complex structural and physical behaviour, where their precise characterisation poses significant challenges. Our newly developed analytic framework can provide both a qualitative and a quantitative characterisations of the dynamical behaviour of a wide range of semi-ordered soft matter systems., Comment: 9 figures

Babinet complementary patterns of a spectrally tunable metamaterial incorporating a nematic liquid crystal are normally assumed to exhibit the same tuning range. Here we show that for a hybrid, terahertz liquid crystal-metamaterial, the sensitivity of its resonances to the variations of the refractive index differs substantially for the two complementary patterns. This is due to a mismatch between the alignment of the liquid crystal and the direction of the local electric field induced in the patterns. Furthermore, and more intriguingly, our experimental data indicate that it is possible to shift the resonance of the positive metamaterial pattern beyond the limit imposed by the alignment mismatch. Our analysis suggests that the observed anomalous frequency shift result from the orientational optical nonlinearity of a nematic liquid crystal., Comment: 11 pages, 6 figures