Topological Learning for the Classification of Disorder: An Application to the Design of Metasurfaces

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. For example, correlated disorder, induced by a minimum inter-nanostructure distance or by hyperuniformity properties, is particularly beneficial for light extraction. Inspired by topology, we introduce numerical descriptors to provide quantitative measures of disorder with universal properties, suitable to treat both uncorrelated and correlated disorder at all length scales. The accuracy of these topological descriptors is illustrated both theoretically and experimentally by using them to design plasmonic metasurfaces with controlled disorder that we then correlate to the strength of their surface lattice resonances. These descriptors are an example of topological tools that can be used for the fast and accurate design of disordered structures or as aid in improving their fabrication methods.