Modeling and understanding of effects of randomness in arrays of resonant meta-atoms

In this review presentation we will discuss approaches to modeling and understanding electromagnetic properties of 2D and 3D lattices of small resonant particles (meta-atoms) in transition from regular (periodic) to random (amorphous) states.

Nanostructured metasurfaces (2D) and metamaterials (3D) are arrangements of optically small but resonant particles (meta-atoms). We will present our results on analytical modeling of metasurfaces with periodical and random arrangements of electrically and magnetically resonant meta-atoms with identical or random sizes, both for the normal and oblique-angle excitations. We show how the electromagnetic response of metasurfaces is related to the statistical parameters of the structure. Furthermore, we will discuss the phenomenon of anti-resonance in extracted effective parameters of metamaterials and clarify its relation to the periodicity (or amorphous nature) of the arrangements of meta-atoms.