Diffractive stacks of metamaterial lattices with a complex unit cell : Self-consistent long-range bianisotropic interactions in experiment and theory

Metasurfaces and metamaterials promise arbitrary rerouting of light using two-dimensional (2D) planar arrangements of electric and magnetic scatterers, respectively, 3D stacks built out of such 2D planes. An important problem is how to self-consistently model the response of these systems in a manner that retains dipole intuition yet does full justice to the self-consistent multiple scattering via near-field and far-field retarded interactions. We set up such a general model for metamaterial lattices of complex 2D unit cells of poly-atomic basis as well as allowing for stacking in a third dimension. In particular, each scatterer is quantified by a magnetoelectric polarizability tensor and Ewald lattice summation deals with all near-field and long-range retarded electric, magnetic, and magnetoelectric couplings self-consistently. We show in theory and experiment that grating diffraction orders of dilute split ring lattices with complex unit cells show a background-free signature of magnetic dipole response. For denser lattices experiment and theory show that complex unit cells can reduce the apparent effect of bianisotropy, i.e., the strong oblique-incidence handed response that was reported for simple split ring lattices. Finally, the method is applied to calculate transmission of finite stacks of lattices. Thereby our simple methodology allows us to trace the emergence of effective material constants when building a 3D metamaterial layer by layer, as well as facilitating the design of metasurfaces.