From optical magnetism to second-order spatial dispersion in self-assembled metamaterials

The magnetic susceptibility of all natural materials is vanishingly small at high frequencies [1]. The metamaterials community has shown that optical magnetism could be realized using top-down fabricated structures, though at... [ view full abstract ]

The magnetic susceptibility of all natural materials is vanishingly small at high frequencies [1]. The metamaterials community has shown that optical magnetism could be realized using top-down fabricated structures, though at the expense of a high degree of anisotropy. We have shown experimentally that isotropic bulk optical magnetism can be produced by self-assembling dense materials made of magnetic meta-atoms composed of spherical plasmonic nanoclusters of well-controlled morphology [2]. These meta-atoms are composed of dielectric cores surrounded by metallic satellites that are either spheres or patches. Our bottom-up hierarchical approach permits the chemical synthesis of meta-atoms with tailored magnetic dipole moments characterized by polarization-resolved static light scattering spectroscopy, followed by microfluidic assembly of dense metamaterials that exhibit a resonance of the magnetic permeability at optical frequencies, characterized by variable–angle spectroscopic ellipsometry. Numerical simulations guide all our investigations. Figure 1(a-d) are scanning electron micrographs of the assembled metamaterial arranged into microfluidic channels. Figure 1(e) shows the experimental measurement of the real part of the magnetic permeability in the visible regime.

The magnetism observed arises from circulating polarization currents within the meta-atom analogous to atomic circulating currents that arise from the angular momentum of the orbiting electron in the classical picture. This magnetic response originates from second-order spatial dispersion and is only valid in the case of divergent-free solutions (when the divergence of the electric field is null).

A full description of the optical properties of our metamaterials actually requires taking the locally non-zero divergence of the electric-field into account. This description requires three electromagnetic parameters.

In this talk, we shall review the realizations of optical magnetism based on the bottom-up approach of material chemistry and describe the emergence of a third nonlocal parameter required to fully describe our metamaterials.

 [1] L. D. Landau and E.M. Lifshitz. Electrodynamics of Continuous Media, Pergamon Press. Oxford, 1960.

 [2] S. Gomez-Grana, A. Le Beulze, …, A. Baron, D. Torrent, and P. Barois, “Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies”, Materials Horizons, 3(6), 596-601 (2016).