We explain the Lorentz resonances in plasmonic crystals that consist of two-dimensional nano-dielectric inclusions as the interaction between resonant material properties and geometric resonances of electrostatic nature. One example of such plasmonic crystals are graphene nanosheets that are periodically arranged within a non-magnetic bulk dielectric. We identify local geometric resonances on the length scale of the small-scale period. From a materials perspective, the graphene surface exhibits a dispersive surface conductance captured by the Drude model. Together these phenomena conspire to generate Lorentz resonances at frequencies controlled by the surface geometry and the surface conductance. The Lorentz resonances found in the frequency response of the effective dielectric tensor of the bulk metamaterial are shown to be given by an explicit formula, in which material properties and geometric resonances are decoupled. This formula is rigorous and obtained directly from corrector fields describing local electrostatic fields inside the heterogeneous structure. Our analytical findings can serve as an efficient computational tool to describe the general frequency dependence of periodic optical devices. As a concrete example, we investigate two prototypical geometries composed of nanotubes and nanoribbons.
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Controlling the dispersion of metamaterials in three dimensions
We provide a platform to examine the effect of inclusion geometry on three-dimensional metamaterial crystals to tune frequency-dependent effective properties for control of leading order dispersive behaviour. The crystal is non-magnetic and made from all dielectric components. The design provides novel dispersive properties using subwavelength resonances controlled by the geometry of the media. We numerically calculate the effective tensors of the metamaterial to identify frequency intervals where the metamaterial exhibits band gaps as well as intervals of normal dispersion and double negative dispersion. The frequency intervals can be explicitly controlled by adjusting the geometry and placement of the dielectric inclusions within the period cell of the crystal.
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- Award ID(s):
- 1813698
- NSF-PAR ID:
- 10354600
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 478
- Issue:
- 2263
- ISSN:
- 1364-5021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2022.0194
