Greenleaf, A;
Kettunen, H;
Kurylev, Y;
Lassas, M;
Uhlmann, G;
(2018)
Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry.
SIAM Journal on Applied Mathematics
, 78
(1)
pp. 437-456.
10.1137/17M1130964.
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Abstract
We introduce a fundamentally new method for the design of metamaterial arrays. These behave superdimensionally, exhibiting a higher local density of resonant frequencies, giant focusing of rays, and stronger concentration of waves than expected from the physical dimension. This sub-Riemannian optics allows planar designs to function effectively as 3- or higher-dimensional media, and bulk material as dimension 4 or higher. Valid for any waves modeled by the Helmholtz equation, including scalar optics and acoustics, and with properties derived from the behavior of waves in sub-Riemannian geometry, these arrays can be assembled from nonresonant metamaterial cells and are potentially broadband. Possible applications include antenna design and energy harvesting.
| Type: | Article |
|---|---|
| Title: | Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/17M1130964 |
| Publisher version: | https://doi.org/10.1137/17M1130964 |
| Language: | English |
| Additional information: | This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | transformation optics, metamaterials, sub-Riemannian geometry |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1462504 |
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