Gyrotropy of a Metamolecule: Wire on a Torus

N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev

Phys. Rev. Lett. 103, 093901 – Published 26 August 2009

Abstract

Sharing topology with numerous organic molecules, a wire helix bend into a torus gives a curious object with a gyrotropic behavior which is far from obvious. While a continuous constant current in opposite sections of the torus would create mutually cancelling contributions to its gyrotropic response, an array of tori can show strong circular dichroism linked to the excitation of standing current waves. Here we present the experimental study of optical activity in a chiral toroidal metamaterial and discuss its response in terms of multipole moments, including the elusive toroidal moment.

Received 11 June 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.093901

Authors & Affiliations

N. Papasimakis^*, V. A. Fedotov, K. Marinov^†, and N. I. Zheludev

Optoelectronics Research Centre, University of Southampton, SO17 1BJ, United Kingdom

^*N.Papasimakis@soton.ac.uk
^†Present address: STFC Daresbury Laboratory, ASTeC, Daresbury, Warrington, WA44AD, U.K. kiril.marinov@stfc.ac.uk

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Vol. 103, Iss. 9 — 28 August 2009

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Images

Figure 1
Examples of chiral toroidal structures: (a) the head-tail connector of the bacteriophage $ϕ 29$ [7]; (b) a torus-shaped fullerene [10]. (c) The enantiomeric forms of a chiral toroidal coil are connected by a mirror reflection.Reuse & Permissions
Figure 2
(a) Top and (b) side views of the unit cell of the toroidal metamaterial. In the experimental measurements, the toroids are arranged into a $13 \times 13$ metamaterial array (c) so that the normally incident electromagnetic wave propagates perpendicular to the axes of the toroids.Reuse & Permissions
Figure 3
(a) Transmission $t$ for a right (blue line) and a left (red line) circularly polarized wave. The circular dichroism $Δ t$ is represented by the solid green curve (experimental) and the black solid circles (numerical). The positions of the main dichroism resonances at $ν_{2}$ , $ν_{4}$ , and $ν_{6}$ are marked by the green strips. Inset: Sketch of the toroidal metamaterial unit cell and direction of wave propagation. Panel (b) shows the left-right differential phase delay $Δ φ = φ_{+} - φ_{-}$ .Reuse & Permissions
Figure 4
Finite element simulations of toroidal metamaterial. (a) and (b) show electric density (color maps) and power flow lines at the 4 GHz resonance for a right and left circularly polarized incident wave, respectively. (c) and (d) present the induced current oscillation as a function of position on the wire winding for right (red line) and left (blue line) circularly polarized light, at the 4 and 10 GHz resonances, respectively.Reuse & Permissions
Figure 5
Radiated power from the different multipole moments of the (numerically simulated) current configuration on the wire windings, normalized to the incident power. Insets: Idealized resonant currents modes on the toroidal solenoid and leading terms of the multipole expansion for current configurations with two, four, and six nodes (from left to right). For $n = 2$ the leading terms are the electric $p$ and magnetic $m$ dipole moments, while for $n = 4$ , these moments vanish and the electric quadrupole moment $Q$ dominates the response of the structure. In the case $n = 6$ , both dipole and quadrupole moments are present. Dashed vertical lines show positions of gyrotropy resonances.Reuse & Permissions
Figure 6
Magnetic toroidal moment. A static poloidal current on a torus creates a ringlike configuration of magnetic dipoles, which in turn leads to a magnetic toroidal dipole moment $τ$ (a). A constant current flowing along the chiral toroidal coil results in a (magnetic) toroidal $τ$ and magnetic dipole $m$ moments. The latter depends on the chirality of the coil (b).Reuse & Permissions

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