Many-Body Subradiant Excitations in Metamaterial Arrays: Experiment and Theory

Stewart D. Jenkins, Janne Ruostekoski, Nikitas Papasimakis, Salvatore Savo, and Nikolay I. Zheludev

Phys. Rev. Lett. 119, 053901 – Published 3 August 2017

Abstract

Subradiant excitations, originally predicted by Dicke, have posed a long-standing challenge in physics owing to their weak radiative coupling to environment. Here we engineer massive coherently driven classical subradiance in planar metamaterial arrays as a spatially extended eigenmode comprising over 1000 metamolecules. By comparing the near- and far-field response in large-scale numerical simulations with those in experimental observations we identify strong evidence for classically correlated multimetamolecule subradiant states that dominate the total excitation energy. We show that similar spatially extended many-body subradiance can also exist in plasmonic metamaterial arrays at optical frequencies.

Received 31 October 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.053901

Physics Subject Headings (PhySH)

Light propagation, transmission & absorption Metamaterials Superradiance & subradiance

Atomic, Molecular & Optical

Authors & Affiliations

Stewart D. Jenkins¹ and Janne Ruostekoski¹

¹Mathematical Sciences and Centre for Photonic Metamaterials, University of Southampton, Southampton SO17 1BJ, United Kingdom

Nikitas Papasimakis², Salvatore Savo^2,3, and Nikolay I. Zheludev^2,4

²Optoelectronics Research Centre and Centre for Photonic Metamaterials, University of Southampton, Southampton SO17 1BJ, United Kingdom
³TetraScience Inc., 114 Western Ave, Boston, Massachusetts 02134, USA
⁴Centre for Disruptive Photonic Technologies, School of Physical and Mathematical Sciences and The Photonics Institute, Nanyang Technological University, Singapore 637378, Singapore

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Vol. 119, Iss. 5 — 4 August 2017

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Images

Figure 1
(a) A schematic illustration of the planar metamaterial array consisting of asymmetric split-ring metamolecules. Each metamolecule has two constituent circuit resonator arcs, or meta-atoms, whose out-of-phase oscillating currents produce a strong net magnetic dipole perpendicular to the array. The arrows on the plane (blue arrows) represent the electric dipole of each arc and the arrows normal to the plane (red arrows) represent the magnetic dipoles generated by pairs of arcs. In a collective pure phase-coherent magnetic (PM) mode all magnetic dipoles in the array oscillate in phase. [(b) and (c)] Numerically calculated magnetic dipole (b) and electric dipole (b) excitation profiles for this mode.
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Figure 2
(a) Experimentally measured reflectance (black line) and numerically calculated back-scattered intensity (red dashed line) spectra from a $30 \times 36$ ASR microwave metamaterial array with a lattice spacing of $a = 0.28 λ$ . We also show calculated spectra (red dash-dot line) for arrays of plasmonic resonators ( $a = 0.2 λ$ ). (b) Calculated spectra from microwave arrays of noninteracting metamolecules (black line), and arrays with a large lattice spacing of $a = 1.9 λ$ (dashed blue line) and thus weakened interactions. The frequencies are in the units of the single arc decay rate $Γ$ , centered at the resonance frequency $ω_{m}$ of the phase coherent magnetic eigenmode of the corresponding SSR array.
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Figure 3
(a) The contribution of a pure phase-coherent magnetic (PM; solid red line), pure phase-coherent electric (PE; dashed blue line) mode, and all the other eigenmodes of the symmetric system (dash-dot black line) to the steady-state excitation of the spectrum in Fig. 2. The phase-coherent magnetic dipole mode is dominant at the Fano resonance, while the phase-coherent electric dipole mode is significantly excited only outside the resonance. (b) The dependence of the Fano resonance depth [defined as $c = (I_{\max} - I_{\min}) / I_{\max}$ , where $I_{\min}$ is the minimum reflected intensity on resonance, and $I_{\max}$ is the reflected intensity at the lesser of the adjacent local maxima; blue line] and inverse linewidth, $γ_{sub}^{- 1}$ , of the dominant subradiant eigenmode of the array (red line) on the size of the metamaterial array, $N$ . In the absence of the Fano resonance $c = 0$ , while $c = 1$ implies full reflection at the resonance frequency.
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Figure 4
Numerically calculated [(a)–(c)] and experimental (d) near-field excitations of a microwave metamaterial array at the transmission peak: (a) electric $| d_{ℓ} |^{2}$ and (b) magnetic $| m_{ℓ} |^{2}$ dipole intensity, (c) total excitation $| d_{ℓ} |^{2} + | m_{ℓ} |^{2}$ , and (d) experimentally measured electric field intensity.
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