Tuning Trapped-mode Resonances in a Planar Metamaterial

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1 Progress n Electromagnetics Research Smposium Proceedings, Suzhou, China, Sept , Tuning Trapped-mode Resonances in a Planar Metamaterial J. H. Shi 1, E. Plum 2, V. A. Fedotov 2, and N.. Zheludev 2 1 College of Science, Harbin Engineering Universit, Harbin 151, China 2 Optoelectronics Research Center, Universit of Southampton, Southampton SO17 1BJ, UK Abstract We demonstrate tuning of trapped-mode resonances in a smmetric planar metamaterial both eperimentall and theoreticall. B controlling the ecitation of the Fano-tpe trapped-mode resonance via the angle of incidence, its qualit factor is controlled and the resonance is red-shifted b up to 21%. 1. NTRODUCTON The asmmetric Fano resonance, which has long been known as a characteristic feature of interacting quantum sstems, has more recentl been found in plasmonic nanostructures and metamaterials [1, 2]. The steep dispersion of the Fano resonance profile promises applications in slow light [3 9], sensor [1, 11], nonlinear [12] and switching [13] applications. Fano resonances in metamaterials were first observed in arras of asmmetricall split rings [14], consisting of two wire arcs of different lengths. ncident electromagnetic waves with the electric polarization parallel to these asmmetric wires can ecite a high-q mode formed b counter-propagating currents, i.e., a so-called trapped mode resonance that is associated with an asmmetric Fano-tpe line shape [14]. The qualit factor of such trapped-mode resonances is mainl limited b losses and attempts to compensate or eliminate Joule losses using opticall-pumped gain media such as semiconductor quantum dots [15, 16] and superconducting metamaterials [17] have been reported. The tunabilit of Fano resonances is another ke issue. Tuning of a Fano resonance was observed when crossing the superconducting transition temperature of a superconducting metamaterial [17]. Most generall, the properties of Fano resonances can be controlled b the metamaterial design [14, 18 2]. However, it is etremel difficult to change the geometrical size of elements once the are fabricated. Therefore, a practical wa of controlling Fano resonances is of great importance for developing metamaterials for real applications [21]. n this paper, we report that trapped-mode Fano-tpe resonances in a planar metamaterial can be efficientl controlled via the angle of incidence, offering an eas-to-implement wa of achieving local field tunabilit in metamaterials. We demonstrate tuning of the trapped-mode qualit factor and its spectral localization eperimentall and numericall. 2. EXPERMENTAL AND SMULATED RESULTS We investigate resonance tuning in a meta-surface based on smmetricall split rings (SSR), see Fig. 1. The SSR consists of two identical wire arcs corresponding to 16 and each copper split ring has a radius of 6 mm and a width of.8 mm. Due to its high smmetr, this structure does not allow the ecitation of anti-smmetric currents at normal incidence. The metamaterial consists of a square meta-molecule arra with a period of 15 mm and an overall size of about 2 2 mm 2. t was etched from 35 µm copper cladding covering FR4 PCB substrate of 1.6 mm thickness. Detailed dimensions of the SSR unit cell are given in Fig. 1. The SSR metamaterial transmission was measured at angles of incidence from to 5 in the 9 14 GHz frequenc range. The eperiments were carried out in an anechoic chamber using broadband horn antennas (Schwarzbeck BBHA912D) equipped with dielectric lens concentrators and a vector network analzer (Agilent E8364B). The electromagnetic response of the SSR metamaterial was also simulated using a full threedimensional Mawell finite element method solver in the frequenc domain, where copper was treated as a perfect electric conductor and a permittivit ε = 4.5 i.5 was assumed for the loss dielectric substrate. For the results presented below, both the polarization of the incident wave and the ais around which the metamaterial was tilted to achieve oblique incidence were perpendicular to the SSR wires (i.e., the -ais), see Fig. 1. Figures 2 and 3 show simulated and measured transmission and reflection spectra of the SSR metamaterial as a function of the angle of incidence α. At normal incidence onto the metamaterial -polarized electromagnetic waves can onl ecite one electric dipole resonance at about 11.3 GHz.

2 568 PERS Proceedings, Suzhou, China, September 12 16, 211 Figure 1: Metamaterial structure. The angle of incidence α is measured between the incident wave vector k and the metamaterial s surface normal n. Here metamaterial transmission and reflection are studied for -polarized electromagnetic waves at oblique incidence which is realized b tilting the metamaterial around its -ais. Smmetricall split ring (SSR) unit cell. Transmission (db) Frequenc (GHz) Reflection (db) Frequenc (GHz) Figure 2: Simulated transmission and reflection of the SSR metamaterial for various angles of incidence. The resonant modes corresponding to resonances,, and are shown in Fig. 4 for α = 5. The ecitation of the trapped mode, which consists of anti-smmetric current oscillations in opposite wire arcs, is prohibited b the high eperimental smmetr in this case. However, when the metamaterial pattern is tilted around the -ais, the trapped-mode resonance appears: a narrow pass band (reflectivit minimum) which ma also be discussed in terms of electromagneticall induced transparenc (ET) [3] forms between two transmission minima. t is obvious from Figs. 2 and 3 that the SSR metamaterial ehibits large frequenc tunabilit of the trapped-mode resonance. With increasing α, the pass band becomes more pronounced and as illustrated b Fig. 3 its qualit factor measured as Q = f/ f increases to about 18 at α = 5 (peak width f =.6 GHz at 3 db below maimum). Simulations [Fig. 2] and eperimental results [Fig. 3] agree well with each other, however, the resonant feature is more pronounced in the simulations. This deviation is linked to scattering from the edges of the eperimental sample, which was assumed to be an infinite periodic structure in the simulations. Oblique incidence leads to a small dela between the ecitation of the two arcs of the SSR. This dela is sufficient to allow the ecitation of an antismmetric trapped current mode associated with transmission maimum (reflection minimum), which gives rise to a strong magnetic dipole [see Fig. 4]. n contrast to this magnetic dipole mode, resonances and are electric dipole resonances with no significant net magnetic field [see Figs. 4 and (c)]. At normal incidence, the ecited magnetic fields show perfect smmetr with respect to the mirror line of the SSR and completel cancel each other, leading to a vanishing magnetic dipole moment. The anti-smmetric current oscillations of the trapped-mode resonance are largel dominated b the -directional surface currents propagating along the wire arcs. Fig. 5 shows the frequenc dependence of the -directional surface current densit at different angles of incidence. At normal incidence, the net -component of the surface current is zero in each arc. As the angle of incidence increases, currents of equal magnitude oscillating in anti-phase in the two wire arcs appear. n particular the increasing angle of incidence results in a 1-fold enhancement of the magnitude of the ecited currents and a remarkabl large red-shift of the trapped-mode resonance, which can be tuned from 13.2 GHz to 1.4 GHz. The large magnitude of the anti-smmetric currents results from

Progress n Electromagnetics Research Smposium Proceedings, Suzhou, China, Sept. 12 16, 211 569 Transmission (db) -1-2 -25 1 2 3 4 5 Qualit factor 2 15 1 5 sim ep -3 9. 1. 11. 12. 13. 14.

Qualit factor for the pass band as a function of the angle of incidence (dashed line: simulation, solid line: eperiment). Magnetic field, z component [A/m] 4.5e-4 7.2e-4 5.6e-4 α =5 α =5 α =5-4.

The arrows indicate the instantaneous direction of the ecited currents and the dashed lines correspond to the SSR mirror line along the -ais. Surface current densit, component [arb.

the fact that an fields emitted from opposite arcs would destructivel interfere in the far-field and therefore the electromagnetic energ is trapped at the meta-surface, ensuring a high qualit factor

3 Progress n Electromagnetics Research Smposium Proceedings, Suzhou, China, Sept , Transmission (db) Qualit factor sim ep Frequenc (GHz) Angle of incidence (deg) Figure 3: Measured transmission and qualit factor. Measured transmission spectra for various angles of incidence. Qualit factor for the pass band as a function of the angle of incidence (dashed line: simulation, solid line: eperiment). Magnetic field, z component [A/m] 4.5e-4 7.2e-4 5.6e-4 α =5 α =5 α =5-4.5e-4-7.2e-4.6e-4 (c) Figure 4: Snapshots of the normal magnetic field at resonances - at α = 5, compare Fig. 2. All field maps show the field amplitude at its maimum. The arrows indicate the instantaneous direction of the ecited currents and the dashed lines correspond to the SSR mirror line along the -ais. Surface current densit, component [arb. units] Figure 5: X-component of the instantaneous surface current densit as a function of frequenc at, 3 and 5 oblique incidence. the fact that an fields emitted from opposite arcs would destructivel interfere in the far-field and therefore the electromagnetic energ is trapped at the meta-surface, ensuring a high qualit factor of the pass band. 3. CONCLUSONS n summar, we eperimentall and numericall demonstrate that the ecitation of trapped-mode resonances in SSR metamaterials can be controlled via the angle of incidence. n particular, we have realized trapped mode on/off switching, tuning of the resonance qualit factor and a 21% red-shift of the trapped-mode resonance via the angle of incidence for a simple, planar model structure based on smmetricall split rings. The structure is well-suited for eisting micro-and nanofabrication technologies and tuning via the incidence angle can be easil applied anwhere in the electromagnetic spectrum. The ET-like behavior of the SSR metamaterial makes it a promising candidate

4 57 PERS Proceedings, Suzhou, China, September 12 16, 211 for slow light applications, while local energ confinement provides in interesting platform for nonlinear and gain metamaterials and the lasing spaser. ACKNOWLEDGMENT Financial support of The Leverhulme Trust, The Roal Societ and the UK s Engineering and Phsical Sciences Research Council, UK is acknowledged. The author J. H. Shi also thanks for support provided b the Natural Science Foundation of Heilongjiang Province in China under grant LC216 and in part b the Special Foundation for Basic Scientific Research of Harbin Engineering Universit under grant HEUCF and HEUCF REFERENCES 1. Fano, U., Effects of configuration interaction on intensities and phase shifts, Phs. Rev., Vol. 124, , Luk anchuk, B., N.. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. Chong, The Fano resonance in plasmonic nanostructures and metamaterials, Nat. Mater., Vol. 9, , Papasimakis, N., V. A. Fedotov, N.. Zheludev, and S. L. Prosvirnin, Metamaterial analog of electromagneticall induced transparenc, Phs. Rev. Lett., Vol. 11, No. 25, 25393, Zhang, S., D. A. Genov, Y. Wang, M. Liu, and X. Zhang, Plasmon-induced transparenc in metamaterials, Phs. Rev. Lett., Vol. 11, No. 4, 4741, Tassin, P., L. Zhang, T. Koschn, E. N. Economou, and C. M. Soukoulis, Low-loss metamaterials based on classical electromagneticall induced transparenc, Phs. Rev. Lett., Vol. 12, No. 5, 5391, Chiam, S. Y., R. Singh, C. Rockstuhl, F. Lederer, W. L. Zhang, and A. A. Bettiol, Analogue of electromagneticall induced transparenc in a terahertz metamaterial, Phs. Rev. B, Vol. 8, No. 15, 15313, Liu, N., L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, Plasmonic analogue of electromagneticall induced transparenc at the Drude damping limit, Nat. Mater., Vol. 8, No. 9, , Papasimakis, N. and N.. Zheludev, Metamaterial-induced transparenc, Opt. Photonics News, Vol. 2, No. 1, 22 27, Miroshnichenko, A. E., S. Flach, and Y. S. Kivshar, Fano resonances in nanoscale structures, Rev. Mod. Phs., Vol. 82, , Liu, N., T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, Planar metamaterial analogue of electromagneticall induced transparenc for plasmonic sensing, Nano Lett., Vol. 1, No. 4, , Lahiri, B., A. Z. Khokhar, R. M. De La Rue, S. G. McMeekin, and N. P. Johnson, Asmmetric split ring resonators for optical sensing of organic materials, Opt. Epress, Vol. 17, No. 2, , Nikolaenko, A. E., F. De Angelis, S. A. Boden, N. Papasimakis, P. Ashburn, E. DiFabrizio, and N.. Zheludev, Carbon nanotubes in a photonic metamaterial, Phs. Rev. Lett., Vol. 14, 15392, Sámson, Z. L., K. F. MacDonald, F. DeAngelis, B. Gholipour, K. Knight, C. C. Huang, E. Di- Fabrizio, D. W. Hewak, and N.. Zheludev, Metamaterial electro-optic switch of nanoscale thickness, Appl. Phs. Lett., Vol. 96. No. 14, 14315, Fedotov, V. A., M. Rose, S. L. Prosvirnin, N. Papasimakis, and N.. Zheludev, Sharp trappedmode resonances in planar metamaterials with a broken structural smmetr, Phs. Rev. Lett., Vol. 99, No. 14, 14741, Plum, E., V. A. Fedotov, P. Kuo, D. P. Tsai, and N.. Zheludev, Towards the lasing spaser: Controlling metamaterial optical response with semiconductor quantum dots, Opt. Epress, Vol. 17, No. 1, , Tanaka, K., E. Plum, J. Y. Ou, T. Uchino, and N.. Zheludev, Multifold enhancement of quantum dot luminescence in plasmonic metamaterials, Phs. Rev. Lett., Vol. 15, No. 22, 22743, Fedotov, V. A., A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N.. Zheludev, Temperature control of Fano resonances and transmission in superconducting metamaterials, Opt. Epress, Vol. 18, , 21.

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Temperature control of Fano resonances and transmission in superconducting metamaterials

Temperature control of Fano resonances and transmission in superconducting metamaterials V.A. Fedotov 1,*, A. Tsiatmas 1, J. H. Shi 1,4, R. Buckingham 2, P. de Groot 2, Y. Chen 3, S. Wang 5, and N.I. Zheludev