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To Super-Radiating Manipulation of a Dipolar Emitter Coupled to a Toroidal Metastructure From non- to super-radiating manipulation of a dipolar emitter coupled to a toroidal metastructure Jie Li,1 Xing-Xing Xin,1 Jian Shao,1 Ying-Hua Wang,1 Jia-Qi Li,1 Lin Zhou,2 and Zheng- Gao Dong1,* 1Physics Department and Jiangsu Key Laboratory of Advanced Metallic Materials, Southeast University, Nanjing 211189, China 2School of Physics and Electronic Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China * [email protected] Abstract: Toroidal dipolar response in a metallic metastructure, composed of double flat rings, is utilized to manipulate the radiation pattern of a single dipolar emitter (e.g., florescent molecule/atom or quantum dot). Strong Fano-type radiation spectrum can be obtained when these two coupling dipoles are spatially overlapped, leading to significant radiation suppression (so-called nonradiating source) attributed to the dipolar destructive interference. Moreover, this nonradiating configuration will become a directionally super-radiating nanoantenna after a radial displacement of the emitter with respect to the toroidal flat-ring geometry, which emits linearly polarized radiation with orders of power enhancement in a particular orientation. The demonstrated radiation characteristics from a toroidal- dipole-mediated dipolar emitter indicate a promising manipulation capability of the dipolar emission source by intriguing toroidal dipolar response. ©2015 Optical Society of America OCIS codes: (160.3918) Metamaterials; (250.5403) Plasmonics. References and links 1. L. B. Zel’dovich, “The relation between decay asymmetry and dipole moment of elementary particles,” Sov. Phys. JETP 6, 1148 (1958). 2. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010). 3. C. Schwartz, “Theory of hyperfine structure,” Phys. Rev. 97(2), 380–395 (1955). 4. E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4 4 Pt 2B), 046609 (2002). 5. V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non- trivial non-radiating excitations in toroidal metamaterials,” Sci. Rep. 3, 2967 (2013). 6. Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012). 7. V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2. 8. K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007). 9. Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012). 10. Y. W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y. F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012). 11. Y. W. Huang, W. T. Chen, P. C. Wu, V. A. Fedotov, N. I. Zheludev, and D. P. Tsai, “Toroidal lasing spaser,” Sci. Rep. 3, 1237 (2013). 12. A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015). 13. Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015). #250469 Received 22 Sep 2015; revised 28 Oct 2015; accepted 28 Oct 2015; published 2 Nov 2015 © 2015 OSA 16 Nov 2015 | Vol. 23, No. 23 | DOI:10.1364/OE.23.029384 | OPTICS EXPRESS 29384 14. V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014). 15. G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic-field of elementary time-dependent toroidal sources,” J. Phys. A 28(16), 4565–4580 (1995). 16. W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015). 17. W. Liu, J. F. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564-570 (2015). 18. A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015). 19. A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005). 20. Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87(24), 245429 (2013). 21. J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014). 22. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). 23. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). 24. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000). 25. I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014). 26. T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008). 27. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010). 28. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012). 29. W. Liu, J. Zhang, B. Lei, H. Ma, W. Xie, and H. Hu, “Ultra-directional forward scattering by individual core- shell nanoparticles,” Opt. Express 22(13), 16178–16187 (2014). 30. W. Liu, A. E. Miroshnichenko, and Y. S. Kivshar, “Control of light scattering by nanoparticles with optically- induced magnetic responses,” Chin. Phys. B 23(4), 047806 (2014). 1. Introduction The toroidal moment, firstly proposed by Zel’dovich in 1957 to interpret the parity violation on the weak interaction in nuclear and particle physics [1], fertilizes the area of classical but incomplete electromagnetic theory of multipole decomposition [2–4]. Unlike electric and magnetic dipoles resulting from a pair of charges and circulating currents respectively, the intriguing toroidal dipole is caused by a current flowing on the surface of a torus along its meridian [5,6]. However, the toroidal dipolar response is much weaker than conventional dipoles and, consequently, difficult to be detected in naturally occurring media [7]. Therefore, to find dominant toroidal dipolar responses by artificial composites is an emerging exploration field. Recently, it was claimed that toroidal metamaterials could be constructed to strengthen the toroidal dipolar response while suppressing other electric and magnetic multipoles [2,5,6,8–13]. Though it is well known that a toroidal dipole has a radiation pattern identical to an electric or magnetic dipole [14], an interesting phenomenon associated with the toroidal dipole is the nonradiating characteristic when it interacts with an electric dipole, which can be regarded as a nontrivial anapole [2,5,12,15–18]. It has been numerically demonstrated that such a hypothetical nonradiating system can be converted into a directional emission source in dependence of the interface contrast of index of refraction between the dipolar system and surroundings [19]. In addition, it should be interesting to explore the interaction phenomena between a toroidal dipole and other multipoles. For example, it was reported that the toroidal dipolar response could be enhanced by coupling to electric or magnetic dipole, resulting in an analogy of electromagnetically-induced transparency [5,12,15,18]. In this paper, a toroidal metastructure by double metallic flat-rings is proposed to numerically investigate the scattering characteristic of its interaction with a dipolar emitter. It #250469 Received 22 Sep 2015; revised 28 Oct 2015; accepted 28 Oct 2015; published 2 Nov 2015 © 2015 OSA 16 Nov 2015 | Vol. 23, No. 23 | DOI:10.1364/OE.23.029384 | OPTICS EXPRESS 29385 is interesting to find that the interaction can be either radiating enhanced or suppressed (i.e., nonradiating), depending on constructive or destructive interference, respectively. Moreover, the nonradiating phenomenon can be sensitively manipulated to be a super-radiating one with both pronounced directionality and linear polarization conversion, once the dipole emitter is shifted away from the axis of toroidal dipole. 2. Numerical model The passive composite metastructure proposed in this paper is shown in Fig. 1, comprising double metallic flat-ring elements for the toroidal dipolar response with a silicon-oxide gap ε = layer as spacer ( SiO2 2.4 ). The flat-ring inner and outer radii are 100 and 300 nm, respectively, and the gap between 40-nm-thick metallic flat rings is 30 nm.
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