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Electromagnetic toroidal excitations in matter and free space

Nature Materials volume 15, pages 263–271 (2016)Cite this article

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Abstract

The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information.

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Figure 1: Toroidal structures at different length scales.
Figure 2: The 'multipole zoo'.
Figure 3: Toroidal metamaterials.
Figure 4: Non-radiating configurations.
Figure 5: Focused doughnut pulses.

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Acknowledgements

The authors are grateful to Din Ping Tsai, Ian Youngs and Janne Ruostekoski for fruitful discussions and acknowledge the support of the MOE Singapore (grant MOE2011-T3-1-005), the UK's Engineering and Physical Sciences Research Council (grants EP/G060363/1, EP/M008797/1), the Defence Science and Technology Laboratory (grant DSTLX-1000068886) and the Leverhulme Trust.

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  1. Optoelectronics Research Centre & Centre for Photonic Metamaterials, University of Southampton, SO17 1BJ, Highfield, UK

    N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould & N. I. Zheludev

  2. TPI and Centre for Disruptive Photonic Technologies, Nanyang Technological University, 637378, Singapore, Singapore

    N. I. Zheludev

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  1. N. Papasimakis
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  2. V. A. Fedotov
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  3. V. Savinov
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  5. N. I. Zheludev
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All authors made equal contributions to the review and edited the text and figures.

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Correspondence to N. Papasimakis.

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Papasimakis, N., Fedotov, V., Savinov, V. et al. Electromagnetic toroidal excitations in matter and free space. Nature Mater 15, 263–271 (2016). https://doi.org/10.1038/nmat4563

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