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Dielectric metasurfaces can show multi-resonant response with high Q-factors in the visible range due to multipole coupling. This work suggests that these collective resonances in all-dielectric metasurfaces can be modified if adjacent to…

We show how the elusive toroidal dipole moment appears as a radiative excitation eigenmode in a metamolecule resonator that is formed by pairs of plasmonic nanorods. We analyze one such nanorod configuration - a toroidal metamolecule. We…

The toroidal response is numerically investigated in a multifold double-ring metamaterials at the antibonding magnetic-dipole mode (i.e., antiparallel magnetic dipoles in one double-ring fold). This intriguing toroidal resonance in…

Optics · Physics 2012-12-27 Zheng-Gao Dong , Peigen Ni , Jie Zhu , Xiaobo Yin , X. Zhang

Toroidal modes enable high-Q resonances, but electric toroidal excitations remain unexplored compared to magnetic ones. This work establishes electric-magnetic toroidal duality in a hexagonal metasurface. Using finite element simulations,…

Optics · Physics 2026-05-26 Oleksiy Breslavets , Yuri Savin , Zoya Eremenko

We present a thorough investigation of the electromagnetic resonant modes supported by systems of polaritonic rods placed at the vertices of canonical polygons. The study is conducted with rigorous finite-element eigenvalue simulations. To…

The excitation of toroidal multipoles in metamaterials was investigated for high-Q response at a subwavelength scale. In this study, we explored the optimization of toroidal excitations in a planar metamaterial comprised of asymmetric split…

Optics · Physics 2017-04-11 Yuancheng Fan , Fuli Zhang , Quanhong Fu , Zeyong Wei , Hongqiang Li

We demonstrate that, owing to the unique topology of the toroidal dipolar mode, its electric/magnetic field can be spatially confined within subwavelength, externally accessible regions of the metamolecules, which makes the toroidal planar…

Dynamic metamolecules (DMMs) are composed of a dielectric core made of hydrogel surrounded by randomly-packed plasmonic beads that can display magnetic resonances when excited by light at optical frequencies. Their optical properties can be…

Herein, we discuss the conditions for excitation of symmetry-protected toroidal dipole modes in all-dielectric metasurfaces composed of trimer or twin-trimer clusters of dielectric disks. Such metasurfaces permit enhanced light-matter…

Living in a world of resonances, there have been significant progresses in the field of excitation high-quality and multifunctional moments across a wide range of optical frequencies. Among all acknowledged resonances, the toroidal…

Optics · Physics 2018-10-17 Burak Gerislioglu , Arash Ahmadivand

The toroidal dipole is an exquisite electromagnetic momentum apart from the classical multipoles family that can be localized and squeezed in an extremely tiny spot. This mode, in optical nanosystems, can be particularly distinguished as a…

Optics · Physics 2018-07-23 Arash Ahmadivand , Burak Gerislioglu

Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here we propose and theoretically study all-dielectric…

The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode…

Optics · Physics 2026-01-27 Sergey Gladyshev , Kristina Frizyuk , Andrey Bogdanov

We demonstrate that the toroidal dipolar response can be realized in the optical regime by designing a feasible nanostructured metamaterial, comprising asymmetric double-bar magnetic resonators assembled into a toroid-like configuration. It…

Optics · Physics 2015-03-13 Zheng-Gao Dong , J. Zhu , Junsuk Rho , Jia-Qi Li , Changgui Lu , Xiaobo Yin , X. Zhang

We revisit the fundamental topic of light scattering by single homogenous nanoparticles from the new perspective of excitation and manipulation of toroidal dipoles. It is revealed that besides within all-dielectric particles, toroidal…

Optics · Physics 2015-10-28 Wei Liu , Jianhua Shi , Bing Lei , Haojun Hu , Andrey E. Miroshnichenko

Optically resonant particles are key building blocks of many nanophotonic devices such as optical antennas and metasurfaces. Because the functionalities of such devices are largely determined by the optical properties of individual…

The optical properties of infinite planar array of scattering particles, metasurfaces and metagratings, are attracting special attention lately for their rich phenomenology, including both plasmonic and high-refractive-index dielectric…

Resonant modes determine the response of electromagnetic devices, including dielectric and plasmonic resonators. Relying on the degrees of freedom that metamaterials provide, this contribution shows how to design, at will, the resonant…

A toroidal dipole represents an often overlooked electromagnetic excitation distinct from the standard electric and magnetic multipole expansion. We show how a simple arrangement of strongly radiatively coupled atoms can be used to…

Optics · Physics 2020-08-05 Kyle E. Ballantine , Janne Ruostekoski

A general analytical approach to the study of electromagnetic resonances of metasurfaces consisting of meta-atoms with anisotropic electric and magnetic dipole polarizabilities and irradiated with obliquely incident light is developed in…

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