Toroidal Dipole Moment Research Articles

Geometry-Independent Excitation of Dark Modes Using Dipole Moment Transitions

Despite numerous potential advantages of subradiative dark modes due to an extremely high quality ( ${Q}$ ) factor, the practicality still depends on the consistency of excitations for a tight fabrication tolerance. This article proposes a novel approach to adaptive transitions between different dipole moments to allow for consistent excitation of Fano and electric quadrupole resonances that are extremely sensitive to geometric errors. The proposed geometry of each metamolecule consists of four strips printed on a thin dielectric film with four gaps between the strips, and the geometric error is described as structural deformation by adjusting the strip lengths and gap sizes in the vertical direction. In each deformed state, current and magnetic-field distributions are analyzed to interpret operating principles, and multipole moments are calculated based on the multipole expansion using the current distributions. The results demonstrate that the consistent excitation of the electric quadrupole moment is enabled based on a simultaneous transition between toroidal and electric dipole moments, and the Fano resonance is consistently excited by the magnetic-to-electric dipole moment transition. For verification, original and deformed metasurfaces are fabricated, and their transmission and reflection coefficients are measured in a semianechoic chamber to experimentally validate the proposed dipole moment transitions. The results confirm that the proposed approach has great potential to bring advances in recent sensing and energy harvesting applications where an extremely high ${Q}$ -factor is essential.

Toroidal dipole-induced coherent forward scattering from a miniaturized cloaking structure

The physical existence of microwave toroidal dipole in a dogbone metallic inclusion-based miniaturized cloaking structure is verified in this paper. The excitation of toroidal dipole moments on the studied composite is verified using multipole scattering formalism. The presence of the toroidal Fano resonance significantly enhances resonant forward scattering from the structure for normal incidence. Multipolar contribution from the electric, magnetic and toroidal moments significantly enhances the scattering cross-section of the composite as compared to a bare cylindrical metallic object. Applicability of the proposed scheme is tested inside an anechoic chamber using reflection measurements on the fabricated structure and is subsequently validated in computer simulations in the microwave frequency regime.

Excitation of high Q toroidal dipole resonance in an all-dielectric metasurface

In metamaterial systems, toroidal dipole (TD) plays an important role in determining their optical properties. Here, we proposed an all-dielectric metasurface consisting of two silicon split-ring resonators (SRRs) that can support strong TD resonance. The TD resonance is excited by TD moments both inside the unit cell and between the neighboring unit cells, and can be easily manipulated by altering the gap size or distance of the SRRs, leading to powerful electric and magnetic near-field enhancement. In addition, symmetric unprotected TD bound state in the continuum (TD-BIC) was achieved in closed-ring-resonator (CRR) metasurface, and transformed into leaky resonances with ultrahigh Q factors by adjusting the distance of CRRs. The proposed structure provides a good platform for us to better understand the coupling of SRRs, which is useful for the design and application of TD metasurfaces in biological sensors, nonlinear interactions and other photonic devices.

Toroidal Dipole Mode Observation In Situ

Besides classical dipole moments, the metaparticles are characterized by toroidal dipole moments that are important for numerous applications ranging from strong field localizations to anapole modes and the dynamic Aharonov–Bohm effect. On the other hand, the toroidal and electric dipole radiation are undistinguished by external observers due to identical radiation patterns. Therefore, the importance of toroidal dipole moments in multipole expansion is questioned by many researchers. However, a long‐awaited unanswered question is—what is going on inside a toroidal metamolecule and is its near‐field distribution distinct from the electric dipole field? Herein, the toroidal dipole mode is experimentally confirmed in situ by proof‐of‐concept measurements of electric and magnetic fields inside properly fabricated water metamolecules with toroidal topology in the microwave frequency range.

Tailoring the excitation of two kinds of toroidal dipoles in all-dielectric metasurfaces

In this paper, the simultaneous excitation of the toroidal dipoles within the unit cell and between neighboring unit cells is theoretically proposed and demonstrated in an all-dielectric metasurface composed of silicon bars. We referred to the toroidal dipole moment within the unit cell as the intra-toroidal dipole moment, and the toroidal dipole moment between the unit cells as the inter-toroidal dipole moment. We found that the contribution of the weak free-space coupling of the inter-toroidal dipole and intra-toroidal dipole can be dramatically increased by decreasing the distance between the adjacent silicon bars, so the electric and magnetic field is significantly confined both inside and between the silicon bars. Hence the radiation loss is greatly suppressed and a toroidal resonance with the high Q-factor of 63,000 is achieved. The proposed all-dielectric metasurface is low loss, simple structure and operating in the near infrared regime, which has potential applications in biochemical sensing, non-linear devices, slow light-based devices, and other optical devices.

Demonstration of Robust Plexcitonic Coupling in Organic Molecules‐Mediated Toroidal Meta‐Atoms

AbstractHybridized plexcitonic states are conventionally excited via robust coupling between resonantly coordinated plasmonic modes and molecular excitons. Here, numerical and experimental studies for the strong plexcitonic coupling and Rabi splitting of dynamic toroidal dipole moment in a plasmonic meta‐atom are presented. It is shown that introducing semiconductor PbS quantum dot aggregates, as a narrow gap semiconductor, with a bulk bandgap of 0.41 eV and a large exciton Bohr radius (tunable over the entire near‐infrared band) to the developed toroidal plasmonic metamaterial allows for the substantially strong plexcitonic coupling with the Rabi splitting of 150 meV in the near‐infrared wavelengths. By computing the density of states for photons, the enhancement in the intensity of the photoluminescence spectra is quantitatively and qualitatively demonstrated. The results verified the luminescence enhancement due to the strong near‐field coupling in the proposed unit cell, and cavity quantum electrodynamics Purcell effect. It is believed that this understanding paves a new method to study the plexcitonic coupling principle in nontraditional resonances and high‐order modes to employ them as novel approaches in the coming generation and modern nanophotonic technologies.

Polarization-independent Fano metasurface with directional toroidal dipole for magnetic field tunability

We have designed and numerically investigated an all-dielectric metasurface consisting of four nanorings located apart with a cross nanobar resonator in between, which supports polarization-independent Fano resonance arising from destructive interference between electric and toroidal dipole moments. Exploiting polarization dependency of toroidal dipole, the polarization of incident light can actively control the direction of toroidal dipole but does not affect Fano resonance. Moreover, our results also manifest that local magnetic field can be dynamically switched on and off based on directional toroidal dipole while maintaining polarization-independent Fano resonance, indicating potential application in efficient switch, light trapping and magnetic hot-spot generation.

C-shaped split ring resonator terahertz toroidal dipole metasurfaces

We designed and fabricated terahertz toroidal dipole metasurfaces based on a C-shaped split ring resonator metallic pattern fabricated on a flexible dielectric material (mylar). The toroidal dipole moment (Ty) was demonstrated as the dominant contribution to two different resonances at low frequency (ω1) and at high frequency (ω2). Simulation and LC circuit model analysis offered a quantitative explanation to the blue shift of the resonant frequencies at ω1 and ω2 as the increase of the opening angle(θ). The resonant frequencies showed a red shift at ω1 and ω2 as the increase of the outer ring radius (QR). Furthermore, the enhancement of the Q factor was attributed to the increase of Ty and the decrease of radiative loss. It was further proven that the model provided a new scheme for designing the toroidal dipole metasurfaces under a terahertz band, which was expected to be used as terahertz functional devices.

Radiation of Dynamic Toroidal Moments.

Dynamic toroidal dipoles, a distinguished class of fundamental electromagnetic sources, receive increasing interest and participate in fascinating electrodynamic phenomena and sensing applications. As described in the literature, the radiative nature of dynamic toroidal dipoles is sometimes confounded, intermixing with static toroidal dipoles and plasmonic dark modes. Here, we elucidate this issue and provide proof-of-principle experiments exclusively on the radiation behavior of dynamic toroidal moments. Optical toroidal modes in plasmonic heptamer nanocavities are analyzed by electron energy loss spectroscopy and energy-filtered transmission electron microscopy supported by finite-difference time-domain numerical calculations. Additionally, their corresponding radiation behaviors are experimentally investigated by means of cathodoluminescence. The observed contrasting behaviors of a single dynamic toroidal dipole mode and an antiparallel toroidal dipole pair mode are discussed and elucidated. Our findings further clarify the electromagnetic properties of dynamic toroidal dipoles and serve as important guidance for the use of toroidal dipole moments in future applications.

Optical Anapoles: Concepts and Applications

AbstractInterference of electromagnetic modes supported by subwavelength photonic structures is one of the key concepts that underpins the nanoscale control of light in metaoptics. It drives the whole realm of all‐dielectric Mie‐resonant nanophotonics with many applications for low‐loss nanoscale optical antennas, metasurfaces, and metadevices. Specifically, interference of the electric and toroidal dipole moments results in a very peculiar, low‐radiating optical state associated with the concept of optical anapole. Here, the physics of multimode interferences and multipolar interplay in nanostructures is uncovered with an intriguing example of the optical anapole. The recently emerged field of anapole electrodynamics is reviewed, explicating its relevance to multipolar nanophotonics, including direct experimental observations, manifestations in nonlinear optics, and rapidly expanding applications in nanoantennas, active photonics, and metamaterials.

Perforated all-dielectric anapole metamaterials

In this work, we propose a novel type of perforated silicon metamaterials, exhibiting anapole mode in optics. The interplay of electric and toroidal dipole moments leads to transparency of the system at resonant frequency due to destructive interference between them. This type of metamaterials is demanding for practical nanophotonics application due to one-step simple fabrication and fascinating properties inherent to anapole mode excitation.

Light emission by accelerated electric, toroidal, and anapole dipolar sources

Emission of electromagnetic radiation by accelerated particles with electric, toroidal and anapole dipole moments is analyzed. It is shown that ellipticity of the emitted light can be used to differentiate between electric and toroidal dipole sources, and that anapoles, elementary neutral non-radiating configurations, which consist of electric and toroidal dipoles, can emit light under uniform acceleration. The existence of non-radiating configurations in electrodynamics implies that it is impossible to fully determine the internal makeup of the emitter given only the distribution of the emitted light. Here we demonstrate that there is a loop-hole in this `inverse source problem'. Our results imply that there may be a whole range of new phenomena to be discovered by studying the electromagnetic response of matter under acceleration.

Anapole Mode Sustaining Silicon Metamaterials in Visible Spectral Range

AbstractThis paper is dedicated to a type of perforated silicon metamaterials, possessing anapole mode in visible spectral range due to destructive interference between electric and toroidal dipole moments. The proposed structure gains both in attainable material and simplified fabrication. Such a material exhibits a desirable physical effect and has obvious practical application: it supports the anapole mode without complicated 3D toroidal geometry and can be processed in one step by nanofabrication methods. The metamaterial paves the way for advanced optical devices on the base of all‐dielectric metamaterials. Besides inherently low dissipative losses and strong anapole response, such an optical metamaterial can demonstrate subtle sensing, nonradiative data transfer, Aharonov‐Bohm effect and other tempting applications in nanophotonics.

Nanofocusing of Toroidal Dipole for Simultaneously Enhanced Electric and Magnetic Fields Using Plasmonic Waveguide

Optical toroidal dipole and electromagnetic field enhancement have attracted much interest owing to their interesting physical features and various potential nanophotonic applications. In this paper, novel antireflective nanofocusing methods to deliver and squeeze toroidal dipole moment with simultaneous enhancement of electric and magnetic fields are suggested. By coupling the two fundamental modes of a metal–insulator–metal waveguide with a partial mirror in a waveguide and a nanocavity, resonant squeezing of longitudinal and perpendicular toroidal dipoles in an ultracompact nanocavity (∼ λ 2 / 190) is achieved at the near-telecom wavelengths. Moreover, electric and magnetic field enhancements occur simultaneously in a designated nanocavity. We expect that the proposed scheme would pave a way to engineer nanophotonic waveguide based light-matter interactions by enhancing both electric and magnetic fields. This study would interest both nanophotonics and quantum optics communities.

Resonance Coupling between Molecular Excitons and Nonradiating Anapole Modes in Silicon Nanodisk-J-Aggregate Heterostructures

The nonradiating nature of anapole modes owing to the compositions of electric and toroidal dipole moments makes them distinct from conversional radiative resonances, and they have been suggested for the design of nanophotonic devices such as nanolasers based on light–matter interactions tailor by nanodisks. Therefore, the investigation of resonance coupling between molecular excitons and anapole modes is not only of fundamental interest, but is also promising for practical applications. To this end, a heterostructure composed of a silicon nanodisk and a uniform molecular J-aggregate ring is used to achieve the resonance coupling between the exciton transition and the anapole mode. In contrast with that of the conversional resonances, the resonance coupling is evidenced by a scattering peak around the exciton transition frequency, and the anapole mode splits into a pair of eigenmodes characterized as pronounced scattering dips, which are termed as the formation of two hybrid anapole modes caused by the co...

Toroidal dipolar response in plasmonic nanoparticle clusters

A closed loop of magnetic dipoles gives rise to a toroidal dipole, where magnetic dipoles serve as the basic elements. However, magnetic responses are much weaker than electric ones at optical frequencies. Here, we show that toroidal dipole moments can be induced by collective modes in plasmonic nanoparticle clusters instead of using magnetic dipoles. When the geometric parameters of plasmonic clusters are optimized, a dominant radiation from toroidal dipole can be realized guaranteed by the symmetry properties of clusters. Compared to the toroidal model with triple plasmonic nanoparticles, the plane-wave excitation of toroidal dipolar mode can be angular independent for the cluster with particle number N ⩾ 4. These findings of toroidal moments based on collective modes in plasmonic nanoparticle clusters may find potential applications in optical sensing, nano-antennas, and nonlinear optics, etc.

Destructive interference between electric and toroidal dipole moments in TiO2 cylinders and frustums with coaxial voids

We demonstrate numerically the possibility of multipole interference in the TiO2 (titanium dioxide) microcylinders and microfrustums in the wavelength range 210-300 μm. Resonantly strong destructive interference between toroidal and electric dipole contributions to the scattered field is achieved by a geometry tuning. The toroidal and electric dipole mode overlapping at the resonant wavelength with almost total suppression of the total electric dipole moment is achieved.

\u201cOptical and Surface Enhanced Raman Scattering properties of Ag modified silicon double nanocone array\u201d

Surface enhanced Raman scattering (SERS) systems with large number of active sites exhibit superior capability in detection of low concentration analytes. In this paper, we present theoretical as well as experimental studies on the optical properties of a unique hybrid nanostructure, Ag NPs decorated silicon double nanocones (Si-DNCs) array, which provide high density of hot spots. The Si-DNC array is fabricated by employing electron beam lithography together with plasma etching process. Multipole analysis of the scattering spectra, based on the multipole expansion theory, confirms that the toroidal dipole moment dominates over other electric and magnetic multipole moments in the Si-DNCs array. This response occurs as a result of generating current densities flowing in opposite directions and consequently generating H-field vortexes inside the nanocones. Moreover, SERS applicability of this type of nanostructure is examined. For this purpose, the Si-DNCs array is decorated with Ag nanoparticles (NPs) by means of electroless deposition method. Simulation results indicate that combination of multiple resonances, including LSPR resonance of Ag NPs, longitudinal standing wave resonance of Ag layer and inter-particle interaction in the gap region, result in a significant SERS enhancement. Our experimental results demonstrate that Si-DNC/Ag NPs array substrate provides excellent reproducibility and ultrahigh sensitivity.

Toroidal and magnetic Fano resonances in planar THz metamaterials

The toroidal dipole moment, a localized electromagnetic excitation of torus magnetic fields, has been observed experimentally in metamaterials. However, the metamaterial based toroidal moment was restricted at higher frequencies by the complex three-dimensional structure. Recently, it has been shown that toroidal moment could also be excited in a planar metamaterial structure. Here, we use asymmetric Fano resonators to illustrate theoretically and experimentally the underlying physics of the toroidal coupling in an array of planar metamaterials. It is observed that the anti-parallel magnetic moment configuration shows toroidal excitation with higher quality (Q) factor Fano resonance, while the parallel magnetic moment shows relatively lower Q factor resonance. Moreover, the electric and toroidal dipole interferes destructively to give rise to an anapole excitation. The magnetic dipole-dipole interaction is employed to understand the differences between the toroidal and magnetic Fano resonances. We further study the impact of intra unit-cell coupling between the Fano resonator pairs in the mirrored and non-mirrored arrangements. The numerical and theoretical approach for modelling the near-field effects and experimental demonstration of toroidal and magnetic Fano resonances in planar systems are particularly promising for tailoring the loss in metamaterials across a broad range of the electromagnetic spectrum.

Unidirectional scattering induced by the toroidal dipolar excitation in the system of plasmonic nanoparticles.

The interference between conventional multipoles (e.g., electric and magnetic dipole, electric quadrupole, etc.) is known as the cause of unidirectional backward and forward scattering of nanoparticles. However, an unconventional multipole moment, toroidal dipole moment is generally overlooked in the unidirectional scattering. In this work, we systematically investigate the unidirectional scattering in the system of plasmonic nanoparticles. It is found that the toroidal dipole moment can play a significant role in the unidirectional backward scattering. The structural tunability of the unidirectional scattering is also demonstrated. Our results can find applications in the design of nanoantennas.