Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials

Radiationless optical modes in metasurfaces: recent progress and applications

Non-radiative optical modes attracted enormous attention in optics due to strong light confinement and giant Q-factor at its spectral position. The destructive interference of multipoles leads to zero net-radiation and strong field trapping. Such radiationless states disappear in the far-field, localize enhanced near-field and can be excited in nano-structures. On the other hand, the optical modes turn out to be completely confined due to no losses at discrete point in the radiation continuum, such states result in infinite Q-factor and lifetime. The radiationless states provide a suitable platform for enhanced light matter interaction, lasing, and boost nonlinear processes at the state regime. These modes are widely investigated in different material configurations for various applications in both linear and nonlinear metasurfaces which are briefly discussed in this review.

Probing optical anapoles with fast electron beams

Optical anapoles are intriguing charge-current distributions characterized by a strong suppression of electromagnetic radiation. They originate from the destructive interference of the radiation produced by electric and toroidal multipoles. Although anapoles in dielectric structures have been probed and mapped with a combination of near- and far-field optical techniques, their excitation using fast electron beams has not been explored so far. Here, we theoretically and experimentally analyze the excitation of optical anapoles in tungsten disulfide (WS2) nanodisks using Electron Energy Loss Spectroscopy (EELS) in Scanning Transmission Electron Microscopy (STEM). We observe prominent dips in the electron energy loss spectra and associate them with the excitation of optical anapoles and anapole-exciton hybrids. We are able to map the anapoles excited in the WS2 nanodisks with subnanometer resolution and find that their excitation can be controlled by placing the electron beam at different positions on the nanodisk. Considering current research on the anapole phenomenon, we envision EELS in STEM to become a useful tool for accessing optical anapoles appearing in a variety of dielectric nanoresonators.

Optically transparent and flexible-assembled metasurface rasorber for infrared-microwave camouflage based on a hybrid anapole state

Hybrid anapole state, originating from the destructive interference of more than one basic electromagnetic multipole moments with their toroidal counterparts, enables the simultaneous suppression of multiple leading scattering channels, thereby demonstrates promising applications in perfect absorption and electromagnetic camouflage. However, the formation of hybrid anapoles is challenging because a careful overlap of electromagnetic multipoles with their toroidal counterparts is required. In this study, we propose and experimentally demonstrate a transparent and flexible assembled metasurface rasorber supporting hybrid anapole states for infrared and microwave camouflage, which not only supports low IR emissivity in the range of 8-14 μm but also exhibits an absorption-transmission-absorption response in the microwave band. In addition, the conformal and tunable performances of the fabricated metasurface rasorber are experimentally demonstrated. Our study provides a new strategy for designing multispectral camouflage metasurfaces.

Resonant coupling of molecular excitons and optical anapoles in silicon nanosphere-J-aggregate heterostructures under vector beam illumination

Resonant excitation of high-index dielectric nanostructures and their coupling with molecular excitons provide great opportunities for engineering adaptable platforms for hybrid functional optical devices. Here, we numerically calculate resonance coupling of nonradiating anapole states to molecular excitons within silicon nanosphere-J-aggregate heterostructures under illumination with radially polarized cylindrical vector beams. The results show that the resonance coupling is accompanied by a scattering peak around the exciton transition frequency, and the anapole state splits into a pair of anticrossing eigenmodes with a mode splitting energy of ≈200m e V. We also investigate the resonance coupling as a function of the J-aggregate parameters, such as thickness, exciton transition linewidth, and oscillator strength. Resonant coupling of the anapole states and J-aggregate heterostructures could be a promising platform for future nanophotonic applications such as in information processing and sensing.

The Rise of Toroidal Electrodynamics and Spectroscopy

Toroidal electrodynamics is now massively influencing research in toroidal (Marinov et al. New J. Phys. 2007, 9, 234; Basharin et al. Phys. Rev. X 2015, 5, 011036; Jeong et al. ACS Photonics 2020, 7, 1699) and anapole metamaterials (Basharin et al. Phys. Rev. B 2017, 95, 035104; Wu et al. ACS Nano 2018, 12, 1920), optical properties of nanoparticles (Miroshnichenko et al. Nature Commun. 2015, 6, 8069; Gurvitz et al. Laser Photonics Rev. 2019, 13, 1800266), plasmonics (Ogut et al. Nano Lett. 2012, 12, 5239; Yezekyan et al. Nano Lett. 2022, 22, 6098), sensors (Gupta et al. Appl. Phys. Lett. 2017, 110, 121108; Ahmadivand et al. Mater. Today 2020, 32, 108; Wang et al. Nanophotonics 2021, 10, 1295; Yao et al. Photonix 2022, 3, 23), and lasers (Huang et al. Sci. Rep. 2013, 3, 1237; Hwang et al. Nanophotonics 2021, 10, 3599), while a recent publication on toroidal optical transitions in hydrogen-like atoms (Kuprov et al. Sci. Adv. 2022, 8, eabq7651) promises to launch a new chapter in spectroscopy. In this Viewpoint, we review these progresses.

Classical Analog and Hybrid Metamaterials of Tunable Multiple-Band Electromagnetic Induced Transparency

The electromagnetic induced transparency (EIT) effect originates from the destructive interference in an atomic system, which contributes to the transparency window in its response spectrum. The implementation of EIT requires highly demanding laboratory conditions, which greatly limits its acceptance and application. In this paper, an improved harmonic spring oscillation (HSO) model with four oscillators is proposed as a classical analog for the tunable triple-band EIT effect. A more general HSO model including more oscillators is also given, and the analyses of the power absorption in the HSO model conclude a formula, which is more innovative and useful for the study of the multiple-band EIT effect. To further inspect the analogizing ability of the HSO model, a hybrid unit cell containing an electric dipole and toroidal dipoles in the metamaterials is proposed. The highly comparable transmission spectra based on the HSO model and metamaterials indicate the validity of the classical analog in illustrating the formation process of the multiple-band EIT effect in metamaterials. Hence, the HSO model, as a classical analog, is a valid and powerful theoretical tool that can mimic the multiple-band EIT effect in metamaterials.

Toroidal optical transitions in hydrogen-like atoms

It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions involving electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also involve toroidal multipoles-toroidal absorption lines have been observed in electromagnetic metamaterials. Here, we show that a previously unexplored type of spectroscopy of the hitherto largely neglected toroidal dipolar interaction becomes feasible if, apart from the classical r × r × p toroidal dipole density term responsible for the toroidal transitions in metamaterials, the spin-dependent r × σ term (which only occurs in relativistic quantum mechanics) is taken into account. Toroidal dipole operators are odd under parity and time-reversal symmetries; toroidal dipole transitions can therefore be distinguished from electric multipole and magnetic dipole transitions.

Excitation of Asymmetric Resonance with Symmetric Split-Ring Resonator

In this paper, a new approach to excite sharp asymmetric resonances using a single completely symmetric split-ring resonator (SRR) inside a rectangular waveguide is proposed. The method is based on an asymmetry in the excitation of a symmetric split-ring resonator by placing it away from the center of the waveguide along its horizontal axis. In turn, a prominent asymmetric resonance was observed in the transmission amplitude of both the simulated results and the measured data. Using a single symmetric SRR with an asymmetric distance of 6 mm from the center of a rectangular waveguide led to the excitation of a sharp resonance with a Q-factor of 314 at 6.9 GHz. More importantly, a parametric study simulating different overlayer analytes with various refractive indices revealed a wavelength sensitivity of 579,710 nm/RIU for 150 μm analyte thickness.

Electric field enhancement by a hybrid dielectric-metal nanoantenna with a toroidal dipole contribution

Plasmonic nanocavities enable extreme light-matter interactions by pushing light down to the nanoscale. The numerical simulation is carried out systematically on the slotted Φ-shaped Si disk system with the super-dipole mode based on the analysis of the scattering strength of electric and toroidal dipoles. New blocks are introduced to the zero-field strength region of a slotted Si disk system as a function of the field enhancement factors. The far-field scattering characteristics and near-field electromagnetic field distributions are investigated by a multipole decomposition analysis to elucidate the intrinsic causes of the field enhancement. In the hybrid metal-dielectric nanoantenna, the Φ-shaped Si structure is prepared by superimposing Au nanoantennas for further field enhancement. In addition, the effects of the placement of an electric dipole emitter on the Purcell factor are derived. The geometric volume of the system is increased, and the electric field strength is improved, leading to an electric field increase of ∼30. Coupling between the super-dipole mode of the dielectric nanostructure and plasmonic modes of the metallic nanoantenna produces an enhancement as large as 16 times. Our results reveal a greatly enhanced super-dipole mode by electromagnetic coupling in composite structures, which will play a significant role in enhanced nonlinear photonics, near-field enhancement spectroscopy, and strong photon-exciton coupling.

Pure toroidal dipole in a single dielectric disk

The toroidal dipole is a peculiar electromagnetic excitation and has attracted increasing interests because of unusual radiation characteristics. However, the realization of toroidal moment requires complicated structure and are often disturbed by the conventional electric and magnetic multipoles. In this paper, we explore the electromagnetic properties of a simple dielectric disk illuminated by a focused radially polarized beam and demonstrate a pure toroidal dipolar response. A comprehensive approach is proposed to suppress other undesirable electromagnetic multipolar resonances step by step. The disk with optimized geometry is employed to construct an all-dielectric electric mirror dominated by toroidal dipolar resonance. And two kinds of anapole modes with total suppression of far-field radiation are investigated, which proves electric and magnetic non-radiating sources, respectively. Besides, by simultaneously introducing the asymmetry in both structure and incidence, a transformation from Mie-type mode to trapped mode is observed. Our study provides an opportunity to realize a unique pure toroidal dipole and may boost the relevant light-matter interaction.

Anapole States in Gap-Surface Plasmon Resonators

Anapole states associated with the destructive interference between dipole and toroidal moments result in suppressed scattering accompanied by strongly enhanced near fields. In this work, we comprehensively examine the anapole state formation in metal-insulator-metal configurations supporting gap surface-plasmon (GSP) resonances that are widely used in plasmonics. Using multipole decomposition, we show that in contrast to the common case of dielectric particles with out-of-phase superposition of electric and toroidal dipoles anapole states in GSP resonators are formed due to the compensation of magnetic dipole moments. Unlike anapole states in dielectric particles, magnetic anapole states in GSP resonator does not provide a pronounced suppression of scattering, but it features huge electric field enhancement, which we verify by numerical simulations and two-photon luminescence measurements. This makes the GSP resonator configuration very promising for use in a wide range of applications, ranging from nonlinear harmonic generation to absorption enhancement and sensing.

Enhanced Thermo-optical Response by Means of Anapole Excitation

High refractive index (HRI) dielectric nanostructures offer a versatile platform to control the light-matter interaction at the nanoscale as they can easily support electric and magnetic modes with low losses. An additional property that makes them extraordinary is that they can support low radiative modes, so-called anapole modes. In this work, we propose a spectrally tunable anapole nanoheater based on the use of a dielectric anapole resonator. We show that a gold ring nanostructure, a priori nonresonant, can be turned into a resonant unit by just filling its hole with an HRI material supporting anapole modes, resulting in a more efficient nanoheater able to amplify the photothermal response of the bare nanoring. As proof of concept, we perform a detailed study of the thermoplasmonic response of a gold nanoring used as heating source and a silicon disk, designed to support anapole modes, located in its center acting as an anapolar resonator. Furthermore, we utilize the anapole excitation to easily shift the thermal response of these structures from the shortwave infrared range to the near-infrared range.

Highly-sensitive sensor based on toroidal dipole governed by bound state in the continuum in dielectric non-coaxial core-shell cylinder

The electromagnetic fields distributed on the surface region of the nanostructure is very important to improve the performance of the sensor. Here, we proposed a highly sensitive sensor based on toroidal dipole (TD) governed by bound state in the continuum (BIC) in all-dielectric metasurface consisting of single non-coaxial core-shell cylinder nanostructure array. The excitation of TD resonance in a single nanostructure is still challenging. The designed nanostructure not only supports TD resonance in a single nanostructure but also has very high Q-factor. More importantly, its electric field distributes at the surface of outer cylinder-shell, which is very suitable for biosensing. To evaluate the sensing performance of our proposed structure, we investigated the sensitivity and the figure of merit (FOM) of nanostructure with different structural parameters. Maximum sensitivity and FOM can reach up to 342 nm/RIU and 1295 when the asymmetric parameter d =10 nm. These results are of great significance to the research of TD resonance and the development of ultrasensitive sensor.

Design and simulation of a GST-based metasurface with strong and switchable circular dichroism

Circular dichroism (CD) is required in the applications of biological detection, analytical chemistry, etc. Here, we numerically demonstrated large-range switchable CD by controlling the phase change of Ge₂Sb₂Te₅ (GST) in a zigzag array. At the amorphous state of GST (a-GST), the strong and dual-waveband CD effects are realized via the selective excitations of electric, magnetic, and toroidal resonances. With the transition from a-GST to crystalline state GST, CD strengths are tailored dynamically in large ranges. In detail, the CD magnitudes change by about 0.93 and the modulation depths exceed 94% at dual wavebands. The strong CD effects and large-range switch capability in the GST-based metasurfaces will boost the development of active chiroptical devices.

Incident-angle-insensitive toroidal metamaterial

The incident-angle-insensitive toroidal dipole resonance on an asymmetric double-disk metamaterial is investigated in the near infrared band. Numerical results show that when the incident angle of excitation light varies from 0° to 90°, our metastructure not only always maintains stable toroidal dipole resonance characteristics, but also presents an excellent local field confinement. Under normal incidence, the polarization angle accessible to a dominant toroidal dipole resonance can be expanded to 70° in spite of the weakened electric field amplitude probed in the gap-layer. Moreover, the dependent relationships of toroidal dipole resonance on the radial asymmetry Δr and gap distance are also explored. The local electric field amplitude can also reach a maximum by structural optimization. The works enrich the research of toroidal moment and provide more application potentials in optical devices.

Dual-band polarization-insensitive toroidal dipole quasi-bound states in the continuum in a permittivity-asymmetric all-dielectric meta-surface

Ultra-high quality (Q) factor resonances derived from the bound states in the continuum (BICs) have drawn much attention in optics and photonics. Especially in meta-surfaces, they can enable ultrasensitive sensors, spectral filtering, and lasers because of their enhanced light-matter interactions and rare superiority of scalability. In this paper, we propose a permittivity-asymmetric all-dielectric meta-surface, comprising high-index cuboid tetramer clusters with symmetric structural parameters and configuring periodically on a glass substrate. Simulation results offer dual-band quasi-BICs with high Q values of 4447 and 11391, respectively. Multipolar decomposition in cartesian and electromagnetic distributions are engaged to analyze the physical mechanism of dual quasi-BIC modes, which reveals that they are both governed by magnetic quadrupole (MQ) and in-plane toroidal dipole (TD). The polarization-insensitive and scalable characteristics are also investigated. Additionally, we appraise the sensing performances of the proposed structure. As an example, our work supports an uncommon route to design dual-band polarization-insensitive TD quasi-BICs resonators and facilitates their applications in optic and photonics, such as low-threshold lasers and sensing.

Toroidal electromagnetically induced transparency based meta-surfaces and its applications

The vigorous research on low-loss photonic devices has brought significance to a new kind of electromagnetic excitation, known as toroidal resonances. Toroidal excitation, possessing high-quality factor and narrow linewidth of the resonances, has found profound applications in metamaterial (MM) devices. By the coupling of toroidal dipolar resonance to traditional electric/magnetic resonances, a metamaterial analogue of electromagnetically induced transparency effect (EIT) has been developed. Toroidal induced EIT has demonstrated intriguing properties including steep linear dispersion in transparency windows, often leading to elevated group refractive index in the material. This review summarizes the brief history and properties of the toroidal resonance, its identification in metamaterials, and their applications. Further, numerous theoretical and experimental demonstrations of single and multiband EIT effects in toroidal-dipole-based metamaterials and its applications are discussed. The study of toroidal-based EIT has numerous potential applications in the development of biomolecular sensing, slow light systems, switches, and refractive index sensing.

Invisible Mie scatterer

Dielectric Mie scatterers possessing simultaneously magnetic and electric resonances can be used to tailor scattering utilizing the interference among electromagnetic multipole moments. Cloaking for this type of Mie scatterer is important for various applications. However, the existing cloaking mechanisms mainly focus on the elimination of net electric dipole moments, which have not been generalized to a Mie scatterer with both magnetic and electric responses yet. Herein, we propose and experimentally demonstrate an invisible Mie scatterer utilizing a hybrid skin cloak. The hybrid mechanism relies on the realization of a magnetic analog of a plasmonic cloak and the electric anapole condition to eliminate the net magnetic and electric dipole moments simultaneously. Microwave experiments are provided to validate the proposal. Our results not only introduce a new concept of skin cloaking for electromagnetic scatterers, but also provide new insight for the invisibility and illusion of Mie scatterers.

Multiband transparency effect induced by toroidal excitation in a strongly coupled planar terahertz metamaterial

The multiband transparency effect in terahertz (THz) domain has intrigued the scientific community due to its significance in developing THz multiband devices. In this article, we have proposed a planar metamaterial geometry comprised of a toroidal split ring resonator (TSRR) flanked by two asymmetric C resonators. The proposed geometry results in multi-band transparency windows in the THz region via strong near field coupling of the toroidal excitation with the dipolar C-resonators of the meta molecule. The geometry displays dominant toroidal excitation as demonstrated by a multipolar analysis of scattered radiation. High Q factor resonances of the metamaterial configuration is reported which can find significance in sensing applications. We report the frequency modulation of transparency windows by changing the separation between TSRR and the C resonators. The numerically simulated findings have been interpreted and validated using an equivalent theoretical model based upon three coupled oscillators system. Such modeling of toroidal resonances may be utilized in future studies on toroidal excitation based EIT responses in metamaterials. Our study has the potential to impact the development of terahertz photonic components useful in building next generation devices.

Anapole Meta-Atoms: Nonradiating Electric and Magnetic Sources

The existence of classical nonradiating electromagnetic sources is one of the puzzling questions to date. Here, we investigate radiation properties of physical systems composed of a single ultrahigh permittivity dielectric hollow disk excited by electric or magnetic pointlike dipole antennas, placed inside the inner bore. Using analytical and numerical methods, we demonstrate that such systems can support anapole states with total suppression of far-field radiation and thereby exhibit the properties of electric or magnetic nonradiating sources. It is shown that the suppression of the far-field radiated power is a result of the destructive interference between radiative contributions of the pointlike dipole antennas and the corresponding induced dipole moments of the hollow disk. The experimental investigation of the nonradiating electric source has been performed to confirm our theoretical predictions. Our results pave the way to create and realize compact nonradiative sources for applications in modern wireless power transfer systems, sensors, RFID tags, and medical technologies.

High Q-factor with spoof-anapole mode excitation in metamaterials

In this Letter, numerical and experimental studies for the spoof-anapole effect are presented. Different from the anapole modes, when electric and toroidal dipole intensities are minimized, the spoof-anapole effect can be generated. The spoof-anapole effect can reduce the radiation losses with a high $Q$-factor. The concept is valid in various frequency bands from microwave range for millimeter-sized objects to visible range for nanoparticles. The spoof-anapole modes are first experimentally realized in microwave metamaterials. Almost perfect spoof-anapole behavior is observed, which produces an extremely high $Q$-factor at the resonance frequency. The experimental results agree well with the analytical ones and pave way to excite the non-radiating electromagnetic sources.

Third-harmonic light polarization control in magnetically resonant silicon metasurfaces

Nonlinear metasurfaces have become prominent tools for controlling and engineering light at the nanoscale. Usually, the polarization of the total generated third harmonic is studied. However, diffraction orders may present different polarizations. Here, we design an high quality factor silicon metasurface for third harmonic generation and perform back focal plane imaging of the diffraction orders, which present a rich variety of polarization states. Our results demonstrate the possibility of tailoring the polarization of the generated nonlinear diffraction orders paving the way to a higher degree of wavefront control.

Toroidal dipole resonance in an asymmetric double-disk metamaterial

Toroidal dipole response in metamaterials was usually based on a complex structure with special arrangements or symmetries. In this paper, we propose an asymmetric double-disk metamaterial to numerically and experimentally demonstrate the toroidal dipole response in microwave frequency range. When the upper disk has an offset angle θ ranging from 0 to 100 degrees with respect to the lower one, the toroidal dipole resonance always plays the decisive role, which has been proved by calculating the scattered power in terms of the multipole scattering theory. Besides, the dependence of toroidal dipole response on structural parameters has been explored. Our works enrich the research of toroidal moment and, meanwhile, present more application potentials in meta-devices from microwave to optical regime.

Anapole moment of localized spoof plasmon polaritons based on a hybrid coupling mechanism

In the past several years, the anapole mode has received increasing interest and has been used in numerous applications. However, little relevant work exists on localized spoof plasmon polaritons (LSSPs), which are limited by the excitation of the electric dipole in a symmetrical structure. The lack of an electric dipole makes the excitation of the anapole moment difficult. In this study, we experimentally demonstrate that compact planar metadisks can exhibit a radiationless anapole mode of LSSPs at microwave frequencies. By integrating large and small split-ring resonators, the strong interaction between conductive and inductive coupling is shown to excite the electric dipole. The necessary condition for excitation of the electric dipole using the hybrid coupling mechanism is derived by analyzing equivalent LCR circuits. The proposed structure exhibits nearly equal magnitudes of the toroidal and electric dipoles. Moreover, analytical and numerical approaches are developed to explain the physics of the hybrid coupling mechanism accurately. Further experimental measurements confirm the theoretical predictions.

Radiative Toroidal Dipole and Anapole Excitations in Collectively Responding Arrays of Atoms

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 synthesize a toroidal dipole where the toroidal topology is generated by radiative transitions forming an effective poloidal electric current wound around a torus. We extend the protocol for methods to prepare a delocalized collective excitation mode consisting of a synthetic lattice of such toroidal dipoles and a nonradiating, yet oscillating charge-current configuration, dynamic anapole, for which the far-field radiation of a toroidal dipole is identically canceled by an electric dipole.

Optical Kerr nonlinearity of arrays of all-dielectric high-index nanodisks in the vicinity of the anapole state

The nonlinear optical properties of the high-index nanoparticles are boosted at the anapole state. Researchers intensively study this phenomenon as being promising for various applications. In this Letter, the nonlinear optical Kerr effect of disordered and square lattice metasurfaces of GaP nanodisks is investigated as a function of the disk size in the vicinity of the anapole state at the wavelength of 532 nm. When the sizes of the nanodisks are close to the anapole state, the effective second-order refractive index of the metasurface increases exponentially. On approaching the anapole state, the sign of the effective second-order refractive index is inverted. The absolute value of the effective nonlinear Kerr coefficient of the square lattice metasurface is higher than that of the disordered array of nanodisks. The absolute value of the effective second-order refractive index in proximity to the anapole state is an order of magnitude higher than that at non-anapole resonances of the disordered metasurfaces consisting of the nanodisks or spheres.

Toroidal dipole bound states in the continuum metasurfaces for terahertz nanofilm sensing

A novel terahertz nanofilm sensor consisting of toroidal dipole bound states in the continuum (TD-BIC) inspired Fano resonance metasurface is proposed and investigated, which exhibits both the TD character and BIC feature. When the mirror symmetry of the unit cell was broken, the TD resonance was excited and demonstrated by anti-aligned magnetic dipoles and calculated scattering powers and the BIC mode was verified with the quality factor satisfying the inverse square law. Combined with the amplitude difference referencing technique, the TD-BIC inspired Fano resonance was utilized for nanofilm sensing at THz frequencies for the first time. Simulation results show that the amplitude difference can be easily observed by comparing the resonance frequency shift under difference thicknesses of germanium overlayer. Moreover, by coating with a 40 nm-thick analyte overlayer, the sensitivity of amplitude difference can achieve 0.32/RIU, which is a significant value and more suitable for sensing nanofilm analytes than the traditional frequency shift method. These advantages make our proposed structure have potential applications in sensing nanofilm analytes.

Enhanced toroidal localized spoof surface plasmons in homolateral double-split ring resonators

In this paper, toroidal localized spoof surface plasmons (LSSPs) based on homolateral double-split ring resonators is proposed and experimentally demonstrated at microwave frequencies. By introducing a new split in the conventional single-split ring resonator, the magnetic field in resonator is locally modified. The double-split ring resonator can create the mixed coupling in the structure, leading to the enhancement of magnetic field. Both numerical simulations and experiments are in good agreement. Compared with traditional toroidal LSSPs based on the single-split ring resonators, the imperfection of toroidal LSSPs is resolved, the intensity of toroidal resonance and the figure of merit (FoM) are significantly enhanced. To understand and clarify the enhanced magnetic field phenomena, we analyze the role of the double-split ring resonator. The effect of location of source and spacing between two splits on the resonance intensity are also discussed. A higher intensity of toroidal LSSPs resonance could be achieved by changing the spacing between two splits. Additionally, it is experimentally demonstrated that the enhanced toroidal LSSPs resonance is sensitivity to the background medium. The results of our research provide a new idea for exciting the enhanced toroidal dipole.

Nonradiating anapole condition derived from Devaney-Wolf theorem and excited in a broken-symmetry dielectric particle

In this work, we first derive the nonradiating anapole condition with a straightforward theoretical demonstration exploiting one of the Devaney-Wolf theorems for nonradiating currents. Based on the equivalent volumetric and surface electromagnetic sources, it is possible to establish a unique compact conditions directly from Maxwell's Equations in order to ensure nonradiating anapole state. In addition, we support our theoretical findings with a numerical investigation on a broken-symmetry dielectric particle, building block of a metamaterial structure, demonstrating through a detailed multiple expansion the nonradiating anapole condition behind these peculiar destructive interactions.

Optical radiation manipulation of Si-Ge2Sb2Te5 hybrid metasurfaces

Active optical metadevices have attracted growing interest for the use in nanophotonics owing to their flexible control of optics. In this work, by introducing the phase-changing material Ge₂Sb₂Te₅ (GST), which exhibits remarkably different optical properties in different crystalline states, we investigate the active optical radiation manipulation of a resonant silicon metasurface. A designed double-nanodisk array supports a strong toroidal dipole excitation and an obvious electric dipole response. When GST is added, the toroidal response is suppressed, and the toroidal and electric dipoles exhibit pronounced destructive interference owing to the similarity of their far-field radiation patterns. When the crystallization ratio of GST is varied, the optical radiation strength and spectral position of the scattering minimum can be dynamically controlled. Our work provides a route to flexible optical radiation modulation using metasurfaces.

Excitation of Nonradiating Anapoles in Dielectric Nanospheres

Although the study of nonradiating anapoles has long been part of fundamental physics, the dynamic anapole at optical frequencies was only recently experimentally demonstrated in a specialized silicon nanodisk structure. We report excitation of the electrodynamic anapole state in isotropic silicon nanospheres using radially polarized beam illumination. The superposition of equal and out-of-phase amplitudes of the Cartesian electric and toroidal dipoles produces a pronounced dip in the scattering spectra with the scattering intensity almost reaching zero-a signature of anapole excitation. The total scattering intensity associated with the anapole excitation is found to be more than 10 times weaker for illumination with radially vs linearly polarized beams. Our approach provides a simple, straightforward alternative path to realizing nonradiating anapole states at the optical frequencies.

Mantle cloaking due to ideal magnetic dipole scattering

One of the most exciting applications of metaparticles and metasurfaces consists in the magnetic light excitation. However, the principal limitation is due to parasitic extra multipoles of electric family excited in magnetic dipole meta-particles characterized by a radiating nature and corresponding radiating losses. In this paper, we propose the “ideal magnetic dipole” with suppressed additional multipoles except of magnetic dipole moment in the scattered field from a cylindrical object by using mantle cloaking based on metasurface and on anapole concept. The considered metasurface consists of a periodic width modulated microstrip line, with a sinusoidally shaped profile unit cell printed on a dielectric substrate.

Generating Third Harmonic Vacuum Ultraviolet Light with a TiO2 Metasurface

Dielectric metasurfaces have recently been shown to provide an excellent platform for the harmonic generation of light due to their low optical absorption and to the strong electromagnetic field enhancement that can be designed into their constituent meta-atoms. Here, we demonstrate vacuum ultraviolet (VUV) third harmonic generation from a specially designed dielectric metasurface consisting of a titanium dioxide (TiO₂) nanostructure array. The metasurface was designed to enhance the generation of VUV light at a wavelength of 185 nm by tailoring its geometric design parameters to achieve an optical resonance at the fundamental laser wavelength of 555 nm. The metasurface exhibits an enhancement factor of nominally 180 compared to an unpatterned TiO₂ thin film of the same thickness, evidence of strong field enhancement at the fundamental wavelength. Mode analysis reveals that the origin of the enhancement is an anapole resonance near the pump wavelength. This work demonstrates an effective strategy for the compact generation of VUV light that could enable expanded access to this useful region of the electromagnetic spectrum.

Strong Coupling between Dark Plasmon and Anapole Modes

Plasmonic nanocavities enable extreme light-matter interaction by pushing light down to the nanoscale. The dipolar feature of bright modes allows coupling with the external excitation from free space but results in a radiating background, whereas nonradiating dark plasmon modes can hardly be excited. Here, we report for the first time on strong coupling between dark plasmon and anapole modes in a hybrid metal-dielectric nanostructure. With the aid of vanishing dipole characteristics of the anapole and dark plasmons, the hybrid modes exhibit minimum far-field scattering and maximum near-field enhancement. The dark mode coupling in the metal-dielectric nanostructure offers a nonradiating air cavity with greatly improved field enhancement in a broadened band, thus providing a background-free experimental platform for spectroscopic applications. The proposed approach to dark plasmon excitation, i.e., via anapole, may boost practical exploitation of dark plasmons by allowing linearly polarized light illumination and scalable arrays of individual nanostructure units.

Nonradiating anapole states in nanophotonics: from fundamentals to applications

Nonradiating sources are nontrivial charge-current distributions that do not generate fields outside the source domain. The pursuit of their possible existence has fascinated several generations of physicists and triggered developments in various branches of science ranging from medical imaging to dark matter. Recently, one of the most fundamental types of nonradiating sources, named anapole states, has been realized in nanophotonics regime and soon spurred considerable research efforts and widespread interest. A series of astounding advances have been achieved within a very short period of time, uncovering the great potential of anapole states in many aspects such as lasing, sensing, metamaterials, and nonlinear optics. In this review, we provide a detailed account of anapole states in nanophotonics research, encompassing their basic concepts, historical origins, and new physical effects. We discuss the recent research frontiers in understanding and employing optical anapoles and provide an outlook for this vibrant field of research.

Design of anapole mode electromagnetic field enhancement structures for biosensing applications

The design of an all-dielectric nanoantenna based on nonradiating "anapole" modes is studied for biosensing applications in an aqueous environment, using FDTD electromagnetic simulation. The strictly confined electromagnetic field within a circular or rectangular opening at the center of a cylindrical silicon disk produces a single point electromagnetic hotspot with up to 6.5x enhancement of |E|, for the 630-650 nm wavelength range, and we can increase the value up to 25x by coupling additional electromagnetic energy from an underlying PEC-backed substrate. We characterize the effects of the substrate design and slot dimensions on the field enhancement magnitude, for devices operating in a water medium.

Ultrahigh-quality factor resonant dielectric metasurfaces based on hollow nanocuboids

In this work, a dielectric metasurface consisting of hollow dielectric nanocuboids, with ultrahigh quality factor, is theoretically proposed and demonstrated. The variation of the hole size of the cuboid allows for the tuning of the resonant anapole mode in the nanoparticles. The metasurface is designed to operate in two complementary modes, namely electromagnetically induced transparency and narrowband selective reflection. Thanks to the non-radiative nature of the anapole resonances, the minimal absorption losses of the dielectric materials, and the near-field coupling among the metasurface nanoparticles, a very high quality factor of Q=2.5×10⁶ is achieved. The resonators are characterized by a simple bulk geometry and the subwavelength dimensions of the metasurface permit operation in the non-diffractive regime. The high quality factors and strong energy confinement of the proposed devices open new avenues of research on light-matter interactions, which may find direct applications, e.g., in non-linear devices, biological sensors, laser cavities, and optical communications.

Multipolar passive cloaking by nonradiating anapole excitation

In this paper, we demonstrate the relation between cloaking effect and its nonradiating state by considering the destructive multipolar interaction between near-field scattering by bare object and surrounding coating located in its proximity. This cloaking effect is underpinned by anapole mode excitation and it occurs as destructive interference between the electric dipole moment, generated by a bare object (here a central metallic scatterer) and the toroidal moment, formed inside the cloak (a surrounding cluster of dielectric cylinders). Numerical results show how a cloaking effect based on the formation of the anapole mode can lead to an overall nonradiating metamolecule with all-dielectric materials in the coating region.

High-Q Fano resonances via direct excitation of an antisymmetric dark mode

The engineering of metal-insulator-metal metasurfaces (MSs) displaying sharp spectral features based on Fano-type interference between a symmetric bright mode and an antisymmetric dark mode is reported. The proposed mechanism for direct excitation of antisymmetric mode avoids the necessity of mode hybridization through near-field coupling. Modeling and experimental results bring evidence that such MSs operating in the microwave or terahertz domains provide greater flexibility for Fano resonance engineering and provide strong enhancement of the spectral selectivity factor. It is shown that the occurring Fano resonance interference is related to the broken eigenmode orthogonality in open systems and is independent of hybridization mechanism.

Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation

Nonradiating electromagnetic configurations in nanostructures open new horizons for applications due to two essential features: a lack of energy losses and invisibility to the propagating electromagnetic field. Such radiationless configurations form a basis for new types of nanophotonic devices, in which a strong electromagnetic field confinement can be achieved together with lossless interactions between nearby components. In our work, we present a new design of free-standing disk nanoantennas with nonradiating current distributions for the optical near-infrared range. We show a novel approach to creating nanoantennas by slicing III-V nanowires into standing disks using focused ion-beam milling. We experimentally demonstrate the suppression of the far-field radiation and the associated strong enhancement of the second-harmonic generation from the disk nanoantennas. With a theoretical analysis of the electromagnetic field distribution using multipole expansions in both spherical and Cartesian coordinates, we confirm that the demonstrated nonradiating configurations are anapoles. We expect that the presented procedure of designing and producing disk nanoantennas from nanowires becomes one of the standard approaches to fabricating controlled chains of standing nanodisks with different designs and configurations. These chains can be essential building blocks for new types of lasers and sensors with low power consumption.

Excitation of nonradiating magnetic anapole states with azimuthally polarized vector beams

Nonradiating current configurations have been drawing the attention of the physics community for many years. It has been demonstrated recently that dielectric nanoparticles provide a unique platform to host such nonradiating modes, called "anapoles". Here we study theoretically the excitation of such exotic anapole modes in silicon nanoparticles using structured light. Alternative illumination configurations, properly designed, are able to unlock hidden behavior of scatterers. Particularly, azimuthally polarized focused beams enable us to excite ideal anapole modes of magnetic type in dielectric nanoparticles. Firstly, we perform the decomposition of this type of excitation into its multipolar content and then we employ the T-matrix method to calculate the far-field scattering properties of nanoparticles illuminated by such beams. We propose several configuration schemes where magnetic anapole modes of simple or hybrid nature can be detected in silicon nanospheres, nanodisks and nanopillars.

Toroidal Localized Spoof Plasmons on Compact Metadisks

Localized spoof surface plasmons (LSSPs) have recently emerged as a new research frontier due to their unique properties and increasing applications. Despite the importance, most of the current researches only focus on electric/magnetic LSSPs. Very recent research has revealed that toroidal LSSPs, LSSPs modes with multipole toroidal moments, can be achieved at a point defect in a 2D groove metal array. However, this metamaterial shows the limitations of large volume and poor compatibility to photonic integrated circuits. To overcome the above challenges, here it is proposed and experimentally demonstrated compact planar metadisks based on split ring resonators to support the toroidal LSSPs at microwave frequencies. Additionally, it is experimentally demonstrated that the toroidal LSSPs resonance is very sensitive to the structure changes and the background medium. These might facilitate its utilization in the design and application of plasmonic deformation sensors and the refractive index sensors.

Optical Anapole Metamaterial

The toroidal dipole is a localized electromagnetic excitation independent from the familiar magnetic and electric dipoles. It corresponds to currents flowing along minor loops of a torus. Interference of radiating induced toroidal and electric dipoles leads to anapole, a nonradiating charge-current configuration. Interactions of induced toroidal dipoles with electromagnetic waves have recently been observed in artificial media at microwave, terahertz, and optical frequencies. Here, we demonstrate a quasi-planar plasmonic metamaterial, a combination of dumbbell aperture and vertical split-ring resonator, that exhibits transverse toroidal moment and resonant anapole behavior in the optical part of the spectrum upon excitation with a normally incident electromagnetic wave. Our results prove experimentally that toroidal modes and anapole modes can provide distinct and physically significant contributions to the absorption and dispersion of slabs of matter in the optical part of the spectrum in conventional transmission and reflection experiments.

Metamaterial engineered transparency due to the nullifying of multipole moments

Here we propose, to the best of our knowledge, a novel transparency effect in cylindrical all-dielectric metamaterials. We show that the cancellation of multipole moments of the same kind leads to almost zero radiation losses in all-dielectric metamaterials due to the counter-directed multipolar moments in metamolecule. The nullifying of multipoles, mainly dipoles, and suppression of higher multipoles, results in the ideal transmission of an incident wave through the designed metamaterial. The observed effect could pave the road to the new generation of light-manipulating transparent metadevices such as filters, waveguides, and cloaks.

A Toroidal Metamaterial Switch

Toroidal dipole is a localized electromagnetic excitation that plays an important role in determining the fundamental properties of matter due to its unique potential to excite nearly nonradiating charge-current configuration. Toroidal dipoles are recently discovered in metamaterial systems where it is shown that these dipoles manifest as poloidal currents on the surface of a torus and are distinctly different from the traditional electric and magnetic dipoles. Here, an active toroidal metamaterial switch is demonstrated in which the toroidal dipole can be dynamically switched to the fundamental electric dipole or magnetic dipole, through selective inclusion of active elements in a hybrid metamolecule design. Active switching of nonradiating toroidal configuration into highly radiating electric and magnetic dipoles can have significant impact in controlling the electromagnetic excitations in free space and matter that can have potential applications in designing efficient lasers, sensors, filters, and modulators.

Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States

Anapole states associated with the resonant suppression of electric-dipole scattering exhibit minimized extinction and maximized storage of electromagnetic energy inside a particle. Using numerical simulations, optical extinction spectroscopy, and amplitude-phase near-field mapping of silicon dielectric disks, we demonstrate high-order anapole states in the near-infrared wavelength range (900-1700 nm). We develop the procedure for unambiguously identifying anapole states by monitoring the normal component of the electric near-field and experimentally detect the first two anapole states as verified by far-field extinction spectroscopy and confirmed with the numerical simulations. We demonstrate that higher-order anapole states possess stronger energy concentration and narrower resonances, a remarkable feature that is advantageous for their applications in metasurfaces and nanophotonics components, such as nonlinear higher-harmonic generators and nanoscale lasers.

Rapid Detection of Infectious Envelope Proteins by Magnetoplasmonic Toroidal Metasensors

Unconventional characteristics of magnetic toroidal multipoles have triggered researchers to study these unique resonant phenomena by using both 3D and planar resonators under intense radiation. Here, going beyond conventional planar unit cells, we report on the observation of magnetic toroidal modes using artificially engineered multimetallic planar plasmonic resonators. The proposed microstructures consist of iron (Fe) and titanium (Ti) components acting as magnetic resonators and torus, respectively. Our numerical studies and following experimental verifications show that the proposed structures allow for excitation of toroidal dipoles in the terahertz (THz) domain with the experimental Q-factor of ∼18. Taking the advantage of high-Q toroidal line shape and its dependence on the environmental perturbations, we demonstrate that room-temperature toroidal metasurface is a reliable platform for immunosensing applications. As a proof of concept, we utilized our plasmonic metasurface to detect Zika-virus (ZIKV) envelope protein (with diameter of 40 nm) using a specific ZIKV antibody. The sharp toroidal resonant modes of the surface functionalized structures shift as a function of the ZIKV envelope protein for small concentrations (∼pM). The results of sensing experiments reveal rapid, accurate, and quantitative detection of envelope proteins with the limit of detection of ∼24.2 pg/mL and sensitivity of 6.47 GHz/log(pg/mL). We envision that the proposed toroidal metasurface opens new avenues for developing low-cost, and efficient THz plasmonic sensors for infection and targeted bioagent detection.

On the dynamic toroidal multipoles from localized electric current distributions

We analyze the dynamic toroidal multipoles and prove that they do not have an independent physical meaning with respect to their interaction with electromagnetic waves. We analytically show how the split into electric and toroidal parts causes the appearance of non-radiative components in each of the two parts. These non-radiative components, which cancel each other when both parts are summed, preclude the separate determination of each part by means of measurements of the radiation from the source or of its coupling to external electromagnetic waves. In other words, there is no toroidal radiation or independent toroidal electromagnetic coupling. The formal meaning of the toroidal multipoles is clear in our derivations. They are the higher order terms of an expansion of the multipolar coefficients of electric parity with respect to the electromagnetic size of the source.