Electromagnetic toroidal excitations in matter and free space

The Observation of High-Order Charge–Current Configurations in Plasmonic Meta-Atoms: A Numerical Approach

Living in a world of resonances, there have been significant progresses in the field of excitation of pronounced and multifunctional moments across a wide range of optical frequencies. Among all acknowledged resonances, the toroidal multipoles have received copious interest in recent years due to possessing inherent signatures in nature. As a fundamental member, toroidal dipole is a strongly localized electromagnetic excitation based on charge–current configurations, which can be squeezed into an extremely small spot. Although there have been extensive studies on the behavior and properties of toroidal dipoles in order to develop all-optical devices based on this technology, so far, all analyses are restricted to the first (1st) order toroidal dipoles. In this work, using a practical technique, we successfully observed exquisite multi-loop super-toroidal (MLST) spectral features in a planar multipixel metallodielectric meta-atom. Employing the theory behind the excitation of multi-loop currents, we numerically and theoretically demonstrated that a traditional toroidal dipole can be transformed into a super-toroidal moment by varying the dielectric permittivity of the capacitive gaps between proximal pixels. This understanding introduces a new approach for the excitation of complex multi-loop toroidal moments in plasmonic metamaterials with high sensitivity, applicable for various nanophotonics applications from sensing to filtering.

Double toroidal spoof localized surface plasmon resonance excited by two types of coupling mechanisms

The double toroidal spoof localized surface plasmons (LSPs) on combined split ring resonators (SRRs) are proposed and experimentally demonstrated at microwave frequencies. Based on conventional printed circuit board techniques on a dielectric substrate, the designed metamaterial clearly shows two toroidal spoof LSP resonances. Two toroidal spoof LSP resonances are excited due to the conductive coupling and magneto-inductive coupling, respectively. Both numerical simulations and experiments are in good agreement. It is shown that the toroidal spoof LSP resonance is sensitivie to the local dielectric environments. Hence, the combined SRRs may be used as plasmonic sensors and find potential applications in the microwave and terahertz frequencies.

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.

Exceptional singular resonance in gain mediated metamaterials

We study the scattering of optical field by a hybridized metamaterial with properly imprinted gain. We predict that an occasionally real-eigen valued singularity in the interaction matrix of the coupled dark-bright meta-molecule would produce a high-Q resonance. This effect is demonstrated in full-wave three-dimensional finite element optical simulation. Field is efficiently amplified at this resonance. Further investigation shows that the resonance is associated with an exceptional point. The difference of this exceptional singularity from other high-Q resonances such as the spectral singularities in the scattering or transfer matrixes of parity-time symmetric systems and the bound states in the continuum is discussed. The non-Hermitian nature of the exceptional singularity promises some nonlinear applications.

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.

Terahertz toroidal metamaterial with tunable properties

We present a tunable metamodulator to work at terahertz frequencies by employing the dependency of toroidal dipolar resonance on the conductivity of vanadium dioxide. Numerical results show that toroidal dipolar resonance in the proposed planar structure can be observed around 0.288 THz in transmission spectrum. From the distribution of the anti-phase current flowing in the symmetric split ring resonator, the formation of toroidal dipole is validated. Our design may have potential applications in advanced terahertz devices, such as filter, plasmonic sensor, and fast switch.

Active control of anapole states by structuring the phase-change alloy Ge2Sb2Te5

High-index dielectric nanoparticles supporting a distinct series of Mie resonances have enabled a new class of optical antennas with unprecedented functionalities. The great wealth of multipolar responses has not only brought in new physical insight but also spurred practical applications. However, how to make such a colorful resonance palette actively tunable is still elusive. Here, we demonstrate that the structured phase-change alloy Ge2Sb2Te5 (GST) can support a diverse set of multipolar Mie resonances with active tunability. By harnessing the dramatic optical contrast of GST, we realize broadband (Δλ/λ ~ 15%) mode shifting between an electric dipole resonance and an anapole state. Active control of higher-order anapoles and multimodal tuning are also investigated, which make the structured GST serve as a multispectral optical switch with high extinction contrasts (>6 dB). With all these findings, our study provides a new direction for realizing active nanophotonic devices.

Toroidal Dipole-Enhanced Third Harmonic Generation of Deep Ultraviolet Light Using Plasmonic Meta-atoms

The harmonic generation of light with plasmonic and all-dielectric nanostructures has gained much recent interest. This approach is especially promising for short wavelength (i.e., ultraviolet (UV)) generation, where conventional nonlinear crystals reach their limits both in transparency and in their ability to achieve phase-matching between the input and output fields. Here, we demonstrate that the third harmonic generation of deep UV light in an indium tin oxide (ITO) film can be substantially enhanced by a metasurface consisting of metallic toroidal meta-atoms covered with an alumina layer for protection against laser-induced damage. This approach combines the benefits of the large nonlinear susceptibility of ITO with the unique field enhancement properties of a toroidal metasurface. This ITO-meta-atom combination produces a third harmonic signal at a wavelength of 262 nm that is nominally five times larger than that of an ITO film patterned with a conventional hotspot-enhanced plasmonic dimer array. This result demonstrates the potential for toroidal meta-atoms as the active engineered element in a new generation of enhanced nonlinear optical materials and devices.

Non-Mie optical resonances in anisotropic biomineral nanoparticles

The optical properties of nanoparticles have attracted continuous attention owing to their high fundamental and applied importance across many disciplines. A recently emerged field of all-dielectric nanophotonics employs optically induced electric and magnetic Mie resonances in dielectric nanoparticles with a high refractive index. This property allows obtaining additional valuable degrees of freedom to control the optical responses of nanophotonic structures. Here we propose a conceptually distinct approach towards reaching optical resonances in dielectric nanoparticles. We show that, lacking conventional Mie resonances, low-index nanoparticles can exhibit a novel anisotropy-induced family of non-Mie eigenmodes. Specifically, we investigate light interactions with calcite and vaterite nanospheres and compare them with the Mie scattering by a fused silica sphere. Having close permittivities and the same dimensions, these particles exhibit significantly different scattering behavior owing to their internal structure. While a fused silica sphere does not demonstrate any spectral features, the uniaxial structure of the permittivity tensor for calcite and the non-diagonal permittivity tensor for vaterite result in a set of distinguishable peaks in scattering spectra. Multipole decomposition and eigenmode analysis reveal that these peaks are associated with a new family of electric and magnetic resonances. We identify magnetic dipole modes of ordinary, extraordinary and hybrid polarization as well as complex electric dipole resonances, featuring a significant toroidal electric dipole moment. As both vaterite and calcite are biominerals, naturally synthesized and exploited by a variety of living organisms, our results provide an indispensable toolbox for understanding and elucidating the mechanisms behind the optical functionalities of true biological systems.

Pairing Toroidal and Magnetic Dipole Resonances in Elliptic Dielectric Rod Metasurfaces for Reconfigurable Wavefront Manipulation in Reflection

A novel approach for reconfigurable wavefront manipulation with gradient metasurfaces based on permittivity-modulated elliptic dielectric rods is proposed. It is shown that the required 2π phase span in the local electromagnetic response of the metasurface can be achieved by pairing the lowest magnetic dipole Mie resonance with a toroidal dipole Mie resonance, instead of using the lowest two Mie resonances corresponding to fundamental electric and magnetic dipole resonances as customarily exercised. This approach allows for the precise matching of both the resonance frequencies and quality factors. Moreover, the accurate matching is preserved if the rod permittivity is varied, allowing for constructing reconfigurable gradient metasurfaces by locally modulating the permittivity in each rod. Highly efficient tunable beam steering and beam focusing with ultrashort focal lengths are numerically demonstrated, highlighting the advantage of the low-profile metasurfaces over bulky conventional lenses. Notably, despite using a matched pair of Mie resonances, the presence of an electric polarizability background allows to perform the wavefront shaping operations in reflection, rather than transmission. This has the advantage that any control circuitry necessary in an experimental realization can be accommodated behind the metasurface without affecting the electromagnetic response.

Dual Toroidal Dipole Resonance Metamaterials under a Terahertz Domain

We proposed and fabricated a flexible, planar, U-shape-modified structure metamaterial (MM) that was composed of two metallic pattern layers separated by a polyimide layer, where each metallic pattern layer consists of two U-shaped split ring resonators (USRRs). The coupling effect between the two USRRs in the same metallic layer was vital to the formation of dual toroidal dipole (TD) resonances. The measured and simulated results showed that both low quality factor (Q) (~1.82) and high Q (~10.31) TD resonances were acquired synchronously at two different frequencies in the MMs by adjusting the distance between the two coplanar USRRs. With the interaction of the USRRs, the energy levels of the USRRs were split into inductance-capacitance (LC)-induced TD resonance at low frequency and dipole-induced TD resonance at high frequency. Thus, the electric multipole interaction played an important role in determining the energy level of the TD resonance. The better strength of the high frequency TD resonance can be confined to an electromagnetic field inside a smaller circular region, and thus, a higher Q was obtained. In order to investigate the TD mechanism more in depth, the power of the electric dipole, magnetic dipole, electric circular dipole, and TD were quantitatively calculated. Dual TD MMs on a freestanding substrate will have potential applications in functional terahertz devices for practical applications.

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.

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.

Bio-field array: a dielectrophoretic electromagnetic toroidal excitation to restore and maintain the golden ratio in human erythrocytes

Erythrocytes must maintain a biconcave discoid shape in order to efficiently deliver oxygen (O2 ) molecules and to recycle carbon dioxide (CO2 ) molecules. The erythrocyte is a small toroidal dielectrophoretic (DEP) electromagnetic field (EMF) driven cell that maintains its zeta potential (ζ) with a dielectric constant (ԑ) between a negatively charged plasma membrane surface and the positively charged adjacent Stern layer. Here, we propose that zeta potential is also driven by both ferroelectric influences (chloride ion) and ferromagnetic influences (serum iron driven). The Golden Ratio, a function of Phi φ, offers a geometrical mathematical measure within the distinct and desired curvature of the red blood cell that is governed by this zeta potential and is required for the efficient recycling of CO2 in our bodies. The Bio-Field Array (BFA) shows potential to both drive/fuel the zeta potential and restore the Golden Ratio in human erythrocytes thereby leading to more efficient recycling of CO2 . Live Blood Analyses and serum CO2 levels from twenty human subjects that participated in immersion therapy sessions with the BFA for 2 weeks (six sessions) were analyzed. Live Blood Analyses (LBA) and serum blood analyses performed before and after the BFA immersion therapy sessions in the BFA pilot study participants showed reversal of erythrocyte rheological alterations (per RBC metric; P = 0.00000075), a morphological return to the Golden Ratio and a significant decrease in serum CO2 (P = 0.017) in these participants. Immersion therapy sessions with the BFA show potential to modulate zeta potential, restore this newly defined Golden Ratio and reduce rheological alterations in human erythrocytes.

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.

All-silicon-based nano-antennas for wavelength and polarization demultiplexing

We propose an all-silicon-based nano-antenna that functions as not only a wavelength demultiplexer but also a polarization one. The nano-antenna is composed of two silicon cuboids with the same length and height but with different widths. The asymmetric structure of the nano-antenna with respect to the electric field of the incident light induced an electric dipole component in the propagation direction of the incident light. The interference between this electric dipole and the magnetic dipole induced by the magnetic field parallel to the long side of the cuboids is exploited to manipulate the radiation direction of the nano-antenna. The radiation direction of the nano-antenna at a certain wavelength depends strongly on the phase difference between the electric and magnetic dipoles interacting coherently, offering us the opportunity to realize wavelength demultiplexing. By varying the polarization of the incident light, the interference of the magnetic dipole induced by the asymmetry of the nano-antenna and the electric dipole induced by the electric field parallel to the long side of the cuboids can also be used to realize polarization demultiplexing in a certain wavelength range. More interestingly, the interference between the dipole and quadrupole modes of the nano-antenna can be utilized to shape the radiation directivity of the nano-antenna. We demonstrate numerically that radiation with adjustable direction and high directivity can be realized in such a nano-antenna which is compatible with the current fabrication technology of silicon chips.

The correct and unusual coordinate transformation rules for electromagnetic quadrupoles

Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat space-time due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived, which are particularly unusual as they involve second derivatives of the coordinate transformation and an integral. Transformations involving integrals have not been seen before. This is significantly different from the familiar transformation rules for a dipole, where the components transform as tensors. It enables quadrupoles to be correctly defined in general relativity and to prescribe the equations of motion for a quadrupole in a coordinate system adapted to its motion and then transform them to the laboratory coordinates. An example is given of another unusual feature: a quadrupole which is free of dipole terms in polar coordinates has dipole terms in Cartesian coordinates. It is shown that dipoles, electric dipoles, quadrupoles and electric quadrupoles can be defined without reference to a metric and in a coordinates-free manner. This is particularly useful given their complicated coordinate transformation.

High-quality-factor multiple Fano resonances for refractive index sensing

We design and numerically analyze a high-quality (Q)-factor, high modulation depth, multiple Fano resonance device based on periodical asymmetric paired bars in the near-infrared regime. There are four sharp Fano peaks arising from the interference between subradiant modes and the magnetic dipole resonance mode that can be easily tailored by adjusting different geometric parameters. The maximal Q-factor can exceed 10⁵ in magnitude, and the modulation depths ΔT can reach nearly 100%. Combining the narrow resonance line-widths with strong near-field confinement, we demonstrate an optical refractive index sensor with a sensitivity of 370 nm/RIU and a figure of merit of 2846. This study may provide a further step in sensing, lasing, and nonlinear optics.

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.

Giant intrinsic chiro-optical activity in planar dielectric nanostructures

The strong optical chirality arising from certain synthetic metamaterials has important and widespread applications in polarization optics, stereochemistry and spintronics. However, these intrinsically chiral metamaterials are restricted to a complicated three-dimensional (3D) geometry, which leads to significant fabrication challenges, particularly at visible wavelengths. Their planar two-dimensional (2D) counterparts are limited by symmetry considerations to operation at oblique angles (extrinsic chirality) and possess significantly weaker chiro-optical responses close to normal incidence. Here, we address the challenge of realizing strong intrinsic chirality from thin, planar dielectric nanostructures. Most notably, we experimentally achieve near-unity circular dichroism with ~90% of the light with the chosen helicity being transmitted at a wavelength of 540 nm. This is the highest value demonstrated to date for any geometry in the visible spectrum. We interpret this result within the charge-current multipole expansion framework and show that the excitation of higher-order multipoles is responsible for the giant circular dichroism. These experimental results enable the realization of high-performance miniaturized chiro-optical components in a scalable manner at optical frequencies.

Extreme sensitive metasensor for targeted biomarkers identification using colloidal nanoparticles-integrated plasmonic unit cells

Engineered terahertz (THz) plasmonic metamaterials have emerged as promising platforms for quick infection diagnosis, cost-effective and real-time pharmacology applications owing to their non-destructive and harmless interaction with biological tissues in both in vivo and in vitro assays. As a recent member of THz metamaterials family, toroidal metamaterials have been demonstrated to be supporting high-quality sharp resonance modes. Here we introduce a THz metasensor based on a plasmonic surface consisting of metamolecules that support ultra-narrow toroidal resonances excited by the incident radiation and demonstrate detection of an ultralow concertation targeted biomarker. The toroidal plasmonic metasurface was designed and optimized through extensive numerical studies and fabricated by standard microfabrication techniques. The surface then functionalized by immobilizing the antibody for virus-envelope proteins (ZIKV-EPs) for selective sensing. We sensed and quantified the ZIKV-EP in the assays by measuring the spectral shifts of the toroidal resonances while varying the concentration. In an improved protocol, we introduced gold nanoparticles (GNPs) decorated with the same antibodies onto the metamolecules and monitored the resonance shifts for the same concentrations. Our studies verified that the presence of GNPs enhances capturing of biomarker molecules in the surrounding medium of the metamaterial. By measuring the shift of the toroidal dipolar momentum (up to Δω~0.35 cm^-1) for different concentrations of the biomarker proteins, we analyzed the sensitivity, repeatability, and limit of detection (LoD) of the proposed toroidal THz metasensor. The results show that up to 100-fold sensitivity enhancement can be obtained by utilizing plasmonic nanoparticles-integrated toroidal metamolecules in comparison to analogous devices. This approach allows for detection of low molecular-weight biomolecules (≈13 kDa) in diluted solutions using toroidal THz plasmonic unit cells.

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.

Electrically Tunable Fano Resonance from the Coupling between Interband Transition in Monolayer Graphene and Magnetic Dipole in Metamaterials

Fano resonance modulated effectively by external perturbations can find more flexible and important applications in practice. We theoretically study electrically tunable Fano resonance with asymmetric line shape over an extremely narrow frequency range in the reflection spectra of metamaterials. The metamaterials are composed of a metal nanodisk array on graphene, a dielectric spacer, and a metal substrate. The near-field plasmon hybridization between individual metal nanodisks and the metal substrate results into the excitation of a broad magnetic dipole. There exists a narrow interband transition dependent of Fermi energy E_f, which manifests itself as a sharp spectral feature in the effective permittivity ε_g of graphene. The coupling of the narrow interband transition to the broad magnetic dipole leads to the appearance of Fano resonance, which can be electrically tuned by applying a bias voltage to graphene to change E_f. The Fano resonance will shift obviously and its asymmetric line shape will become more pronounced, when E_f is changed for the narrow interband transition to progressively approach the broad magnetic dipole.

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.

Asymmetric Nanoantennas for Ultrahigh Angle Broadband Visible Light Bending

Wavefront manipulation in metasurfaces typically relies on phase mapping with a finite number of elements. In particular, a discretized linear phase profile may be used to obtain a beam bending functionality. However, discretization limits the applicability of this approach for high angle bending due to the drastic efficiency drop when the phase is mapped by a small number of elements. In this work, we discuss a novel concept for energy redistribution in diffraction gratings and its application in the visible spectrum range, which helps overcome the constraints of ultrahigh angle (above 80°) beam bending. Arranging asymmetric dielectric nanoantennas into diffractive gratings, we show that one can efficiently redistribute the power between the grating orders at will. This is achieved by precise engineering of the scattering pattern of the nanoantennas. The concept is numerically and experimentally demonstrated at visible frequencies using several designs of TiO₂ (titanium dioxide) nanoantennas for medium (∼55°) and high (∼80°) angle light bending. Results show efficient broadband visible-light operation (blue and green range) of transmissive devices, reaching efficiencies of ∼90% and 50%, respectively, at the optimized wavelength. The presented design concept is general and can be applied for both transmission and reflection operation at any desired wavelength and polarization.

Generalized Magnetic Mirrors

We propose generalized magnetic mirrors that can be achieved by excitations of sole electric resonances. Conventional approaches to obtain magnetic mirrors rely heavily on exciting the fundamental magnetic dipoles, whereas here we reveal that, besides magnetic resonances, electric resonances of higher orders can be also employed to obtain highly efficient magnetic mirrors. Based on the electromagnetic duality, it is also shown that electric mirrors can be achieved by exciting magnetic resonances. We provide direct demonstrations of the generalized mirrors proposed in a simple system of a one-dimensional periodic array of all-dielectric wires, which may shed new light on many advanced fields of photonics related to resonant multipolar excitations and interferences.

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.

Toroidal response in all-dielectric metamaterials based on water

We experimentally demonstrate for the first time the toroidal dipolar response in metamaterials based on clusters of cylindrical dielectric particles in microwave frequency range. Instead of expensive ceramic elements we used distilled water with permittivity at room temperature is about 75, while the dielectric loss tangent is not large at frequencies up to 4 GHz. Moreover, we show all-dielectric metamaterial consisting of water box with hollow tubes which is more practical for future applications. Our findings also demonstrate that the proposed ideas can be applicable in optics with low-index dielectrics.

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.

Simultaneous excitation of extremely high-Q-factor trapped and octupolar modes in terahertz metamaterials

Achieving high-Q-factor resonances allows dramatic enhancement of performance of many plasmonic devices. However, the excitation of high-Q-factor resonance, especially multiple high-Q-factor resonances, has been a big challenge in traditional metamaterials due to the ohmic and radiation losses. Here, we experimentally demonstrate simultaneous excitation of double extremely sharp resonances in a terahertz metamaterial composed of mirror-symmetric-broken double split ring resonators (MBDSRRs). In a regular mirror-arranged SRR array, only the low-Q-factor dipole resonance can be excited with the external electric field perpendicular to the SRR gap. Breaking the mirror-symmetry of the metamaterial leads to the occurrence of two distinct otherwise inaccessible ultrahigh-Q-factor modes, which consists of one trapped mode in addition to an octupolar mode. By tuning the asymmetry parameter, the Q factor of the trapped mode can be linearly modulated, while the Q factor of the octupolar mode can be tailored exponentially. For specific degree of asymmetry, our simulations revealed a significantly high Q factor (Q>100) for the octupolar mode, which is more than one order of magnitude larger than that of conventional metamaterials. The mirror-symmetry-broken metamaterial offers the advantage of enabling access to two distinct high-Q-factor resonances which could be exploited for ultrasensitive sensors, multiband filters, and slow light devices.

Optically resonant dielectric nanostructures

Rapid progress in nanophotonics is driven by the ability of optically resonant nanostructures to enhance near-field effects controlling far-field scattering through intermodal interference. A majority of such effects are usually associated with plasmonic nanostructures. Recently, a new branch of nanophotonics has emerged that seeks to manipulate the strong, optically induced electric and magnetic Mie resonances in dielectric nanoparticles with high refractive index. In the design of optical nanoantennas and metasurfaces, dielectric nanoparticles offer the opportunity for reducing dissipative losses and achieving large resonant enhancement of both electric and magnetic fields. We review this rapidly developing field and demonstrate that the magnetic response of dielectric nanostructures can lead to novel physical effects and applications.

Anapole nanolasers for mode-locking and ultrafast pulse generation

Nanophotonics is a rapidly developing field of research with many suggestions for a design of nanoantennas, sensors and miniature metadevices. Despite many proposals for passive nanophotonic devices, the efficient coupling of light to nanoscale optical structures remains a major challenge. In this article, we propose a nanoscale laser based on a tightly confined anapole mode. By harnessing the non-radiating nature of the anapole state, we show how to engineer nanolasers based on InGaAs nanodisks as on-chip sources with unique optical properties. Leveraging on the near-field character of anapole modes, we demonstrate a spontaneously polarized nanolaser able to couple light into waveguide channels with four orders of magnitude intensity than classical nanolasers, as well as the generation of ultrafast (of 100 fs) pulses via spontaneous mode locking of several anapoles. Anapole nanolasers offer an attractive platform for monolithically integrated, silicon photonics sources for advanced and efficient nanoscale circuitry.

Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance

A planar terahertz metamaterial consisting of square split ring resonators is proposed, and the excitation of toroidal dipolar resonance is demonstrated. Moreover, we theoretically investigate the strong interaction between graphene and toroidal dipolar resonance of the metamaterial. By varying its Fermi energy, the simulations show that graphene can actively modulate the transmission amplitude of toroidal dipolar resonance and even switch it off. The interaction of the toroidal dipolar resonance with monolayer graphene further highlights the ultrasensitive sensing characteristic of the planar metamaterial, which can be utilized for other graphene-like two-dimensional materials. These intriguing properties of the proposed metamaterial may have potential applications in terahertz modulators and ultrasensitive sensors.

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.

High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials

With unusual electromagnetic radiation properties and great application potentials, optical toroidal moments have received increasing interest in recent years. 3D metamaterials composed of split ring resonators with specific orientations in micro-/nanoscale are a perfect choice for toroidal moment realization in optical frequency considering the excellent magnetic confinement and quality factor, which, unfortunately, are currently beyond the reach of existing micro-/nanofabrication techniques. Here, a 3D toroidal metamaterial operating in mid-infrared region constructed by metal patterns and dielectric frameworks is designed, by which high-quality-factor toroidal resonance is observed experimentally. The toroidal dipole excitation is confirmed numerically and further demonstrated by phase analysis. Furthermore, the far-field radiation intensity of the excited toroidal dipoles can be adjusted to be predominant among other multipoles by just tuning the incident angle. The related processing method expands the capability of focused ion beam folding technologies greatly, especially in 3D metamaterial fabrication, showing great flexibility and nanoscale controllability on structure size, position, and orientation.

Blueshift and phase tunability in planar THz metamaterials: the role of losses and toroidal dipole contribution

We propose a model of tunable THz metamaterials. The main advantage is the blueshift of resonance and phase tunability due to inductive coupling in planar metallic metamolecules with incorporated silicon wires. We discuss the role of losses and toroidal dipole contribution to metamaterial response.

Ideal Magnetic Dipole Scattering

We introduce the concept of tunable ideal magnetic dipole scattering, where a nonmagnetic nanoparticle scatters light as a pure magnetic dipole. High refractive index subwavelength nanoparticles usually support both electric and magnetic dipole responses. Thus, to achieve ideal magnetic dipole scattering one has to suppress the electric dipole response. Such a possibility was recently demonstrated for the so-called anapole mode, which is associated with zero electric dipole scattering. By spectrally overlapping the magnetic dipole resonance with the anapole mode, we achieve ideal magnetic dipole scattering in the far field with tunable strong scattering resonances in the near infrared spectrum. We demonstrate that such a condition can be realized at least for two subwavelength geometries. One of them is a core-shell nanosphere consisting of a Au core and silicon shell. It can be also achieved in other geometries, including nanodisks, which are compatible with current nanofabrication technology.

Nontrivial nonradiating all-dielectric anapole

Dynamic anapole is a promising element for future nonradiating devices, such as cloaked sources and sensors, quantum emitters, and especially the sources for observing dynamic Aharonov-Bohm effect. However, the anapole response can be damped by the Joule losses. In this paper we theoretically propose and experimentally demonstrate a novel type of active all-dielectric source, which is in some sense, realizes the elementary anapole of Afanasiev, and study its radiative/nonradiative regimes in the microwave range.

Toroidal Dipolar Excitation in Metamaterials Consisting of Metal nanodisks and a Dielectrc Spacer on Metal Substrate

We have investigated numerically toroidal dipolar excitation at optical frequency in metamaterials whose unit cell consists of three identical Ag nanodisks and a SiO₂ spacer on Ag substrate. The near-field plasmon hybridization between individual Ag nanodisks and substrate forms three magnetic dipolar resonances, at normal incidence of plane electromagnetic waves. The strong coupling among three magnetic dipolar resonances leads to the toroidal dipolar excitation, when space-inversion symmetry is broke along the polarization direction of incident light. The influences of some geometrical parameters on the resonance frequency and the excitation strength of toroidal dipolar mode are studied in detail. The radiated power from toroidal dipole is also compared with that from conventional electric and magnetic multipoles.

Suppression of scattering for small dielectric particles: anapole mode and invisibility

We reveal that an isotropic, homogeneous, subwavelength particle with high refractive index can produce ultra-small total scattering. This effect, which follows from the inhibition of the electric dipole radiation, can be identified as a Fano resonance in the scattering efficiency and is associated with the excitation of an anapole mode in the particle. This anapole mode is non-radiative and emerges from the destructive interference of electric and toroidal dipoles. The invisibility effect could be useful for the design of highly transparent optical materials.This article is part of the themed issue 'New horizons for nanophotonics'.

Multipolar interference effects in nanophotonics

Scattering of electromagnetic waves by an arbitrary nanoscale object can be characterized by a multipole decomposition of the electromagnetic field that allows one to describe the scattering intensity and radiation pattern through interferences of dominating multipole modes excited. In modern nanophotonics, both generation and interference of multipole modes start to play an indispensable role, and they enable nanoscale manipulation of light with many related applications. Here, we review the multipolar interference effects in metallic, metal-dielectric and dielectric nanostructures, and suggest a comprehensive view on many phenomena involving the interferences of electric, magnetic and toroidal multipoles, which drive a number of recently discussed effects in nanophotonics such as unidirectional scattering, effective optical antiferromagnetism, generalized Kerker scattering with controlled angular patterns, generalized Brewster angle, and non-radiating optical anapoles. We further discuss other types of possible multipolar interference effects not yet exploited in the literature and envisage the prospect of achieving more flexible and advanced nanoscale control of light relying on the concepts of multipolar interference through full phase and amplitude engineering.This article is part of the themed issue 'New horizons for nanophotonics'.

Coherent selection of invisible high-order electromagnetic excitations

Far-field spectroscopy and mapping of electromagnetic near-field distribution are the two dominant tools for analysis and characterization of the electromagnetic response in nanophotonics. Despite the widespread use, these methods can fail at identifying weak electromagnetic excitations masked by stronger neighboring excitations. This is particularly problematic in ultrafast nanophotonics, including optical sensing, nonlinear optics and nanolasers, where the broad resonant modes can overlap to a significant degree. Here, using plasmonic metamaterials, we demonstrate that coherent spectroscopy can conveniently isolate and detect such hidden high-order photonic excitations. Our results establish that the coherent spectroscopy is a powerful new tool. It complements the conventional methods for analysis of the electromagnetic response, and provides a new route to designing and characterizing novel photonic devices and materials.

Sharp Toroidal Resonances in Planar Terahertz Metasurfaces

A toroidal dipole in metasurfaces provides an alternate approach for the excitation of high-Q resonances. In contrast to conventional multipoles, the toroidal dipole interaction strength depends on the time derivative of the surrounding electric field. A characteristic feature of toroidal dipoles is tightly confined loops of oscillating magnetic field that curl around the fictitious arrow of the toroidal dipole vector.

Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances

Strong Mie-type magnetic dipole resonances in all-dielectric nanostructures provide novel opportunities for enhancing nonlinear effects at the nanoscale due to the intense electric and magnetic fields trapped within the individual nanoparticles. Here we study third-harmonic generation from quadrumers of silicon nanodisks supporting high-quality collective modes associated with the magnetic Fano resonance. We observe nontrivial wavelength and angular dependencies of the generated harmonic signal featuring a multifold enhancement of the nonlinear response in oligomeric systems.