Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible

Highly efficient vortex generation at the nanoscale

Control of the angular momentum of light at the nanoscale is critical for many applications of subwavelength photonics, such as high-capacity optical communications devices, super-resolution imaging and optical trapping. However, conventional approaches to generate optical vortices suffer from either low efficiency or relatively large device footprints. Here we show a new strategy for vortex generation at the nanoscale that surpasses single-pixel phase control. We reveal that interaction between neighbouring nanopillars of a meta-quadrumer can tailor both the intensity and phase of the transmitted light. Consequently, a subwavelength nanopillar quadrumer is sufficient to cover a 2lπ phase change, thus efficiently converting incident light into high-purity optical vortices with different topological charges l. Benefiting from the nanoscale footprint of the meta-quadrumers, we demonstrate high-density vortex beam arrays and high-dimensional information encryption, bringing a new degree of freedom to many designs of meta-devices.

Electron Beam Induced Circularly Polarized Light Emission of Chiral Gold Nanohelices

Chiral plasmonic nanostructures possess a chiroptical response orders of magnitude stronger than that of natural biomolecular systems, making them highly promising for a wide range of biochemical, medical, and physical applications. Despite extensive efforts to artificially create and tune the chiroptical properties of chiral nanostructures through compositional and geometrical modifications, a fundamental understanding of their underlying mechanisms remains limited. In this study, we present a comprehensive investigation of individual gold nanohelices by using advanced analytical electron microscopy techniques. Our results, as determined by angle-resolved cathodoluminescence polarimetry measurements, reveal a strong correlation between the circular polarization state of the emitted far-field radiation and the handedness of the chiral nanostructure in terms of both its dominant circularity and directional intensity distribution. Further analyses, including electron energy-loss measurements and numerical simulations, demonstrate that this correlation is driven by longitudinal plasmonic modes that oscillate along the helical windings, much like straight nanorods of equal strength and length. However, due to the three-dimensional shape of the structures, these longitudinal modes induce dipolar transverse modes with charge oscillations along the short axis of the helices for certain resonance energies. Their radiative decay leads to observed emission in the visible range. Our findings provide insight into the radiative properties and underlying mechanisms of chiral plasmonic nanostructures and enable their future development and application in a wide range of fields, such as nano-optics, metamaterials, molecular physics, biochemistry, and, most promising, chiral sensing via plasmonically enhanced chiral optical spectroscopy techniques.

Enhancing Faraday and Kerr rotations based on the toroidal dipole mode in an all-dielectric magneto-optical metasurface

The magneto-optical Faraday and Kerr effects are widely used in modern optical devices. In this Letter, we propose an all-dielectric metasurface composed of perforated magneto-optical thin films, which can support the highly confined toroidal dipole resonance and provide full overlap between the localized electromagnetic field and the thin film, and consequently enhance the magneto-optical effects to an unprecedented degree. The numerical results based on the finite element method show that the Faraday and Kerr rotations can reach -13.59° and 8.19° in the vicinity of toroidal dipole resonance, which are 21.2 and 32.8 times stronger than those in the equivalent thickness of thin films. In addition, we design an environment refractive index sensor based on the resonantly enhanced Faraday and Kerr rotations, with sensitivities of 62.96 nm/RIU and 73.16 nm/RIU, and the corresponding maximum figures of merit 132.22°/RIU and 429.45°/RIU, respectively. This work provides a new, to the best of our knowledge, strategy for enhancing the magneto-optical effects at nanoscale, and paves the way for the research and development of magneto-optical metadevices such as sensors, memories, and circuits.

Polarization-selective narrow band dual-toroidal-dipole resonances in a symmetry-broken dielectric tetramer metamaterial

Here we propose a metasurface consisting of symmetry-broken dielectric tetramer arrays, which can generate polarization-selective dual-band toroidal dipole resonances (TDR) with ultra-narrow linewidth in the near-infrared region. We found, by breaking the C_4v symmetry of the tetramer arrays, two narrow-band TDRs can be created with the linewidth reaching ∼ 1.5 nm. Multipolar decomposition of scattering power and electromagnetic field distribution calculations confirm the nature of TDRs. A 100% modulation depth in light absorption and selective field confinement has been demonstrated theoretically by simply changing the polarization orientation of the exciting light. Intriguingly, it is also found that absorption responses of TDRs on polarization angle follow the equation of Malus' law in this metasurface. Furthermore, the dual-band toroidal resonances are proposed to sense the birefringence of an anisotropic medium. Such polarization-tunable dual toroidal dipole resonances with ultra-narrow bandwidth offered by this structure may find potential applications in optical switching, storage, polarization detection, and light emitting devices.

Plasmonic vortices for tunable manipulation of target particles, using arrays of elliptical holes in a gold layer

Here, we numerically prove that light with linear polarization can be coupled to surface plasmon polaritons at an elliptical hole perforated in a gold layer to generate plasmonic vortex (PV). Benefiting from the smooth variation of the minor to major ellipse axes, a gradual variation in the phase profile of the generated PV is achieved. Regarding this, three types of independent arrays of elliptical holes are presented, which can produce uniform and high quality PVs with different topological charges at the center of the arrays. The first array can produce PV with topological charges of + 1 and - 1, depending on the polarization orientation of the incident light. In the second one, the topological charge of the PV can be switched between 0 and + 2, by switching the polarization direction of the incident light. In the third array, a robust PV with topological charge of + 1 is generated independent of possible tolerances in the polarization orientation. In order to use the generated PVs for plasmonic tweezing application, there are side fringes around the central vortex of the arrays that should be eliminated. To produce a single vortex, we propose metal-insulator-metal (MIM) structures, screening excessive fringes and allowing the central PVs to leak out. It is also demonstrated by simulation that target particles, such as gold and polystyrene spheres of subwavelength dimensions, can be efficiently manipulated by our MIM designs, suitable for different applications including local mixing, and applying switchable torque or force to target particles to explore their complete elastic characteristics.

Toroidal Dipole Excitation in Metamaterial Perfect Absorber Consisting of Dielectric Nanodisks Quadrumer Clusters and Spacer on Metal Substrate

We proposed an infrared narrowband metamaterial perfect absorber (MPA) which is induced by toroidal dipole resonance in a dielectric-metal hybrid system. The MPA is composed of amorphous-silicon (a-Si) nanodisk quadrumer clusters, dielectric spacer, and Au substrate, where the dielectric spacer is inserted between Si disk quadrumer and Au substrate. Near field distribution and multipole decomposition of far-field, scattering powers show that toroidal dipole mode is formed by opposite phase magnetic dipoles in neighboring Si nanodisks. The effects of geometric and material parameters on absorption characteristics were explored. The sensing performance of the MPA was also evaluated. The proposed MPA has potential applications in air sensing applications. Since the nanodisks quadrumer of the MPA retains C4v symmetry, perfect absorption band is polarization independent. Furthermore, the absorption quality factor of the hybrid dielectric-metal hybrid absorber is higher than that of all-metal perfect absorbers, thanks to the low loss feature of the dielectric resonator.

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.

Benchmarking Density Functional Approximations for Diamagnetic and Paramagnetic Molecules in Nonuniform Magnetic Fields

In this article, correlated studies on a test set of 36 small molecules are carried out with both wavefunction (HF, MP2, CCSD) and density functional (LDA, KT3, cTPSS, cM06-L) methods. The effect of correlation on exotic response properties such as molecular electronic anapole susceptibilities is studied and the performance of the various density functional approximations are benchmarked against CCSD and/or MP2. Atoms and molecules are traditionally classified into "diamagnetic" and "paramagnetic" based on their isotropic response to uniform magnetic fields. However, in this article, we propose a more fine-grained classification of molecular systems on the basis of their response to generally nonuniform magnetic fields. The relation of orientation to different qualitative responses is also considered.

Probing plasmonic excitation mechanisms and far-field radiation of single-crystalline gold tapers with electrons

Conical metallic tapers represent an intriguing subclass of metallic nanostructures, as their plasmonic properties show interesting characteristics in strong correlation to their geometrical properties. This is important for possible applications such as in the field of scanning optical microscopy, as favourable plasmonic resonance behaviour can be tailored by optimizing structural parameters like surface roughness or opening angle. Here, we review our recent studies, where single-crystalline gold tapers were investigated experimentally by means of electron energy-loss and cathodoluminescence spectroscopy techniques inside electron microscopes, supported by theoretical finite-difference time-domain calculations. Through the study of tapers with various opening angles, the underlying resonance mechanisms are discussed. This article is part of a discussion meeting issue 'Dynamic in situ microscopy relating structure and function'.

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.

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.

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.

Magnetic toroidal dipole response in individual all-dielectric nanodisk clusters

Multipole electromagnetic resonances and their couplings are of crucial importance for both the fundamental understanding of light scattering by high-index all-dielectric nanostructures and lots of nanophotonic applications based on those nanostructures. Here, we show that magnetic dipole modes in a dielectric nanodisk cluster can easily form a magnetic toroidal dipole (MTD) mode. The cluster consists of five silicon nanodisks, where each nanodisk holds a magnetic dipole mode. These magnetic dipole modes can collectively couple with each other and form a MTD mode under suitable excitation. The MTD mode is confirmed by multipole expansion calculations and near field distributions, where two closed loops of magnetic field with opposite directions are seen. The response of the MTD is strong and comparable to that of a common electric dipole or magnetic dipole mode. It is also found that the MTD resonance is accompanied by an electric toroidal quadrupole mode in the cluster. The MTD mode is tunable by varying the geometries. We also fabricated silicon nanoparticle clusters and verified the MTD mode in the experiment. Our results illustrate the controllable excitation of strong high-order electromagnetic modes and these modes may open new opportunities for light manipulation at the nanoscale.

Dual-toroidal dipole excitation on permittivity-asymmetric dielectric metasurfaces

Magnetic and electric toroidal dipoles possess interesting properties differing from traditional electric and magnetic dipoles. In order to generate both the magnetic and electric toroidal dipoles simultaneously in one single structure, a permittivity-asymmetric dielectric metasurface is proposed, which is composed of clusters of four high-index dielectric nano-disks with asymmetric permittivity distribution. These two types of toroidal dipole responses can be separately observed at different spectral positions. This study reveals that symmetry-breaking in a broad sense is crucial for exciting toroidal responses, and the proposed metasurface points to a unique routine of exciting and enhancing the toroidal responses, which may be used to realize efficient light-matter interaction in the area of meta-optics.

Direct Observation of Infrared Plasmonic Fano Antiresonances by a Nanoscale Electron Probe

In this Letter, we exploit recent breakthroughs in monochromated aberration-corrected scanning transmission electron microscopy (STEM) to resolve infrared plasmonic Fano antiresonances in individual nanofabricated disk-rod dimers. Using a combination of electron energy-loss spectroscopy and theoretical modeling, we investigate and characterize a subspace of the weak coupling regime between quasidiscrete and quasicontinuum localized surface plasmon resonances where infrared plasmonic Fano antiresonances appear. This work illustrates the capability of STEM instrumentation to experimentally observe nanoscale plasmonic responses that were previously the domain only of higher-resolution infrared spectroscopies.

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.

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.

Spectral field mapping in plasmonic nanostructures with nanometer resolution

Plasmonic nanostructures and -devices are rapidly transforming light manipulation technology by allowing to modify and enhance optical fields on sub-wavelength scales. Advances in this field rely heavily on the development of new characterization methods for the fundamental nanoscale interactions. However, the direct and quantitative mapping of transient electric and magnetic fields characterizing the plasmonic coupling has been proven elusive to date. Here we demonstrate how to directly measure the inelastic momentum transfer of surface plasmon modes via the energy-loss filtered deflection of a focused electron beam in a transmission electron microscope. By scanning the beam over the sample we obtain a spatially and spectrally resolved deflection map and we further show how this deflection is related quantitatively to the spectral component of the induced electric and magnetic fields pertaining to the mode. In some regards this technique is an extension to the established differential phase contrast into the dynamic regime.

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.

Toroidal resonance based optical modulator employing hybrid graphene-dielectric metasurface

In this paper, we demonstrate the combination of a dielectric metasurface with a graphene layer to realize a high performance toroidal resonance based optical modulator. The dielectric metasurface consists of two mirrored asymmetric silicon split-ring resonators (ASSRRs) that can support strong toroidal dipolar resonance with narrow line width (~0.77 nm) and high quality (Q)-factor (~1702) and contrast ratio (~100%). Numerical simulation results show that the transmission amplitude of the toroidal dipolar resonance can be efficiently modulated by varying the Fermi energy EF when the graphene layer is integrated with the dielectric metasurface, and a max transmission coefficient difference up to 78% is achieved indicating that the proposed hybrid graphene/dielectric metasurface shows good performance as an optical modulator. The effects of the asymmetry degree of the ASSRRs on the toroidal dipolar resonance are studied and the efficiency of the transmission amplitude modulation of graphene is also investigated. Our results may also provide potential applications in optical filter and bio-chemical sensing.

"Optical and Surface Enhanced Raman Scattering properties of Ag modified silicon double nanocone array"

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

Optical reconfiguration and polarization control in semi-continuous gold films close to the percolation threshold

Controlling and confining light by exciting plasmons in resonant metallic nanostructures is an essential aspect of many new emerging optical technologies. Here we explore the possibility of controllably reconfiguring the intrinsic optical properties of semi-continuous gold films, by inducing permanent morphological changes with a femtosecond (fs)-pulsed laser above a critical power. Optical transmission spectroscopy measurements show a correlation between the spectra of the morphologically modified films and the wavelength, polarization, and the intensity of the laser used for alteration. In order to understand the modifications induced by the laser writing, we explore the near-field properties of these films with electron energy-loss spectroscopy (EELS). A comparison between our experimental data and full-wave simulations on the exact film morphologies hints toward a restructuring of the intrinsic plasmonic eigenmodes of the metallic film by photothermal effects. We explain these optical changes with a simple model and demonstrate experimentally that laser writing can be used to controllably modify the optical properties of these semi-continuous films. These metal films offer an easy-to-fabricate and scalable platform for technological applications such as molecular sensing and ultra-dense data storage.

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.

Super-radiating manipulation of a nano-emitter by active toroidal metamaterials

The far-field radiation of a single dipolar emitter can be controlled by coupling to toroidal dipole resonance attached to metallic double flat rings, realizing a conversion from non- to super-radiating. The underlying physical mechanism is the hybridization interference of toroidal and electric dipoles under an asymmetric configuration by introducing a radial displacement of the dipolar emitter. By embedding gain medium in the gap spacer between double flat rings, the directional far-field super-radiating power can achieve a tremendous enhancement with a moderate requirement on the gain coefficient, promoting light-matter interaction manipulation.

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.

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.

Optical force enhancement and annular trapping by plasmonic toroidal resonance in a double-disk metastructure

Optical forces can be enhanced by surface plasmon resonances with various interesting characteristics. Here, we numerically calculated the optical forces enhanced by a new kind of toroidal dipolar resonance in a double-disk metastructure. The results show that this kind of optical force is competitive with ordinary plasmonic forces and typically can reach-182.5pNμm²mW^-1. Influences of geometric parameters are discussed for the enhancement characteristic of optical force. Finally, we make a contrastive investigation on the optical trapping characteristic on a 5-nm-diameter nanoparticle, and show that the unique annular trapping region can be utilized for nanoscale applications.

Reflection and Phase Matching in Plasmonic Gold Tapers

We investigate different dynamic mechanisms, reflection and phase matching, of surface plasmons in a three-dimensional single-crystalline gold taper excited by relativistic electrons. Plasmonic modes of gold tapers with various opening angles from 5° to 47° are studied both experimentally and theoretically, by means of electron energy-loss spectroscopy and finite-difference time-domain numerical calculations, respectively. Distinct resonances along the taper shaft are observed in tapers independent of opening angles. We show that, despite their similarity, the origin of these resonances is different at different opening angles and results from a competition between two coexisting mechanisms. For gold tapers with large opening angles (above ∼20°), phase matching between the electron field and that of higher-order angular momentum modes of the taper is the dominant contribution to the electron energy-loss because of the increasing interaction length between electron and the taper near-field. In contrast, reflection from the taper apex dominates the EELS contrast in gold tapers with small opening angles (below ∼10°). For intermediate opening angles, a gradual transition of these two mechanisms was observed.

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.

Coupling of plasmonic nanopore pairs: facing dipoles attract each other

Control of the optical properties of nano-plasmonic structures is essential for next-generation optical circuits and high-throughput biosensing platforms. Realization of such nano-optical devices requires optical couplings of various nanostructured elements and field confinement at the nanoscale. In particular, symmetric coupling modes, also referred to as dark modes, have recently received considerable attention because these modes can confine light energy to small spaces. Although the coupling behavior of plasmonic nanoparticles has been relatively well studied, couplings of inverse structures, that is, holes and pores, remain partially unexplored. Even for the most fundamental coupling system of two dipolar holes, comparison of the symmetric and anti-symmetric coupling modes has not been performed. Here we present, for the first time, a systematic study of the symmetric and anti-symmetric coupling of nanopore pairs using cathodoluminescence by scanning transmission electron microscopy and electromagnetic simulation. The symmetric coupling mode, approximated as a pair of facing dipoles, is observed at a lower energy than that of the anti-symmetric coupling mode, indicating that the facing dipoles attract each other. The anti-symmetric coupling mode splits into the inner- and outer-edge localized modes as the coupling distance decreases. These coupling behaviors cannot be fully explained as inverses of coupled disks. Symmetric and anti-symmetric coupling modes are also observed in a short-range ordered pore array, where one pore supports multiple local resonance modes, depending on the distance to the neighboring pore. Accessibility to the observed symmetric modes by far field is also discussed, which is important for nanophotonic device applications.

Engineering non-radiative anapole modes for broadband absorption enhancement of light

In this paper, we propose a novel, frequency- and angularly- broadband approach to achieve absorption rate enhancement in high-index dielectric nanostructures through the engineering of non-radiative anapole modes. We employ multipolar decomposition of numerically computed current distributions and analyze the far-field scattering power of multipole moments. By leveraging the destructive interference of electric dipole and toroidal dipole moments, we design non-radiating anapole modes and demonstrate significantly enhanced absorbed power in silicon and germanium nanostructures. We demonstrate wide wavelength tunability of the anapole-driven peak absorption enhancement for nano-disks and square nano-pixel geometries, which can be conveniently fabricated with current lithography. Finally, by combining nano-disks and nano-pixels of different sizes into functional surface units, we design nanostructured arrays with enhanced bandwidth and absorption rates that can be useful for the engineering of broadband semiconductor photodetectors driven by controllable anapole responses.

Wedge Dyakonov Waves and Dyakonov Plasmons in Topological Insulator Bi2Se3 Probed by Electron Beams

Bi2Se3 has recently attracted a lot of attention because it has been reported to be a platform for the realization of three-dimensional topological insulators. Due to this exotic characteristic, it supports excitations of a two-dimensional electron gas at the surface and, hence, formation of Dirac-plasmons. In addition, at higher energies above its bandgap, Bi2Se3 is characterized by a naturally hyperbolic electromagnetic response, with an interesting interplay between type-I and type-II hyperbolic behaviors. However, still not all the optical modes of Bi2Se3 have been explored. Here, using mainly electron energy-loss spectroscopy and corresponding theoretical modeling we investigate the full photonic density of states that Bi2Se3 sustains, in the energy range of 0.8 eV-5 eV. We show that at energies below 1 eV, this material can also support wedge Dyakonov waves. Furthermore, at higher energies a huge photonic density of states is excited in structures such as waveguides and resonators made of Bi2Se3 due to the hyperbolic dispersion.

Electromagnetic toroidal excitations in matter and free space

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

Evolution of Plasmonic Metamolecule Modes in the Quantum Tunneling Regime

Plasmonic multinanoparticle systems exhibit collective electric and magnetic resonances that are fundamental for the development of state-of-the-art optical nanoantennas, metamaterials, and surface-enhanced spectroscopy substrates. While electric dipolar modes have been investigated in both the classical and quantum realm, little attention has been given to magnetic and other "dark" modes at the smallest dimensions. Here, we study the collective electric, magnetic, and dark modes of colloidally synthesized silver nanosphere trimers with varying interparticle separation using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). This technique enables direct visualization and spatially selective excitation of individual trimers, as well as manipulation of the interparticle distance into the subnanometer regime with the electron beam. Our experiments reveal that bonding electric and magnetic modes are significantly impacted by quantum effects, exhibiting a relative blueshift and reduced EELS amplitude compared to classical predictions. In contrast, the trimer's electric dark mode is not affected by quantum tunneling for even Ångström-scale interparticle separations. We employ a quantum-corrected model to simulate the effect of electron tunneling in the trimer which shows excellent agreement with experimental results. This understanding of classical and quantum-influenced hybridized modes may impact the development of future quantum plasmonic materials and devices, including Fano-like molecular sensors and quantum metamaterials.

Toroidal dipolar response by a dielectric microtube metamaterial in the terahertz regime

Due to metal losses in plasmonic metamaterials, high-refractive-index dielectrics are promising to improve optical performances of their metallic counterparts. In this paper, a LiTaO(3) microtube metamaterial is numerically investigated to explore the toroidal dipolar resonance based on the multipole expansion theory. The local field strength probed on the central axis of the microtube is greatly enhanced for the toroidal dipolar mode, forming a strong hot spot concentrated in the deep-subwavelength scale. Furthermore, we also show the influences of geometrical parameter on the quality (Q) factor of the toroidal mode. The high Q factor and strongly concentrated field strength in the toroidal microtube metamaterial offer application potentials such as sensing, energy havesting, particle trapping, and nonlinear optical effects.

Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles

We revisit the fundamental topic of light scattering by single homogenous nanoparticles from the new perspective of excitation and manipulation of toroidal dipoles. It is revealed that besides within all-dielectric particles, toroidal dipoles can also be efficiently excited within homogenous metallic nanoparticles. Moreover, we show that those toroidal dipoles excited can be spectrally tuned through adjusting the radial anisotropy parameters of the materials, which paves the way for further more flexible manipulations of the toroidal responses within photonic systems. The study into toroidal multipole excitation and tuning within nanoparticles deepens our understanding of the seminal problem of light scattering, and may incubate many scattering related fundamental researches and applications.

Nonradiating anapole modes in dielectric nanoparticles

Nonradiating current configurations attract attention of physicists for many years as possible models of stable atoms. One intriguing example of such a nonradiating source is known as ‘anapole'. An anapole mode can be viewed as a composition of electric and toroidal dipole moments, resulting in destructive interference of the radiation fields due to similarity of their far-field scattering patterns. Here we demonstrate experimentally that dielectric nanoparticles can exhibit a radiationless anapole mode in visible. We achieve the spectral overlap of the toroidal and electric dipole modes through a geometry tuning, and observe a highly pronounced dip in the far-field scattering accompanied by the specific near-field distribution associated with the anapole mode. The anapole physics provides a unique playground for the study of electromagnetic properties of nontrivial excitations of complex fields, reciprocity violation and Aharonov–Bohm like phenomena at optical frequencies.

The anapole is an intriguing example of a nonradiating source useful in the study of electromagnetic properties in complex phenomena. Here, Miroshnichenko et al. demonstrate that a single dielectric nanoparticle can exhibit a radiationless anapole mode at visible wavelengths.

Investigating hybridization schemes of coupled split-ring resonators by electron impacts

We present a comprehensive theoretical and experimental investigation of the plasmon hybridization of coupled split-ring resonators by means of the electron energy-loss spectroscopy. Split-ring resonator is a key element in design of negative refractive index metamaterials, and has been therefore intensively studied in the literature. Here, our aim is the study of hybridization effects for higher-order non-dipolar modes, which have been not investigated beforehand. We provide a complete scheme of the multimodal distribution of the coupled and single-element split-ring resonators, with a precise attention to the hybridization of those modes according to the induced moments. Our study suggests a clear dominance of electric and magnetic dipole moments over higher-order modes in the far-field radiation spectrum.

Plasmonic Toroidal Dipolar Response under Radially Polarized Excitation

Plasmonic toroidal resonance has attracted growing interests because of its low loss electromagnetic properties and potential high sensitive nanophotonic applications. However, the realization in a metamaterial requires three-dimensional complicated structural design so far. In this paper, we design a simple metal-dielectric-metal (MIM) sandwich nanostructure, which exhibits a strong toroidal dipolar resonance under radially polarized excitation. The toroidal dipole moment as the dominant contribution for the scattering is demonstrated by the mirror-image method and further analyzed by Lagrangian hybridization model. The proposed toroidal configuration also shows a highly tolerant for misalignment between the structure center and the incident light focus. Our study proves the way for the toroidal plasmonic application with the cylindrical vector beams.

Invisible nanowires with interfering electric and toroidal dipoles

By studying the scattering of normally incident plane waves by a single nanowire, we reveal the indispensable role of toroidal multipole excitation in multipole expansions of radiating sources. It is found that for both p-polarized and s-polarized incident waves, toroidal dipoles can be effectively excited within homogenous dielectric nanowires in the optical spectrum regime. We further demonstrate that the plasmonic core-shell nanowires can be rendered invisible through destructive interference of the electric and toroidal dipoles, which may inspire many nanowire-based light-matter interaction studies, and incubate biological and medical applications that require noninvasive detections and measurements.

Excitation of plasmon toroidal mode at optical frequencies by angle-resolved reflection

Plasmon toroidal mode is a unique electromagnetic resonance that cannot be expanded by general electronic or magnetic multipoles. Usually, this mode excitation needs complicated nanostructures, which is a challenge for sample fabrications, especially for nanodesigns with optical resonant frequencies. In this work, we designed a circular V-groove array and studied its toroidal-mode excitation by angle-resolved reflection experimentally and numerically. Our results show that a plasmon toroidal mode around wavelength 700 nm can be excited in this simple nanostructure for incident angles larger than 20°. Compared to reported papers, our design can realize the optical excitation of plasmon toroidal mode, which is useful in high-sensitivity plasmon sensors.

Near- and far-field properties of plasmonic oligomers under radially and azimuthally polarized light excitation

We present a comprehensive experimental and theoretical study on the near- and far-field properties of plasmonic oligomers using radially and azimuthally polarized excitation. These unconventional polarization states are perfectly matched to the high spatial symmetry of the oligomers and thus allow for the excitation of some of the highly symmetric eigenmodes of the structures, which cannot be excited by linearly polarized light. In particular, we study hexamer and heptamer structures and strikingly find very similar optical responses, as well as the absence of a Fano resonance. Furthermore, we investigate the near-field distributions of the oligomers using near-field scanning optical microscopy (NSOM). We observe significantly enhanced near-fields, which arise from efficient excitation of the highly symmetric eigenmodes by the radially and azimuthally polarized light fields. Our study opens up possibilities for tailored light-matter interaction, combining the design freedom of complex plasmonic structures with the remarkable properties of radially and azimuthally polarized light fields.

Rapid prototyping of Fresnel zone plates via direct Ga(+) ion beam lithography for high-resolution X-ray imaging

A significant challenge to the wide utilization of X-ray microscopy lies in the difficulty in fabricating adequate high-resolution optics. To date, electron beam lithography has been the dominant technique for the fabrication of diffractive focusing optics called Fresnel zone plates (FZP), even though this preparation method is usually very complicated and is composed of many fabrication steps. In this work, we demonstrate an alternative method that allows the direct, simple, and fast fabrication of FZPs using focused Ga(+) beam lithography practically, in a single step. This method enabled us to prepare a high-resolution FZP in less than 13 min. The performance of the FZP was evaluated in a scanning transmission soft X-ray microscope where nanostructures as small as sub-29 nm in width were clearly resolved, with an ultimate cutoff resolution of 24.25 nm, demonstrating the highest first-order resolution for any FZP fabricated by the ion beam lithography technique. This rapid and simple fabrication scheme illustrates the capabilities and the potential of direct ion beam lithography (IBL) and is expected to increase the accessibility of high-resolution optics to a wider community of researchers working on soft X-ray and extreme ultraviolet microscopy using synchrotron radiation and advanced laboratory sources.

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

Engaging strongly resonant interactions allows dramatic enhancement of functionalities of many electromagnetic devices. However, resonances can be dampened by Joule and radiation losses. While in many cases Joule losses may be minimized by the choice of constituting materials, controlling radiation losses is often a bigger problem. Recent solutions include the use of coupled radiant and sub-radiant modes yielding narrow asymmetric Fano resonances in a wide range of systems, from defect states in photonic crystals and optical waveguides with mesoscopic ring resonators to nanoscale plasmonic and metamaterial systems exhibiting interference effects akin to electromagnetically-induced transparency. Here we demonstrate theoretically and confirm experimentally a new mechanism of resonant electromagnetic transparency, which yields very narrow isolated symmetric Lorentzian transmission lines in toroidal metamaterials. It exploits the long sought non-trivial non-radiating charge-current excitation based on interfering electric and toroidal dipoles that was first proposed by Afanasiev and Stepanovsky in [J. Phys. A Math. Gen. 28, 4565 (1995)].

From isolated metaatoms to photonic metamaterials: evolution of the plasmonic near-field

Metamaterials are artificial media which can provide optical properties not available from natural materials. These properties often result from the resonant excitation of plasmonic modes in the metallic building blocks ("metaatoms") of the metamaterial. Electromagnetic interactions between the metaatoms significantly modify the resonances of the individual metaatoms and influence the optical properties of the whole metamaterial. To better understand these interactions, we study in this Letter the evolution of the plasmonic near-field in the course of the transition from an isolated metaatom, in our case a split-ring resonator (SRR), to a photonic metamaterial via electron energy-loss spectroscopy. For small SRR ensembles, we observe the formation of discrete optical bright and dark modes due to coupling of the metaatoms. Large SRR arrays reveal a quasi-continuum of modes in the interior and distinct edge modes at the boundaries of the array. Our experimental results are in excellent agreement with numerical calculations.