Electromagnetic toroidal excitations in matter and free space

Supertoroidal light pulses as electromagnetic skyrmions propagating in free space

Topological complex transient electromagnetic fields give access to nontrivial light-matter interactions and provide additional degrees of freedom for information transfer. An important example of such electromagnetic excitations are space-time non-separable single-cycle pulses of toroidal topology, the exact solutions of Maxwell's equations described by Hellwarth and Nouchi in 1996 and recently observed experimentally. Here we introduce an extended family of electromagnetic excitation, the supertoroidal electromagnetic pulses, in which the Hellwarth-Nouchi pulse is just the simplest member. The supertoroidal pulses exhibit skyrmionic structure of the electromagnetic fields, multiple singularities in the Poynting vector maps and fractal-like distributions of energy backflow. They are of interest for transient light-matter interactions, ultrafast optics, spectroscopy, and toroidal electrodynamics.

High-quality-factor dual-band Fano resonances induced by dual bound states in the continuum using a planar nanohole slab

In photonics, it is essential to achieve high-quality (Q)-factor resonances to improve optical devices' performances. Herein, we demonstrate that high-Q-factor dual-band Fano resonances can be achieved by using a planar nanohole slab (PNS) based on the excitation of dual bound states in the continuum (BICs). By shrinking or expanding the tetramerized holes of the superlattice of the PNS, two symmetry-protected BICs can be induced to dual-band Fano resonances and their locations as well as their Q-factors can be flexibly tuned. Physical mechanisms for the dual-band Fano resonances can be interpreted as the resonant couplings between the electric toroidal dipoles or the magnetic toroidal dipoles based on the far-field multiple decompositions and the near-field distributions of the superlattice. The dual-band Fano resonances of the PNS possess polarization-independent feature, and they can be survived even when the geometric parameters of the PNS are significantly altered, making them more suitable for potential applications.

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

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

Lasing Action from Anapole Metasurfaces

We study active dielectric metasurfaces composed of two-dimensional arrays of split-nanodisk resonators fabricated in InGaAsP membranes with embedded quantum wells. Depending on the geometric parameters, such split-nanodisk resonators can operate in the optical anapole regime originating from an overlap of the electric dipole and toroidal dipole Mie-resonant optical modes, thus supporting strongly localized fields and high-Q resonances. We demonstrate room-temperature lasing from the anapole lattices of engineered active metasurfaces with low threshold and high coherence.

The 2021 Magnonics Roadmap

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years.

Electric Factors in Wound Healing

Significance: Electric factors such as electric charges, electrodynamic field, skin battery, and interstitial exclusion permeate wound healing physiology and physiopathology from injury to re-epithelialization. The understanding of how electric factors contribute to wound healing and how treatments may interfere with them is fundamental for the development of better strategies for the management of pathological scarring and chronic wounds. Recent Advances: Angiogenesis, cell migration, macrophage activation hemorheology, and microcirculation can interfere and be interfered with electric factors. New treatments with various types of electric currents, laser, light emitting diode, acupuncture, and weak electric fields applied directly on the wound have been developed to improve wound healing. Critical Issues: Despite the basic and clinical development, pathological scars such as keloids and chronic wounds are still a challenge. Future Directions: New treatments can be developed to improve skin wound healing taking into account the influence of electrical charges. Monitoring electrical activity during skin healing and the influence of treatments on hemorheology and microcirculation are examples of how to use knowledge of electrical factors to increase their effectiveness.

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

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

Multiple Fano resonances excitation on all-dielectric nanohole arrays metasurfaces

Both toroidal dipoles, electric dipoles and magnetic dipoles belong to one type of electromagnetic excitation. In this paper, we present an all-dielectric metasurface composed of an array of square nanoholes. It can simultaneously generate four resonance responses excited by TD, EQ and MD in the continuous near-infrared band. By introducing the in-plane symmetry breaking of the unit cell, asymmetric dielectric nanohole arrays are used to achieve two quasi-BIC resonance modes with high Q-factors excited by EQ and MD. The paper theoretically analyzes and demonstrates the relationship between structural asymmetry and the radiative Q-factor of two Fano resonances, that are governed by symmetry-protected BICs. And multipole decomposition and near-field analysis are performed to demonstrate the dominant role of various electromagnetic excitations in the four modes. The spectra response is also calculated for different incident polarization angles and medium refractive indices. The proposed metasurface is more feasible and practical compared to other complex nanostructures, which may open avenues for the development of applications such as biochemical sensing, optical switches and optical modulators, and provide a reference for the design of devices with polarization-independent properties.

Toroidal dipole Fano resonances supported by lattice-perturbed dielectric nanohole arrays in the near-infrared region

The toroidal dipole (TD) plays an important role in light-matter interactions. In this paper, a lattice-perturbed dielectric nanohole array structure has been put forward to excite dominant TD Fano resonances in the near-infrared region. Herein, the numerical investigations and experimental demonstrations have been performed to characterize the TD Fano resonances with a series of lattice perturbations. The scattering power of TD and quality (Q)-factor of the resonance can be tailored by tuning perturbation. By using the lattice perturbation of 53 nm, the highest experimental Q-factor of 584 is obtained.

Strongly resonant silicon slot metasurfaces with symmetry-protected bound states in the continuum

In this work, a novel all-dielectric metasurface made of arrayed circular slots etched in a silicon layer is proposed and theoretically investigated. The structure is designed to support both Mie-type multipolar resonances and symmetry-protected bound states in the continuum (BIC). Specifically, the metasurface consists of interrupted circular slots, following the paradigm of complementary split-ring resonators. This configuration allows both silicon-on-glass and free-standing metasurfaces and the arc length of the split-rings provides an extra tuning parameter. The nature of both BIC and non-BIC resonances supported by the metasurface is investigated by employing the Cartesian multipole decomposition technique. Thanks to the non-radiating nature of the quasi-BIC resonance, extremely high Q-factor responses are calculated, both by fitting the simulated transmittance spectra to an extended Fano model and by an eigenfrequency analysis. Furthermore, the effect of optical losses in silicon on quenching the achievable Q-factor values is discussed. The metasurface features a simple bulk geometry and sub-wavelength dimensions. This novel device, its high Q-factors, and strong energy confinement open new avenues of research on light-matter interactions in view of new applications in non-linear devices, biological sensors, and optical communications.

Momentum space toroidal moment in a photonic metamaterial

Berry curvature, the counterpart of the magnetic field in the momentum space, plays a vital role in the transport of electrons in condensed matter physics. It also lays the foundation for the emerging field of topological physics. In the three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains of Berry curvature. Here, we demonstrate a toroidal moment of Berry curvature with flux approaching to π in judiciously engineered metamaterials. The Berry curvature exhibits a vortex-like configuration without any source and drain in the momentum space. Experimentally, the presence of Berry curvature toroid is confirmed by the observation of conical-frustum shaped domain-wall states at the interfaces formed by two metamaterials with opposite toroidal moments.

The appearance of toroidal multipolar moments in electrodynamics interrogates the question for their existence in Berry curvature, which can be seen as the “magnetic field” in the momentum space. Here, the authors observe 3D vortex distributions in the Berry curvature within a photonic metamaterial.

Resonance-trapped bound states in the continuum in metallic THz metasurfaces

The realization of bound states in the continuum (BICs) in optical systems has been relying mainly on symmetry breaking. In contrast, another mechanism, known as resonance-trapped (or Friedrich-Wintgen) scenario, has been reported in the limited scope of dielectric resonant inclusions or at off-Γ points. In this Letter, we demonstrate that the coupling coefficient between two coplanar metallic split-ring resonators can be tuned to satisfy the Friedrich-Wintgen BIC condition with normal terahertz (THz) incidence when metals are modeled as perfect electric conductors. Temporal coupled-mode theory is applied to validate the results. Experimentally, a BIC-induced cloaking effect has been observed, owing to the intrinsic dissipation loss of the constitutive materials. Our findings suggest an alternative strategy to construct BICs in metallic metasurfaces apart from conventional symmetry-breaking methods.

Non-isolated sources of electromagnetic radiation by multipole decomposition for photonic quantum technologies on a chip with nanoscale apertures

The creation of single photon sources on a chip is a mid-term milestone on the road to chip-scale quantum computing. An in-depth understanding of the extended multipole decomposition of non-isolated sources of electromagnetic radiation is not only relevant for a microscopic description of fundamental phenomena, such as light propagation in a medium, but also for emerging applications such as single-photon sources. To design single photon emitters on a chip, we consider a ridge dielectric waveguide perturbed with a cylindrical inclusion. For this, we expanded classical multipole decomposition that allows simplifying and interpreting complex optical interactions in an intuitive manner to make it suitable for analyzing light-matter interactions with non-isolated objects that are parts of a larger network, e.g. individual components such as a single photon source of an optical chip. It is shown that our formalism can be used to design single photon sources on a chip.

Functionalized terahertz plasmonic metasensors: Femtomolar-level detection of SARS-CoV-2 spike proteins

Effective and efficient management of human betacoronavirus severe acute respiratory syndrome (SARS)-CoV-2 virus infection i.e., COVID-19 pandemic, required sensitive and selective sensors with short sample-to-result durations for performing desired diagnostics. In this direction, one appropriate alternative approach to detect SARS-CoV-2 virus protein at low level i.e., femtomolar (fM) is exploring plasmonic metasensor technology for COVID-19 diagnostics, which offers exquisite opportunities in advanced healthcare programs, and modern clinical diagnostics. The intrinsic merits of plasmonic metasensors stem from their capability to squeeze electromagnetic fields, simultaneously in frequency, time, and space. However, the detection of low-molecular weight biomolecules at low densities is a typical drawback of conventional metasensors that has recently been addressed using toroidal metasurface technology. This research is focused on the fabrication of a miniaturized plasmonic immunosensor based on toroidal electrodynamics concept that can sustain robustly confined plasmonic modes with ultranarrow lineshapes in the terahertz (THz) frequencies. By exciting toroidal dipole mode using our quasi-infinite metasurface and a judiciously optimized protocol based on functionalized gold nanoparticles (AuNPs) conjugated with the specific monoclonal antibody specific to spike protein (S1) of SARS-CoV-2 virus onto the metasurface, the resonance shifts for diverse concentrations of the spike protein are monitored. Possessing molecular weight around ~76 kDa allowed to detect the presence of SARS-CoV-2 virus protein with significantly low as limit of detection (LoD) was achieved as ~4.2 fM. We envisage that outcomes of this research will pave the way toward the use of toroidal metasensors as practical technologies for rapid and precise screening of SARS‐CoV‐2 virus carriers, symptomatic or asymptomatic, and spike proteins in hospitals, clinics, laboratories, and site of infection.

Integrated Molar Chiral Sensing Based on High-Q Metasurface

Circular dichroism (CD) spectroscopy is conventionally utilized for the enantiomer-specific analysis of chiral samples, which is of great significance in academia and industry. Recently, metasurfaces have been introduced for enhancing the sensitivity of CD spectroscopy. However, the obtained CD spectrum alone cannot provide the enantiomer composition of a chiral sample. It should be normalized by the molar concentration of chiral molecules, which is usually measured on a different platform. Here, for the first time we demonstrate the integrated acquisition of CD spectrum and molar concentration over an individual metasurface with high sensitivities. High-Q resonances are supported on the metasurface, governed by bound states in the continuum. The generated superchiral field enables a 59-times enhancement of CD signal. Meanwhile, the refractive index-based detection of molar concentration achieves a large figure-of-merit of 80.6. Accordingly, a standard procedure is established for the integrated molar chiral sensing with high sensitivity.

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

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

Spectral Modulation through the Hybridization of Mie-Scatterers and Quasi-Guided Mode Resonances: Realizing Full and Gradients of Structural Color

Metasurfaces made up of subwavelength arrays of Mie scatterers can be engineered to control the optical properties of incident light. The hybridization of the fundamental Mie resonances with lattice resonances greatly enhances the scattering cross-section of individual Mie scatterers. Through careful design of the locations of these hybridized modes using two differently engineered hydrogenated amorphous silicon nanorods, we numerically calculate and experimentally fabricate two examples of full color printing; one with spectral colors comparable to the Adobe RGB gamut, and another with gradients of color. We identify and characterize the mechanisms behind each and provide a framework that can be used to design any all-dielectric metasurfaces of subwavelength Mie scatterers for spectral modulation.

Planar Achiral Metasurfaces-Induced Anomalous Chiroptical Effect of Optical Spin Isolation

Planar chiral structures respond differently for oppositely handed incident light, and thus can produce extraordinary chiroptical effects such as circular conversion dichroism (CCD) and asymmetric transmission (AT). Such chiroptical effects are powerful tools to realize the fundamental principle of optical spin isolation, which leads to a plethora of applications such as optical conversion diodes, chiral imaging, and sensing. Here, we demonstrate the chiroptical effects of simultaneous CCD and AT through meticulously designed single-layered achiral nanofins. Our metamolecule consists of four achiral hydrogenated amorphous silicon (a-Si:H) nanofins that are carefully oriented and optimized to exhibit considerable CCD and AT. The device demonstrates a circular conversion dichroism of 55% and an asymmetric transmission of 58% at a wavelength of 633 nm. Right-hand circularly polarized light (RHCP) is completely absorbed, while left-hand circularly polarized light (LHCP) is transmitted with a polarization conversion, making it a perfect circular polarization wave isolator with negligible backscattering (due to low reflectance). This unique design and its underlying working mechanism are described comprehensively with three different techniques. These methods validate the proposed design and its methodology. For practical applications such as imaging, the proposed design realizes the Pancharatnam-Berry (PB) phase, achieving a 0-2π phase coverage for transmitted circular polarization. For the proof of concept, a metahologram is designed and demonstrated by employing the achieved full-phase control. The measured response of the fabricated metadevice not only validates the CCD and AT but also exhibits a simulated polarization conversion efficiency of up to 71% and measured efficiency up to 52%, comparable to state-of-the-art metahologram demonstrations.

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.

Spin-Selective Full-Dimensional Manipulation of Optical Waves with Chiral Mirror

Realizing arbitrary manipulation of optical waves, which still remains a challenge, plays a key role in the implementation of optical devices with on-demand functionalities. However, it is hard to independently manipulate multiple dimensions of optical waves because the optical dimensions are basically associated with each other when adjusting the optical response of the devices. Here, the concise design principle of a chiral mirror is utilized to realize the full-dimensional independent manipulation of circular-polarized waves. By simply changing three structural variables of the chiral mirror, the proposed design principle can arbitrarily and independently empower the spin-selective manipulation of amplitude, phase, and operation wavelength of circular-polarized waves with a large modulation depth. This approach provides a simple solution for the realization of spin-selective full-dimensional manipulation of optical waves and shows ample application possibilities in the areas of optical encryption, imaging, and detection.

Generalized Maxwell projections for multi-mode network Photonics

The design of optical resonant systems for controlling light at the nanoscale is an exciting field of research in nanophotonics. While describing the dynamics of few resonances is a relatively well understood problem, controlling the behavior of systems with many overlapping states is considerably more difficult. In this work, we use the theory of generalized operators to formulate an exact form of spatio-temporal coupled mode theory, which retains the simplicity of traditional coupled mode theory developed for optical waveguides. We developed a fast computational method that extracts all the characteristics of optical resonators, including the full density of states, the modes quality factors, and the mode resonances and linewidths, by employing a single first principle simulation. This approach can facilitate the analytical and numerical study of complex dynamics arising from the interactions of many overlapping resonances, defined in ensembles of resonators of any geometrical shape and in materials with arbitrary responses.

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

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

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

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

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.

Polarization-independent toroidal dipole resonances driven by symmetry-protected BIC in ultraviolet region

Optical resonances have gained great attention in nanophotonics attributing to their large enhancement of local field. In this work, we investigate polarization-independent toroidal dipole responses governed by bound state in the continuum (BIC) in the ultraviolet region. By introducing symmetry breaking, an asymmetric dielectric nanohole array is employed to excite two symmetry-protected BICs. Far-field contribution and near-field analysis are performed to demonstrate the dominant role of toroidal dipole in the above two modes. Our design shows the same responses under incident plane wave with different polarizations. The calculated enhancement factors also validate that these resonances can produce strong local field enhancement. Our work may provide a route towards resonators with polarization-independent responses and good performance.

Infrared dielectric metamaterials from high refractive index chalcogenides

High-index dielectric materials are in great demand for nanophotonic devices and applications, from ultrathin optical elements to metal-free sub-diffraction light confinement and waveguiding. Here we show that chalcogenide topological insulators are particularly apt candidates for dielectric nanophotonics architectures in the infrared spectral range, by reporting metamaterial resonances in chalcogenide crystals sustained well inside the mid-infrared, choosing Bi2Te3 as case study within this family of materials. Strong resonant modulation of the incident electromagnetic field is achieved thanks to the exceptionally high refractive index ranging between 7 and 8 throughout the 2-10 μm region. Analysis of the complex mode structure in the metamaterial allude to the excitation of circular surface currents which could open pathways for enhanced light-matter interaction and low-loss plasmonic configurations by coupling to the spin-polarized topological surface carriers, thereby providing new opportunities to combine dielectric, plasmonic and magnetic metamaterials in a single platform.

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

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

Angle-dependent optical response of the plasmonic nanoparticle clusters with rotational symmetry

Plasmonic nanoparticle clusters are widely considered experimentally and numerically. In the clusters consisting of one central particle and N satellite particles, not only the magnetic modes but also the toroidal modes can exist. Here, the eigenmodes of such clusters and the corresponding excitation efficiency under the illumination of a plane wave are studied analytically by using the eigen-decomposition method. The angular dependence of the optical response of these clusters is clearly demonstrated. The behavior of excitation efficiency is dependent on both the value and the parity of N, the number of satellite particles. Our results may provide a guide for the selective excitation of plasmonic modes in the plasmonic nanoparticle clusters.

Optical radiation manipulation of Si-Ge2Sb2Te5 hybrid metasurfaces

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

Excitation of Nonradiating Anapoles in Dielectric Nanospheres

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

Electromagnetic Waves in Annular Regions

In suitable bounded regions immersed in vacuum, time periodic wave solutions solving a full set of electrodynamics equations can be explicitly computed. Analytical expressions are available in special cases, whereas numerical simulations are necessary in more complex situations. The attention here is given to selected three-dimensional geometries, which are topologically equivalent to a toroid, where the behavior of the waves is similar to that of fluid-dynamics vortex rings. The results show that the shape of the sections of these rings depends on the behavior of the eigenvalues of a certain elliptic differential operator. Time-periodic solutions are obtained when at least two of such eigenvalues attain the same value. The solutions obtained are discussed in view of possible applications in electromagnetic whispering galleries or plasma physics.

Spin-preserving chiral photonic crystal mirror

Chirality refers to a geometric phenomenon in which objects are not superimposable on their mirror image. Structures made of nanoscale chiral elements can exhibit chiroptical effects, such as dichroism for left- and right-handed circularly polarized light, which makes these structures highly suitable for applications ranging from quantum information processing and quantum optics to circular dichroism spectroscopy and molecular recognition. At the same time, strong chiroptical effects have been challenging to achieve even in synthetic optical media, and chiroptical effects for light with normal incidence have been speculated to be prohibited in thin, lossless quasi-two-dimensional structures. Here, we report an experimental realization of a giant chiroptical effect in a thin monolithic photonic crystal mirror. Unlike conventional mirrors, our mirror selectively reflects only one spin state of light while preserving its handedness, with a near-unity level of circular dichroism. The operational principle of the photonic crystal mirror relies on guided-mode resonance (GMR) with a simultaneous excitation of leaky transverse electric (TE-like) and transverse magnetic (TM-like) Bloch modes in the photonic crystal slab. Such modes are not reliant on the suppression of radiative losses through long-range destructive interference, and even small areas of the photonic crystal exhibit robust circular dichroism. Despite its simplicity, the mirror strongly outperforms earlier reported structures and, contrary to a prevailing notion, demonstrates that near-unity reflectivity contrast for opposite helicities is achievable in a quasi-two-dimensional structure.

Mantle cloaking due to ideal magnetic dipole scattering

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

Functional Charge Transfer Plasmon Metadevices

Reducing the capacitive opening between subwavelength metallic objects down to atomic scales or bridging the gap by a conductive path reveals new plasmonic spectral features, known as charge transfer plasmon (CTP). We review the origin, properties, and trending applications of this modes and show how they can be well-understood by classical electrodynamics and quantum mechanics principles. Particularly important is the excitation mechanisms and practical approaches of such a unique resonance in tailoring high-response and efficient extreme-subwavelength hybrid nanophotonic devices. While the quantum tunneling-induced CTP mode possesses the ability to turn on and off the charge transition by varying the intensity of an external light source, the excited CTP in conductively bridged plasmonic systems suffers from the lack of tunability. To address this, the integration of bulk plasmonic nanostructures with optothermally and optoelectronically controllable components has been introduced as promising techniques for developing multifunctional and high-performance CTP-resonant tools. Ultimate tunable plasmonic devices such as metamodulators and metafilters are thus in prospect.

Optical nanoheating of resonant silicon nanoparticles

The photothermal characteristics of nanoparticles are of particular interest to biophotonic and biomedical applications due to their ability to efficiently localize thermal energy down to the nanometer scale. However, few works had demonstrated an efficient dissipation of heat to their nanoscale surrounding in response to optical excitation. Here, we demonstrate an efficient platform for optical nanoheating based on silicon nanocuboids. Based on Green's tensor formalism and temperature-dependent Raman spectroscopy analyses, we found that the significant nanoheating effect is a consequence of the resonant modes specifically, to the high degree of overlap between the different resonant modes of the silicon nanocuboids. Currently, the temperature rise of up to 300 K was measured with incident power density of 2.9 mW/µm². Such effective nanoheating platform would be suitable in applications where controllable optical nanoheating is crucial, such as nanosurgery, photochemistry, and nanofabrication.

Chirality selective metamaterial absorber with dual bands

In this paper, a sensitive chirality selective metamaterial absorber (CSMA) is constructed by using 'I-shaped' resonator with asymmetric twisted metallic wires. Absorption of 95.18% and 91.77% at two resonant frequencies can be achieved for left-handed circularly polarized (LCP) incident wave, with little loss of right-handed circularly polarized (RCP) incident wave, which results in significant absorptive circular dichroism. Not only can the CSMA intensely absorb LCP illumination with dual bands, but also circularly polarized (CP) conversion for RCP wave is achieved over a broad bandwidth. The spin-dependent absorption, closely linked to chiral symmetry breaking, is investigated through oblique incidence, power loss distribution and scanning parameters optimization. The proposed strategy is further demonstrated in mid-infrared band which could advance the applications in polarization manipulation to circularly polarized detectors/lasers, chiral sensing/bolometers, and molecular spectroscopy.

Anapole: Its birth, life, and death

Despite the recent extensive study of the nonradiating (anapole) mode in the resonant light scattering by nanoparticles, the key questions, about the dynamics of its excitation at the leading front of the incident pulse and collapse behind the trailing edge, still remain open. We answer the questions, first, by direct numerical integration of the complete set of the Maxwell equations, describing the scattering of a rectangular laser pulse by a dielectric cylinder. The simulation shows that while the excitation and the collapse periods, both have the same characteristic time-scale, the dynamics of these processes are qualitatively different. The relaxation to the steady-state scattering at the leading front is accompanied by high-amplitude oscillatory modulations of the envelope of the basic electromagnetic oscillations, while behind the trailing edge the decay of the envelope is monotonic. Then, we present the general arguments showing that this is the case for the anapole excited in any classical system. Next, we introduce a simple, exactly integrable yet accurate, physically transparent model describing the dynamics of the anapole. The model admits generalization to a broad class of resonant phenomena and may be regarded as a compliment to the commonly used Temporal Coupled-Mode Theory.

Strong Coupling between Dark Plasmon and Anapole Modes

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

Propagation of toroidal localized spoof surface plasmons using conductive coupling

Here, on a platform of two split-ring resonator (SRR) disks in the microwave regime, we have numerically and experimentally investigated the coupling of toroidal localized spoof surface plasmons (LSSPs). The coupling effect is investigated both theoretically and experimentally. We observe that magnetic dipole coupling exists in the toroidal LSSPs coupling and causes a rearrangement of the toroidal LSSPs, which suppresses the propagation of toroidal LSSPs. To realize the propagation of toroidal LSSPs, we introduce conductive coupling into the SRR disks. The conductive coupling can correct magnetic dipole coupling and enhance toroidal LSSPs coupling. Both numerical simulations and experiments are in good agreement. The toroidal LSSPs can be effectively propagated, even in the three right-angle-bent SRR disks. This study paves the way toward a better understanding of toroidal LSSPs coupling and finds many applications in the transfer of electromagnetic energy using toroidal moments.

Light emission driven by magnetic and electric toroidal dipole resonances in a silicon metasurface

Dielectric nanoparticles supporting pronounced toroidal and anapole resonances have enabled a new class of optical antennas with unprecedented functionalities. In this work, we propose a light-emitting silicon metasurface which simultaneously supports both magnetic toroidal dipole and electric toroidal dipole resonances in the near-infrared region. The metasurface consists of a square array of split nanodisks with embedded germanium quantum dots. By varying the width of the split air-gap, the spectral positions and quality factors of the two toroidal dipoles are flexibly tuned. Large photoluminescence enhancement is experimentally demonstrated at the toroidal resonances, which is attributed to the unique near- and far-field characteristics of the resonant modes. Moreover, the light emissions driven by the two toroidal dipoles are of different polarization, which further suggests versatile polarization-engineered radiation properties. Our work shows enormous potential in light emission manipulation and provides a route for high-efficiency, ultra-compact LEDs and potentially functional dielectric metasurface lasers.

Organometallic complexes of carbon nanotori

New organometallic complexes of carbon nanotori were designed and theoretically described by means of density functional theory. After a systematic structural search, it was found that energetically favorable complexes were formed by the metal atoms Cr and Ni, both located at the center of a nanotorus with diameter around 5 Å and 120 carbon atoms. The nature of the metal-nanotorus interaction shows a partial polar-covalent character, different from those found in other well-known organometallic compounds. Interactions were studied through molecular orbitals and thermodynamic stability. Ten bonds are set up between the metal atom and nanotorus, confirmed by electron density topology analysis, showing ten bond critical points among the metal atoms and the surrounding carbon atoms. The response of the induced electron current caused by a magnetic field perpendicular to the nanotorus was analyzed to explain the electron delocalization and aromaticity of the complexes. Only in the case of the chromium complex, the electron density is fully delocalized on the whole complex. According to a geometry-based index of aromaticity, interaction with the metal atom only changes the aromatic character of the carbon rings slightly. Also, induced currents were used to elucidate the presence of a ferrotoroidal behavior. The isolated nanotorus and its compound with a single Ni atom have well-defined ferrotoroidal behavior because they present broken symmetries and could help to design a topological insulator. Meanwhile, the nanotorus with a Cr atom at the center lacks ferrotoroidal behavior as a consequence of the absence of magnetic vortices. Graphical abstract Organometallic complex of carbon nanotorus with chromium and induced currents on it by applying an external magnetic field.

Transition metal dichalcogenide nanodisks as high-index dielectric Mie nanoresonators

Monolayer transition metal dichalcogenides (TMDCs) have recently been proposed as an excitonic platform for advanced optical and electronic functionalities^1-3. However, in spite of intense research efforts, it has not been widely appreciated that TMDCs also possess a high refractive index^4,5. This characteristic opens up the possibility to utilize them to construct resonant nanoantennas based on subwavelength geometrical modes^6,7. Here, we show that nanodisks, fabricated from exfoliated multilayer WS₂, support distinct Mie resonances and anapole states⁸ that can be tuned in wavelength over the visible and near-infrared range by varying the nanodisk size and aspect ratio. As a proof of concept, we demonstrate a novel regime of light-matter interaction-anapole-exciton polaritons-which we realize within a single WS₂ nanodisk. We argue that the TMDC material anisotropy and the presence of excitons enrich traditional nanophotonics approaches based on conventional high-index materials and/or plasmonics.

Nonradiating anapole states in nanophotonics: from fundamentals to applications

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

High-order elastic multipoles as colloidal atoms

Achieving and exceeding diversity of colloidal analogs of chemical elements and molecules as building blocks of matter has been the central goal and challenge of colloidal science ever since Einstein introduced the colloidal atom paradigm. Recent advances in colloids assembly have been achieved by exploiting the machinery of DNA hybridization but robust physical means of defining colloidal elements remain limited. Here we introduce physical design principles allowing us to define high-order elastic multipoles emerging when colloids with controlled shapes and surface alignment are introduced into a nematic host fluid. Combination of experiments and numerical modeling of equilibrium field configurations using a spherical harmonic expansion allow us to probe elastic multipole moments, bringing analogies with electromagnetism and a structure of atomic orbitals. We show that, at least in view of the symmetry of the "director wiggle wave functions," diversity of elastic colloidal atoms can far exceed that of known chemical elements.

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.