Nonradiating anapole states in nanophotonics: from fundamentals to applications

Anapole states and transverse displacement sensing based on the interaction between cylindrical vector beams and Au core-Si shell nanodisks

Precise optical control at the nanoscale is crucial for advancing photonic devices and sensing technologies. Herein, we theoretically introduce what we believe to be a novel approach for nano-optical manipulation, employing Au core-Si shell nanodisks interacting with tightly focused cylindrical vector beams to achieve electric and magnetic anapole states. Our investigations unveil that the interplay between individual nanodisks and radially polarized beams (RPBs) located in the center of RPBs yields a position-dependent electric anapole state. Conversely, under illumination by azimuthally polarized beams (APBs), the electric anapole state exhibits independence from the nanodisk's positioning and is accompanied by significant magnetic dipole excitations. Furthermore, the interaction between APBs and nanodisk multimers enables the formation of a magnetic anapole state, marking an advancement in nano-optical control. This study further explores the application of the position-dependent electric anapole state for nanoscale transverse displacement sensing, which allows for precise determination of the nanodisk's position within a plane. These findings not only facilitate versatile control over anapole states but also set a foundation for integrated displacement sensing technologies on-chip.

Wide angle anapole excitation in stacked resonators

In the search for resonances with high localized field strengths in all-dielectric nanophotonics, novel states such as anapoles, hybrid anapoles and bound states in the continuum have been realized. Of these, the anapoles are the most readily achievable. Interaction between vertically stacked disks supporting anapole resonances increases the field localization further. When fabricated from materials with high non-linear coefficients, such stacked disk pillars can be used as non-linear antennas. The excitation of such 3D pillars often includes off normal incidence when using focusing optics. Therefore, it is important to evaluate the angular and polarization response of such pillars. In the paper we fabricate pillars with three AlGaAs disks in a stack separated by stems of GaAs. The angular and polarization responses are evaluated experimentally with integrating sphere measurements and numerically through simulation, multipole decomposition and quasi-normal modes. We find that the stacked geometry shows hybridized anapole excitation for a broad span of incidence angles, with tunability of the individual multipolar response up to octupoles, including an electric octupole anapole, and we show how the average enhanced confined energy varies under angled excitation. The results show that the vertical stacked geometry can be used with highly focusing optics for efficient in-coupling to the hybridized anapole.

Probing optical anapoles with fast electron beams

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

Singular optics empowered by engineered optical materials

The rapid development of optical technologies, such as optical manipulation, data processing, sensing, microscopy, and communications, necessitates new degrees of freedom to sculpt optical beams in space and time beyond conventionally used spatially homogenous amplitude, phase, and polarization. Structuring light in space and time has been indeed shown to open new opportunities for both applied and fundamental science of light. Rapid progress in nanophotonics has opened up new ways of "engineering" ultra-compact, versatile optical nanostructures, such as optical two-dimensional metasurfaces or three-dimensional metamaterials that facilitate new ways of optical beam shaping and manipulation. Here, we review recent progress in the field of structured light-matter interactions with a focus on all-dielectric nanostructures. First, we introduce the concept of singular optics and then discuss several other families of spatially and temporally structured light beams. Next, we summarize recent progress in the design and optimization of photonic platforms, and then we outline some new phenomena enabled by the synergy of structured light and structured materials. Finally, we outline promising directions for applications of structured light beams and their interactions with engineered nanostructures.

Germanium metasurface assisted broadband detectors

The demand on broadband near-infrared photodetections with high responsivity is becoming increasingly eminent; however its realization remains a significant technological challenge. Here we design, fabricate, and characterize a broadband Ge photodetector (1000-1600 nm), composed of densely packed 230-nm-thick Ge disks of different diameters (255 nm, 320 nm, and 500 nm), placed on top of a 105-nm-thin Ge layer. Using experimentally measured and calculated transmission and absorption spectra, we demonstrate that the absorption and detector responsivity are increased by nearly 2 orders of magnitude, compared to the unstructured Ge photodetector, due to the excitation of magnetic dipole resonances in Ge disks, while preserving a relatively low dark current. Our approach is simple and can be easily adapted to other semiconductor material platforms and operation wavelengths to enable performance improvements of broadband photodetector devices.

Tailoring the resonant modes in liquid crystal based all-dielectric metasurfaces

High refractive index dielectic metasurfaces are being increasingly studied for their novel light-matter interactions such as Huygen's lens, absolute transmission and complete absorption. Liquid crystal is a versatile medium with high dielectric anisotropy and hence interaction of light with the dielectric metasurfaces immersed in liquid crystal medium show complex behaviour compared to isotropic media. Most of the investigations on liquid crystal based electromagnetic response of dielectric metasurfaces focus on tunability of resonant frequencies and switching between the resonant states as a function of external stimuli such as electric field, temperature, etc. In the current work we present a detailed numerical investigation based on studies of scattering response, near-field and far-field radiation profiles of cubic Tellurium metasurfaces as a function of liquid crystal orientations in infrared frequencies. We show that the near-field and far-field radiation profiles of primary resonant modes-electric dipoles and magnetic dipoles reorient as a function of liquid crystal orientations. In particular, we study the effect of liquid crystal orientations on novel non-radiative states called anapoles. It is observed that liquid crystal orientations effect the excitation and orientation of anapole states within the Tellurium structures. This paves way for design of an electrically-driven switch between non-radiative and radiative states. Further, controlling the near-field and far-field radiation profiles opens up possibilities in designing liquid crystal based tunable multi-functional metasurfaces which can change the directionality of incident light.

Low loss sensitivity of the anapole mode in localized defective nanoparticles

The excitation of a nonradiating anapole in a high-index dielectric nanosphere is an effective pathway for enhancing light absorption. Here, we investigate the effect of localized lossy defects on the nanoparticle based on Mie scattering and multipole expansion theories and find its low sensitivity to absorption loss. The scattering intensity can be switched by tailoring the defect distribution of the nanosphere. For a high-index nanosphere with homogeneous loss distributions, the scattering abilities of all resonant modes reduce rapidly. By introducing loss in the strong field regions of the nanosphere, we achieve independent tuning of other resonant modes without breaking the anapole mode. As the loss increases, the electromagnetic scattering coefficients of the anapole and other resonant modes show opposite trends, along with strongly suppressed corresponding multipole scattering. While regions with strong electric fields are more susceptible to loss, the anapole's inability to emit or absorb light as a dark mode makes it hard to change. Our findings provide new opportunities for the design of multi-wavelength scattering regulation nanophotonic devices via local loss manipulation on dielectric nanoparticles.

Tunable localization of light using nested invisible metasurface cavities

An invisible cavity is an open resonant device that confines a localized field without producing any scattering outside of the device volume. By exploiting the scatter-less property of such device, it is possible to nest two invisible cavities, as the outer cavity would simply not notice the presence of the inner one, regardless of their relative position. As a result, the position of the inner cavity becomes a means to easily control the field localized inside the cavity and its quality factor. In this paper, we discuss the properties of nested invisible cavities as a simple method to achieve stronger localized fields and high tunable quality factor. Furthermore, we show that in optics, these cavities can be implemented using nanodisk-based dielectric metasurfaces that operate near their electric resonances.

Meta-Atoms with Toroidal Topology for Strongly Resonant Responses

A conductive meta-atom of toroidal topology is studied both theoretically and experimentally, demonstrating a sharp and highly controllable resonant response. Simulations are performed both for a free-space periodic metasurface and a pair of meta-atoms inserted within a rectangular metallic waveguide. A quasi-dark state with controllable radiative coupling is supported, allowing to tune the linewidth (quality factor) and lineshape of the supported resonance via the appropriate geometric parameters. By conducting a rigorous multipole analysis, we find that despite the strong toroidal dipole moment, it is the residual electric dipole moment that dictates the electromagnetic response. Subsequently, the structure is fabricated with 3D printing and coated with silver paste. Importantly, the structure is planar, consists of a single metallization layer and does not require a substrate when neighboring meta-atoms are touching, resulting in a practical, thin and potentially low-loss system. Measurements are performed in the 5 GHz regime with a vector network analyzer and a good agreement with simulations is demonstrated.

Temperature-resilient anapole modes associated with TE polarization in semiconductor nanowires

Polarization-dependent scattering anisotropy of cylindrical nanowires has numerous potential applications in, for example, nanoantennas, photothermal therapy, thermophotovoltaics, catalysis, sensing, optical filters and switches. In all these applications, temperature-dependent material properties play an important role and often adversely impact performance depending on the dominance of either radiative or dissipative damping. Here, we employ numerical modeling based on Mie scattering theory to investigate and compare the temperature and polarization-dependent optical anisotropy of metallic (gold, Au) nanowires with indirect (silicon, Si) and direct (gallium arsenide, GaAs) bandgap semiconducting nanowires. Results indicate that plasmonic scattering resonances in semiconductors, within the absorption band, deteriorate with an increase in temperature whereas those occurring away from the absorption band strengthen as a result of the increase in phononic contribution. Indirect-bandgap thin ([Formula: see text]) Si nanowires present low absorption efficiencies for both the transverse electric (TE, [Formula: see text]) and magnetic (TM, [Formula: see text]) modes, and high scattering efficiencies for the TM mode at shorter wavelengths making them suitable as highly efficient scatterers. Temperature-resilient higher-order anapole modes with their characteristic high absorption and low scattering efficiencies are also observed in the semiconductor nanowires ([Formula: see text] nm) for the TE polarization. Herein, the GaAs nanowires present [Formula: see text] times greater absorption efficiencies compared to the Si nanowires making them especially suitable for temperature-resilient applications such as scanning near-field optical microscopy (SNOM), localized heating, non-invasive sensing or detection that require strong localization of energy in the near field.

Deterministic Excitation of Polarization-Sensitive Extrinsic Anapole State in Si Nanodisk Clusters

Nanoparticle clusters provide new degrees of freedom for light control due to their mutual interaction compared with an individual one. Here, the authors demonstrate theoretically and experimentally a type of optical anapole (a nonradiating state) termed as extrinsic anapole, with mode field spreading across Si nanodisk dimers unlike the intrinsic one that is confined within individual nanodisks. The extrinsic anapole is sensitive to the polarized excitation. When the electric vector E of excitation is perpendicular to the dimer axis, the coupled toroidal dipole (TD) mode is largely enhanced and broadened to be spectrally overlapped with the electric dipole (ED) mode. The destructive interference of these two modes results in the generation of the extrinsic anapole. However, it vanishes when E is parallel to the dimer axis. Such polarization dependence can be relieved with the participation of the third nanodisk. Scattering spectra of Si nanodisk trimers stay almost unchanged under different polarized excitations, although the near-field distributions are quite different. Finally, enhanced white-light emission is observed in Si nanodisk clusters, which can be attributed to the near-infrared absorption enhancement induced by extrinsic anapole states. The findings manifest that high-index all-dielectric nanodisk clusters are promising for light manipulation based on mode interference.

Manipulating light scattering and optical confinement in vertically stacked Mie resonators

High index dielectric nanoresonators have gained prominence in nanophotonics due to lower losses compared to plasmonic systems and their ability to sustain both electric and magnetic resonances. The resonances can be engineered to create new types of optical states, such as bound-states in a continuum (BIC) and anapoles. In this work, we report on the optical properties of vertically stacked AlGaAs nanodisk Mie resonators. The nanodisks are designed to support an anapole state in the visible wavelength region (400-700 nm). The vertically stacked nanodisk resonators are fabricated from AlGaAs/GaAs multilayer samples with a fast and scalable patterning method using charged sphere colloidal lithography. Both measurements and finite difference time domain (FDTD) simulations of two and three stacked resonators show a sharp dip in the reflectance spectra at the anapole wavelength. For the 2 and 3 disk stacks the reflectance dip contrast at the anapole wavelength becomes very pronounced in the specular reflectance and is attributed to increased directional scattering due to an antenna effect. FDTD simulations show there is enhanced field confinement in all the disks at the anapole wavelength and the confined energy within the individual disks in the stack is at least 2-5 times greater compared to an isolated single nanodisk of the same dimension. Furthermore, the field confinement consistently increases with adding more disks in the stack. These vertically stacked AlGaAs nanodisk resonators can be a very exciting platform to engineer light matter interactions for linear and non-linear optical applications. The general principles of the fabrication method can be adapted to other wavelength ranges and can also be adapted for other III-V material combinations as well as for Si/SiO2.

An All-Dielectric Metasurface Polarimeter

The polarization state of light is a key parameter in many imaging systems. For example, it can image mechanical stress and other physical properties that are not seen with conventional imaging and can also play a central role in quantum sensing. However, polarization is more difficult to image, and polarimetry typically involves several independent measurements with moving parts in the measurement device. Metasurfaces with interleaved designs have demonstrated sensitivity to either linear or circular/elliptical polarization states. Here, we present an all-dielectric meta-polarimeter for direct measurement of any arbitrary polarization state from a single-unit-cell design. By engineering a completely asymmetric design, we obtained a metasurface that can excite eigenmodes of the nanoresonators, thus displaying a unique diffraction pattern for not only any linear polarization state but all elliptical polarization states (and handedness) as well. The unique diffraction patterns are quantified into Stokes parameters with a resolution of 5° and with a polarization state fidelity of up to 99 ± 1%. This holds promise for applications in polarization imaging and quantum state tomography.

Designing two-dimensional temperature profiles using tunable thermoplasmonics

Heat flow generation and manipulation in nanometer-sized solids using light represents one of the up-and-coming tasks in thermonanophotonics. Enhanced light-matter interaction due to plasmon resonance permits metallic nanostructures to absorb light energy efficiently, and it results in extra optical heating. The net temperature increment of nanostructures is directly dependent on heat exchange with a thermostat. However, to the best of our knowledge, precise tailoring of optical heating at a fixed pump power is still of no practical implementation. In this paper, we focus on the tunable optical heating of a plasmonic nanostructure exposed to moderate light intensity (MW cm^-2) based on slowing down heat exchange through a 1D waveguide heatsink bridging the nanostructure and the highly thermal conducting thermostat. The rationale for this concept is evidenced through optical heating of a 2D array of stacked titanium nitride (TiN) (plasmonic refractory nanoheater) and height-controlled silicon (Si) (1D waveguide heatsink) cylinders. Depending on the Si pillar height, the temperature rise of a TiN : Si voxel ranges from a few up to thousands of degrees at a fixed pump power. The temperature of the TiN : Si voxel is remotely measured from the Raman shift of the Si pillar. Using ellipsometry, we find a temperature threshold of 400 °C, above which the thin TiN film is chemically degraded due to oxidation. The latter enables fine tailoring of thermal gradients using TiN : Si voxels of equal size but different permittivity. These findings contribute towards the development of tunable thermoplasmonics by demonstrating programmable non-uniform temperature profiles in the steady-state regime under continuous-wave laser illumination for a variety of thermo-optical applications.

Anapole States in Gap-Surface Plasmon Resonators

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

Toroidal dipole-modulated dipole-dipole double-resonance in colloidal gold rod-cup nanocrystals for improved SERS and second-harmonic generation

Colloidal metal nanocrystals (NCs) show great potential in plasmon-enhanced spectroscopy owing to their attractive and structure-depended plasmonic properties. Herein, unique Au rod-cup NCs, where Au nanocups are embedded on the one or two ends of Au nanorods (NRs), are successfully prepared for the first time via a controllable wet-chemistry strategy. The Au rod-cup NCs possess multiple plasmon modes including transverse and longitudinal electric dipole (TED and LED), magnetic dipole (MD), and toroidal dipole (TD) modulated LED resonances, producing large extinction cross-section and huge near-field enhancements for plasmon-enhanced spectroscopy. Particularly, Au rod-cup NCs with two embedded cups show excellent surface-enhanced Raman spectroscopy (SERS) performance than Au NRs (75.6-fold enhancement excited at 633 nm) on detecting crystal violet owing to the strong electromagnetic hotspots synergistically induced by MD, LED, and TED-based plasmon coupling between Au cup and rod. Moreover, the strong TD-modulated dipole-dipole double-resonance and MD modes in Au rod-cup NCs bring a 37.3-fold enhancement of second-harmonic generation intensity compared with bare Au NRs, because they can efficiently harvest photoenergy at fundamental frequency and generate large near-field enhancements at second-harmonic wavelength. These findings provide a strategy for designing optical nanoantennas for plasmon-enhanced applications based on multiple plasmon modes.

Electronic Supplementary Material

Supplementary material (SEM image of Au rod-one-cup NCs; TEM image of Au/PbS hybrids; SEM image of Au rod-two-cup NCs; low-amplification SEM image of Au rod-two-cup NCs; experimental extinction and calculated electric field distributions of Au NR excited at different wavelengths; calculated absorption and scattering spectra of Au rod-one-cup NCs; schematic illustration of the cut plane and the corresponding magnetic field distribution under L3 excitation; Raman spectra of CV (10-6 M) adsorbed on Au rod-cup NCs with different cup sizes; calculated magnetic field distribution of Au rodcup NCs excited at 532 and 633 nm; calculated electric field distributions of Au rod-one-cup NC excited at 600 nm along TE and LE; the models of Au rod-cup NCs used in the simulations) is available in the online version of this article at 10.1007/s12274-022-4562-5.

Multifunctional and Transformative Metaphotonics with Emerging Materials

Future technologies underpinning multifunctional physical and chemical systems and compact biological sensors will rely on densely packed transformative and tunable circuitry employing nanophotonics. For many years, plasmonics was considered as the only available platform for subwavelength optics, but the recently emerged field of resonant metaphotonics may provide a versatile practical platform for nanoscale science by employing resonances in high-index dielectric nanoparticles and metasurfaces. Here, we discuss the recently emerged field of metaphotonics and describe its connection to material science and chemistry. For tunabilty, metaphotonics employs a variety of the recently highlighted materials such as polymers, perovskites, transition metal dichalcogenides, and phase change materials. This allows to achieve diverse functionalities of metasystems and metasurfaces for efficient spatial and temporal control of light by employing multipolar resonances and the physics of bound states in the continuum. We anticipate expanding applications of these concepts in nanolasers, tunable metadevices, metachemistry, as well as a design of a new generation of chemical and biological ultracompact sensing devices.

Free-form optimization of nanophotonic devices: from classical methods to deep learning

Nanophotonic devices have enabled microscopic control of light with an unprecedented spatial resolution by employing subwavelength optical elements that can strongly interact with incident waves. However, to date, most nanophotonic devices have been designed based on fixed-shape optical elements, and a large portion of their design potential has remained unexplored. It is only recently that free-form design schemes have been spotlighted in nanophotonics, offering routes to make a break from conventional design constraints and utilize the full design potential. In this review, we systematically overview the nascent yet rapidly growing field of free-form nanophotonic device design. We attempt to define the term "free-form" in the context of photonic device design, and survey different strategies for free-form optimization of nanophotonic devices spanning from classical methods, adjoint-based methods, to contemporary machine-learning-based approaches.

Toroidal dipole resonances by a sub-wavelength all-dielectric torus

Electromagnetic toroidal excitations open up a new avenue for strong light-matter interactions. Although toroidal dipole resonances (TDRs) based on artificial meta-molecules were reported intensely, the TDRs supported in a single dielectric particle remain largely unknown. In this work, we show that an all-dielectric sub-wavelength torus can support a dominant TDR. The magnetic field can be enhanced greatly, and it shows a "vortex-like" configuration in the torus, confirming the toroidal excitation. The evolutions of the TDRs due to the geometrical parameters, dielectric permittivity, and polarization are discussed. It is found that the toroidal excitation is achieved mainly for TM polarization, while the anapole state is uncovered for TE polarization. This work suggests a new strategy for toroidal excitations based on a simple dielectric resonator.

Invisible Mie scatterer

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

Enhanced Chiral Mie Scattering by a Dielectric Sphere within a Superchiral Light Field

A superchiral field, which can generate a larger chiral signal than circularly polarized light, is a promising mechanism to improve the capability to characterize chiral objects. In this paper, Mie scattering by a chiral sphere is analyzed based on the T-matrix method. The chiral signal by circularly polarized light can be obviously enhanced due to the Mie resonances. By employing superchiral light illumination, the chiral signal is further enhanced by 46.8% at the resonance frequency. The distribution of the light field inside the sphere is calculated to explain the enhancement mechanism. The study shows that a dielectric sphere can be used as an excellent platform to study the chiroptical effects at the nanoscale.

Anapole Meta-Atoms: Nonradiating Electric and Magnetic Sources

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

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.

Strong couplings between magnetic quantum emitters and subwavelength all-dielectric resonators with whispering gallery modes

Here we theoretically investigate the coherent interactions between the quantum emitters with magnetic dipole transitions and subwavelength all-dielectric resonators of whispering gallery modes (WGMs). We extend a semi-analytical method which can efficiently calculate the far-field spectrum of a general hybrid system. Then, a subwavelength sphere with refractive index around n = 3.5 is chosen as the dielectric resonator. Due to the high magnetic field enhancements of the WGMs of the sphere, strong couplings between magnetic quantum emitters and subwavelength WGMs can occur, where a clear Rabi splitting appears on the extinction spectrum of the hybrid system. The match between the relaxation times of the WGMs and emitters are important to efficiently achieve a strong enough coupling. The other parameters including the order of a WGM, the radius, the refractive index, the transition dipole moment and excitation intensity are also important factors that can affect the couplings. Our results pave the way for strong interactions between light and magnetic emitters mediated by subwavelength all-dielectric resonators.

Near-field nonlinear imaging of an anapole mode beyond diffraction limit

Nonlinear nanophotonics, as an emerging field in nanophotonics, eagerly calls for experimental techniques for probing and analyzing near-field nonlinear optical signals with subwavelength resolution. Here, we report an aperture-type scanning near-field optical microscopic method for probing near-field nonlinear optical processes. As a demonstration, near-field third-harmonic generation from an anapole dark-mode state generated by a silicon nanodisk is probed and imaged. The measured results agree well with the simulations, with a spatial resolution down to $0.14{\lambda _0}$ and a sensitivity of 0.1 nW. This method provides a powerful tool for characterizing nonlinear light-matter interactions at the nanoscale, which can help, for example, to unveil crystal properties involving subwavelength defects or dislocations.

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.

Collective photonic response of high refractive index dielectric metasurfaces

Sub-wavelength periodic nanostructures give rise to interesting optical phenomena like effective refractive index, perfect absorption, cloaking, etc. However, such structures are usually metallic which results in high dissipative losses and limitations for use; therefore, dielectric nanostructures are increasingly considered as a strong alternative to plasmonic (metallic) materials. In this work, we show light-matter interaction in a high refractive index dielectric metasurface consisting of an array of cubic dielectric nano-structures made of very high refractive index material, Te in air, using computer modelling. We observe a distinct band-like structure in both transmission and reflection spectra resulting from the near-field coupling of the field modes from neighboring dielectric structures followed by a sharp peak in the transmission at higher frequencies. From the spatial distribution of the electric and magnetic fields and a detailed multipole analysis in both spherical harmonics and Cartesian components, the dominant resonant modes are identified to be electric and magnetic dipoles. Specifically at lower frequency (60 THz) a novel anapole-like state characterized by strong-suppression in reflection and absorption is observed, reported very recently as 'lattice-invisibility' state. Differently, at higher frequency (62 THz), strong absorption and near-zero far field scattering are observed, which combined with the field profiles and the multipole analysis of the near-fields indicate the excitation of an anapole. Notably the observed novel modes occur in the simple geometry of dielectric cubes and are a result of collective response of the metasurfaces. Periodicity of the cubic metasurface is shown as the significant material tuning parameter, allowing for the near-field and far-field coupling effects of anapole metasurface. More generally, our work is a contribution towards developing far-fetching applications based on metamaterials such as integrated devices and waveguides consisting of non-radiating modes.

Anapole mediated giant photothermal nonlinearity in nanostructured silicon

Featured with a plethora of electric and magnetic Mie resonances, high index dielectric nanostructures offer a versatile platform to concentrate light-matter interactions at the nanoscale. By integrating unique features of far-field scattering control and near-field concentration from radiationless anapole states, here, we demonstrate a giant photothermal nonlinearity in single subwavelength-sized silicon nanodisks. The nanoscale energy concentration and consequent near-field enhancements mediated by the anapole mode yield a reversible nonlinear scattering with a large modulation depth and a broad dynamic range, unveiling a record-high nonlinear index change up to 0.5 at mild incident light intensities on the order of MW/cm². The observed photothermal nonlinearity showcases three orders of magnitude enhancement compared with that of unstructured bulk silicon, as well as nearly one order of magnitude higher than that through the radiative electric dipolar mode. Such nonlinear scattering can empower distinctive point spread functions in confocal reflectance imaging, offering the potential for far-field localization of nanostructured Si with an accuracy approaching 40 nm. Our findings shed new light on active silicon photonics based on optical anapoles.

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.

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

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

Optical radiation manipulation of Si-Ge2Sb2Te5 hybrid metasurfaces

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

Strong field enhancement in individual Φ-shaped dielectric nanostructures based on anapole mode resonances

Due to their ability to produce high electric field enhancements in relatively large nanoscale volumes with minimum absorption and nonradiating properties, anapole modes excited in high index dielectric nanostructures have attracted considerable attentions in these years. We propose a design strategy to simultaneously excite the anapole mode efficiently and maintain its resonant wavelength, which has been remained as a challenge in the conventional dielectric nanostructures. Based on analyzing the relationship between the field enhancement factor and scattering intensity of the electric and toroidal dipoles, we introduce two and four nanocuboids into the nil field intensity areas in the silicon disk system, respectively. The geometric volume of the system can be increased effectively and the electric field enhancement is boosted to be 190% and 250% while the resonant wavelength of the anapole mode is almost maintained constant. The systems combined with a slot in the strongest field intensity area also follow the same law, revealing that the design strategy can be easily extended to other geometric, material and frequency systems. Different from the design strategy to add new components into the areas with strong field intensity, the incorporations occurring at the minimum intensity area is another design scheme to engineer the properties of the resonant systems and can find broad applications in nano-device designs.

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.