Toroidal Dipole Research Articles

Spin–Orbit Coupling Free Nonlinear Spin Hall Effect in a Triangle-Unit Collinear Antiferromagnet with Magnetic Toroidal Dipole

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is Drude-type, while the nonlinear spin conductivity has Hall-type characterization. We demonstrate the emergence of both spin conductivities in a breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with triangular geometry give rise to rich spin conductive phenomena.

High-Q magnetic toroidal dipole resonance in all-dielectric metasurfaces

High quality (Q) factor toroidal dipole (TD) resonances have played an increasingly important role in enhancing light–matter interactions. Interestingly, TDs share a similar far-field distribution as the conventional electric/magnetic dipoles but have distinct near-field profiles from them. While most reported works focused on the electric TD, magnetic TDs (MTDs), particularly high-Q MTD, have not been fully explored yet. Here, we successfully realized a high-Q MTD by effectively harnessing the ultrahigh Q-factor guided mode resonances supported in an all-dielectric metasurface, that is, changing the interspacing between silicon nanobar dimers. Other salient properties include the stable resonance wavelength but a precisely tailored Q-factor by interspacing distance. A multipole decomposition analysis indicates that this mode is dominated by the MTD, where the electric fields are mainly confined within the dielectric nanostructures, while the induced magnetic dipole loops are connected head-to-tail. Finally, we experimentally demonstrated such high-Q MTD resonance by fabricating a series of silicon metasurfaces and measuring their transmission spectra. The MTD resonance is characterized by a sharp Fano resonance in the transmission spectrum. The maximum measured Q-factor is up to 5079. Our results provide useful guidance for realizing high-Q MTD and may find exciting applications in boosting light–matter interactions.

Dielectric terahertz metasurface governed by symmetry-protected BIC for ultrasensitive sensing

The non-radiative bound states in the continuum (BIC) have attracted much attention in achieving theoretically infinite quality (Q) factor. In this paper, a dielectric terahertz metasurface with C 4v symmetry is proposed, and a toroidal dipole resonance is easily obtained under incident plane wave. Moreover, by slightly tuning the asymmetry parameter δ to break the in-plane symmetry of the structure (side length perturbation), a magnetic dipole BIC mode radiates as quasi-BIC (QBIC) with extremely narrow linewidth and ultrahigh Q of 1.2 × 104 at δ = 0.4 μm. It shows significant performance in THz sensing with the sensitivity around 446 GHz/RIU and figure of merit (FoM) up to 2267. The designed metasurface in the case of symmetry-breaking by position perturbation also achieves ultrasensitive sensing. Additionally, the effects of geometric parameters on the resonance modes have been comprehensively investigated. Our work provides a route to design symmetry-protected BIC metasurface with simple structure, and the Q factor as well as resonant frequency can be controlled using a single geometric parameter, which may facilitate designing high-performance metasurface in sensing applications.

High-Performance Refractive Index and Temperature Sensing Based on Toroidal Dipole in All-Dielectric Metasurface.

This article shows an all-dielectric metasurface consisting of "H"-shaped silicon disks with tilted splitting gaps, which can detect the temperature and refractive index (RI). By introducing asymmetry parameters that excite the quasi-BIC, there are three distinct Fano resonances with nearly 100% modulation depth, and the maximal quality factor (Q-factor) is over 104. The predominant roles of different electromagnetic excitations in three distinct modes are demonstrated through near-field analysis and multipole decomposition. A numerical analysis of resonance response based on different refractive indices reveals a RI sensitivity of 262 nm/RIU and figure of merit (FOM) of 2183 RIU-1. This sensor can detect temperature fluctuations with a temperature sensitivity of 59.5 pm/k. The proposed metasurface provides a novel method to induce powerful TD resonances and offers possibilities for the design of high-performance sensors.

Electric and magnetic toroidal dipole excitations in core-shell spheres

Electric and magnetic toroidal dipole excitations in core-shell spheres

Dual-band high-Q near-perfect absorption by tilted Si-assisted metasurfaces.

All-dielectric metasurface perfect absorbers (MPAs) based on quasibound states in the continuum (QBICs) play a crucial role in optical and photonic devices as they can excite high-Q resonances. These structures require adding back reflectors or placing at least two asymmetric elements in each unit to break the absorption limit of 50%, which will increase the design complexity. In this work, we propose a high-Q monolayer MPA (MMPA) composed of a tilted Si nanocube array. By tuning the tilted angle of the nanocube, dual-QBIC modes at two different wavelengths are excited, which corresponds to magnetic quadrupole (MQ) and toroidal dipole (TD) modes, respectively. The high-reflection but low-Q magnetic dipole (MD) background mode excited by such a dual-band structure can decrease the radiative loss of transmission of MQ and TD modes, enabling the structure to break the absorption limit of 50%. The maximum absorption achieves 94% simultaneously at the wavelength of 933 and 961 nm, with the Q factors of 759 and 986, respectively. Our work provides a simple paradigm for designing dual-band high-Q MMPAs, which would greatly expand their range of applications, such as multiplexed optical nanodevices.

Mechanism of formation and evolution of bound states in the continuum of split-hole all-dielectric metasurface under asymmetric displacement perturbation

Bound states in the continuum (BICs) with ultra-high Q properties have attracted much attention for their perfect localization in the continuous spectral range coexisting with extended waves. In this study, breaking the traditional excitation form of structure breakage or excitation field asymmetry, a monolithic silicon nanodisk array with relative displacement generated by the complete splitting of square nanopores is proposed based on the unique electromagnetic properties of all-dielectric metamaterials. During the introduction of perturbations by asymmetric displacements of splitting holes, it is shown by numerical simulations that two BICs at different wavelengths can be realized. Combined with eigenmodes of group theory, the symmetric matching relationship between the symmetry-protected BICs and the free-space radiation during the evolution process is analytically demonstrated, and the formation mechanism and the evolution law of the BICs excited by this metasurface are deeply investigated. meanwhile, it also provides a theoretical basis for the polarization dependence of quasi-BICs excitation and the ultra-high Q factor expression of BICs. Furthermore, near-field distribution and multipole decomposition show that the field distribution and surface currents support the excitation of BIC-driven toroidal dipole and magnetic quadrupole dual modes. This study not only provides an effective reference for the stability of high-Q resonance wavelengths, but also solves the problem of the lack of universality in analyzing the resonance mechanism based on resonance phenomena, and provides solid theoretical support for the study of displacement-mediated BICs resonance excitation and evolution.

Enhanced spontaneous radiation of quantum dots based on modulated anapole states in dielectric metamaterial

Dielectric nanostructures exhibit low-loss electrical and magnetic resonance, making them ideal for quantum information processing. In this study, the periodic double-groove silicon nanodisk (DGSND) is used to support the anapole state. Based on the distribution properties of the electromagnetic field in anapole states, the anapoles are manipulated by cutting the dielectric metamaterial. Quantum dots (QDs) are used to stimulate the anapole and control the amplification of the photoluminescence signal within the QDs. By opening symmetrical holes in the long axis of the nanodisk in the dielectric metamaterial, the current distribution of Mie resonance can be adjusted. As a result, the toroidal dipole moment is altered, leading to an enhanced electric field (E-field) and Purcell factor. When the dielectric metamaterial is deposited on the Ag substrate separated by the silicon dioxide (SiO2) layer, the structure exhibits ultra-narrow perfect absorption with even higher E-field and Purcell factor enhancement compared to silicon (Si) nanodisks.

Highly Sensitive Qualitative and Quantitative Identification of Cashmere and Wool Based on Terahertz Electromagnetically Induced Transparent Metasurface Biosensor.

Cashmere and wool are both natural animal fibers used in the textile industry, but cashmere is of superior quality, is rarer, and more precious. It is therefore important to distinguish the two fibers accurately and effectively. However, challenges due to their similar appearance, morphology, and physical and chemical properties remain. Herein, a terahertz electromagnetic inductive transparency (EIT) metasurface biosensor is introduced for qualitative and quantitative identification of cashmere and wool. The periodic unit structure of the metasurface consists of four rotationally symmetric resonators and two cross-arranged metal secants to form toroidal dipoles and electric dipoles, respectively, so that its effective sensing area can be greatly improved by 1075% compared to the traditional dipole mode, and the sensitivity will be up to 342 GHz/RIU. The amplitude and frequency shift changes of the terahertz transmission spectra caused by the different refractive indices of cashmere/wool can achieve highly sensitive label-free qualitative and quantitative identification of both. The experimental results show that the terahertz metasurface biosensor can work at a concentration of 0.02 mg/mL. It provides a new way to achieve high sensitivity, precision, and trace detection of cashmere/wool, and would be a valuable application for the cashmere industry.

Triple-band transparency effect by multiple couplings based on toroidal dipole resonance

We explored multiple couplings properties in composite metastructure. One part is the asymmetric double rings, supporting the narrow toroidal dipole resonance, and the other component is an upright rod that excites the broad electric dipole resonance. When these two resonant modes coincide in the spectrum, dual-band plasmon induced transparency (PIT) behavior can be obtained, which is attributed to in-phase and out-of-phase couplings between the toroidal dipole and electric dipole modes. Meanwhile, the dual-band features will become a single PIT band by varying the rotation offset angle between the upper- and lower-rings. Moreover, by introducing lateral displacement of the rod with respect to the toroidal component, a triple-band PIT effect can be achieved. In particular, under a large lateral displacement, a broadband transparency window appears across a wavelength range greater than 120 nm, where the transmission exceeds 0.9. It is derived from the hybrid coupling between toroidal dipole, electric dipole and induced high-order resonance modes. The toroidal-based PIT metamaterials not only promote the understanding of toroidal dipole moment but also provide a positive reference for toroidal-based meta-devices.

Multiple toroidal dipole Fano resonances from quasi-bound states in the continuum in an all-dielectric metasurface

In this paper, a highly sensitive sensor consisting of a silicon nanorod and symmetric rings (SNSR) is presented. Theoretically, three Fano resonances with high Q-factors are excited in the near-infrared range by breaking the symmetry structure based on quasi-bound states in the continuum (Q-BICs). The electromagnetic near-field analysis confirms that the resonances are mainly controlled by toroidal dipole (TD) resonance. The structure is optimized by adjusting different geometrical parameters, and the maximum Q-factor of the Fano resonances can reach 7427. To evaluate the sensing performance of the structure, the sensitivity and the figure of merit (FOM) are calculated by adjusting the environmental refractive index: the maximum sensitivity of 474 nm/RIU and the maximum FOM of 3306 RIU-1. The SNSR can be fabricated by semiconductor-compatible processes, which is experimentally evaluated for changes in transmission spectra at different solution concentrations. The results show that the sensitivity and the Q-factor of the designed metasurface can reach 295 nm/RIU and 850, while the FOM can reach 235 RIU-1. Therefore, the metasurface of SNSR is characterized by high sensitivity and multi-wavelength sensing, which are current research hotspots in the field of optics and can be applied to biomedical sensing and multi-target detection.

Numerical simulation on high quality anapole resonator with large electric field concentration in all-dielectric metasurface

In the field of nanophotonics, the manipulation of light using high refractive index dielectric materials has garnered significant attention in recent years. This occurs because dielectric materials with a high refractive index demonstrate lower losses in comparison to metallic plasmonic materials. Furthermore, the interference between internal toroidal dipole moment and electric dipole moment leads to destructive interference in the radiation field, resulting in the formation of an anapole state and localization of energy in the near-field. In this work, we initially excite the anapole state in a silicon nanodisk with a periodic nanostructured disk. By introducing a cross slit and adjusting the structural parameters, the anapole state is further optimized, and achieving highly concentrated near-field energy within the cross air slit of the silicon nanodisk. Specially designed, with a full width at halfmaximum (FWHM) of the transmitted spectrum of only 0.09 nm, and a Q factor of up to 9745, close to 104. Additionally, the structure can produce up to 571 times the electric field enhancement. The remarkable performance of a high Q factor and localized near-field energy holds great potential for various applications, including enhancing nonlinear effects, surface enhanced Raman scattering (SERS) and designing nanolasers.

Configurable dual-topological-interface-states induced reflection in hybrid multilayers consisting of a Ge2Sb2Te5 film

Active control of induced reflection is crucial for many potential applications ranging from slowing light to biosensing devices. However, most previous approaches require patterned nanostructures to achieve controllable induced reflection, which hinders their further applications due to complicated architectures. Herein, we propose a lithography-free multilayered structure to achieve the induced reflection through the coupling of dual-topological-interface-states. The multilayers consist of two one-dimensional (1D) photonic crystals (PCs) and an Ag film separated by a Spacer, topological edge state (TES) and topological Tamm state (TTS) can be excited simultaneously and their coupling induces the reflection window. The coupled-oscillator model is proposed to mimic the coupling between the TES and TTS, and the analytical results are in good agreement with finite element method (FEM). In addition, the TES-TTS induced reflection is robust to the variation of structural parameters. By integrating an ultra-thin phase-change film of Ge2Sb2Te5 (GST) into the multilayers, the induced reflection can be switched through the phase transition of the GST film. The multipole decomposition reveals that the vanished reflection window is arising from the disappearance of TTS associated with the toroidal dipole (TD) mode.

Multiple fano resonances based on all-dielectric metastructure for refractive index sensing

We investigate an optical refractive index sensor based on an all-dielectric metastructure in the near-infrared regime for achieving high sensitivity and high quality factor (Q-factor). By introducing the asymmetry in the metastructure, four sharp Fano resonances with high Q-factor are generated owing to the transition from symmetry-protected bound states in the continuum (BIC) to quasi-BIC, and the magnetic quadrupole (MQ) resonance, magnetic dipole (MD) resonance, and toroidal dipole (TD) resonance are analyzed by a combination of the field distributions. By evaluating the sensing performance with finite difference time domain (FDTD), the highest Q-factor can reach 6900, the modulation depth is close to 100 %, the sensitivity can reach 288 nm/RIU, and the figure of merit (FOM) is 888 RIU−1. Furthermore, the sensor is prepared using electron beam lithography (EBL), and inductively coupled plasma reactive ion etch (ICP-RIE), and high sensitivity is achieved in liquids with different refractive indices in the near-infrared. The results show a good sensing performance of the designed metastructure. Our findings will give access to the development of applications in non-linear devices, narrow-band filters, optical switches, and quantum nanophotonics.

High-Q quasi-bound states in the continuum in C2-symmetric metasurface with enhanced second harmonic generation in two-dimensional materials

Quasi-bound states in the continuum (Quasi-BIC) possess a high quality-factor (Q-factor) that can amplify local electromagnetic fields and nonlinear effects such as second harmonic generation (SHG). In this paper, we propose a silicon metasurface with C2 symmetry. By tuning the structural parameters without breaking the C2 symmetry, three symmetric protected BICs (SP-BICs) are transformed into sharp quasi-BICs dominated by different modes in the nearinfrared spectrum. The quasi-BICs exhibit Q-factors as high as 10370 in C2 symmetric metasurface. Numerical simulations reveal that the toroidal dipole (TD) and magnetic dipole (MD) enhance intercellular coupling and local electromagnetic fields, laying the foundation for generating metasurface with high Q-factor. Furthermore, the longitudinal radiative component of electric quadrupole (EQ) outside the facet promotes enhanced light interaction with the 2D material. Leveraging the robust local electromagnetic fields and radiation characteristics of these quasi-BICs, we have achieved substantial SHG enhancement across multiple wavelengths under continuous wave (CW) operation. The SHG from 2D GaSe flake reaches 14189-fold enhancement. Our results not only offer insights into designing metasurface structures with high Q-factors but also explore the methods of enhancing the interaction between metasurface and 2D materials. The proposed nanostructure has numerous potential applications in nonlinear optics, optoelectronics and signal processing.

Near-perfect absorption of a honeycomb metasurface through QBICs.

All-dielectric high-Q metasurface absorbers based on quasi-bound states in the continuum (QBICs) are essential for optical and photonic devices. However, achieving perfect absorption requires adding back reflectors at the bottom or placing at least four asymmetric elements in each unit of monolayer metasurfaces, which will increase the design complexity. This work proposes a honeycomb structure with units periodically arranged as a hexagonal lattice. Each unit cell is made of two nanopost elements. By only tuning the radius difference of two elements to break the in-plane symmetry, two orthogonal QBIC modes corresponding to toroidal dipole (TD) and electric dipole (ED) modes are excited, respectively. The maximum absorption reaches 92.3% at 955 nm with a Q factor of 1501, breaking the monolayer limit of 50% by the degenerate critical coupling. Our work may provide a promising route for designing high-Q all-dielectric metasurface absorbers applied in ultrafast optoelectronic devices.

Multi-function sensing applications based on high Q-factor multi-Fano resonances in an all-dielectric metastructure.

A multi-function sensor based on an all-dielectric metastructure for temperature and refractive index sensing simultaneously is designed and analyzed in this paper. The structure is composed of a periodic array of silicon dimers placed on the silicon dioxide substrate. By breaking the symmetry of the structure, the ideal bound states in the continuum can be converted to the quasi-bound states in the continuum, and three Fano resonances are excited in the near-infrared wavelength. Combining with the electromagnetic field distributions, the resonant modes of three Fano resonances are analyzed as magnetic dipole, magnetic toroidal dipole, and electric toroidal dipole, respectively. The proposed sensor exhibits an impressive maximal Q-factor of 9352, with a modulation depth approaching 100%. Our investigation into temperature and refractive index sensing properties reveals a maximum temperature sensitivity of 60 pm/K. Regarding refractive index sensing, the sensitivity and figure of merit are determined to be 279.5 nm/RIU and 2055.1 RIU-1, respectively. These findings underscore the potential of the all-dielectric metastructure for simultaneous multi-parameter measurements. The sensor's versatility suggests promising applications in biological and chemical sensing.

From non-scattering to super-scattering with Mie-tronics

Electric anapoles, arising from the destructive interference of primitive and toroidal electric dipole moments, have recently emerged as a fundamental class of non-scattering sources. On the other hand, super-scattering states represent the opposite regime wherein the scattering cross-section of a subwavelength particle exceeds the single-channel limit, leading to a strong scattering behavior. Here, we demonstrate that the interplay between the topology of light and the subwavelength scatterer can lead to these two opposite responses within an isolated all-dielectric meta-atom. In particular, we present the emergence of a new non-scattering state, referred to as hybrid anapole, which surpasses conventional electric dipole anapoles by achieving a remarkable 23-fold enhancement in the suppression of far-field radiation and almost threefold enhancement in the confinement of electromagnetic energy inside the meta-atom. We also explore the role of particle orientation and its inversion symmetry in the scattering response and predict the possibility of switching between non-scattering and super-scattering states within the same platform. The presented study elucidates the role of light and matter topologies in the scattering response of subwavelength meta-atoms, uncovering two opposite regimes of light-matter interaction and opening new avenues in applications such as nonlinear optics and spectroscopy.

Toroidal metamaterial-assisted terahertz biosensor with high sensitivity

In this paper, a toroidal metamaterial for achieving highly sensitive sensors in the terahertz (THz) frequency range is proposed. Such a subwavelength structure consists of a pair of mirror-symmetric metal split-ring resonators and a single metal wire. By exciting the structure with vertically incident electromagnetic waves, high-Q transmission peaks are generated at 2.40 and 2.44[Formula: see text]THz. Near-field analysis reveals that the reverse-flowing currents in the metal split-ring resonators and the metal wire create a pair of magnetic dipoles connected end to end, resulting in a vortex-like magnetic field known as a toroidal dipole. Calculations of multipole scattering energy further confirm that the rapidly enhanced toroidal dipole is the primary factor responsible for the high-Q transmission peaks. This toroidal metamaterial can be used to design refractive index sensors with a sensitivity of up to 20[Formula: see text]GHz/RIU, enabling the detection of subtle changes in the surrounding environment’s parameters. Our strategy paves an alternative route to the development of highly sensitive sensors for biological and chemical molecules in the THz frequency range.

Terahertz Lattice enhanced Quasi-Anapole Immunosensor assisted by protein antibody and AuNPs

Terahertz (THz) metasurface immunosensor has the characteristics of label-free detection, good biocompatibility and high specificity because the antibody-modified of biomarkers has the ability to specifically recognize corresponding biomarkers and increase the detection sensitivity to the concentration of the recognized antigen. The limit of detection (LoD) of THz metasurface immunosensor is highly dependent on resonant field enhancement of metasurface. The anapole mode shows a radiationless state with nontrivial oscillating current configuration. To observe such mode in farfield, in this work, the concept of quasi-anapole (QA) mode is presented which is induced when the electric and toroidal dipoles with identical intensity radiate in antiphase on the metasurface with the unit cell of two split ring resonators (SRRs) on both sides of the central cut-wire. In addition, by coupling the first-order lattice mode to the QA mode, lattice-enhanced QA mode (LQA) was investigated and observed to further enhance field confinement and decrease radiative loss. As a practical application, immunosensor was designed and fabricated by functionalized gold nanoparticles conjugated with the specific monoclonal antibody onto the LQA metasurface to detect the cell concentration of SARS-CoV-2 spike protein. The experimental results indicate that the response of LQA immunosensor depends heavily on the concentration of the Anti-S modified on its surface. When the concentration of Anti-S is 50 pg/ml, the LoD reaches to 3 pg/ml (39 fmol). Such THz LQA immunosensor also shows good specific identification and validates its effectiveness in biomedical sensing.