Toroidal Dipole Research Articles

High-Q Resonances Induced by Toroidal Dipole Bound States in the Continuum in Terahertz Metasurfaces

The radiation mode of the interaction between electromagnetic waves and materials has always been a research hotspot in nanophotonics, and bound states in the continuum (BICs) belong to one of the nonradiative modes. Owing to their high-quality factor characteristics, BICs are extensively employed in nonlinear harmonic generators and sensors. Here, the influence of structural parameters on radiation modes has been systematically analyzed using band theory; the mechanisms of quasi-BIC mode and BIC mode were also analyzed through multipole decomposition of scattered power and near-field distribution. Notably, this study presents the discovery that the toroidal dipole-BIC (TD-BIC) arises from the interference and cancellation of electric and toroidal dipoles. The research results indicate that the structure, which supports symmetry-protected BICs, is sensitive to variations in the concentration of NaCl solution in its surroundings, making it applicable for liquid detection in miniaturized metal sensors. The proposed scheme broadens the applicability of BIC-based sensors and provides a prospective platform for biological and chemical sensing.

Simultaneously enhance electric and magnetic Purcell factor by strong coupling between toroidal dipole quasi-BIC and electric dipole

The larger electric or magnetic Purcell factor demonstrates that the structure can be utilized as an electric or magneto-optical emission project. Their simultaneous realization offers the potential for integrated circuits to achieve selective photon sources. In this study, we put forth a proposal for the simultaneous attainment of substantial electrical and magnetic Purcell enhancements. In our hybrid metal–dielectric metasurface, the toroidal dipole (TD) quasi bound states in the continuum mode and the electric dipole (ED) mode are strongly coupled, so the hybrid mode combines the advantages of both, with a large Q factor and a small mode volume. The design implements a Rabi splitting energy of 222 meV between the TD quasi-BIC and ED modes, achieving an electric Purcell factor of 43 and a magnetic Purcell factor of 684, which are greater than those observed for the metal rod and dielectric structure, respectively. This paves the way for the development of high-performance hybrid optoelectronic applications.

Numerical simulation of electromagnetically induced transparency in composite metamaterial

Abstract In high-refractive-index dielectric nanostructure, the Mie resonance become evident, and the destructive interference of the radiation fields from electric and toroidal dipole moments results in the excitation of anapole state, which has the unique optical properties of a dark state and can support the excitation of more diverse optical phenomena, such as the electromagnetically induced transparency (EIT) effect. In this study, we performed numerical simulations of a composite metamaterial consisting of Si nanocubes and gold nanorods. The Au-Si composite structure produces an electromagnetically induced transparency spectrum based on the coupling of the optical dark channel (i. e. anapole state) and bright channel (i. e. localized surface plasmon resonance). By tailoring the surface structure of the dielectric Si cube, the surface charge and current distributions can be modified, and finally, the nonradiative anapole state may be influenced and manipulated. The results show that the modified metal/dielectric metamaterial can realize an electromagnetically induced transparency effect with a transmission of up to 95% and a refractive index sensitivity of 170 nm RIU−1.

Toroidal dipole resonances enhanced second-harmonic generation with shallow etching of lithium niobate metasurface.

Lithium niobate (LiNbO3) has shown great potential for applications in nonlinear metasurfaces, thanks to its large second-order nonlinear coefficients and high integration capabilities. Optical resonances play a crucial role in further enhancing the nonlinear optical responses of LiNbO3 metasurfaces (LNMS). In this study, both numerically and experimentally, we designed and fabricated a metasurface structure that supports toroidal dipole (TD) resonance to enhance second-harmonic generation (SHG). This structure, which consists of an array of shallow-etched square columns on a continuous thin film, intensifies the SHG signal at 400 nm within the LiNbO3 film by means of strong local field confinement. Experimental results indicate that this signal is ten times stronger compared to that of lithium niobate on insulator (LNOI). These findings emphasize the potential of TD resonance in enhancing the performance of LiNbO3 in integrated nonlinear nanophotonic applications.

Dynamic tunable multi-channel ultra-narrowband absorber based on hollowed-out trapezoidal Si–graphene–Au metasurface

Abstract Dynamic tunable metasurfaces are of great interest for their optical modulation properties. This study proposes a metasurface with a rectangular hole etched from a silicon square. By converting this rectangular hole into a trapezoid, we disrupt the symmetry, transforming the symmetry-protected bound states in the continuum (BICs) into a quasi-BIC state, achieving triple Fano resonances with a maximum Q factor of 1074. The results of the multipole analysis suggest resonance modes are toroidal dipole, electric quadrupole and magnetic dipole, respectively. A typical dielectric/dielectric/metal structure is then formed by adding an Au layer below the original structure. The polarized-light absorption of the metasurface is found to be unaffected by the angle of incident light. An analysis of the thickness of the Si is studied on the effect of absorption. Eventually, a single layer of graphene is incorporated at the bottom of the Si. The dynamic modulation of the three absorption peaks of the composite metasurface is achieved by controlling the bias voltage to alter the Fermi level E f of graphene. The Si–graphene–Au structure has a sensitivity of 252.5 nm RIU−1 and the maximum performance value of 126.25 RIU−1 at E f = 1 eV. These results indicate that this composite metasurface has potential applications in the research of sensor direction.

Dual polarization-independent quasi-bound states in the continuum in a hetero-out-of-plane dielectric metasurface.

Symmetry-protected quasi-bound states in the continuum (qBICs) in metasurfaces with broken in-plane symmetry are extensively investigated to achieve high quality-factor (Q-factor) resonances. Herein, we propose the hetero-out-of-plane (H-OP) dielectric metasurface, which is composed of Si cuboids tetramer broken out-of-plane symmetry by adding a layer of silica. Dual polarization-independent qBICs are realized. The multipolar decomposition of scattering powers and near-field distributions reveal the physical mechanism of dual qBICs modes, which are dominated by the magnetic quadrupole and the toroidal dipole. The two symmetry-protected qBICs in the H-OP metasurface have robust Q-factors and stable resonance wavelengths compared with these in the out-of-plane metasurface. Our results provide a route to achieve the high Q-factor resonator with better performance applied in many optical and optoelectronic devices.

Candidate Toroidal Electric Dipole Mode in the Spherical Nucleus ^{58}Ni.

Dipole toroidal modes appear in many fields of physics. In nuclei, such a mode was predicted more than 50years ago, but clear experimental evidence was lacking so far. Using a combination of high-resolution inelastic scattering experiments with photons, electrons, and protons, we identify for the first time candidates for toroidal dipole excitations in the nucleus ^{58}Ni and demonstrate that transverse electron scattering form factors represent a relevant experimental observable to prove their nature.

Optimizing the chiral optical response in nanostructures using plasmonic Fano resonance

This study investigates the chiral enhancement effects of plasmonic Fano resonance modes in planar metallic nanostructures. The nanostructure consists of a central Z-shaped or 卍-shaped element surrounded by six clustered gold nanorods, focusing on the coupling between these doubly rotationally symmetric structures. This coupling induces plasmonic Fano resonance, which significantly enhances the chiral response. Under normal incidence of circularly polarized light, the maximum chiral response can reach up to 41%. Finite-difference time-domain simulation and multipole expansion analysis reveal the fundamental origin of this enhanced chiral response: the selective excitation of electric dipoles and toroidal dipoles in polarization. The study demonstrates that rotationally symmetric structures and coupling effects play a crucial role in modulating the chiral response of nanostructures.

High-Q triple-mode quasi-bound states in the continuum in an asymmetric dielectric metamaterial

Bound states in the continuum (BICs) in metamaterials have attracted much attention due to their high efficiency in field enhancing. In this paper, we numerically demonstrated the triple-mode symmetry-protected BICs (SP-BICs) in an all-dielectric microtube metamaterial. By moving the hollows transversely and longitudinally in microtubes, three SP-BICs are transformed into high quality-factor (Q-factor) quasi-BICs (q-BICs), which are supported by asymmetric magnetic toroidal dipole electric hexapolar resonances respectively. The maximum Q-factor of q-BICs enabled by asymmetric magnetic toroidal dipole reaches 67647. This high Q-factor triple-mode q-BICs in all-dielectric microtube metamaterial has great potential in the applications of sensing, laser generation, and nonlinear optics.

Analogue of electromagnetically-induced transparency by toroidal dipole in a symmetry-breaking metamaterial

Analogue of electromagnetically-induced transparency (EIT) in metamaterials was typically based on the destructive interference between electric and magnetic dipolar resonances. In this work, a dipolar toroidal response is demonstrated by a plasmonic metamaterial composed of a ring and a disk. We theoretically demonstrate that the toroidal dipole can couple with the magnetic dipolar response (subradiant mode) and thus induce the EIT-like phenomenon by breaking the geometrical symmetry of the considered metamaterial. The result also shows a promising potential for applications of high-sensitivity resonant transmission associated with the intriguing toroidal moment.

Quasi-bound states in the continuum with stable dual-resonance wavelengths in mid-infrared metasurface for ultrasensitive refractive index sensing and molecular vibrations of strong coupling.

In this paper, a dual-resonances mid-infrared all-dielectric metasurface sensor based on asymmetric cross dimer, which is driven by quasi-bound states in the continuum (QBIC), is proposed and investigated. The metasurface sensor maintains the total permittivity constant when the asymmetric parameter is adjusted, thereby ensuring the stability of the QBIC resonance wavelengths, which exhibit Q-factors of 6351 and 13561, respectively. The multiple decompositions and electromagnetic field distributions reveal that the toroidal dipole is the dominant component of the dual-resonance modes. The sensitivities to the refractive index are 3559 nm/RIU and 1146 nm/RIU, with corresponding figures of merit of 4449 RIU-1 and 2453 RIU-1, respectively. Further numerical simulations have demonstrated a strong coupling phenomenon between the QBIC and the molecular vibrations of polymethyl methacrylate (PMMA), resulting in a significant enhancement of the infrared absorption signal. With the 50-nm-thick PMMA layer, the enhancement of molecular signal is 90.614%.

Spontaneous Magnetization Induced by Antiferromagnetic Toroidal Ordering.

The magnetic toroidal dipole moment, which is induced by a vortex-type spin texture, manifests itself in parity-breaking physical phenomena, such as a linear magnetoelectric effect and nonreciprocal transport. We elucidate that a staggered alignment of the magnetic toroidal dipole can give rise to spontaneous magnetization even under antiferromagnetic structures. We demonstrate the emergence of uniform magnetization by considering the collinear antiferromagnetic structure with the staggered magnetic toroidal dipole moment on a bilayer zigzag chain. Based on the model calculations, we show that the interplay between the collinear antiferromagnetic mean field and relativistic spin-orbit coupling plays an important role in inducing the magnetization.

Enhanced high-harmonic generation in a polarization-insensitive all-dielectric metasurface exploiting dual-Fano resonance

Nonlinear optics demands efficacious techniques for nonlinear properties engineering. Metasurfaces, as a flat technology with easy fabrication in various arrangements and without the need for phase-matching conditions, are suitable platforms for nonlinear optics. This study proposes a silicon metasurface with special geometry that provides high conversion efficiency by exploiting Fano resonances and the excitation of magnetic and toroidal dipoles. The results indicate the high efficiencies of third harmonic generation of 5.17×10−3 W−2 and fifth harmonic generation of 7.92×10−9 W−4 under 1 GW/cm2 pump intensity in the near-infrared regime. More specifically, linear and nonlinear optical responses of the structure are completely polarization-independent.

All-dielectric ellipsoidal tetramer metasurface sensor with multi-resonances from the bound states in the continuum.

We demonstrate an all-dielectric tetramer metasurface that achieves high-precision refractive index sensing through the excitation of toroidal dipole, magnetic dipole, and electric quadrupole modes, driven by bound states in the continuum (BIC). The metasurface exhibits exceptional performance, with a quality factor of 4.65 × 104, a sensitivity parameter of 649 nm/RIU, and a figure of merit of 1.51 × 104 RIU-1, achieved by optimizing symmetry and lattice perturbations in periodic silicon tetramer ellipsoidal nanodisks on a SiO2 substrate. Additionally, the sensor effectively distinguishes analytes with extinction coefficient differences as small as 0.01 through enhanced broadband absorption. This innovation demonstrates substantial potential for label-free sensing applications in microfluidic chip integration.

High quality factor of bound states in continuum in hBN metasurface

A bound state in the continuum (BIC) metasurface (MS) was designed to achieve an ultrahigh quality factor(Q factor) using natural hyperbolic materials, such as hexagonal boron nitride. To investigate the structure's dispersion and Q factor, a unit cell of the MS comprising semicircles and rectangles was designed. This MS structure supports symmetry-protected BICs and exhibits a Q factor of approximately 13 000 at 4.43964 × 1013 Hz. By breaking the MS symmetry, the BICs are converted into quasi-BICs, resulting in quasi-BIC resonance with a high Q factor. Further analysis of the reflection spectra and multipole theory indicates that the toroidal dipole (TD) has the most significant influence on the resonance. Thus, the symmetry-protected BIC can be transformed into the TD resonance with a Q factor by breaking symmetry.

The investigation of an inspired type toroidal dipole flexible metasurfaces at terahertz frequencies

We theoretically and experimentally carried out an inspired type of toroidal dipole (TD) metasurfaces, which composed of a metamolecule of symmetric aluminium semicircles with a bar in the middle fabricated on polyimide substrate in the terahertz (THz) regime. It was found that the three resonances show red-shift tendency due to the increase of inductance and capacitance with the increase of semicircle's outer radius. Meanwhile, both the TD resonances and the current flowing in the metallic bar can generate the head-to-tail magnetic field distribution, which is the most prominent feature of TD phenomenon. The generation of this phenomenon is discussed deeply via the power of the multipoles, which are calculated according to the volume current density distribution data extracted from the simulations. The low frequencies (∼0.5 THz) head-to-tail magnetic field distribution is mainly attributed to TD resonance generated via the mutual effect between the two semicircles, while the same phenomenon at high frequencies (∼0.8 THz) is mainly attributed to the current flowing the middle metallic bar. The enhancement of head-to-tail magnetic field distribution leads to the increase of quality (Q) factor, and the Q factor of fabricated sample is as high as 24.5. Moreover, the electromagnetic properties in TD metasurfaces could be adjusted by the metal bar's width. The optimization of TD resonances provides opportunity to design the high Q-factor metasurfaces, and it opens up potential applications in terahertz high sensitivity devices.

Efficient second-harmonic generation in a lithium niobate metasurface governed by high-Q magnetic toroidal dipole resonances.

Lithium niobate (LN) is an excellent nonlinear optical material due to its large nonlinear coefficient, low loss, and broad optical transparency window. So, it is widely used in the generation of nonlinear harmonics. Magnetic toroidal dipole (MTD) resonance is a special optical resonance mode, which can effectively localize the light field inside the device, thus enhancing the nonlinear effects of the materials. In this work, we numerically study the second-harmonic generation (SHG) effect of the LN metasurface based on the MTD mode with a high quality factor (Q-factor). The designed LN nanorod dimer metasurface supports high Q-factor MTD guided mode resonances (GMRs), which are excited by varying the center spacing of the two nanorods, and the Q-factor can be controlled by the offset distance. The excited MTD can effectively confine the electric field within the device, which enables the LN metasurface SHG conversion efficiency to reach 1.15 × 10-2. In addition, by adjusting the structural parameters, it is possible to effectively modulate the wavelength and conversion efficiency of the SHG. Our results provide a new route for high-quality nonlinear light sources.

Excitation and manipulation of toroidal dipole response in an antenna

The toroidal dipole is always overlooked due to its relatively weak interaction with the electromagnetic fields, but it actually exhibits tremendous potential for the design of advanced photonic devices. Here, we demonstrate the existence of toroidal dipole in plasma antenna system, which is rarely observed in the antenna design. It consists of a half-wavelength antenna and eight plasma rings to excite the toroidal dipole to enhance the electromagnetic radiation of the whole antenna system, whose mechanism is different from conventional antenna, which is a multiband antenna. We further confirm that the hybrid mode, which combines the toroidal dipole and multipole moments, can be dynamically adjusted to control both return loss and the opening of operating windows. This allows for flexible tuning of the multiband antenna simply by manipulating the response of the toroidal dipole. Furthermore, the toroidal dipole antenna is stable in dusty plasma, making it suitable for solving the problem of ‘blackout’ phenomena in aerospace communications, which exhibits the additional benefits of reduced cost and easier to manufacture.

Terahertz meta-biosensor for subtype detection and chemotherapy monitoring of glioma cells

Rapid and precise identification of glioma subtypes can assist surgeons in quickly determining patients’ conditions and developing treatment plans. However, current methods face challenges such as high cost and limited sensitivity, thereby significantly hindering diagnostic efficiency. In this paper, we proposed a spectral sensing strategy by introducing terahertz biosensors for glioma subtype recognition and therapeutic efficacy monitoring. Our findings demonstrated that both the resonance frequency and amplitude of the transmission spectra varied as the cell increased. The two-dimensional fingerprint diagram could help us rapidly recognize cell subtypes. Additionally, we conducted a theoretical analysis of the sensing performance. We confirmed that the high Q-factor (∼27.8) results from toroidal dipole resonance and examined the impact of dielectric loss and the refractive index of the analyte on the resonance dip. Furthermore, we applied the biosensor in therapeutic drug screening and showed that as the concentration of tubastatin A increased, the resonance frequency shifted from 183.1 GHz to 76.2 GHz. This result indicates that the toroidal dipole constructed by the metasurface enables ultrasensitive light-matter interactions that amplify subtle cellular changes to the resonance spectrum. The proposed THz meta-biosensor demonstrates significant potential for rapid intraoperative recognition of glioma cell subtypes and therapeutic efficacy monitoring.

Double rectangular-grooves metasurface for highly efficient electric modulation

With the rapid development of optical communication, how to achieve efficient modulation (fast response speed and high modulation depth) of optical signals has attracted more and more attention from researchers. Among all electro-optical modulator (EOM) designs, the electro-optical metasurface is undoubtedly a competitive solution for optical signal modulation in free space. Although current research on electro-optical metasurfaces has realized improving response speed owing to the Pockels effect, there are still difficulties in achieving high modulation depth under CMOS-compatible voltage and developing rational designs of metasurfaces to achieve voltage application that trigger electro-optical effects. In this work, an ultrahigh-Q factor BaTiO3 (BTO) electro-optical metasurface, which consists of a periodic array of rectangular grooves, was designed to provide a feasible solution to address these shortcomings. Based on bound states in the continuum (BIC) theory, ultrahigh-Q factor (2.87 × 105) quasi-BIC (Q-BIC) was obtained around 1550 nm by breaking the in-plane symmetry of the two rectangular grooves in a unit cell, which could significantly deepen the modulation depth. The concave and continuous structure of rectangular grooves made the application of voltage more efficient. The simulation results show that an optical signal modulation in free space with a modulation depth of 100% could be achieved. Multipole decomposition indicated that toroidal dipole (TD) was dominant in this Q-BIC. Our work may further promote the development of electro-optical modulation towards faster and deeper modulation.