Toroidal Dipole Research Articles

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.

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.

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.

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.

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.

Active dual quasi-BICs in a dielectric metasurface with VO2 for slow light and optical modulation.

We investigate the temperature tunable dual quasi-bound states in the continuum (qBICs) in a silicon/vanadium dioxide (Si/VO2) hybrid metasurface with Q-factor being as large as 9.3 × 106 and 2.8 × 107 by breaking the in-plane C2 symmetry. The far-field scattering of multipoles and near-field distributions confirm that the toroidal dipole and magnetic quadrupole dominate the dual qBICs resonance. The high performance of slow light with ultralarge group index exceeding 5.6 × 105 and the inverse quadratic law between the group index and asymmetric parameter are achieved. By temperature tuning of the VO2 thin film at the sub-10 K scale, a modulation depth of 90% and the ON/OFF ratio exceeding 12.8 dB are obtained. The proposed temperature tunable dual qBICs have potential applications in the fields of tunable slow light, temperature switches, and sensors.

The high-Q THz stereo metasurface sensor based on double toroidal dipole with wide operating angle bandwidth

A highly sensitive terahertz stereo metasurface sensor, characterized by a high quality factor (Q-factor) and based on dual toroidal dipole (TD) resonance, has been proposed. The optimal structural parameters are ascertained by comparing the pertinent parameters of the stereo and planar structures in relation to TD modal excitation. The effective excitation of the TD mode is demonstrated using the calculations of multipole scattered power, reflection spectra, surface currents, electric fields, and magnetic field distributions. It is crucial that the stereo metasurface exhibits simplicity and that the dual TD resonance can be readily excited through simple adjustments in the distance and height of the intermediate gap. It also demonstrates exceptionally high sensitivity and Q-factor, both of which are essential for sensing applications. Moreover, the proposed stereo terahertz metasurface sensor still shows excellent sensing performance in a wide range of incidence angles (±40°), which is of great significance for practical applications. In conclusion, this structure offers a novel design framework for high-performance terahertz sensors based on the TD mode.

Sensing and frequency selecting with toroidal resonance in metasurface

A double M-shaped metasurface is proposed and produced to realize a high Q-factor resonance at 13 GHz. The numerical and experimental results show that the high Q excitation of the structure is caused by the strong toroidal dipole. The novel toroidal metasurface can be a refractive index sensor with a high sensitivity of 3.2 GHzRIU−1. In addition, the double layer metasurface can achieve frequency selection with a bandwidth of 0.27 GHz. The proposed metasurface further extends the application of toroidal dipole in the field of sensing, frequency selective surface and so on.

Polarization-independent tetramer metastructure with multi-Fano resonances governed by quasi-bound states in the continuum

We propose what we believe to be a novel metastructure consisting of silicon nanoblock tetramer clusters and investigated theoretically and experimentally how to enhance surface sensing capabilities with polarization-independent properties through bound states in the continuum (BICs). By introducing square defects, three quasi-BIC modes are excited at the wavelengths of 1013.29 nm, 1109.57 nm, and 1310.73 nm with a modulation depth up to 100% and a Q-factor of 16618, while achieving a sensitivity of 256 nm/RIU and a figure of merit of 2519.7 RIU−1. Utilizing the finite-difference method in the time domain (FDTD), we have analyzed the electromagnetic near-field distributions, polarization properties, and robustness corresponding to resonance dips at different wavelengths. Our results reveal that the distinct electromagnetic near-field distributions excited by the quasi-BIC modes are characterized by the strong field confinement within the silica nanoblock tetramer clusters. The modes are primarily governed by magnetic quadrupole (MQ) resonance and toroidal dipole (TD) moment. Additionally, the polarization-independent properties of the metastructure are demonstrated to ensure that they can effectively respond to the incident light regardless of its polarization state, while the robustness is investigated to show the stability and reliability by shifting square defects. Moreover, the transmission spectra of the metastructure is experimentally verified by immersing the sample into CaCl2 solutions in different concentrations. This work plays a pivotal role in creating further novel and high-performance optical metastructures while demonstrating the potential applications of quasi-BIC modes in precision sensing in the future.

Asymmetric dumbbell dimers simultaneously supporting quasi-bound states in continuum and anapole modes for terahertz biosensing

Abstract Multi-resonant metasurfaces are of great significance in the applications of multi-band nanophotonics. Here, we propose a novel metasurface design scheme for simultaneously supporting quasi-bound states in continuum (QBIC) and other resonant modes, in which QBIC resonance is generated by mirror or rotational symmetry breaking in oligomers while other resonant modes can be simultaneously excited by rationally designing the shapes of meta-atoms within oligomers. As an example, the simultaneous excitation of QBIC and anapole modes are demonstrated in a dimer metasurface composed of asymmetric dumbbell-shaped apertures. Based on the far-field multipole decomposition and near-field electromagnetic field distributions, the origin mechanisms of QBIC and anapole mode are elucidated. The symmetry breaking of dumbbell-shaped dimer results in QBIC. Within a certain asymmetric variation range, the contributions of toroidal dipole moment and electric dipole moment with approximately equal magnitudes remain dominant, which allows the anapole mode to always present. The effectiveness of the proposed design scheme is further confirmed by the experimental results identical with the evolutions of numerical simulation. In terahertz biosensing experiments, the anapole mode exhibits a higher sensitivity of 271.3 GHz (nmol/μl)−1, whereas the QBIC can achieve a lower detection limit of 0.015 nmol/μl and expands the detection range by almost an order of magnitude. Our findings are beneficial to designing multi-resonant metasurfaces with different resonance modes and promote the corresponding applications in the fields of biosensing, lasers, filtering, and nonlinearity.

Double-parameter analysis of an asymmetric herringbone temperature and refractive index sensor based on all-dielectric metasurface

The all-dielectric metasurface is a tremendously efficacious path to seek out planar optical manipulators. The application of extremely sensitive optical sensors is expected to benefit from the Fano resonances created in all-dielectric metasurface. An optical sensor basaed on the all-dielectric hollow herringbone metasurface is tuned for high-sensitivity temperature sensing and refractive index sensing. In the continuous near-infrared band, two resonance responses activated by magnetic toroidal dipole and magnetic quadrupole can be generated simultaneously. According to the simulation results, a superior properties refractive index sensor holding a Q factor as high as 2.6 × 104 is achieved, its maximum FOM of 3980 RIU−1 is displayed, and its sensitivity is 232 nm/RIU. And sensitivity of the temperature sensor is proved to be 63 pm/K, which shows a prominent improvement in temperature sensing. After analyzing it in the experiment, it is found that the Q factor is 5366 and FOM of 465 RIU−1, with the sensitivity of 178 nm/RIU. This refractive sensor provides a favorable groundwork for developing high-sensitivity sensing devices in many biochemical disciplines, which also increases the extensive application possibilities for biochemical analysis and environmental detection.

Dynamic tunable and switchable broadband near-infrared absorption modulator based on graphene-hybrid metasurface

The integration of graphene with metasurfaces enables devices with remarkable dynamic tunability, propelling electromagnetic (EM) manipulations to new heights by transitioning from static to dynamic control. In this study, we theoretically investigate a broadband absorption modulator with dynamic tunability based on a graphene hybrid metasurface. The metasurface consists of a monolayer graphene sheet sandwiched between a square silver block and a silica layer. The excitation of the magnetic toroidal dipole (MTD) leads to a significant enhancement of graphene’s electromagnetic absorption. By arranging four blocks as a supercell to support multi-resonance, we achieve a broadband modulator spanning from 1000 to 1210 nm, with graphene absorption exceeding 57 %. Notably, there is no plasmonic hybridization among adjacent components within the super unit. By tuning the Fermi energy of graphene, narrow-band tunability can be achieved at any wavelength within the operation spectrum. Furthermore, the designed device exhibits a perfect modulation depth (∼100 %). We demonstrate the switchability of the proposed device by showcasing its ON/OFF status at representative wavelengths of 1205 nm, 1119 nm, and 1052 nm. Thus, the proposed graphene-based hybrid metasurface fulfills the requirements for broadband tunability and switchability, offering a high ON/OFF ratio, full modulation depth, and a small switch voltage gap. This design holds significant potential for future developments.

Toroidal dipole bound states in the continuum in asymmetric dimer metasurfaces

Structural symmetry plays a pivotal role in the emergence of symmetry-protected bound states in the continuum (BICs), often observed at the Γ-point within the first Brillouin zone. However, structural symmetry is not an absolute requirement for the formation of BICs at the Γ-point. In this work, we demonstrate that all-dielectric metasurfaces and photonic crystal slabs, made of dimer nanostructures with different sizes and shapes, can sustain BICs at the Γ-point. We show that the nature of these BICs is well preserved, irrespective of the size mismatch/difference, as long as the center-to-center distance between two nanodisks is equal to half of the lattice constants of a superunit cell. The BICs are transformed into quasi-BICs (QBICs) with finite quality (Q) factors by varying the interspacing of dimer nanodisks. Multipole decomposition indicates that this BIC is primarily governed by a toroidal dipole, with a secondary contribution from a magnetic dipole and magnetic quadrupole. Furthermore, we establish that such a BIC is robust against the shape of nanodisks. Notably, we observe that the Q-factor of QBICs for right nanodisks displaced along the y-axis is three orders of magnitude higher than those along the x-axis, suggesting an effective approach to realizing ultrahigh-Q resonances. Finally, we present an experimental demonstration of such a BIC by fabricating silicon dimer metasurfaces and photonic crystal slabs with dimer nanoholes. The trend of measured Q-factors and resonant wavelengths of QBICs shows good agreement with theoretical predictions. The maximum Q-factor is up to 22 633. These results not only advance our understanding of BICs within compound metasurfaces but also hold great promise in enhancing light–matter interactions.

Cluster Odd-Parity Multipoles by Staggered Orbital Ordering in Locally Noncentrosymmetric Crystals

Odd-parity multipoles in crystals manifest themselves not only in their peculiar electronic orderings but also in unconventional parity-violating physical phenomena. We here report the emergence of odd-parity multipoles by considering staggered orbital orderings in a locally noncentrosymmetric crystal system with the global inversion center but without the inversion center at each lattice site. We show that various odd-parity multipoles, such as the electric toroidal monopole, electric dipole, and electric toroidal quadrupole, are realized depending on the type of orbital orderings in the one-dimensional zigzag chain. Such odd-parity multipoles give rise to an antisymmetric spin splitting in the electronic band structure with the aid of the relativistic spin–orbit coupling. We also show that similar states with odd-parity multipoles are realized in other locally noncentrosymmetric crystals, such as the two-dimensional honeycomb and three-dimensional diamond structures.

Terahertz Sensing Based on Floating Bilayer Metasurface with Toroidal Dipole Resonance Toward Ultra‐High Sensitivity

AbstractMetasurface structures have proven to be effective in enhancing terahertz sensing signals and can thus be used as sensors to improve terahertz detection sensitivity. However, the sensitivity is limited by the poor spatial overlap between the analytes and the local electric field of the metasurface. In this work, a novel design of a floating bilayer metasurface structure for terahertz sensing is proposed and investigated. This structure supports a sharp toroidal dipole resonance and can concentrate near‐field energy on the analyte and metal atoms rather than on the substrate surface by floating the metal atoms. Consequently, the sensitivity is significantly improved to as high as 362 GHz RIU−1; theoretically, this is approximately 2.6 times higher than that of the common metasurface. The ability of the floating bilayer metasurface to quantitatively detect chlorothalonil is experimentally demonstrated. The resonance peak shows a significant frequency shift of 7 GHz for a change of 0.0001 mg dL−1 in chlorothalonil concentration, reaching up to 86 GHz when the change in chlorothalonil concentration is 100 mg dL−1; this is approximately 6.6 times higher than that of the common metasurface. This work provides opportunities for metasurface to realize ultrasensitive sensing in the terahertz regime.