Toroidal Dipole Mode Research Articles

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 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.

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.

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.

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.

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.

Magnetically Reconfigurable Toroidal Metasurfaces

AbstractHarnessing electron spin within limited dimensions under applied magnetic fields can lead to spin‐assisted tunable light‐matter interactions, which form a crucial step in developing frequency‐agile opto‐spintronic structures toward next generation photonic devices. For this purpose, spin‐dependent magneto transport phenomena derived from ferromagnetic (FM)/nonmagnetic (NM) multilayer structures have recently emerged as a useful tool for dynamically tailoring electromagnetic waves. With this pretext, five layers of aluminum (Al)/nickel (Ni) based multilayer thin films in sub skin depth regime are studied in terahertz domain under low‐intensity (0 to 30 mT) magnetic fields while systematically varying the NM spacer layer (sandwiched between the FM layers) from 8 to 18 nm. Such thin multi‐layer films demonstrate conductivity variations up to ≈40% for 30 mT of applied field. Utilizing the same multilayer configurations, magnetic field induced tunability in a metasurface design is investigated that simultaneously manifests toroidal, dipolar, and other higher‐order modes. Further, multipolar analysis reveals that the nonradiative toroidal and radiative dipole modes can be enhanced by almost 56% and 183%, respectively, under 0–30 mT magnetic fields. Such magnetic field‐induced simultaneous control over radiative and non‐radiative resonances can be pivotal for next generation terahertz magnetophotonic devices.

Switchable multiple quasibound states in the continuum based on the phase transition of vanadium dioxide

Resonant dielectric nanostructures have achieved significant advancements in the manipulation of light at the nanoscale. Particularly, bound states in the continuum (BICs) based on dielectric metasurfaces have greatly enhanced the intensity of light–matter interaction. However, most BICs in dielectric metasurfaces are fixed in their functionality once they are made. In this study, we present the development of switchable multiple quasi-BICs by combining dielectric nanostructures with vanadium dioxide. The resulting hybrid dielectric metasurface can support three types of BICs with different multipole origins for vanadium dioxide in the insulating phase. By introducing structural asymmetry through width adjustment, one quasi-BIC with a longitudinal toroidal dipole characteristic is excited under x-polarized incidence. Further, tuning the width allows for the generation of two additional quasi-BICs with distinct electromagnetic sources under y-polarized incidence. Additionally, the hybrid dielectric metasurface also supports a high-Q transverse toroidal dipole mode. Moreover, all quasi-BICs and toroidal dipole modes can be turned off when vanadium dioxide transitions into the metallic phase. The switchable multiple quasi-BICs hold promise for applications in optical modulators, tunable harmonic generation, and biosensors.

Hollow Mie resonators based on toroidal magnetic dipole mode with enhanced sensitivity in refractometric sensing

We propose a refractometric sensor based on hollow silicon Mie resonators of a toroidal magnetic dipole mode. This mode has a pair of antiparallel electric dipoles perpendicular to the silica substrate; thus, the radiation of the mode is suppressed, resulting in an ultra-narrow reflection peak linewidth of 0.35 nm. In addition, the hollow structure enhances the interaction between the enhanced electric field and the surrounding medium, thus improving the sensitivity. The proposed Mie resonators achieve a sensitivity of 486 nm RIU−1 and a figure of merit up to 1389 RIU−1, which are ideal for refractometric sensing.

High-performance mid-infrared refractive index sensing all-dielectric metasurface with dual resonance excited by bound states in the continuum and toroidal dipole mode

Converting bound states in the continuum (BICs) domain to quasi-BICs regime effectively achieves high Q-factor excitation, enabling refractive index sensing. In this paper, we propose an all-dielectric metasurface consisting of four silicon nanopore cylinders. While maintaining a four-fold symmetry, an asymmetric distribution of nanopores is introduced, creating two resonances in the mid-infrared range. Through near-field analysis and multipole decomposition, it is demonstrated that magnetic dipoles (MD) and toroidal dipoles (TD) dominate the resonance modes, and the sensing performance of the structure is investigated. The quality factor (Q) and sensitivity reach 6688 and 1140nm/RIU, respectively. The sensing characteristics in different refractive index (RI) media are analyzed, and the results show that the refractive index sensing capability of the dielectric metasurface is influenced by its structural parameters and exhibits a significant linear response relationship. Furthermore, by varying the structural parameters of the dielectric metasurface, we also discovered the differences in sensing performance within different wavelength ranges. We study all polarization angle robust quasi-BICs in the mid-infrared spectral region, which can provide new references for polarization-insensitive metasurfaces with dual resonances. Polarization-insensitive technology can avoid the need for compensating the polarization state of the light signal in the sensor and improve the performance and reliability of the sensor.

Dual high-Q resonance sensing for refractive index and temperature based on all-dielectric asymmetric metasurface

In this work, we present a high-quality (Q) dual-resonance sensor based on all-dielectric metasurface for refractive index and temperature sensing simultaneously. The all-dielectric metasurface was composed of a periodic array of Si nanocluster placed on the commercially available glass substrate. Two distinct optical resonance modes with extremely high Q factors of 13500 and 14900, a magnetic quadrupole mode (MQ), and toroidal dipole mode (TD), are observed at 1614.12 nm, and 1639.02 nm in the reflection spectra, and confirmed by the electromagnetic field distribution of each resonance. To further reveal the underlying coupling effects of the two resonances, we also perform a systematic analysis of the influence of the differences in radius (ΔR) and gap (Δx and Δy). At last, the refractive index and temperature sensing performance were investigated. More specifically, the proposed sensor exhibits a maximum refractive index sensitivity of 418 nm/RIU for the analyte refractive index range between 1.33 and 1.37, and maximum temperature sensitivity of 86.4 pm/°C in the range of 0 °C–40 °C, which demonstrates great linear relationship and is much better than the previous sensors based on all-dielectric structure. The proposed all-dielectric metasurface is an effective way to achieve refractive index and temperature dual-parameter sensing, which will facilitate wide applications in unstable environment, such as the measurement of temperature and salinity in seawater.

Switchable high-Q electromagnetically induced transparency based on the Ge2Sb2Te5 nanodisk dimers

Bound states in the continuum (BICs) based on metasurfaces have gained significant attention recently to enhance the strength of light-matter interaction. However, most BIC metasurfaces possess fixed optical properties once they have been fabricated. In this study, we introduce the concept of BICs to the phase-change metasurfaces composed of Ge2Sb2Te5 nanodisk dimers. The Ge2Sb2Te5 nanodisk dimers can support a low-Q transverse magnetic dipole resonance, a high-Q toroidal dipole resonance and a high-Q longitudinal magnetic dipole resonance. By adjusting geometric parameter, the high-Q longitudinal magnetic dipole resonance can be converted into a BIC mode. Notably, when Ge2Sb2Te5 is in the amorphous phase, high-Q electromagnetically induced transparency (EIT)-like resonances can be achieved due to the interaction between a low-Q transverse magnetic dipole mode and either a high-Q toroidal dipole mode or a high-Q longitudinal magnetic dipole mode. However, the EIT resonances are switched off when Ge2Sb2Te5 is transformed into the crystalline phase. Furthermore, the high-Q EIT resonances enable the realization of an ultrahigh group refractive index, and can be tuned through the phase transition of Ge2Sb2Te5. The switchable high-Q EIT resonances hold potential applications in slow-light devices, optical modulators, and biosensors.

Bound states in the continuum driven by multiple modes for high Q refractive index sensing in metasurfaces

Bound states in the continuum (BICs) have attracted much attention in the field of refractive index sensing. In this paper, we propose multi-mode symmetry-protected BICs (SP-BICs) and the Freidrich–Wintgen BIC (FW-BIC) in terahertz metasurfaces consisted of periodic open split ring resonators. Firstly, multi-mode SP-BICs are subject to the magnetic dipole, electric dipole (ED), and toroidal dipole (TD) modes. Moreover, we demonstrate the FW-BIC by strongly coupling the electric quadrupole and TD modes. For micron film sensing of the ED mode, simulation results show that the Q factor, the sensitivity of sensing (S), and the corresponding figure of merit can simultaneously reach 1561, 141 GHz/RIU, and 306, respectively. Our quasi-BICs have potential applications in micro-sensing.

Enhancing Faraday and Kerr rotations based on the toroidal dipole mode in an all-dielectric magneto-optical metasurface.

The magneto-optical Faraday and Kerr effects are widely used in modern optical devices. In this Letter, we propose an all-dielectric metasurface composed of perforated magneto-optical thin films, which can support the highly confined toroidal dipole resonance and provide full overlap between the localized electromagnetic field and the thin film, and consequently enhance the magneto-optical effects to an unprecedented degree. The numerical results based on the finite element method show that the Faraday and Kerr rotations can reach -13.59° and 8.19° in the vicinity of toroidal dipole resonance, which are 21.2 and 32.8 times stronger than those in the equivalent thickness of thin films. In addition, we design an environment refractive index sensor based on the resonantly enhanced Faraday and Kerr rotations, with sensitivities of 62.96 nm/RIU and 73.16 nm/RIU, and the corresponding maximum figures of merit 132.22°/RIU and 429.45°/RIU, respectively. This work provides a new, to the best of our knowledge, strategy for enhancing the magneto-optical effects at nanoscale, and paves the way for the research and development of magneto-optical metadevices such as sensors, memories, and circuits.

Dual-band polarization-independent high quality factor Fano resonances using a twisted tetrameric nanohole slab

The Fano profile inspired by bound states in the continuum (BICs) has emerged as an effective approach to obtain high quality factor (QF) resonances. However, achieving polarization-independent high QF Fano resonances through the excitation of BICs is still challenging. Herein, we demonstrate that dual-band polarization-independent high QF Fano resonances can be realized by using a twisted tetrameric nanohole slab (TTNS). By twisting the nanoholes of the tetramerized slab, two quasi-BICs can be transformed into dual-band high QF Fano resonances due to the Brillouin zone folding as well as the symmetry breaking from C4v to C2v of the structure. The variation of the twist angle (θ) significantly alters the location of the Fano resonance in the longer wavelength, but it has slight influence on the Fano resonance in the shorter wavelength. A larger QF corresponds to a larger average electric-field enhancement-factor (AEE) for both of the Fano resonances, but the QF of the Fano resonance at the longer wavelength is more robust to the variation of θ due to its larger scaling rule as QF∼|θ|−6. According to multipole decompositions, Fano resonances at the longer and shorter wavelength correspond to toroidal dipole (TD) mode and hybrid TD-magnetic quadrupole (MQ) mode, respectively. In addition, both the two Fano resonances survive even if the structural parameters are significantly altered, and they exhibit polarization-independent features because the rotational symmetry of the structure can be maintained as θ is varied.

Independently tunable Fano resonance from quasibound state in the continuum in hybrid graphene–dielectric metasurface for magnetic field tunability

We study an independently tunable Fano resonance from quasibound state in the continuum and polarization-independent toroidal dipole resonance in hybrid graphene–dielectric metasurface consisting of a nanoring and a cross-shaped nanobar. The unique structural properties of the proposed metasurface can support directional toroidal dipole mode, where the asymmetric magnetic field enhancement can be dynamically switched on and off while maintaining polarization-independent Fano spectral response. Through reducing or increasing inner radius of nanoring, an additional quasi-BIC dominated by magnetic dipole moment can be excited and independently tuned by altering the polarization direction of the incident wave. In addition, the quasi-BIC can be effectively modulated via adjusting the Fermi energy and layer numbers of the graphene. Our results can be of practical interest for a variety of applications including optical modulator, filter, switches, and light trapping.

Asymmetric Cross Metasurfaces with Multiple Resonances Governed by Bound States in the Continuum.

The bound state in the continuum (BIC) has paved a new way to achieve excellent localization of the resonant mode coexisting with a continuous spectrum in the metasurface. Here, we propose an all-dielectric metasurface consisting of periodic pairs of asymmetric crosses that supports multiple Fano resonances. Due to the sufficient degrees of freedom in the unit cell, we displaced the vertical bars horizontally to introduce in-plane perturbation, doubling the unit cell structure. Dimerization directly resulted in the folding of the Brillouin zone in k space and transformed the BIC modes into quasi-BIC resonances. Then, simultaneous in-plane symmetry breaking was introduced in both the x and y directions to excite two more resonances. The physical mechanisms of these BIC modes were investigated by multipole decomposition of the scattering cross section and electromagnetic near-field analysis, confirming that they are governed by toroidal dipole (TD) modes and magnetic dipole (MD) modes. We also investigated the flexible tunability and evaluated the sensing performance of our proposed metasurface. Our work is promising for different applications requiring stable and tunable resonances, such as optical switching and biomolecule sensing.

Light Guidance Aided by the Toroidal Dipole and the Magnetic Quadrupole in Silicon Slotted-Disk Chains.

Far-field scattering of high-index nanoparticles can be hugely reduced via interference of multipolar moments giving rise to the so-called anapole states. It has been suggested that this reduced scattering can contribute to efficient transmission along periodic chains of such nanoparticles. In this work, we analyze via numerical simulation and experiments the transmission of light along chains of regular and slotted silicon disks in the frequency region over the light cone. We do not observe transmission at wavelengths corresponding to the excitation of the first electric anapole for regular disks. However, large transmission along straight and curved chains is observed for slotted disks due to the simultaneous excitation of the toroidal dipole and magnetic quadrupole modes in the disks. Photonic band calculations unveil that such large transmission can be ascribed to leaky resonances, though bound states in the continuum do not appear in the structures under analysis. Experiments at telecom wavelengths using silicon disk chains confirm the numerical results for straight and bent chains. Our results provide new insights into the role of radiationless states in light guidance along nanoparticle chains and offer new avenues to utilize Mie resonances of simple nanophotonic structures for on-chip dielectric photonics.

Giant optical chirality in dielectric metasurfaces induced by toroidal dipole resonances.

Although toroidal dipole (TD) resonance is a highly localized mode with a high quality (Q) factor, in most chiral structures the TD resonance is much weaker than the electric or magnetic dipole resonances and contributes little to the chiral response. In this Letter, we theoretically propose a chiral all-dielectric TD metasurface that possesses giant optical chirality with a certain degree of incident-angle robustness induced by a strong TD resonance. Interestingly, the symmetry of the system can be broken simultaneously at oblique incidence to produce chiral quasi-bound states in the continuum. The nearly unchanged high-Q TD resonance within a certain range of incident angles can avoid the problem of a reduced image quality caused by the incident-angle sensitivity, as demonstrated by the polarization-multiplexed-field image displays. The giant chirality with a certain degree of incident-angle robustness induced by the TD mode would be useful in some applications, including high-quality optical imaging, high-performance asymmetric transmission, and sensing.

Unlocking Novel Ultralow-Frequency Band Gap: Assembled Cellular Metabarrier for Broadband Wave Isolation.

Admittedly, the design requirements of compactness, low frequency, and broadband seem to constitute an impossible trinity, hindering the further development of elastic metamaterials (EMMs) in wave shielding engineering. To break through these constraints, we propose theoretical combinations of effective parameters for wave isolation based on the propagation properties of Lamb waves in the EMM layer. Accordingly, we design compact EMMs with a novel ultralow-frequency bandgap, and the role of auxeticity in the dissociation between the dipole mode and the toroidal dipole mode is clearly revealed. Finally, under the guidance of the improved gradient design, we integrate multiple bandgaps to assemble metamaterial barriers (MMBs) for broadband wave isolation. In particular, the original configuration is further optimized and its ultralow-frequency and broadband performance are proven by transmission tests. It is foreseeable that our work will provide a meaningful reference for the application of the new EMMs in disaster prevention and protection engineering.