Toroidal Dipole Resonance Research Articles

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.

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.

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.

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.

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-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.

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.

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.

Nonreciprocal toroidal dipole resonance and one-way quasi-bound state in the continuum.

Bound states in the continuum (BICs) provide an alternative way of trapping light at nanoscale. Although the last 10 years have witnessed tremendous progress on BICs from fundamentals to applications, nonreciprocal BICs and their potential applications have not been fully exploited yet. In this study, we demonstrated a one-way quasi-BIC by leveraging an all-dielectric magneto-optical (MO) metasurface. We show that the key point for achieving a one-way quasi-BIC is to excite a magnetization-induced leaky resonance. Here we adopt the longitudinal toroidal dipole (TD) resonance characterized by a vortex distribution of head-to-tail magnetic dipoles parallel to the plane of the MO metasurface. We show that, by breaking the time-reversal symmetry, at critical conditions, the TD resonance can be enhanced in the forward channel and perfectly canceled in the time-reversed channel, resulting in a one-way quasi-BIC. The demonstrated phenomena hold significant promise for practical applications such as magnetic field optical sensing, nonreciprocal optical switching, isolation, and modulation.

Laplace Differentiator Based on Metasurface with Toroidal Dipole Resonance

AbstractAs an important method of image processing, image differentiation enables edge detection of targets to achieve recognition of object features and information compression and the computation speed can be boosted by optical information techniques. Traditional optical image differentiation methods mainly rely on spatial spectrum filtering by using classical 4f system, while some work focus on 1D or single‐direction differentiation. It is only in recent years that the rapid development of metasurfaces has facilitated image differentiation methods. In this work, a Laplace operation device is demonstrated based on a silicon hollow brick dielectric resonant metasurface for incident light field. The optical transfer function (OTF) required by the optical Laplace operation can be obtained by exciting an angularly selective toroidal dipole (TD) resonance supported by the metasurface. This hollow silicon brick differentiator not only realizes 2D second‐order edge detection but also has a numerical aperture close to 0.4 and a broad working wavelength range >100 nm and can be directly integrated with imaging systems. Such metadevice may be potentially applied in the fields of optical sensing, microscopy, machine vision, biomedical imaging, etc.

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.

Strong coupling of excitons and electric/magnetic toroidal dipole modes in perovskite metasurfaces.

Effective manipulation of the interactions between light and matter is crucial for the advancement of various high-performance optoelectronic devices. It is noted that the toroidal dipole resonance refers to an electromagnetic excitation that exists beyond the conventional understanding of electric and magnetic multipoles, which shows great potential for enhancing light-matter interactions. In this work, we investigate the strong coupling properties of electric toroidal dipole (ETD) and magnetic toroidal dipole (MTD) with excitons in (PEA)2PbI4 perovskite metasurfaces. The nanostructure consists of two identical nanobars on a SiO2 substrate, which support ETD and MTD responses. The strong coupling between ETD/MTD modes and perovskite excitons is achieved when adjusting oscillator strength f0, which can be charactered by the clearly anti-crossing behavior appeared in the transmission spectra. The Rabi splitting can be readily tuned by controlling f0. When f0 increases to 1.0, their Rabi splitting values reach as high as 371 meV and 300 meV, respectively. The proposed strong coupling between excitons and ETD/MTDs paves the way for large-scale, low-cost integrated polaritonic devices operating at room temperature.

Dynamic modulation of electric and magnetic toroidal dipole resonance and light trapping in Si-GSST hybrid metasurfaces.

The weak coupling of a toroidal dipole (TD) to an electromagnetic field offers great potential for the advanced design of photonic devices. However, simultaneous excitation of electric toroidal dipoles (ETDs) and magnetic toroidal dipoles (MTDs) is currently difficult to achieve. In this work, we propose a hybrid metasurface based on Si and phase transition material G e 2 S b 2 S e 4 T e 1 (GSST), which is formed by four Si columns surrounding a GSST column and can simultaneously excite two different TD (ETD and MTD) resonances. We also calculated the electric field distribution, magnetic field distribution, and multipole decomposition of the two resonances, and the results show that the two modes are ETD resonance and MTD resonance, respectively. The polarization characteristics of these two modes are also investigated, and the average field enhancement factor (EF) of the two modes is calculated. The dynamic modulation of the relative transmission and EF is also achieved based on the tunable properties of the phase change material GSST. Our work provides a way to realize actively tunable TD optical nanodevices.

High Q Chiroptical Responses Driven by Toroidal Dipole Resonance in All-Dielectric Metasurfaces

High Q Chiroptical Responses Driven by Toroidal Dipole Resonance in All-Dielectric Metasurfaces

Terahertz toroidal dipole metamaterial sensors for detection of aflatoxin B1

Terahertz metamaterial biosensors have attracted significant attention in the biological field due to their advantages of label-free, real-time and in situ detection. In this paper, a highly sensitive metamaterial sensor with semi-ring mirror symmetry based on toroidal dipole resonance is designed for a new metamaterial biosensor. It is shown that a refractive index sensitivity of 337.5 GHz per refractive index unit can be achieved under an analyte of saturated thickness near a 1.33 THz transmission dip. For biosensor samples where aflatoxin B1 is dropped on the metamaterial surface in our experiment, dip amplitudes of transmission varying from 0.1904 to 0.203 and 0.2093 are observed as aflatoxin B1 concentrations are altered from 0 to 0.001 μg ⋅ml−1 and to 0.01 μg ⋅ml−1, respectively. Furthermore, when aflatoxin B1 concentrations are 0.1 μg ⋅ml−1, 1 μg ⋅ml−1, 10 μg ⋅ml−1 and 100 μg ⋅ml−1, dip amplitudes of 0.2179, 0.226, 0.2384 and 0.2527 and dip redshifts of 10.1 GHz, 20.1 GHz, 27.7 GHz and 37.6 GHz are respectively observed. These results illustrate high-sensitivity, label-free detection of aflatoxin B1, enriching the applications of sensors in the terahertz domain.

Photosensitizing Metasurface Empowered by Enhanced Magnetic Field of Toroidal Dipole Resonance.

Photochemical reaction exploiting an excited triplet state (T1 ) of a molecule requires two steps for the excitation, i.e., electronic transition from the ground (S0 ) to singlet excited (S1 ) states and intersystem crossing to the T1 state. A dielectric metasurface coupled with photosensitizer that enables energy efficient photochemical reaction via the enhanced S0 →T1 magnetic dipole transition is developed. In the direct S0 →T1 transition, the photon energy of several hundreds of meV is saved compared to the conventional S0 → S1 →T1 transition. To maximize the magnetic field intensity on the surface, a silicon (Si) nanodisk array metasurface with toroidal dipole resonances is designed. The surface of the metasurface is functionalized with ruthenium (Ru(II)) complexes that work as a photosensitizer for singlet oxygen generation. In the coupled system, the rate of the direct S0 →T1 transition of Ru(II) complexes is 41-fold enhanced at the toroidal dipole resonance of a Si nanodisk array. The enhancement of a singlet oxygen generation rate is observed when the toroidal dipole resonance of a Si nanodisk array is matched with the direct S0 →T1 transition wavelength of Ru(II) complexes.

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.