Toroidal Dipole Resonance Research Articles

Plasmonic hotspot in toroidal metamaterial

Toroidal dipole resonance under a normal incident excitation can be realized by designing a metallic circular groove with a depth asymmetry. Due to its specific radial charge current configuration, charges gather together on the central circular platform and form a plasmonic hotspot, covering a large circular region with a diameter of 200 nm, where E-field magnitude attains 34-time enhancement than that of the incident light, providing more potentials for energy harvesting or nanoparticle trapping, manipulating of light–matter interaction, and optical data storage.

Dual toroidal dipole resonances in a planar terahertz flexible metasurfaces

We proposed and fabricated planar dual toroidal dipole flexible metasurfaces at terahertz frequencies, and the units cell consists of two asymmetric J-shaped metallic ring resonators fabricated on the mylar medium. Measured and simulated results show that phase difference caused by the asymmetry of the metasurfaces in time and space lead to two strong toroidal dipole resonances in the transmission spectrum. The classical Fano resonance model is applied to the fitting of transmission spectrum, and the good coincidence reveals the metasurfaces resonant coupling mechanism. The resonances of metasurfaces are very sensitive to the dimensional parameters of the unit cell. The development of the sensitive dual-band planar terahertz toroidal dipole metasurfaces will promote the actual implementation of terahertz functional devices.

Toroidal metasurfaces integrated with microfluidic for terahertz refractive index sensing

A terahertz refractive index sensor consisting of toroidal dipole resonance metasurface integrated with microfluidic channel is proposed. The excitation of toroidal dipole resonance in this metasurface and the localized electromagnetic field enhancement in microfluidic channel are investigated comprehensively. Numerical results show that the calculated quality factor and the corresponding figure of merit can reach 1103 and 244, much higher than previously reported terahertz metamaterials sensors. Moreover, the refractive index sensing capabilities of non-polar and polar liquids are also investigated, which demonstrate the resonant frequency shift does not depend on the losses of analytes and show this device can be used for sensing various materials, including highly absorptive materials. This proposed structure can be extended to work in other frequency regions and has potential applications in high performance gases, liquids and biological materials sensing.

Toroidal Dipole Resonances in All‐Dielectric Oligomer Metasurfaces

AbstractDynamic toroidal multipoles have been attracting an increasing amount of attention, thanks to their unique electromagnetic properties. The concept bears great promises in the field of optical sensing as well as electromagnetic energy localization. Metal‐based structures with specific designs have been widely adopted to obtain toroidal responses. However, applications for such structures are often hindered by the significant intrinsic loss when it comes to optical frequencies. Here, several configurations of all‐dielectric metasurfaces, in which the meta‐molecules are composed of disk oligomers (trimer, quadrumer, pentamer, and hexamer), are proposed to support toroidal dipole resonances in the near‐infrared waveband when the polarization of the normally incident excitation plane wave is directed to one of the symmetry axes of the oligomers. Multipole expansion including the toroidal dipole term along with near‐field electromagnetic patterns confirms the existence of strong toroidal dipolar responses within certain wavelength ranges. This work would enrich the diversity of the all‐dielectric optical systems with toroidal dipole resonances.

Tunable Toroidal Dipolar Resonance for Terahertz Wave Enabled by a Vanadium Dioxide Metamaterial

An active toroidal switch is numerically presented in a terahertz metamaterial. Transmission of toroidal dipole can be tuned by the conductivity of vanadium dioxide, and its modulation depth can be up to 32%. The resonance of toroidal dipole is verified by the distribution of electric current. Due to the unique field distribution of the toroidal mode, the proposed design may find potential applications in enhanced absorption and sensing.

Tuning toroidal dipole resonances in dielectric metamolecules by an additional electric dipolar response

With the rise of artificial magnetism and metamaterials, the toroidal family recently attracted more attention for its unique properties. Here, we propose an all-dielectric pentamer metamolecule consisting of nano-cylinders with two toroidal dipolar resonances, whose frequencies, EM distributions, and Q factor can be efficiently tuned due to the additional electric dipole mode offered by a central cylinder. To further reveal the underlying coupling effects and the formation mechanism of toroidal responses, the multiple scattering theory is adopted. It is found that the first toroidal dipole mode, which can be tuned from 2.21 to 3.55μm, is mainly induced by a collective electric dipolar resonance, while the second one, which can be tuned from 1.53 to 1.84μm, relies on the cross coupling of both electric and magnetic dipolar responses. The proposed low-loss metamolecule and mode coupling analyses may pave the way for the efficient design of toroidal responses in advanced optical devices.

Terahertz toroidal metamaterial with tunable properties.

We present a tunable metamodulator to work at terahertz frequencies by employing the dependency of toroidal dipolar resonance on the conductivity of vanadium dioxide. Numerical results show that toroidal dipolar resonance in the proposed planar structure can be observed around 0.288 THz in transmission spectrum. From the distribution of the anti-phase current flowing in the symmetric split ring resonator, the formation of toroidal dipole is validated. Our design may have potential applications in advanced terahertz devices, such as filter, plasmonic sensor, and fast switch.

Light emission driven by magnetic and electric toroidal dipole resonances in a silicon metasurface.

Dielectric nanoparticles supporting pronounced toroidal and anapole resonances have enabled a new class of optical antennas with unprecedented functionalities. In this work, we propose a light-emitting silicon metasurface which simultaneously supports both magnetic toroidal dipole and electric toroidal dipole resonances in the near-infrared region. The metasurface consists of a square array of split nanodisks with embedded germanium quantum dots. By varying the width of the split air-gap, the spectral positions and quality factors of the two toroidal dipoles are flexibly tuned. Large photoluminescence enhancement is experimentally demonstrated at the toroidal resonances, which is attributed to the unique near- and far-field characteristics of the resonant modes. Moreover, the light emissions driven by the two toroidal dipoles are of different polarization, which further suggests versatile polarization-engineered radiation properties. Our work shows enormous potential in light emission manipulation and provides a route for high-efficiency, ultra-compact LEDs and potentially functional dielectric metasurface lasers.

Dual Toroidal Dipole Resonance Metamaterials under a Terahertz Domain.

We proposed and fabricated a flexible, planar, U-shape-modified structure metamaterial (MM) that was composed of two metallic pattern layers separated by a polyimide layer, where each metallic pattern layer consists of two U-shaped split ring resonators (USRRs). The coupling effect between the two USRRs in the same metallic layer was vital to the formation of dual toroidal dipole (TD) resonances. The measured and simulated results showed that both low quality factor (Q) (~1.82) and high Q (~10.31) TD resonances were acquired synchronously at two different frequencies in the MMs by adjusting the distance between the two coplanar USRRs. With the interaction of the USRRs, the energy levels of the USRRs were split into inductance-capacitance (LC)-induced TD resonance at low frequency and dipole-induced TD resonance at high frequency. Thus, the electric multipole interaction played an important role in determining the energy level of the TD resonance. The better strength of the high frequency TD resonance can be confined to an electromagnetic field inside a smaller circular region, and thus, a higher Q was obtained. In order to investigate the TD mechanism more in depth, the power of the electric dipole, magnetic dipole, electric circular dipole, and TD were quantitatively calculated. Dual TD MMs on a freestanding substrate will have potential applications in functional terahertz devices for practical applications.

Toroidal dipole bound states in the continuum

Toroidal multipole moments are usually underestimated as they are quite weak in most cases of light-matter interaction. Herein, we reveal a strong link between the toroidal dipole resonance and the bound state in the continuum in the context of all-dielectric metasurfaces. We introduce the concept of toroidal dipole bound states in the continuum, in which two eigenmodes of the silicon metasurface exhibit an intrinsic toroidal dipolar character and have an infinite lifetime. They can be classified as transverse (trivial) and longitudinal (nontrivial) toroidal dipole modes, which correspond to symmetry unprotected and protected bound states in the continuum, respectively. We demonstrate that such toroidal bound states in the continuum supported by the symmetry metasurface can be turned into ultrahigh-$Q$ resonances with a dominant toroidal dipole excitation, which validates their physical origin associated with the ultrahigh-$Q$ toroidal dipole leaky resonances. A full multipole decomposition with dispersive, lossy, and substrate effects further validates that the proposed concept is general and can also be generalized to other structures.

Pairing Toroidal and Magnetic Dipole Resonances in Elliptic Dielectric Rod Metasurfaces for Reconfigurable Wavefront Manipulation in Reflection.

A novel approach for reconfigurable wavefront manipulation with gradient metasurfaces based on permittivity‐modulated elliptic dielectric rods is proposed. It is shown that the required 2π phase span in the local electromagnetic response of the metasurface can be achieved by pairing the lowest magnetic dipole Mie resonance with a toroidal dipole Mie resonance, instead of using the lowest two Mie resonances corresponding to fundamental electric and magnetic dipole resonances as customarily exercised. This approach allows for the precise matching of both the resonance frequencies and quality factors. Moreover, the accurate matching is preserved if the rod permittivity is varied, allowing for constructing reconfigurable gradient metasurfaces by locally modulating the permittivity in each rod. Highly efficient tunable beam steering and beam focusing with ultrashort focal lengths are numerically demonstrated, highlighting the advantage of the low‐profile metasurfaces over bulky conventional lenses. Notably, despite using a matched pair of Mie resonances, the presence of an electric polarizability background allows to perform the wavefront shaping operations in reflection, rather than transmission. This has the advantage that any control circuitry necessary in an experimental realization can be accommodated behind the metasurface without affecting the electromagnetic response.

Analog of electromagnetically induced transparency in an E-shaped all-dielectric metasurface based on toroidal dipolar response

An analog of electromagnetically induced transparency (EIT) in an asymmetric E-shaped all-dielectric metasurface was proposed and numerically demonstrated in the near infrared spectral region. The E-shaped metasurface supports a strong toroidal dipolar resonance with high quality (Q) factor, which is verified by decomposed scattered powers for multipole moments using a Cartesian coordinate system. A high transmission EIT-like optical response was achieved, and clearly interpreted by the destructive interference between the dark toroidal dipolar moment and bright magnetic dipolar mode through the asymmetric metasurface. The bandwidth of the transparency window can be easily designed by changing the asymmetric parameter of the structure. The proposed E-shaped all-dielectric metasurface gives a new way to realize toroidal dipolar response and has potential applications in bio-chemical sensing, narrowband filters, optical modulations, and slow light based devices.

Individual Low-Energy Toroidal Dipole State in ^{24}Mg.

The low-energy dipole excitations in ^{24}Mg are investigated within the Skyrme quasiparticle random phase approximation for axial nuclei. The calculations with the force SLy6 reveal a remarkable feature: the lowest I^{π}K=1^{-}1 excitation (E=7.92 MeV) in ^{24}Mg is a vortical toroidal state (TS) representing a specific vortex-antivortex realization of the well-known spherical Hill's vortex in a strongly deformed axial confinement. This is a striking example of an individual TS which can be much more easily discriminated in experiment than the toroidal dipole resonance embracing many states. The TS acquires the lowest energy due to the huge prolate axial deformation in ^{24}Mg. The result persists for different Skyrme parametrizations (SLy6, SVbas, SkM*). We analyze spectroscopic properties of the TS and its relation with the cluster structure of ^{24}Mg. Similar TSs could exist in other highly prolate light nuclei. They could serve as promising tests for various reactions to probe a vortical (toroidal) nuclear flow.

Toroidal-dipole induced plasmonic perfect absorber

We present a new kind of perfect absorber which roots in a toroidal dipole resonance. The toroidal metastructure consists of a metallic circular groove with a depth asymmetry, which couples to the toroidal dipole field in the near-infrared region and thus realizes nearly unit absorbance, acting as a perfect absorber. Moreover, this absorber owns a high sensitivity of 609.6 nm/RIU to the dielectric surroundings. Furthermore, by tuning the geometric parameters, both the toroidal dipole resonance and perfect absorbance characteristics are insensitive to the circular groove width, providing profound fabrication tolerance in future experiments.

Surface Plasmon Polariton Mediated Multiple Toroidal Resonances in 3D Folding Metamaterials

Toroidal dipole has attracted tremendous attentions in nuclear, particle, condensed matter and material physics due to its exotic characteristics that are distinct from the fundamental electric and magnetic dipoles. Due to the very weak intensity, toroidal dipolar response is extremely difficult to be detected in natural materials. Although single dynamic toroidal dipole has recently been observed in metamaterials, simultaneous observation of multiple toroidal dipole resonances is still very challenging, and many intriguing physical phenomena associated with them have remained elusive. Here we experimentally demonstrate an approach to achieving toroidal dipole responses with high quality factors in the infrared region via surface-plasmon-polariton excitation. Implementation of this concept leads to simultaneous experimental observation of double toroidal modes in 3D metamaterial. Periodicity and angle dependent transmission measurements clearly reveal the coupling between the surface-plasmon-polariton mod...

Toroidal resonance based optical modulator employing hybrid graphene-dielectric metasurface.

In this paper, we demonstrate the combination of a dielectric metasurface with a graphene layer to realize a high performance toroidal resonance based optical modulator. The dielectric metasurface consists of two mirrored asymmetric silicon split-ring resonators (ASSRRs) that can support strong toroidal dipolar resonance with narrow line width (~0.77 nm) and high quality (Q)-factor (~1702) and contrast ratio (~100%). Numerical simulation results show that the transmission amplitude of the toroidal dipolar resonance can be efficiently modulated by varying the Fermi energy EF when the graphene layer is integrated with the dielectric metasurface, and a max transmission coefficient difference up to 78% is achieved indicating that the proposed hybrid graphene/dielectric metasurface shows good performance as an optical modulator. The effects of the asymmetry degree of the ASSRRs on the toroidal dipolar resonance are studied and the efficiency of the transmission amplitude modulation of graphene is also investigated. Our results may also provide potential applications in optical filter and bio-chemical sensing.

Multipolar response of nonspherical silicon nanoparticles in the visible and near-infrared spectral ranges

Spectral multipole resonances of parallelepiped-, pyramid-, and cone-like shaped silicon nanoparticles excited by linearly polarized light waves are theoretically investigated. The numerical finite element method is applied for the calculations of the scattering cross sections as a function of the nanoparticles geometrical parameters. The roles of multipole moments (up to the third order) in the scattering process are analyzed using the semianalytical multipole decomposition approach. The possibility of scattering pattern configuration due to the tuning of the multipole contributions to the total scattered waves is discussed and demonstrated. It is shown that cubic nanoparticles can provide a strong isotropic side scattering with minimization of the scattering in forward and backward directions. In the case of the pyramidal and conical nanoparticles the total suppression of the side scattering can be obtained. It was found that due to the shape factor of the pyramidal and conical nanoparticles their electric toroidal dipole resonance can be excited in the spectral region of the first electric and magnetic dipole resonances. The influence of the incident light directions on the optical response of the pyramidal and conical nanoparticles is discussed. The obtained results provide important information that can be used for the development of nanoantennas with improved functionality due to the directional scattering effects.

Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance.

A planar terahertz metamaterial consisting of square split ring resonators is proposed, and the excitation of toroidal dipolar resonance is demonstrated. Moreover, we theoretically investigate the strong interaction between graphene and toroidal dipolar resonance of the metamaterial. By varying its Fermi energy, the simulations show that graphene can actively modulate the transmission amplitude of toroidal dipolar resonance and even switch it off. The interaction of the toroidal dipolar resonance with monolayer graphene further highlights the ultrasensitive sensing characteristic of the planar metamaterial, which can be utilized for other graphene-like two-dimensional materials. These intriguing properties of the proposed metamaterial may have potential applications in terahertz modulators and ultrasensitive sensors.

Super-radiating manipulation of a nano-emitter by active toroidal metamaterials

The far-field radiation of a single dipolar emitter can be controlled by coupling to toroidal dipole resonance attached to metallic double flat rings, realizing a conversion from non- to super-radiating. The underlying physical mechanism is the hybridization interference of toroidal and electric dipoles under an asymmetric configuration by introducing a radial displacement of the dipolar emitter. By embedding gain medium in the gap spacer between double flat rings, the directional far-field super-radiating power can achieve a tremendous enhancement with a moderate requirement on the gain coefficient, promoting light-matter interaction manipulation.

Optical force enhancement and annular trapping by plasmonic toroidal resonance in a double-disk metastructure.

Optical forces can be enhanced by surface plasmon resonances with various interesting characteristics. Here, we numerically calculated the optical forces enhanced by a new kind of toroidal dipolar resonance in a double-disk metastructure. The results show that this kind of optical force is competitive with ordinary plasmonic forces and typically can reach-182.5pNμm2mW-1. Influences of geometric parameters are discussed for the enhancement characteristic of optical force. Finally, we make a contrastive investigation on the optical trapping characteristic on a 5-nm-diameter nanoparticle, and show that the unique annular trapping region can be utilized for nanoscale applications.