Toroidal Responses Research Articles

1 nm‐Resolution Sorting of Sub‐10 nm Nanoparticles Using a Dielectric Metasurface with Toroidal Responses

Sorting nanoparticles is of paramount importance in numerous physical, chemical, and biomedical applications. Current technologies for sorting dielectric nanoparticles have a common size limit and resolution approximately of 20 and 10 nm, respectively. It remains a grand challenge to push the limit. Herein, the new physics that deploys toroidal and multipole responses in a dielectric metasurface to exert strong and distinguishable optical forces on sub‐10 nm nanoparticles is unravelled. The electric toroidal dipole, electric dipole, and quadrupole emerge with distinct light and force patterns, which can be leveraged to promise unprecedented high‐precision manipulations, such as sorting sub‐10 nm polystyrene nanoparticles at 1 nm resolution, sorting 20 nm proteins/exsomes at 3 nm resolution, conveying, and concentrating 100 nm gold nanoparticles. Remarkably, the design can also be employed to screen out medium‐sized nanoparticles from a mixture of nanoparticles with over three sizes. This optofluidic manipulation platform opens the new way to explore intriguing optical modes for the powerful manipulation of nanoparticles with nanometer precisions and low laser powers.

Pseudo-anapole regime in terahertz metasurfaces

We present the numerical, theoretical, and experimental study of a terahertz metasurface supporting a pseudo-anapole. Pseudo-anapole effect arises when electric and toroidal dipole moments both tend to a minimum, instead of destructive interference between electric and toroidal dipole moments in conventional anapole mode. Such overlap allows resonance suppression of electric type radiation. Thus it becomes possible to study the multipoles of other families and higher order excitations. We estimate multipole contribution to the metasurface response via the multipole expansion method. The series is extended with such terms as mean-square radii and multipole interference. We also study the metasurface geometrical tunability. Via scaling, we demonstrate that it is possible to control the metasurface toroidal and electric responses independently. This in turn proves the fact that these multipoles have different physical origin. Moreover, we demonstrate that the proposed metasurface allows excitation of coherent magnetic dipole and electric quadrupole modes, which is crucial for planar cavities and lasing spasers in nanophotonics.

Thermally tunable polarization-insensitive ultra-broadband terahertz metamaterial absorber based on the coupled toroidal dipole modes.

In this paper, we propose a thermally tunable ultra-broadband polarization-insensitive terahertz (THz) metamaterial absorber (MMA) excited by the toroidal dipole moments. Due to the destructive interference resulting from two anti-parallel toroidal dipole moments, which depends on the twelve-fold trapezoidal metallic loops rotated by the axis parallel to the z-axis, the proposed MMA can achieve the absorption over 0.9 in a wide band of 2.38-21.13 THz, whose relative absorption band is 159.5%, at the temperature of 340 K. Meanwhile, by virtue of tuning the conductivity of vanadium dioxide (VO2) controlled by temperature, the tunability of absorption, maximum reaching 0.57, in the above band can be attained. On the other hand, the MMA is insensitive to the polarization angle owing to its symmetric configuration and can simultaneously keep the absorption above 0.9 in the high-frequency band from 15 to 25 THz under the incidence with a large angle of nearly 60°. In this study, a new way to enhance the absorption in a wide band which is based on the toroidal dipole modes is presented. Such a metamaterial can assist in further understanding the underlying mechanism with respect to the toroidal dipole electromagnetic responses.

Dual-toroidal dipole excitation on permittivity-asymmetric dielectric metasurfaces.

Magnetic and electric toroidal dipoles possess interesting properties differing from traditional electric and magnetic dipoles. In order to generate both the magnetic and electric toroidal dipoles simultaneously in one single structure, a permittivity-asymmetric dielectric metasurface is proposed, which is composed of clusters of four high-index dielectric nano-disks with asymmetric permittivity distribution. These two types of toroidal dipole responses can be separately observed at different spectral positions. This study reveals that symmetry-breaking in a broad sense is crucial for exciting toroidal responses, and the proposed metasurface points to a unique routine of exciting and enhancing the toroidal responses, which may be used to realize efficient light-matter interaction in the area of meta-optics.

Polarization-independent toroidal dipole resonances driven by symmetry-protected BIC in ultraviolet region

Optical resonances have gained great attention in nanophotonics attributing to their large enhancement of local field. In this work, we investigate polarization-independent toroidal dipole responses governed by bound state in the continuum (BIC) in the ultraviolet region. By introducing symmetry breaking, an asymmetric dielectric nanohole array is employed to excite two symmetry-protected BICs. Far-field contribution and near-field analysis are performed to demonstrate the dominant role of toroidal dipole in the above two modes. Our design shows the same responses under incident plane wave with different polarizations. The calculated enhancement factors also validate that these resonances can produce strong local field enhancement. Our work may provide a route towards resonators with polarization-independent responses and good performance.

Toroidal dipolar excitations in all-dielectric nanostructures

We have numerically investigated toroidal dipolar excitation at optical frequencies in Si nanostructures. Our results show that, through either special structured pump illumination, or by adding an additional layer associated with geometric tuning, we are able to excite strong toroidal dipolar responses with suppressed electric dipolar excitations. These findings may further pave the way to exploit future applications of toroidal resonances including optical nonlinear enhancement, induced transparency for narrow-band filter, etc.

Individual dipole toroidal states: Main features and search in the ( e,e′ ) reaction

Individual low-energy E1 toroidal and compressional states (TS and CS) produced by the convective nuclear current ${\bf j}_{\rm c}$ were recently predicted for $^{24}$Mg in the framework of quasiparticle random-phase-approximation (QRPA) with Skyrme forces. In the present QRPA study with Skyrme parametrization SLy6, we explore in more detail properties of these states (toroidal and compressional responses, current distributions, and transitions probabilities $B(E1K, 0^+0 \to 1^-K),\; B(E3K, 0^+0 \to 3^-K)$, $B(M2K, 0^+0 \to 2^-K)$ with $K=$0 and 1) and analyze the possibility to discriminate and identify TS in inelastic electron scattering to back angles. The interplay of the convective ${\bf j}_{\rm c}$ and magnetization ${\bf j}_{\rm m}$ nuclear currents is thoroughly scrutinized. A two-step scheme for identification of TS in $(e,e')$ reaction is proposed. The key element of the scheme is the strong interference of the orbital and spin contributions, resulting in specific features of E1 and M2 transversal form factors.

Electromagnetically induced transparency in novel dual-band metamaterial excited by toroidal dipolar response

We demonstrated a novel metamaterial with dual-band electromagnetically induced transparency (EIT) via simulation, experiment and numerical analysis, with resonance frequencies of the transparency peaks of 7.60 and 10.27 GHz. The E-e metamaterial unit cells were composed of E-shaped and e-shaped patterns. By analyzing the surface current distribution and the magnetic field, we qualitatively verified the toroidal dipole response in the E-e metamaterial at 10.27 GHz. Meanwhile, by calculating the multipole’s radiated power, we found that the two transparency peaks were due to the excitation of the electric and toroidal dipole responses. By changing the incident angle from 0° to 60°, we observed changes in transmission spectra, and the quality factors (Q-factors) of the two transparency peaks increased. In addition, the proposed E-e metamaterial can be designed to act as a refractive index sensor or other electronic equipment for the control of electromagnetic waves.

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.

Metasurface Engineering through Bound States in the Continuum

Metasurfaces have attracted a lot of attention in recent years due to novel ways they provide for the efficient wavefront control and engineering of the resonant transmission. We discuss an approach allowing effectively control appearance of the sharp Fano resonances in metasurfaces associated with the {\it bound states in the continuum}. We demonstrate that by breaking the symmetry transversely, in the direction perpendicular to a metasurface with a complex unit cell, we can control the number, frequency, and type of high-$Q$ resonances originating from bound states in the continuum. As example, we demonstrate experimentally the metasurfaces with magnetic dipole and toroidal dipole responses governed by the physics of multipolar bound states.

Polarization sensitive toroidal dipole metasurface for switch and magnetic field tunability

We design and numerically investigate an all-dielectric metasurface, a combination of rectangular bar and two nanoring resonators, that exhibits strong toroidal response with high polarization sensitivity and large modulation depth. With coupled-resonator effects, Fano resonance with toroidal response can be switched on and off at orthogonal orientations. Moreover, directional toroidal dipole can be achieved and controlled by symmetry breaking of metasurface, which can effectively tailor the local magnetic field with high Q-factor and strong field enhancements simultaneously, while keeps strong toroidal dipole responses. We envision that strong toroidal response in proposed metasurface has potential applications in designing switching and modulators.

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.

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...

Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles.

We revisit the fundamental topic of light scattering by single homogenous nanoparticles from the new perspective of excitation and manipulation of toroidal dipoles. It is revealed that besides within all-dielectric particles, toroidal dipoles can also be efficiently excited within homogenous metallic nanoparticles. Moreover, we show that those toroidal dipoles excited can be spectrally tuned through adjusting the radial anisotropy parameters of the materials, which paves the way for further more flexible manipulations of the toroidal responses within photonic systems. The study into toroidal multipole excitation and tuning within nanoparticles deepens our understanding of the seminal problem of light scattering, and may incubate many scattering related fundamental researches and applications.

Toroidal dipolar responses in a planar metamaterial

Both the magnetic toroidal dipolar (MTD) response and electric toroidal dipolar (ETD) response have been achieved and studied in the microwave region by designing a feasible planar metamaterial. By changing the polarized direction of a normally incident wave, two different coupling modes are observed, and therefore MTD and ETD responses can be achieved accordingly. It is also confirmed by scattered powers for various multipole moments and field distributions that they dominate over other traditional multipole responses at 5.69 GHz and 11.69 GHz, respectively. In view of the design feasibility of planar metamaterial, these resonance-enhanced MTD and ETD responses could provide an avenue for various interesting phenomena associated with the elusive toroidal moments.

Design of plasmonic toroidal metamaterials at optical frequencies

Toroidal multipoles are the subject of growing interest because of their unusual electromagnetic properties different from the electric and magnetic multipoles. In this paper, we present two new related classes of plasmonic metamaterial composed of purposely arranged of four U-shaped split ring resonators (SRRs) that show profound resonant toroidal responses at optical frequencies. The toroidal and magnetic responses were investigated by the finite-element simulations. A phenomenon of reversed toroidal responses at higher and lower resonant frequencies has also been reported between this two related metamaterials which results from the electric and magnetic dipoles interaction. Finally, we propose a physical model based on coupled LC circuits to quantitatively analyze the coupled system of the plasmonic toroidal metamaterials.

Cross-Section Sensitivity Study for the Toroidal Field Coil Shielding Parameters in the ITER/OTR Design

An extensive analysis of the sensitivity of the fast neutron flux in the superconductor, the dose to the electrical insulator, and the number of displacements per atom in the copper stabilizer to variations of the neutron cross sections for the International Thermonuclear Experimental Reactor (ITER/OTR) inboard region (first wall/blanket/shield/vacuum vessel) was carried out. All of the nuclides with a significant concentration in the ITER/OTR inboard region were investigated, namely, iron, chromium, nickel, lead, oxygen, hydrogen, boron, copper, [sup 6]Li and [sup 7]Li. The integrated total sensitivities of iron, lead, hydrogen, and oxygen were compared with the results for the OTR and Next European Torus (NET) sensitivity analyses. The integrated total sensitivity of both the fast neutron flux and the dose to variation of lead cross sections for the ITER/OTR was much higher than that for the OTR, namely, 3.5 and 1.2, respectively. The difference in the integrated total sensitivities of the inboard toroidal field coil responses to a one standard deviation variation of the iron, hydrogen, and oxygen neutron cross sections was <30%. The most important energy regions and the types of neutron cross sections for shield calculations were identified. The uncertainty of the neutron cross sections in the important more » energy regions needs to be decreased to<10% to decrease the uncertainty of the calculated neutron dose and fast flux behind the ITER/OR inboard shield to <15 to 30%. 36 refs., 15 figs., 1 tab. « less