Bingnan Wang, Jiangfeng Zhou, Thomas Koschny, Costas M. Soukoulis
We demonstrate experimentally and numerically that nonplanar chiral metamaterials give giant optical activity, circular dichroism, and negative refractive index. The transmission, reflection, and the retrieval results of the experiments agree pretty well with the simulations. This is an important step toward the design and fabrication of three-dimensional isotropic chiral metamaterials.
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Because of the strong inherent resonances, the giant optical activity obtained via chiral metamaterials generally suffers from high dispersion, which has been a big stumbling block to broadband applications. In this paper, we propose a type of chiral metamaterial consisting of interconnected metal helix structures with four-fold symmetry, which exhibits nonresonant Drude-like response and can therefore avoid the highly dispersive optical activity resulting from resonances. It shows that the well-designed chiral metamaterial can achieve nondispersive and pure optical activity with high transmit…
The combination of gain and loss in optical systems that respect parity-time (PT)-symmetry has pointed recently to a variety of novel optical phenomena and possibilities. Many of them can be realized by combining the PT-symmetry concepts with metamaterials. Here we investigate the case of chiral metamaterials, showing that combination of chiral metamaterials with PT-symmetric gain-loss enables a very rich variety of phenomena and functionalities. Examining a simple one-dimensional chiral PT-symmetric system, we show that with normally incident waves the PT-symmetric and the chirality-related c…
Artificial magnetism, negative permeability and negative refractive index are demonstrated in 3D-chiral metamaterial that shows giant polarization rotation and circular dichroism.
Here we report the designing of chiral metamaterial with metallic helix array. The effective electric and magnetic dipoles, which originate from the induced surface electric current upon illumination of incident light, are collinear at the resonant frequency. Consequently, for the circularly polarized incident light, negative refractive index is realized. Our design provides a unique approach to tune the optical properties by assembling helices, and demonstrates a different approach in exploring three- dimensional chiral metamaterial.
We demonstrated a 2D helical chiral metamaterial that exhibits broadband strong optical activity resulting nonresonant Drude-like response. The strong chirality leads to broadband negative refractive index with high figure of merit (>90) and extremely low loss (<2% per layer). The optical activity are insensitive to the angles of incident electromagnetic waves, thereby enabling more flexibility in polarization manipulation applicaitons.
Negative index metamaterials (NIMs) give rise to unusual and intriguing properties and phenomena, which may lead to important applications such as superlens, subwavelength cavity and slow light devices. However, the negative refractive index in metamaterials normally requires a stringent condition of simultaneously negative permittivity and negative permeability. A new class of negative index metamaterials - chiral NIMs, have been recently proposed. In contrast to the conventional NIMs, chiral NIMs do not require the above condition, thus presenting a very robust route toward negative refracti…
We propose a resonant microwave absorber based on a chiral metamaterial. We show, with both numerical simulations and experimental measurements, that the absorber works well for a very wide range of incident angles for different polarizations. The proposed absorber has a compact size and the absorption is close to one for a wide range of incident angles and it is a good candidate for potential applications.
Homogenization of metamaterials is a crucial issue as it allows to describe their optical response in terms of effective wave parameters as e.g. propagation constants. In this paper we consider the possible homogenization of chiral metamaterials. We show that for meta-atoms of a certain size a critical density exists above which increasing coupling between neighboring meta-atoms prevails a reasonable homogenization. On the contrary, a dilution in excess will induce features reminiscent to photonic crystals likewise prevailing a homogenization. Based on Bloch mode dispersion we introduce an ana…
We propose a planar composite chiral metamaterial (CCMM) by symmetrically inserting a metallic mesh between two layers of conjugated gammadion resonators. As the elaborate CCMM operates in the frequency region of off-resonance, it therefore presents loss-less and dispersion-free features. It can achieve flat polarization rotation simultaneously accompanied with high transmission and extremely low ellipticity in a broad bandwidth. In the meanwhile, this intriguing CCMM shows more superiorities in polarization rotation power and operating bandwidth than the pure chiral metamaterial just composed…
We report on a numerical study of optical chirality. Intertwined gold helices illuminated with plane waves concentrate right and left circularly polarized electromagnetic field energy to sub-wavelength regions. These spots of enhanced chirality can be smoothly shifted in position and magnitude by varying illumination parameters, allowing for the control of light-matter interactions on a nanometer scale.
Chiral structure can be applied to construct metamaterial with negative refractive index (NRI). In an assembly of double-layered metallic U-shaped resonators with two resonant frequencies wH and wL, the effective induced electric and magnetic dipoles, which are contributed by the specific surface current distributions, are collinear at the same frequency. Consequently, for left circularly polarized light, NRI occurs at wH, whereas for right circularly polarized light it occurs at wL. Our design provides a new example to apply chiral structures to tune electromagnetic properties, and could be e…
We theoretically investigate the electromagnetic response of a novel class of multi-layered metamaterials obtained by alternating graphene sheets and dielectric layers, the whole structure not exhibiting a plane of reflection symmetry along the stacking direction. We show that the electromagnetic response of the structure is characterized by a magneto-electric coupling described by an effective chiral parameter. Exploiting the intrinsic tunability of the graphene-light coupling, we prove that one can tune both the dielectric and the chiral electromagnetic response by varying the graphene chemi…
Designing broadband enhanced chirality is of strong interest to the emerging fields of chiral chemistry and sensing, or to control the spin orbital momentum of photons in recently introduced nanophotonic chiral quantum and classical optical applications. However, chiral light-matter interactions have an extremely weak nature, are difficult to be controlled and enhanced, and cannot be made tunable or broadband. In addition, planar ultrathin nanophotonic structures to achieve strong, broadband, and tunable chirality at the technologically important visible to ultraviolet spectrum still remain el…
We derive an exact expression for the time-averaged electromagnetic energy inside a chiral dispersive sphere irradiated by a plane wave. The dispersion relations correspond to a chiral metamaterial consisting of uncoupled single-resonance helical resonators. Using a field decomposition scheme and a general expression for the electromagnetic energy density in bi-anisotropic media, we calculate the Lorenz-Mie solution for the internal fields in a medium that is simultaneously magnetic and chiral. We also obtain an explicit analytical relation between the internal electromagnetic field and the ab…
We suggest that electromagnetic chirality, generally displayed by 3D or 2D complex chiral structures, can occur in 1D patterned composites whose components are achiral. This feature is highly unexpected in a 1D system which is geometrically achiral since its mirror image can always be superposed onto it by a 180 deg rotation. We analytically evaluate from first principles the bi-anisotropic response of multilayered metamaterials and we show that the chiral tensor is not vanishing if the system is geometrically one-dimensional chiral, i.e. its mirror image can not be superposed onto it by using…
The electronic Lorentz theory is employed to determine the electromagnetic response of planar split-ring metamaterials. Starting from the dynamics of individual free carriers, the effective permittivity tensor of the metamaterial is calculated. Whenever the split ring lacks in-plane mirror symmetry, the corresponding permittivity tensor has a crystallographic structure of an elliptically dichroic medium, and the metamaterial exhibits optical properties of planar chiral structures. Its transmission spectra are different for right-handed vs. left-handed circular polarization of the incident wave…
Chiroptical effects, characterized by different optical responses for left- (LCP) and right- handed circularly polarized light (RCP), are powerful and valuable tools in optics with wide applications in polarization resolved imaging and sensing. Previously observed strong chiroptical effects are limited to metamaterials with complex three-dimensional chiral structures at the sub-wavelength scale. Although asymmetrical transmission of LCP and RCP have been investigated in planar chiral metasurfaces, the observed weak chiroptical effects result from anisotropic Ohmic dissipation of the metal cons…
We study theoretically and experimentally a novel type of metamaterial with hybrid elements composed of twisted pairs of cross-shaped meta-atoms and their complements. We reveal that such two-layer metasurfaces demonstrate large, dispersionless optical activity at the transmission resonance accompanied by very low ellipticity. We develop a retrieval procedure to determine the effective material parameters for this structure, which has lower-order symmetry ($\mathrm {C}_4$) than other commonly studied chiral structures. We verify our new theoretical approach by reproducing numerical and experim…
Optical systems with gain and loss that respect Parity-Time (PT) symmetry can have real eigenvalues despite their non-Hermitian character. Chiral systems impose circularly polarized waves which do not preserve their handedness under the combined space- and time- reversal operations and, as a result, seem to be incompatible with systems possessing PT symmetry. Nevertheless, in this work we show that in certain configurations, PT symmetric permittivity, permeability and chirality is possible; in addition, real eigenvalues are maintained even if the chirality goes well beyond PT symmetry. By obta…
We employ a homogenization technique based on the Lorentz electronic theory to show that planar chiral structures (PCSs) can be described by an effective dielectric tensor similar to that of biaxial elliptically dichroic crystals. Such a crystal is shown to behave like a PCS insofar as it exhibits its characteristic optical properties, namely, co-rotating elliptical polarization eigenstates and asymmetric, direction-dependent transmission for left/right-handed incident wave polarization.
We report the first experiential observation and theoretical analysis of the new phenomenon of planar chiral circular conversion dichroism, which in some aspects resembles the Faraday effect in magnetized media, but does not require the presence of a magnetic field for its observation. It results from the interaction of an electromagnetic wave with a planar chiral structure patterned on the sub-wavelength scale, and manifests itself in asymmetric transmission of circularly polarized waves in the opposite directions through the structure and elliptically polarized eigenstates. The new effect is…
A bilayered chiral metamaterial (CMM) is proposed to realize a 90 degree polarization rotator, whose giant optical activity is due to the transverse magnetic dipole coupling among the metallic wire pairs of enantiomeric patterns. By transmission through this thin bilayered structure of less than λ/30 thick, a linearly polarized wave is converted to its cross polarization with a resonant polarization conversion efficiency (PCE) of over 90%. Meanwhile, the axial ratio of the transmitted wave is better than 40 dB. It is demonstrated that the chirality in the propagation direction makes this effic…
Applying Artmann's formula to the TE-polarized incident waves, we theoretically show that the Goos-Hänchen (GH) shifts near the angle of the pseudo-Brewster dip of the reflection from a slab of chiral metamaterial can be greatly enhanced. The GH shifts are observed for both parallel and perpendicular components of the reflected field. In addition, it is found that the GH shifts depend not only on the slab thickness and the incident angle, but also on the constitutive parameters of the chiral medium. In particular, when the incident angle is close to the critical angle of total reflection for L…
In this paper, a kind of helix-like chiral metamaterial, which can be realized with multiple conventional lithography or electron beam lithographic techniques, is proposed to achieve broadband bianisotropic optical response analogous to helical metamaterial. On the basis of twisted metamaterial, via tailoring the relative orientation within the lattice, the anisotropy of arc is converted into magneto-electric coupling of closely spaced arc pairs, which leads to a broad bianisotropic optical response. By connecting the adjacent upper and lower arcs, the coupling of metasurface pairs is transfor…
After the prediction that strong enough optical activity may result in negative refraction and negative reflection, more and more artificial chiral metamaterials were designed and fabricated at difference frequency ranges from microwaves to optical waves. Therefore, a simple and robust method to retrieve the effective constitutive parameters for chiral metamaterials is urgently needed. Here, we analyze the wave propagation in chiral metamaterials and follow the regular retrieval procedure for ordinary metamaterials and apply it in chiral metamaterial slabs. Then based on the transfer matrix te…
Bi-isotropic and isotropic negative refractive index (NRI) 3D metamaterials made from periodic arrangements of chiral split ring resonators (SRRs) are proposed and demonstrated. An analytical theory for the characterization and design of these metamaterials is provided and validated by careful full-wave electromagnetic simulations. The reported results are expected to pave the way to the design of practical 3D bi-isotropic and isotropic NRI metamaterials made from a single kind of inclusions.
Effective chiral response of anisotropic multilayered metamaterials
本文研究了各向异性多层超材料因反演对称性破缺产生的有效手性响应，推导了正入射和斜入射下的有效手性张量，并确定了使手性响应最大化的层排列方式。
Controlling the broadband enhanced light chirality with L-shaped dielectric metamaterials
本文设计了基于倾斜纳米柱的全介电硅基L形超材料，通过掠射角沉积实现晶圆级制备，在透射模式下获得宽带增强且振幅与频率均可调控的手性光学响应。
Boundary-induced topological chiral extended states in Weyl metamaterial waveguides
该研究在光子Weyl超材料波导中理论并实验发现由边界独立诱导、不依赖波导宽度的拓扑手性扩展体态，可连接不同二维空间的Fermi弧表面态，为无磁场鲁棒手性输运和调控Weyl准粒子提供新途径。
We report that the classical phenomena of optical activity and circular dichroism, which are traditionally associated with chirality (helicity) of organic molecules, proteins and inorganic structures, can be observed in non-chiral artificial media. Intriguingly, our metamaterial structure yields exceptionally strong resonant optical activity, which also leads to the appearance of a backward wave, a characteristic sign of negative-index media.
We report the existence of Weyl points in a class of non-central symmetric metamaterials, which has time reversal symmetry, but does not have inversion symmetry due to chiral coupling between electric and magnetic fields. This class of metamaterial exhibits either type-I or type-II Weyl points depending on its non-local response. We also provide a physical realization of such metamaterial consisting of an array of metal wires in the shape of elliptical helixes which exhibits type-II Weyl points.
We demonstrate numerically and experimentally a conjugated gammadion chiral metamaterial that uniaxially exhibits huge optical activity and circular dichroism, and gives a negative refractive index. This chiral design provides smaller unit cell size and larger chirality compared with other published planar designs. Experiments are performed at GHz frequencies (around 6GHz) and in good agreement with the numerical simulations.
Multiplexed chiral and helical acoustic anomaly bulk states in an inverse-designed metamaterial
本研究通过逆向设计声学超材料，在同一系统中实现了谷和赝自旋自由度的多路复用，并实验验证了多频声能增强，为鲁棒的多路复用声学器件提供了新策略。
We investigate the influence of chirality on the PT-symmetric and PT-broken phase of PT-symmetric chiral systems. Starting from the point that transverse magnetic (TM) and transverse electric (TE) waves have different exceptional points, we show that with circularly polarized waves (which are linear combinations of TM and TE waves) mixed PT-symmetric phases can be realized and the extent of these phases can be highly controlled by either or both the chirality and the angle of incidence. Additionally, while the transmission of both TM and TE waves in non-chiral PT-symmetric systems is the same …
We experimentally demonstrate a three-dimensional chiral optical metamaterial that exhibits an asymmetric transmission for forwardly and backwardly propagating linearly polarized light. The observation of this novel effect requires a metamaterial composed of three-dimensional chiral metaatoms without any rotational symmetry. Our analysis is supported by a systematic investigation of the transmission matrices for arbitrarily complex, lossy media that allows deriving a simple criterion for asymmetric transmission in an arbitrary polarization base. Contrary to physical intuition, in general the p…
Optical activity is a fundamental phenomenon originating from the chiral nature of crystals and molecules. While intrinsic chiroptical responses of ordinary chiral materials to circularly polarized light are relatively weak, they can be enhanced by specially tailored nanostructures. Here, nanorod metamaterials, comprising a dense array of vertically aligned gold nanorods, is shown to provide significant enhancement of the circular dichroism response of an embedded material. A nanorod composite, acting as an artificial uniaxial crystal, is filled with chiral mercury sulfide nanocrystals embedde…
Electromagnetic response of metallic rod dimers is theoretically calculated for arbitrary planar arrangement of rods in the dimer. It is shown that dimers without an in-plane symmetry axis exhibit elliptical dichroism and act as "atoms" in planar chiral metamaterials. Due to a very simple geometry of the rod dimer, such planar metamaterials are much easier in fabrication than conventional split-ring or gammadion-type structures, and lend themselves to a simple analytical treatment based on coupled dipole model. Dependencies of metamaterial's directional asymmetry on the dimer's geometry are es…
A uniaxial chiral metamaterial is constructed by double-layered four "U" split ring resonators mutually twisted by 90 degrees. It shows a giant optical activity and circular dichroism. The retrieval results reveal that a negative refractive index is realized for circularly polarized waves due to the large chirality. The experimental results are in good agreement with the numerical results.
In this letter, we present the first experimental study of a new chiral metamaterial consisting of toroidal wire windings. We show that the metamaterial exhibits three bands of circular dichroism in the GHz range. We discuss the response of the structure in terms of multipole moments, including the (magnetic) toroidal dipole moment.
Advanced photonic nanostructures have enabled the maximization of synthetic chiroptic activities. The unique structuring of these building blocks has empowered chiral selective interactions with electromagnetic waves in plasmonic structures and dielectric media. Given the repertoire of optimized chiral surfaces in the literature and the ubiquity of chirality in the organic realm, the natural direction to consider is the operation of these devices in larger optical systems much like their chiral organic counterparts. In this review, we recapitulate advances in active and nonlinear chiral metama…
We review the basic physics behind light interaction with plasmonic nanoparticles. The theoretical foundations of light scattering on one metallic particle (a plasmonic monomer) and two interacting particles (a plasmonic dimer) are systematically investigated. Expressions for effective particle susceptibility (polarizability) are derived, and applications of these results to plasmonic nanoantennas are outlined. In the long-wavelength limit, the effective macroscopic parameters of an array of plasmonic dimers are calculated. These parameters are attributable to an effective medium corresponding…
Recently it was discovered that periodic lattices of metamaterial scatterers show optical activity, even if the scatterers or lattice show no 2D or 3D chirality, if the illumination breaks symmetry. In this Letter we demonstrate that such `pseudo-chirality' is intrinsic to any single planar metamaterial scatterer and in fact has a well-defined value at a universal bound. We argue that in any circuit model, a nonzero electric and magnetic polarizability derived from a single resonance automatically imply strong bianisotropy, i.e., magneto-electric cross polarizability at the universal bound set…
In the close vicinity of a chiral nanostructure, the circular dichroism of a biomolecule could be greatly enhanced, due to the interaction with the local superchiral fields. Modest enhancement of optical activity using a planar metamaterial, with some chiral properties, and achiral nanoparticles has been previously reported. A more substantial chirality enhancement can be achieved in the local filed of a chiral nanostructure with a three-dimensional arrangement. Using an embossed chiral nanostructure designed for chiroptical sensing, we measure the circular dichroism spectra of two biomolecule…
Recently the possibility of achieving one-way backscatter immune transportation of light by mimicking the topological order present within certain solid state systems, such as topological insulators, has received much attention. Thus far however, demonstrations of non-trivial topology in photonics have relied on photonic crystals with precisely engineered lattice structures, periodic on the scale of the operational wavelength and composed of finely tuned, complex materials. Here we propose a novel effective medium approach towards achieving topologically protected photonic surface states robus…
Focusing of electromagnetic plane wave from a large size paraboloidal reflector, composed of layers of chiral and/or chiral nihility metamaterials, has been studied us- ing Maslov's method. First, the transmission and reflection of electromagnetic plane wave from two parallel layers of chiral and/or chiral nihility metamaterials are cal- culated using transfer matrix method. The effects of change of angle of incidence, chirality parameters and impedances of layers are noted and discussed. Special cases by taking very large and small values of permittivity of second layer, while assuming value …
Some novel quasi-planar chiral inclusions, feasible from standard photo-etching techniques, are proposed. It is shown that such inclusions can be designed in order to present balanced electric, magnetic and magneto-electric polarizabilities. Using these inclusions, random and periodic bi-isotropic artificial metamaterials exhibiting a balanced positive/negative refractive index can be build up. These metamaterials would exhibit reasonable bandwidths and excellent matching to free space.
Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schrödinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently lar…
We show that asymmetric transmission for linear polarizations can be easily achieved by a monolayer of anisotropic chiral metamolecules through the constructive and destructive interferences between the contributions from anisotropy and chirality. Our analysis is based on the interaction of electromagnetic waves with the constituent electric and magnetic dipoles of the metamaterials, and an effective medium formulation. In addition, asymmetric transmission in amplitude can be effectively controlled by the interference between spectrally detuned resonances. Our findings shed light on the design…
This paper presents a first-principle and global perspective of electromagnetic chirality. It follows for this purpose a bottom-up construction, from the description of chiral particles or metaparticles (microscopic scale), through the electromagnetic theory of chiral media (macroscopic scale), to the establishment advanced properties and design principles of chiral materials and metamaterials. It preliminarily highlights the three fundamental concepts related to chirality -- mirror asymmetry, polarization rotation and magnetodielectric coupling -- and points out the nontrivial interdependenci…
Chirality Inversion and Giant Optical Activity in Scalable Self-Assembled Metamaterials
本研究开发了可规模化组装的分级螺旋超材料，实现了强等离子体光学活性与手性反转，还可回收金纳米颗粒，为可持续手性等离子体材料提供了新方案。
Chirality is a universal feature in nature, as observed in fermion interactions and DNA helicity. Much attention has been given to chiral interactions of light, not only regarding its physical interpretation but also focusing on intriguing phenomena in excitation, absorption, refraction, and topological phase. Although recent progress in metamaterials has spurred artificial engineering of chirality, most approaches are founded on the same principle of the mixing of electric and magnetic responses. Here we propose nonmagnetic chiral interactions of light based on low-dimensional eigensystems. E…
Highly sensitive and selective label free devices for real-time identification of specific biomarkers are expected to significantly impact the biosensing field. The ability of plasmonic systems to confine the light in nanometer volume and to manipulate it by tuning the size, shape and material features of the nanostructures, makes these systems promising candidates for biomedical devices. In this work we demonstrate the engineered sensing capabilities of a compact array of 3D metal dielectric core-shell chiral metamaterial. The intrinsic chirality of the nano-helices makes the system circular …
Topological valley photonics has emerged as a new frontier in photonics with many promising applications. Previous valley boundary transport relies on kink states at internal boundaries between two topologically distinct domains. However, recent studies have revealed a novel class of topological chiral edge states (CESs) at external boundaries of valley materials, which have remained elusive in photonics. Here, we propose and experimentally demonstrate the topological CESs in valley photonic metamaterials (VPMMs) by accurately tuning on-site edge potentials. Moreover, the VPMMs work at deep-su…
Unconventional Weyl points (WPs), carrying topological charge 2 or higher, possess interesting properties different from ordinary charge-1 WPs, including multiple Fermi arcs that stretch over a large portion of the Brillouin zone. Thus far, such WPs have been observed in chiral materials and acoustic metamaterials, but there has been no clean demonstration in photonics in which the unconventional photonic WPs are separated from trivial bands. We experimentally realize an ideal symmetry-protected photonic charge-2 WP in a three-dimensional topological chiral microwave metamaterial. We use field…
Optical activity (polarization rotation of light) is one of the most desired features of chiral media, as it is important for many polarization related applications. However, in the THz region, chiral media with strong optical activity are not available in nature. Here, we study theoretically, and experimentally a chiral metamaterial structure composed of pairs of vertical U-shape resonators of "twisted" arms, and we reveal that it demonstrates large pure optical activity (i.e. optical activity associated with negligible transmitted wave ellipticity) in the low THz regime. The experimental dat…
Electromagnetic waves impinging on three-dimensional helical metallic metamaterials have been shown to exhibit chiral effects of large magnitude both theoretically and in experimental realizations. Chirality here describes different responses of scatterers, materials, or metamaterials to left and right circularly polarized electromagnetic waves. These differences can be quantified in terms of electromagnetic chirality measures. In this work we consider the optimal design of thin metallic free-form nanowires that possess measures of electromagnetic chirality as large as fundamentally possible. …
We introduce a chiral metamaterial with strong, non-resonant optical activity, and very low polarization ellipticity. We achieve this by combining a meta-atom and its complementary structure into a meta-molecule, resulting in the coupling of magnetic and electric dipole responses. In contrast to either a pair of crosses, or complementary crosses, this structure has low dispersion in the optical activity at the transmission resonance. We also study the excitation mechanism in this structure, and optimize the optical activity through changing the twist angle.
Unveiling Chirality: Exploring Nature's Blueprint for Engineering Nanostructured Materials
本文概述了手性仿生等离激元学与超材料领域，通过自组装和纳米加工技术设计手性超材料及等离激元纳米结构，实现了对光响应的显著控制与光学手性增强，为传感、催化和光电器件开辟了新前沿。
Robust Optical Pulling of Plasmonic, Chiral, and Dielectric Nanorods in Single and Cluster Configurations Using Hyperbolic Metamaterials
本研究利用双曲超材料基底，通过全波模拟证明等离激元、手性和介电纳米棒在团簇及单体构型下均能产生稳定的光学牵引力，且等离激元在单体时受力最大，为光学操控提供了实用方案。
Efficient homogenization of multicomponent metamaterials: chiral effects
本文将基于 Haydock 表示的均匀化方法推广到任意多组分周期复合材料，并通过计算具有圆偏振带隙的 Bouligand 手性光子晶体验证了该方法与解析解高度一致。
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