Optical properties of a three-dimensional chiral metamaterial

A three-dimensional chiral metamaterial with four-fold rotational symmetry is designed, and its optical properties are investigated by numerical simulations. The results show that this chiral metamaterial has the following features: high polarization conversion, perfect circular dichroism, and asymmetric transmission of circularly polarized light. A comparison of the results of chiral metamaterials without and with weak coupling between the constituent nanostructures enables us to confirm that the optical properties of our proposed nanostructure are closely related to the coupling between the single nanoparticles. This means that the coupling between nanoparticles can enhance the polarization conversion, circular dichroism, and asymmetric transmission. Due to the excellent optical properties, our metamaterial might have potential applications in the development of future multi-functional optical devices.     

Optical properties for topological insulators with metamaterials

The two fields of topological insulators and metamaterials are independent. In this Letter, we firstly investigate the Fresnel coefficients for the reflected and refracted electromagnetic waves across the interface between topological insulators and left-handed metamaterials. Then, we derive the exact analytic expressions for Kerr and Faraday rotations. By way of multiple reflections method, we demonstrate that perfect lens with left-handed metamaterials slab and topological insulators can be designed. On the other hand, the processes of reflection and refraction are investigated in the case of topological insulator and chiral metamaterial. Then, we give the reflection and transmission coefficients of topological insulator with a chiral medium slab. Lastly, the potential applications of these results are discussed.     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

Dual-band asymmetric electromagnetic wave transmission for dual polarizations in chiral metamaterial structure

In this paper, we propose a chiral metamaterial structure that enables dual-band asymmetric transmission effect for different linearly polarized electromagnetic waves. The metamaterial is composed of metallic spirals with two split-ring resonators sandwiching a dielectric slab and connecting with via hole. Strong one-way transmission of two orthogonally polarized waves at different frequency bands has been confirmed through both full-wave simulation and test on fabricated prototype at the microwave band. Analysis also shows such asymmetric transmission can be attributed to the induced asymmetric current distributions in the spiral that support strong polarization conversion and cross-polarization transmission. By scaling down the metamaterial structure, the concept could also be utilized at other frequency bands, such as submillimeter or even terahertz band and find applications in designing one-way electromagnetic wave devices or polarization spectral filters.     

Switching between the Functions of Half-Wave Plate and Quarter-Wave Plate Simply by Using a Vanadium Dioxide Film in a Terahertz Metamaterial

We propose a switchable THz metamaterial that can be switched between two functions of half-wave plate and quarter-wave plate.The two switchable functions can be simply achieved by inserting a VO_2 film in the metamaterial design.Finite-difference time-domain(FDTD) simulation results show that the proposed metamaterial can convert x-polarized incident wave to y-polarized reflected wave when VO_2 is at metal phase,and convert x-polarized wave to circularly polarized wave when VO_2 is at insulator phase.The metamaterial performs well in the two functions,i.e.,the same broad working frequency band and near perfect polarization conversion.The switching effect originates from the switchable Fabry-Perot cavity length induced by the phase change of VO_2.We believe that our findings provide a reference in designing switchable metamaterials.     

An ultra-broadband and highly-efficient tunable terahertz polarization converter based on composite metamaterial

A near perfect, ultra-broadband and highly-efficient terahertz reflective polarization converter based on multilayer metamaterial is proposed in this paper. The hybrid metamaterial unit structure consists of a split-ring metal pattern and a metal sheet separated by a dielectric resonator spacer. The polarization conversion ratio (PCR) is above 90% from 2.06 to 4.26 THz, with an optimal range between 2.98 and 4.16 THz where the efficiency is above 98% for normal incidence. It also shows excellent performance for oblique incidences. Moreover, the working band and the optimized frequency range for the polarization conversion can be manipulated by changing the open angle between the metallic arcs and the substrate thickness, respectively. Based on this design, two types of hybrid metamaterial converters are also investigated to swith off polarization conversion altogether or modify the polarization conversion bandwidth. A polarization converter with temperature controlled PCR is realized by adding a vanadium oxide (VO₂) mask on the designed structure. In addition, by integrating photoconductive silicon islands between the split-ring and metal bar a dual-band polarization converter can be realized. Combining with a polarizer, this window can act as an active THz filter.     

Asymmetric chiral metamaterial circular polarizer based on four U-shaped split ring resonators

An asymmetric chiral metamaterial structure is constructed by using four double-layered U-shaped split ring resonators, which are each rotated by 90° with respect to their neighbors. The peculiarity of the suggested design is that the sizes of the electrically and magnetically excited rings are different, which allows for equalizing the orthogonal components of the electric field at the output interface with a 90° phase difference when the periodic structure is illuminated by an x-polarized wave. As a result, left-hand circular polarization and right-hand circular polarization are obtained in transmission at 5.1 GHz and 6.4 GHz, respectively. The experiment results are in good agreement with the numerical results.     

High Chern number phase in topological insulator multilayer structures: A Dirac cone model study

We employ the Dirac cone model to explore the high Chern number (C) phases that are realized in the magnetic-doped topological insulator (TI) multilayer structures by Zhao et al. [Nature 588 419 (2020)]. The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters, then the Chern number phase diagrams of the TI multilayer structures are obtained. The high-C behavior is attributed to the band inversion of the renormalized Dirac cones, along with which the spin polarization at the $\varGamma$ point will get increased. Moreover, another two TI multilayer structures as well as the TI superlattice structures are studied.     

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one and two dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the pseudo-quantum electrodynamics (PQED). The well-known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well-known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.     

Quantum Anomalous Hall Multilayers Grown by Molecular Beam Epitaxy

Quantum anomalous Hall(QAH) effect is a quantum Hall effect that occurs without the need of external magnetic field. A system composed of multiple parallel QAH layers is an effective high Chern number QAH insulator and the key to the applications of the dissipationless chiral edge channels in low energy consumption electronics. Such a QAH multilayer can also be engineered into other exotic topological phases such as a magnetic Weyl semimetal with only one pair of Weyl points. This work reports the first experimental realization of QAH multilayers in the superlattices composed of magnetically doped(Bi,Sb)_2Te_3 topological insulator and Cd Se normal insulator layers grown by molecular beam epitaxy. The obtained multilayer samples show quantized Hall resistance h/N_e~2, where h is Planck's constant, e is the elementary charge and N is the number of the magnetic topological insulator layers, resembling a high Chern number QAH insulator. The QAH multilayers provide an excellent platform to study various topological states of matter.     

Left-handed chiral metamaterials

In this work, the concept of left-handed chiral metamaterials is analyzed by emphasizing their optical ability on the rotation of the plane of polarization of a wave. The possibilities of a negative phase velocity, negative and positive propagation constants, and basic electromagnetic properties of this novel medium are also presented. After the characterization of left-handed chiral metamaterial, we provide a reflection and transmission study for two planar boundaries of nonchiral-left-handed chiral metamaterial for normal angles of incidence. Some numerical results are also provided to validate the formulation found in the analysis and to show the role of the chirality in the propagation constants, phase velocities, reflection and transmission.      

Guided electromagnetic waves at the interface between a dielectric and a topological insulator

Surface electromagnetic waves that propagate within the interface between a conventional dielectric or a metamaterial and a topological insulator with an undamped surface electric current are considered. Dispersion relations are given for guided waves that are surface waves polarized differently on either side of the media interface and create a coupling state due to the magnetoelectric effect.     

Polarization-independent broadband terahertz chiral metamaterials on flexible substrate

A THz band-reject filter is designed based on chiral four-fold rotational symmetry metamaterial. This filter was fabricated by laser micro-lens array lithography and characterized by terahertz time-domain spectroscopy. The resonant frequencies at different twist angles are almost the same, which demonstrates the polarization independence of the structure. The electric field distribution is simulated to explain the physics mechanism behind the polarization independence. By stacking multiple metamaterial layers together, a THz broadband reject filter at a bandwidth of 0.461 THz is experimentally achieved.     

Optimal helix shape: Equality of dielectric,magnetic, and chiral susceptibilities

The possibility of linearly polarized electromagnetic microwave conversion into a circularly polarized wave using single-turn helices with preliminary calculated optimal parameters is demonstrated. The helices are characterized by equal dielectric, magnetic, and chiral susceptibilities. Such optimal helices can be further used, for example, to develop reflectionless coatings and metamaterials with negative electromagnetic wave refraction. It is demonstrated that the examined helices activated by both electric and magnetic fields, that is, for any arbitrary orientation of the incident wave polarization plane, have optimal characteristics. This is the advantage of the optimal helices over other possible metamaterial elements, for example, rectilinear vibrators or circular resonators.     

Metamaterial polarization converter analysis: limits of performance

In this paper, we analyze the theoretical limits of a metamaterial-based converter with orthogonal linear eigenpolarizations that allow linear-to-elliptical polarization transformation with any desired ellipticity and ellipse orientation. We employ the transmission line approach providing a needed level of the design generalization. Our analysis reveals that the maximal conversion efficiency for transmission through a single metamaterial layer is 50 %, while the realistic reflection configuration can give the conversion efficiency up to 90 %. We show that a double layer transmission converter and a single layer with a ground plane can have 100 % polarization conversion efficiency. We tested our conclusions numerically reaching the designated limits of efficiency using a simple metamaterial design. Our general analysis provides useful guidelines for the metamaterial polarization converter design for virtually any frequency range of the electromagnetic waves.     

Complex energy plane and topological invariant in non-Hermitian systems

Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics. We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.     

Equivariant PT-symmetric real Chern insulators

It was understood that Chern insulators cannot be realized in the presence of PT symmetry.In this paper,we reveal a new class of PT-symmetric Chern insulators,which has internal degrees of freedom forming real representations of a symmetry group with a complex endomorphism field.As a generalization to the conventional 2n-dimensional Chern insulators with integer n≥1,these PT-symmetric Chern insulators have the n-th complex Chern number as their topological invariant,and have a Z classification given by the equivariant orthogonal K theory.Thus,in a fairly different sense,there exist ubiquitously Chern insulators with PT.symmetry.By generalizing the Thouless charge pump argument,we find that,for a PT-symmetric Chern insulator with Chern number v.there are equally many v flavors of coexisting left-and right-handed chiral modes.Chiral modes with opposite chirality are complex conjugates to each other as complex representations of the internal symmetry group,but are not isomorphic.For the physical dimensionality d=2,the PT-symmetric Chern insulators may be realized in artificial systems including photonic crystals and periodic mechanical systems.     

复合结构螺旋超材料对光波前的高效调控

近年来,超材料和超表面因为一些不同于传统材料的新奇性质一直被广泛研究,而基于超材料或者是超表面的波前控制也是其中的一个热门研究领域.迄今为止,已经提出了很多不同的结构来对反射光和透射光的波前进行调控,在已知的结构中,反射光的波前调控效率已经可以达到较高数值,但是很少有报道能够使用超材料简单高效地调制透射光的波前.本文提出了一种由相同几何结构的左旋和右旋结构复合而成的螺旋超材料.通过使用时域有限差分方法进行仿真,发现这种螺旋结构将会在入射光和透射光之间引入一个可控的相位变化,从而可直接对透射光波前进行调控.仿真结果还表明,该复合结构螺旋超材料在较宽的波长范围内可以达到近64%的透射率.最后通过将该螺旋材料沿着X轴排布成有着连续相位变化的阵列,可以在近红外区域(1.0—1.4μm)观察到反常折射现象,仿真结果与理论计算得出的反常折射角十分符合.     

Transmission-type reconfigurable metasurface for linear-to-circular and linear-to-linear polarization conversions

We present a transmission-type polarization conversion metamaterial (PCM) whose functions can be dynamically switched among the linear-to-circular (LTC) and linear-to-linear (LTL) polarization conversions. The proposed PCM consists of a grating, a polarization conversion surface and a reconfigurable polarization selective surface incorporated with PIN diodes. By changing the states of diodes, the PCM can achieve the reconfigurable manipulations for incident waves. The Fabry-Pérot (F-P) resonances excited by the PCM contribute to the polarization conversions, as is illustrated. Moreover, through establishing the F-P-like cavity model and analyzing the electric field components of the transmitted waves, the conditions for realizing LTC polarization conversion are revealed, which can guide the construction of PCM. The prototype of PCM is fabricated and measured, which can achieve LTC and LTL polarization conversions within 3.31-3.56 GHz and 2.76-4.24 GHz, respectively, the polarization conversion ratios of two functions are higher than 0.95. The measurement results are in agreement with the simulation data.