基于六角形晶格的光子晶体零折射率特性及其光学应用研究

运用色散特性分析的方法,在六角形晶格光子晶体能带结构的布里渊区中心找到了狄拉克点,用等效媒质理论验证了在这一点上光子晶体的等效介电常量和等效磁导率同时为零,即存在狄拉克频点,用此六角形晶格光子晶体可以实现零折射率材料.随后运用有限元数值仿真方法,研究了此六角形晶格结构在狄拉克频点及其附近所呈现的零折射率特性.将此种六角形晶格光子晶体经过合理设计用以制作凹透镜,发现可以实现远场的亚波长聚焦.此外在凹透镜的入射面处引入防反射结构可以在一定程度上增强聚焦效果,提高了系统的分辨率.     

基于六角形晶格的光子晶体零折射率特性及其光学应用研究

运用色散特性分析的方法,在六角形晶格光子晶体能带结构的布里渊区中心找到了狄拉克点,用等效媒质理论验证了在这一点上光子晶体的等效介电常量和等效磁导率同时为零,即存在狄拉克频点,用此六角形晶格光子晶体可以实现零折射率材料,随后运用有限元数值仿真方法,研究了此六角形晶格结构在狄拉克频点及其附近所呈现的零折射率特性,将此种六角形晶格光子晶体经过合理设计用以制作凹透镜,发现可以实现远场的亚波长聚焦,此外在凹透镜的入射面处引入防反射结构可以在一定程度上增强聚焦效果,提高了系统的分辨率.     

纵模对光子晶体中类狄拉克点传输特性的影响

本文通过数值仿真分析了无序正方晶格光子晶体中类狄拉克点的光子传输特性. 结构中的无序是通过随机移动氧化铝介质柱的位置来实现. 研究发现, 由于纵模被激发出来, 在类狄拉克点及其附近无序对结构透射率的影响是不同的. 在类狄拉克点, 由于纵模的干扰, 透射率随着无序的增加而减小, 与通带的行为类似. 在不受纵模干扰的类狄拉克点附近, 透射率几乎不受无序的影响, 这主要是由于结构可以等效为近零折射率材料, 等效的波长非常大. 本文的研究结果有助于人们进一步理解光学纵模和零折射率材料.     

各向异性材料对二维六角晶格光子晶体中狄拉克点的影响EI北大核心CSCD

光子能带结构中的狄拉克点是目前光子晶体研究中新兴的热点。选用双轴材料,用六边形介质柱构成了六角晶格各向异性光子晶体。该光子晶体有三个各异的主介电常数εxx、εyy、εzz。依据麦克斯韦方程组,垂直极化(TE)波中的狄拉克点会受到εxx≠εyy的影响,即可以通过调制双轴材料中X、Y方向的主折射率Nx、Ny得到光子晶体中TE波的狄拉克速率,从而调节TE波中狄拉克点在能带结构图中的位置(即调节狄拉克点的归一化频率及其在布里渊区的位置)。研究了Nx、Ny(对应εxx、εyy)与TE波中狄拉克点的存在性的关系,并通过仿真实验验证了提出的观点。这些研究可为研发新型光学器件以及构建光子芯片提供更多的可能。     

二维声子晶体中Zak相位诱导的界面态

界面态具有巨大的实际应用价值,因此寻找界面态是一个既有科学意义也有应用前景的课题.在本文中,我们通过把二维正方晶格声子晶体的结构单元进行倾斜,构造出具有线性狄拉克色散的斜方晶格体系.狄拉克色散引起体能带Zak相位的π跃变,使得位于狄拉克锥投影能带两边的带隙具有不同符号的表面阻抗,从而导致由正方晶体体系与由其“倾斜”的斜方晶格体系构成的界面处存在确定性的界面态.     

各向异性材料对二维六角晶格光子晶体中狄拉克点的影响

光子能带结构中的狄拉克点是目前光子晶体研究中新兴的热点。选用双轴材料,用六边形介质柱构成了六角晶格各向异性光子晶体。该光子晶体有三个各异的主介电常数εxx、εyy、εzz。依据麦克斯韦方程组,垂直极化(TE)波中的狄拉克点会受到εxx≠εyy的影响,即可以通过调制双轴材料中X、Y方向的主折射率Nx、Ny得到光子晶体中TE波的狄拉克速率,从而调节TE波中狄拉克点在能带结构图中的位置(即调节狄拉克点的归一化频率及其在布里渊区的位置)。研究了Nx、Ny(对应εxx、εyy)与TE波中狄拉克点的存在性的关系,并通过仿真实验验证了提出的观点。这些研究可为研发新型光学器件以及构建光子芯片提供更多的可能。     

声子晶体板中的第二类狄拉克点和边缘传输

在弹性板波体系中设计了一种具有第二类狄拉克点的声子晶体板.不同于第一类狄拉克点,第二类狄拉克点附近的色散具有大的倾斜,以致于等频面的几何形状由点状变成交叉的线状.微调结构的几何参数破缺该镜面对称性,可打开第二类狄拉克点简并,实现体系的能带反转.能带反转前后的二维声子晶体板属于不同的能谷拓扑相,不同拓扑相之间存在无带隙的拓扑保护界面态.不仅如此,由于弹性板波界面态的特殊应力分布,单一能谷相声子晶体板的边界上同样支持无带隙的弹性波传输.本文拓展类石墨烯体系中的二维狄拉克点和能谷态到第二类情形中,在同一结构中获得了界面和边界上的弹性波无带隙边缘传输.由于结构设计简单,可在微小尺寸下加工获得,为高频弹性波器件的设计和构造提供了可行的途径.     

正负折射率材料组成的一维光子晶体的能带及电场

计算了由正负折射率材料交替排列组成的一维光子晶体的能带及电场，发现其能带不同于由普通正折射率材料组成的光子晶体的能带.当选择合适的参数时，由正负折射率材料组成的光子晶体的TE模或TM模有完全光子带隙出现，这在普通光子晶体中不出现.导带中的电场波函数与普通光子晶体相比具有很强的局域性.对于负折射率材料层为色散介质的情况，计算了在不同的具有正负折射率区域能带.     

基于磁流体光子晶体的可调谐近似零折射率研究

基于典型水基Fe_3O_4磁流体,建立了工作频率可调的近似零折射率磁流体光子晶体的理论模型.这种近似零折射率材料具有与自由空间阻抗相匹配的优点,更重要的是其工作频率可由外磁场的大小来调节.在满足等效折射率的绝对值小于0.05的条件下,材料的归一化工作频率可由0.716变化到0.750.     

两维光子晶体狄拉克点赝扩散现象实验设计与研究

论文主要介绍了利用微波光子晶体平台对狄拉克点处的光子输运行为展开的实验和仿真研究。利用氧化铝陶瓷柱,分别构造了蜂窝晶格光子晶体和正方晶格光子晶体实验样品,研究了两者在各自的狄拉克点和类狄拉克点处透射率随实验样品长度的变化关系。分析表明,该处频率的透过率和样品长度的乘积基本保持不变,即透过率与长度成反比关系。该结果证明了狄拉克点和类狄拉克点处存在赝扩散现象。微波实验结果和仿真结果相一致,表明了该平台的可靠性。     

Acoustic crystals with Dirac-like cone dispersion mapped to effective zero-index acoustic materials

Different two-dimensional (2D) acoustic crystals are investigated and the conditions under which these acoustic crystals can be mapped to effective zero-index materials are discussed. Acoustic crystals with Dirac-like points can only be mapped to effective zero-index materials when all three of the following conditions are met simultaneously: (i) the Dirac-like point is formed by monopole and dipole moments, (ii) the Dirac-like point is at a low enough frequency, and (iii) in the extended states above the Dirac-like point frequency, there is only one propagating band. The difference between the optical and acoustic regime is the change in the refractive index near the Dirac point frequency.     

Zero Refractive Index Properties of Two-Dimensional Photonic Crystals with Dirac Cones

The zero refractive index properties of two-dimensional photonic crystals(PCs) are studied theoretically. Three necessary conditions for PCs to mimic the zero index materials(ZIMs) are obtained. In addition, through a comparative study of the properties for two representative PC structures with different types of Dirac cones, we find that the PC with a Dirac-like cone which meets the three necessary conditions does not behave as a ZIM in some cases. Further analysis shows that its non-zero index properties originate from the flat dispersion band.These findings clarify the fundamental physical issue of which type of Dirac cone PC can mimic a real ZIM.     

Tailoring edge and interface states in topological metastructures exhibiting the acoustic valley Hall effect

In this study, we investigate the acoustic topological insulator or topological metastructure, where an acoustic wave can exist only in an edge or interface state instead of propagating in bulk. Breaking the structural symmetry enables the opening of the Dirac cone in the band structure and the generation of a new band gap, wherein a topological edge or interface state emerges.Further, we systematically analyze two types of topological states that stem from the acoustic valley Hall effect mechanism;one type is confined to the boundary, whereas the other type can be observed at the interface between two topologically different structures. Results denote that the selection of different boundaries along with appropriately designed interfaces provides the acoustic waves in the band gap range with abilities of one-way propagation, dual-channel propagation, immunity from backscattering at sharp corners, and/or transition between propagation at interfaces and boundaries. Furthermore, we show that the acoustic wave propagation paths can be tailored in diverse and arbitrary ways by combing the two aforementioned types of topological states.     

Tunable multiple layered Dirac cones in optical lattices

We show that multiple layered Dirac cones can emerge in the band structure of properly addressed multicomponent cold fermionic gases in optical lattices. The layered Dirac cones contain multiple copies of massless spin-1/2 Dirac fermions at the same location in momentum space, whose different Fermi velocity can be tuned at will. On-site microwave Raman transitions can further be used to mix the different Dirac species, resulting in either splitting of or preserving the Dirac point (depending on the symmetry of the on-site term). The tunability of the multiple layered Dirac cones allows us to simulate a number of fundamental phenomena in modern physics, such as neutrino oscillations and exotic particle dispersions with E~p(N) for arbitrary integer N.     

Conical Diffraction from Approximate Dirac Cone States in a Superhoneycomb Lattice

Superhoneycomb lattice is an edge‐centered honeycomb lattice that represents a hybrid fermionic and bosonic system. It contains pseudospin‐1/2 and pseudospin‐1 Dirac cones, as well as a flat band in its band structure. In this paper, we cut the superhoneycomb lattice along short‐bearded boundaries and obtain the corresponding band structure. The states very close to the Dirac points represent approximate Dirac cone states that can be used to observe conical diffraction during light propagation in the lattice. In comparison with the previous literature, this research is carried out using the continuous model, which brings new results and is simple, direct, accurate, and computationally efficient.     

Interfacing 2D and 3D topological insulators: Bi(111) bilayer on Bi2Te3

We report the formation of a bilayer Bi(111) ultrathin film, which is theoretically predicted to be in a two-dimensional quantum spin Hall state, on a Bi(2)Te(3) substrate. From angle-resolved photoemission spectroscopy measurements and ab initio calculations, the electronic structure of the system can be understood as an overlap of the band dispersions of bilayer Bi and Bi(2)Te(3). Our results show that the Dirac cone is actually robust against nonmagnetic perturbations and imply a unique situation where the topologically protected one- and two-dimensional edge states are coexisting at the surface.     

Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice

Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson–hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points.     

Vector valley Hall edge solitons in the photonic lattice with type-II Dirac cones

Topological edge solitons represent a significant research topic in the nonlinear topological photonics. They maintain their profiles during propagation, due to the joint action of lattice potential and nonlinearity, and at the same time are immune to defects or disorders, thanks to the topological protection. In the past few years topological edge solitons were reported in systems composed of helical waveguide arrays, in which the time-reversal symmetry is effectively broken. Very recently, topological valley Hall edge solitons have been demonstrated in straight waveguide arrays with the time-reversal symmetry preserved. However, these were scalar solitary structures. Here, for the first time, we report vector valley Hall edge solitons in straight waveguide arrays arranged according to the photonic lattice with innate type-II Dirac cones, which is different from the traditional photonic lattices with type-I Dirac cones such as honeycomb lattice. This comes about because the valley Hall edge state can possess both negative and positive dispersions, which allows the mixing of two different edge states into a vector soliton. Our results not only provide a novel avenue for manipulating topological edge states in the nonlinear regime, but also enlighten relevant research based on the lattices with type-II Dirac cones.