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摘要:
双曲超材料作为电磁超材料的重要分支，因其独特的近场调控特性成为研究的焦点。双曲超表面作为一种特殊新型的平面超材料，具有双曲色散特性，在理论和应用上也与双曲超材料有诸多相似点。与块体双曲超材料相比，由于纵向维度尺寸的大幅度减小从而将电磁波传播限制在二维平面上，双曲超表面表现出更加优异的性能。本文首先介绍双曲超材料的理论、实现和应用，接着介绍双曲超表面及其潜在应用，最后还指出双曲超材料和超表面在真实条件下的局限，及对应用前景作了展望。
Abstract:Abstract:As an important branch of electromagnetic metamaterials, hyperbolic metamaterials become the focus of research for their unique property of controlling near-field waves. Hyperbolic metasurface is a new type of planar metamaterials with hyperbolic dispersion relationship and has many similarities in theory and applications with hyperbolic metamaterial. Compared with the bulk hyperbolic metamaterials, hyperbolic metasurfaces exhibit more excellent performances because the large reduction in the longitudinal dimension limits the propagation of the electromagnetic waves in the two-dimensional plane. In the first part of this review, we introduce hyperbolic metamaterial with its theory, implementation and applications. The latter part of the review is about hyperbolic metasurfaces and their potential applications. We also point out the restrictions of the hyperbolic metamaterials and metasurfaces and the prospect of future applications.
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Key words:
- hyperbolic metamaterials /
- hyperbolic metasurfaces /
- negative refraction /
- hyperlens
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In recent years, with the continuous progress of micro/nano fabrication technique, the interaction of material and electromagnetic wave in the subwavelength scale has attracted widespread attention. Electromagnetic metamaterial is artificial material composed of building blocks whose feature size is much smaller than the working wavelength, with the electromagnetic properties that does not exist in natural materials. As an important branch of electromagnetic metamaterials, hyperbolic metamaterials become the focus of research for their unique characteristic to control near-field waves. By changing the size and arrangement of the components of hyperbolic metamaterials, the excitation intensity and direction of the surface plasmons (SPs) in them can be modulated, so that the unique dispersion curves can be achieved. Hyperbolic metamaterials have been used in many fields, such as subwavelength imaging, light localization and enhanced spontaneous emission. Hyperbolic metasurface is a new type of planar metamaterials with hyperbolic dispersion relationship and has many similarities in theory and applications with hyperbolic metamaterial. Compared with the bulk hyperbolic matematerials, hyperbolic metasurfaces exhibit more excellent performances because the large reduction in the longitudinal dimension limits the propagation of the electromagnetic waves in the two-dimensional plane.
In this review, starting with hyperbolic metamaterials, we introduce their basic theory of dispersion equation and isofrequency surface, and then describe the method of realizing hyperbolic dispersion from two different structures: metal-dielectric multilayer structure and metal nanowire structure. Effective medium theory to calculate the effective dielectric tensor and the choice of real materials are also presented. At the end of this section, we briefly introduce the typical applications of hyperbolic metamaterials, including optical negative refraction and hyperlens imaging. The latter part of the review is about hyperbolic metasurface and we begin with the introduction of the basic theory and isofrequency curve of hyperbolic metasurface. The difference is that in addition to the introduction of ordinary hyperbolic dispersion, we also stress the special case of near the topological transition point, where the dispersion curve is almost flat and the transmission of electromagnetic wave is almost diffraction-free. Then we list the natural hyperbolic materials that can be used to fabricate hyperbolic metasurface, including uniaxial and two-dimensional materials. The artificial method of using graphene to achieve any topological structure on the plane is illustrated. In analogy with the hyperbolic metamaterial, the negative refraction effect and the hyperlens imaging in hyperbolic metasurface are also introduced. In addition, intriguing properties of hyperbolic metasurfaces and their potential applications are described. Finally, we point out the restrictions of the hyperbolic metamaterials and metasurfaces and the prospect of future applications.
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图 2 (a) 金属-介质多层膜结构示意图，ε、μ、d分别代表材料的介电常数、磁导率和薄膜厚度[20]. (b)半导体多层膜结构有效介电常数的实部图，ε⊥、ε||分别表示垂直和平行于多层膜的介电常数[15]. (c)金属纳米线阵列结构示意图，d为金属纳米线阵列周期，r为金属纳米线半径[16].
Figure 2. (a) Schematic of the metal-dielectric multilayer structure, ε, μ, d represent the permittivity, permeability and film thickness respectively [20]. (b) The real part of the permittivity of a semiconductor multilayer structure, ε⊥, ε|| represent the permittivity that are perpendicular and parallel to the film, respectively [15]. (c) Schematic diagram of the nanowire array structure, d is the period of the nanowire array and r is the radius of the metal nanowire [16].
图 3 (a) 基于金属纳米线阵列的双曲超材料的色散特性[17]. (b)理论计算的双曲超材料的负折射现象[16]. (c)利用氧化铝模板制备的金属银纳米线阵列，SEM照片中标尺为500 nm [18].
Figure 3. (a) Hyperbolic dispersion relationship in nanowire array structure [17]. (b) Simulated negative refraction of hyperbolic metamaterials [16]. (c) Schematic of a silver nanowire hyperbolic metamaterial as well as scanning electron microscopy images showing the top and side views of the nanowires. The scale bars indicate 500 nm [18].
图 4 (a) 基于金属介质多层膜的平板形和圆柱形双曲超材料及其各自色散曲线[47]. (b)上图：双曲超透镜结构示意图及仿真结果.下图：双曲超透镜的两种设计思路，切向层叠和径向层叠[6]. (c)左图：超透镜结构示意图，入射波长365 nm；右图：字母“ON”的超越衍射极限图样[7].
Figure 4. (a) Schematic of the planar and cylindrical multilayer hyperbolic structures and their dispersion properties [47]. (b) Schematic of hyperlens and its simulation results (up) and possible realizations of hyperlens——concentric metallic layers alternate with dielectric layers or radially symmetric "slices" alternate in composition between metallic and dielectric (down) [6]. (c) Left: Schematic of the hyperlens and the incident wavelength is 365 nm, Right: The beyond-diffraction image of the word "ON" [7].
图 5 (a) ~(c)当z取向的电偶极子（黑色箭头）位于表面上方时，在不同电导率情况下表面电场z分量的响应，插图为色散等频曲线[12]. (d)损耗较大时的表面等离子激元传播及其等频曲线[58].
Figure 5. (a)~(c) Color maps show the z-component of the electric field excited by a z-directed dipole (black arrow) located above the surface. The insets present the isofrequency contour of each metasurface topology[12]. (d) In the case that the loss cannot be ignored [58].
图 6 (a) 石墨烯超表面上传播的表面等离子体的电场z分量，插图为对应的石墨烯超表面结构示意图[57]. (b)石墨烯超表面x, y垂直方向的电导率虚部随条带宽度和频率变化的谱图，上图对应y方向，下图对应x方向[57].
Figure 6. (a) Ez field component of surface plasmons excited by a z-oriented electric dipole located above homogeneous metasurfaces defined by various conductivity tensors. The insets show possible realizations of the different metasurface topologies using pristine or nanostructured graphene layers [57]. (b) The imaginary part of the effective electric conductivity along y (up) and x (down) direction versus ribbon width W [57].
图 7 (a) 基于光栅结构的超表面结构示意图[74]. (b)光栅在不同入射光下的色散分布图，光栅周期120 nm，宽度60 nm，高度80 nm[74]. (c)光栅超表面的负折射效应，入射波长500 nm，光栅周期100 nm，宽度40 nm，高度100 nm[74]. (d)~(f)入射波长分别为500 nm(左)，543 nm(中)，633 nm(右)时结构表面等离子激元波传播[74].
Figure 7. (a) Schematic of metasurface based on grating structure [74]. (b) The dispersion relationship of the grating metasurface at different wavelengths. The grating period is 120 nm, the width is 60 nm and the height is 80 nm [74]. (c) The simulated negative refraction of the grating metasurface with 500 nm incident wave. The grating period is 100 nm, the width is 40 nm and the height is 100 nm [74]. (d)~(f) Propagation of surface plasmons along the metasurface at three different wavelengths of (d) 500 nm, (e) 543 nm and (f) 633 nm [74].
图 9 (a) 单层石墨烯无衍射传输示意图[12]. (b)图(a)虚线观察线处的电场强度z分量归一化结果[12]. (c)石墨烯加衬底，加偏压转化为双曲超表面的方法示意图[5]. (d)两个电偶极子经过图(c)中石墨烯表面的仿真结果[5]. (e)平面放大超透镜结构示意图[79].
Figure 9. (a) Schematic of the non-diffraction transmission of the monolayer graphene [12]. (b) The normalized z component of the electric field at the observation lines in Figure (a) [12]. (c) The method of adding substrate and bias to transform graphene to hyperbolic metasurface [5]. (d) Simulated SPPs propagation on the graphene metasurface in Figure (c) [5]. (e) Schematic of the planar magnifying hyperlens [79].
图 10 (a) 石墨烯表面散射体辐射电磁波与表面等离子激元耦合示意图[80]. (b)不同传播角度下的场局域性[58]. (c)自发辐射率随电导率虚部的变化[58].
Figure 10. (a) Schematic of the coupling of a dipole emitter to graphene SPPs [80]. (b) Field confinement at different angles of propagation [58]. (c) SER in logarithm scale versus the conductivity components of the structure [58].
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