超构表面:设计原理与应用挑战(特邀) 下载: 1584次创刊五十周年特邀【增强内容出版】
作为一种二维形式的超构材料,超构表面允许以前所未有的自由度对光的振幅、相位、偏振等维度进行灵活高效的调控,有望突破传统光学的限制,实现低成本、高性能、超轻超薄、功能新颖的新型光学元件,近年来引起了学术界和产业界越来越浓厚的研究兴趣。从物理机理、相位调控到正向设计方法,系统回顾了超构表面的设计原理。介绍了这些机理如何用于实现丰富的应用,包括功能复用、宽带宽、大视场、多层级联、非局域超构表面等,涵盖了最主要和最新的发展方向。最后,讨论了超构表面在走向实用化的道路上所面临的器件设计和加工制造上的挑战,并对领域未来的发展进行展望。
Consisting of sub-wavelength scatterers or holes arranged on a plane, the metasurface, as a two-dimensional form of the metamaterial, permits flexible and efficient modulation of the amplitude, phase, polarization and other characteristics of the light with an unprecedented degree of freedom, which is expected to break through the limitations of traditional optics and realize ultra-light, ultra-thin, high-performance, and novel-functional optical devices. In recent years, metasurfaces have attracted increasing research interest in both academia and industry, and a wide range of applications have been achieved in the field of imaging, holography, quantum optics, displacement metrology, virtual reality, optical encryption, and ultrafast optics. Based on the elucidation of the basic design principles of metasurfaces, this review covers the main development directions, research progress, and challenges of current metasurface applications.
The design principles of metasurfaces are now well established and can be understood in three dimensions the most basic meta-atom and its scattering effect, metasurface as an array of meta-atoms, and the topmost design methods. For the first dimension, the physical image of the electromagnetic modulation of the meta-atom is explained, and the three main types of phase modulation mechanisms are introduced, that are, the resonant phase, the propagation phase, and the geometric phase. The selection of appropriate phase modulation mechanisms is significant for realizing the design of metasurfaces with different functions. For the second one, generalized refraction and reflection laws are introduced. For the last one, the forward design method and its theoretical basis are presented.
How these mechanisms are utilized to realize a variety of applications is described in detail, including polarization multiplexing, wavelength multiplexing, wide bandwidth, large field-of-view, multilayer cascades, and nonlocal metasurfaces, covering the most important and recent developments. 1) Polarization multiplexed devices (Fig.3). When operating at a single wavelength, it is theoretically elucidated that a hybrid phase modulation mechanism can achieve arbitrary polarization and phase modulation under the ideal situation of sufficient design freedom of meta-atoms. Based on this theory, the latest research progresses are presented, such as the multiplexing for arbitrary orthogonal states of polarization, multichannel polarization multiplexing, etc.2) Wavelength multiplexed devices (Fig.4). To achieve independent phase modulation of the incident light at different wavelengths, intelligent strategies of space division multiplexing, decoupling with other multiplexing channels, and other methods have been proposed, leading to applications such as full-color holographic displays. 3) Broadband devices (Fig.5). The problem of achromaticity in metalenses has been a difficult problem in this field for several years. Through dispersion engineering, theories and methods for designing achromatic metalenses have been developed, and both polarization-sensitive and polarization-insensitive achromatic lenses have been realized. Recently, the novel idea of quasi-achromatic metalenses has also been proposed to relax the bandwidth limitation of achromaticity. 4) Incident angle multiplexed and wide field-of-view devices (Fig.6). Incident angle multiplexed metasurfaces can be designed by both forward methods and inverse methods such as topology optimization. By selecting the suitable target phase distribution for wide field-of-view imaging and introducing the concept of effective aperture or virtual aperture, metalenses with wide field-of-view have been designed and realized. 5) Multilayer cascaded metasurfaces (Fig.7). The distance between layers in cascaded metasurfaces determines the relationship between adjacent layers, according to different theoretical models and design methods. By cascading multiple layers of metasurfaces, design tasks that are difficult to achieve with a single metasurface can be achieved, such as hysteresis and chromatic aberration correction of metasurface lenses, and novel functions such as dual-wavelength and dual-focus metasurface lenses can be obtained. 6) Nonlocal metasurfaces (Fig.8). By exploiting the nonlocal effect of metasurfaces, the transverse-momentum-dependent electromagnetic response can be modulated to realize novel functions that are difficult to achieve for local metasurfaces, such as image differentiation and free-space compression, which is a latest trend in metasurface design.
Metasurfaces still face many challenges from science and engineering. In terms of the metasurface design, it is still a common problem of the field to realize devices with higher performance and larger size. On the one hand, it is important to clarify the theoretical performance limits of metasurfaces and the constraints of design methods to guide the future development of the metasurface design. On the other hand, it is also essential to make breakthroughs in design methods, such as the further development and promotion of inverse design. In terms of fabrication and manufacturing, there is still a long way to go for the industrialization and commercialization of metasurfaces due to the limitations of the fabrication accuracy, process compatibility, large-scale manufacturing cost, etc. We believe that metasurfaces will play a transformative role in the near future of optics contributing to their ultra-light and ultra-thin planar architectures, powerful electromagnetic modulation properties to support flexible device designs, ease for integration and miniaturization of optical systems, and the promise of low-cost, high-volume manufacturing.
1 引言
1968年,Veselago[1]首次提出左手材料(LHM)的概念,并对其电磁特性进行了系统性的研究。从此,超构材料这一崭新的领域宣告诞生。超构材料是由空间排布的周期性或非周期性的亚波长结构(如金属环、金属棒等)构成的宏观复合材料,其功能不再单单取决于材料的化学成分,而是与结构紧密关联[2]。这意味着,通过精心的结构设计,超构材料可以具备自然材料无法提供的丰富电磁性质,从而使人类对电磁波的调控能力有望达到前所未有的高度。通常,材料特性可以通过介电常数和磁导率来描述。如
图 1. 光频下各向同性材料在介电常数和磁导率空间中的分布。其中, 和 分别为真空的介电常数和磁导率
Fig. 1. Distribution of isotropic materials in permittivity and permeability space under optical frequency. and are permittivity and permeability of vacuum, respectively
作为超构材料的二维形式,超构表面通过在二维平面上排布超构原子——亚波长级别的散射体或者孔洞——实现特定的电磁调控特性。工作原理上,相比于超构材料,超构表面基于界面处的相位突变而非相位的累积,可以占据更小的物理空间(超构原子的厚度甚至可以远小于工作波长[18]),因而具备更低的损耗[19],以满足实际应用的需求。同时,其紧凑的尺寸也非常适合于集成纳米光子学、新颖的微波天线设计等应用场景[20]。此外,维度的降低显著降低了器件的加工制造难度[21]。构成超构材料的单元结构往往需要具有亚波长级别的尺度,因此,器件的加工难度会随着工作波长的减小而增加。在工艺限制下,早期研究中超构材料大多选择工作在微波波长附近[11-12],如果要推广到更短的波长,则其结构设计自由度将严重受限[22]。超构表面则凭借其易于加工的特性,可以在保持充足的设计自由度的同时,将工作波长范围大大延伸,覆盖从微波[23]、太赫兹[24]、红外[25]到可见光[26]甚至紫外[27]的整个光谱范围。凭借上述优良性质,超构表面可以在某些应用中完全替代超构材料(需要指出的是,在更多的应用中二者往往相互补充,无法相互取代)[19],同时在更广泛的领域里具有丰富和重要的应用,例如成像[28]、全息[29]、量子光学[30]、光谱仪[31]、结构光[32]、精密测量[33]、虚拟现实[34]、增强现实[35]、声波操控[36]、生物传感[37]、加密技术[38]、超快光学[39]等等。
在此对与超构表面相互关联或者功能相似的器件进行简要的对比和区分。从工作波长与单元结构长度的关系上,超构表面的结构长度处于亚工作波长的尺度,此时散射体表现出丰富的谐振特性;当结构长度远小于工作波长时,材料为经典的薄膜材料,表现出准静态的行为,此时材料的有效色散特性仅取决于材料的体光学特性本身,与结构设计无关[21];当结构长度接近工作波长时,典型材料为传统的频率选择表面(FSS)材料[40]和光子带隙(PBG)材料[41]。二元光学元件(BOE)与超构表面均是通过引入相位突变来实现电磁调控的。二者的主要区别在于,二元光学元件利用离散的几个相位级别来实现对光的调控,设计上较为简单[42];而超构表面则通过更复杂的结构设计提供接近连续的相位变化。这种设计复杂性的区别进一步表现在二者的应用范围上:相比于超构表面,二元光学的电磁调制功能会比较受限。衍射光学元件(DOE)基于光的衍射理论对光进行调控,在成像、结构光生成、光束整形等领域与超构表面的应用有重叠。相比于已经在工业界取得广泛应用的衍射光学元件,超构表面尽管在商业化道路上仍然面临大规模制造成本等方面的挑战,但是其表现出的对光进行调控的更高自由度,已经催生出性能优于衍射光学元件或者具备衍射光学元件无法实现的新颖功能的设计,例如高效率和高数值孔径(NA)的透镜[43-44]以及偏振敏感和多路复用的全息器件[45-46],并且仍有很大空间在等待学术研究和工业应用去发掘[47]。但需要注意的是,这并不意味着超构表面会完全取代衍射光学元件。实际上,二者具有各自适用的应用范围,例如对于消色差透镜,超构表面适合高数值孔径和适中带宽的应用,而衍射光学元件适合低数值孔径和宽带宽的应用[48]。详细的讨论参见文献[47-50]。
本文首先在理论层面上介绍超构表面的工作原理,尤其关注超构原子的相位调控机制,同时介绍超构表面的基本设计理论;而后,对于超构表面应用的主要发展方向,包括偏振复用、波长复用、宽带宽、大视场、多层级联、非局域超构表面等,分别以具体的一类或者几类典型的超构表面器件为例,介绍设计方法与研究进展;最后,从多个维度上总结了超构表面领域面临的主要挑战,给出其可能的应对之策,并对超构表面的未来发展做一展望。
2 超构表面的设计原理
本质上,超构表面是超构原子的二维阵列。从超构原子的角度出发,超构表面可以分为同质超构表面和异质超构表面两类[51]:前者由同一种超构原子依周期排布构成,整个超构表面的电磁调控特性可以约化到周期性边界条件下的单个超构原子去考察;后者则采用多种不同形状、尺寸或者旋转角度的超构原子,每种超构原子产生特定的电磁响应,通过对各种超构原子进行精心设计的排布,可实现丰富和复杂的应用。可以看到,同质超构表面的工作原理是进一步理解异质超构表面的基础,而理解同质超构表面的核心在于理解超构原子。同质超构表面可视为异质超构表面的一种特殊情形,但在完美吸收体[52]、偏振调控[53]、透射率或反射率增强[54]等方面也有其独特的应用。本文主要关注异质超构表面,对同质超构表面的系统梳理与讨论可以参阅文献[51]。
2.1 超构原子的基本原理和相位调控机制
超构原子是一种亚波长级别的金属或者电介质结构。亚波长结构与光相互作用的研究最早可以追溯到Mie[55]发表于1908年的著名论文。在那篇论文中,Mie用电磁理论推导了单色平面波与一个均匀介质中任意半径与材料的均匀球相互作用的严格解。在之后的研究中,尽管也有研究尝试将球形结构扩展到非球形,但电磁场解的严格解析形式比较复杂,实际中往往采取一定的近似[56]。在超构表面中,超构原子往往采用圆柱、矩形柱、异形柱(柱截面为H形、V形、十字形等形状)等结构,不同超构原子的散射场彼此相干,理论上目前无法提供一般超构原子的解析解,而只能给出某些情况下的近似模型和公式。其中,对同质超构表面进行建模分析的经典方法是有效介质理论[57-58]。该理论试图找出超构原子结构和体材料参量之间的对应关系,但存在很多限制[21]。实际上,Mie理论或等效介质理论等研究很少直接应用于超构原子的设计(尤其是在异质超构表面的设计中)。一般地,人们普遍利用计算电磁学的方法[例如时域有限差分(FDTD)方法]来对超构原子进行全波仿真,求解其电磁响应特性。
超构原子的相位调控机制对于实现不同功能的超构表面设计具有重要意义。在目前的超构表面设计中,应用最多的是三类相位调控机制:谐振相位、传播相位和几何相位。
先介绍谐振相位。金属与电磁场的相互作用主要取决于其中的自由电子,这些传导电子构成了一种等离子体,将在外加电磁场下产生集群响应[59]。通过结构设计,金属超构原子在电磁场激发下发生谐振,会形成某些特定的电谐振模式和磁谐振模式[51]。在超构表面的研究初期,得益于等离子体光学的发展,研究人员对亚波长级别的金属结构的特性已有比较充分的研究,因此大多选用金[60]、银[61]等金属作为超构原子材料。超构表面可以选择工作在反射或者透射模式(两种模式分别对超构表面的反射光和透射光进行电磁调控)。金属具有很高的欧姆损耗,即使是银和金这样的电导率最高的金属,在光频下依然会表现出难以接受的损耗[62],这就导致金属超构表面的效率受限,尤其是对于透射场景下的应用(成像、片上光电子集成等实际应用中往往要求器件工作在透射模式下[43])。即使通过采用金属/绝缘体/金属(MIM)结构的超构原子结构[见
图 2. 超构表面的设计原理。(a)MIM结构示意图;(b)电介质球在磁偶极子谐振、电偶极子谐振、磁四极谐振和电四极谐振四种谐振模式下的场分布[96];(c)超构原子的琼斯矩阵数学分析中建立的坐标系;(d)用于广义折射定律推导的示意图[93];(e)二维情形下的广义折射定律和反射定律示意图[92];(f)用于实现光束偏转的V形超构原子阵列中每一超构原子的散射电场的FDTD仿真结果[93]
Fig. 2. Design principles of metasurfaces. (a) Illustration of MIM structure; (b) field distributions of dielectric sphere under magnetic dipole resonance, electric dipole resonance, magnetic quadrupole resonance and electric quadrupole resonance[96]; (c) coordinate system established in mathematical analysis of meta-atom using Jones matrix; (d) schematic used for derivation of generalized law of refraction[93]; (e) schematic of generalized laws of refraction and reflection in two-dimensional case[92]; (f) FDTD simulation results of scattered electric field for each meta-atom in V-shaped meta-atom array for beam deflection[93]
作为替代,高折射率的电介质或半导体材料,如二氧化钛[66-67]、氮化镓[68-69]、硅[70-71]等,在可见光或近红外等频率范围内具有极低的损耗,同时拥有丰富的谐振特性,有望实现高效率的超构表面器件。同时,硅等材料与现代互补金属氧化物半导体(CMOS)工艺更加兼容,因此更有潜力实现超构表面大规模的批量生产。与金属不同,电介质材料中不存在自由电子,无法形成传导电流。但当入射光穿透纳米电介质结构时,会激发出强烈的位移电流(可被视为金属中的传导电流在电介质中的对应物),对其分布的进一步研究表明,电介质在一定条件下同样存在电谐振和磁谐振的模式[51]。例如,考虑平面波入射到电介质球的情形,此时主要存在四种谐振模式:两种基础米氏谐振——磁偶极子(MD)谐振和电偶极子(ED)谐振,以及两种高阶米氏谐振——磁四极(MQ)谐振和电四极(EQ)谐振,其中磁谐振与电谐振具有可比的强度。这四种谐振模式下的场分布如
通过超构原子的形状设计,可以调节超构原子内的谐振模式,进而对入射光引入依赖波长和偏振态的相位突变。这种相位调控原理被定义为谐振相位[72]。当采取各向同性的超构原子设计(如圆柱、正方形柱)时,谐振模式的对称保证了引入的谐振相位不具有偏振敏感性[73];而当采取各向异性的超构原子设计(如椭圆形柱、矩形柱)时,相位突变量与入射光的线偏振方向相关[74]。显然,各向同性超构原子设计可视为各向异性超构原子的一种特殊情形。
接下来介绍传播相位。当考虑高折射率、高深宽比的电介质超构表面[75]时,可以利用截断波导原理来对超构原子进行描述。此时,超构原子被视为上下截断的波导,只支持低品质因子的谐振模式。相位调控通过入射光作为导波在传播中的相位积累过程来实现,因此支持带宽更宽的电磁调控(相比之下,谐振效应则具有窄带的特性)[76]。超构原子形状和尺寸的改变所带来的传播模式的调节反映于光在超构原子传播中的等效折射率
这种相位调节机制被称为传播相位[77]。设超构原子的材料和包覆超构原子的材料(一般为空气)的折射率分别为
由
从物理原理上,谐振相位和传播相位有比较清晰的区别;但在实际设计中,这种区分的严格边界是难以界定的。例如,文献[78]指出通过传播相位调控机制引入的相位累积也可能会受到谐振相位的影响。鉴于二者表现出来的相位调控特性是比较相似的,即相位改变量都来自于超构原子形状和尺寸的调节,在实际设计中一般也没有特别的必要进行严格区分。
近年来,传播相位调控机制亦有新的发展。与单一电介质材料构成的超构原子不同,Chen课题组Yin等[79]利用金属和电介质交替堆叠的多层结构构成的双曲超构材料波导来构建超构原子。波导在其侧壁支持伪表面等离激元,通过改变波导的几何参数,可以对伪表面等离激元的色散特性进行调节,进而改变超构原子引入的相位突变,实现波前调控等功能。类似的结构后面还被进一步用于二次谐波生成增强[80]等应用。
可以采用琼斯矩阵对谐振相位或传播相位进行数学描述。假设在固定波长下,
最后介绍几何相位。几何相位概念的提出与应用要远早于超构表面。1956年,Pancharatnam[81]已经发现一平面结构的自旋反向的散射光可以获得额外的二倍旋转角的相位因子,并采用庞加莱球对其进行描述。1984年,Berry[82]首次提出了量子力学上的Berry相位的概念。2002年,Hasman课题组Bomzon等[83]应用几何相位原理实现了偏振敏感的衍射光栅的设计,并在实验上对其可行性进行了验证(此时超构表面的概念尚未诞生)。近年来,几何相位原理亦有新的发展[84]。
考虑
式中:
考虑入射光为圆偏振光的情况,设振幅为1,其琼斯矢量表示为
式中:
在入射光与上述超构原子作用后,散射光的琼斯矢量为
在
在实际设计中,往往通过遍历形状尺寸参量来选择具有尽可能高的偏振转换效率的超构原子,以获得更高的器件效率[86]。由
将谐振相位和传播相位这两种非几何相位与几何相位进行对比。从偏振态上,几何相位超构表面对入射光和散射光的偏振态有严格要求,而非几何相位超构表面无此限制。从工作原理上,非几何相位超构表面依赖于特定的超构原子结构,使其对加工误差比较敏感,因此对微纳加工工艺的精度要求比较高;几何相位超构原子通过一种超构原子的旋转来覆盖全相位空间,具有超构原子结构简单的特性,对加工工艺的精度要求也相对更低(一般旋转角度的加工误差很小,即使加工导致超构表面形状与设计存在偏差,也不会影响相位调控的准确性,只是可能在一定程度上降低超构表面的效率)[87]。此外,某一形状的超构原子对不同波长入射光的散射特性存在差异,因此非几何相位超构表面具有波长敏感性;而几何相位只依赖于旋转角度,这意味着同一几何相位超构表面对不同波长入射光引入的相位分布只有常数项的差异,因此几何相位超构表面对工作波长并不敏感(注意偏振转换效率是与波长相关的)。
如果将谐振或者传播相位调控机制与几何相位调控机制结合起来,即采用多种形状尺寸的超构原子,并允许其以一定的角度旋转,此时超构原子具有极高的电磁调控自由度,超构表面设计空间将大为扩展[88],可以实现消色差成像[89]、偏振复用的全息显示[90]等复杂的设计。这种混合相位调控机制的应用将在第3节详细介绍。
2.2 广义的折射和反射定律
对于异质超构表面,其电磁响应特性是二维空间的函数。广义的折射和反射定律可以用来描述界面处空间分布的相位突变对光在两种介质间折射和反射特性的影响。考虑一维的情形,如
式中:
类似地,广义反射定律为
式中:
上述定律表明,通过设计界面处的相位分布以改变其相位梯度,适当选取周围介质的折射率,折射和反射光束可以在各自的半入射面内弯曲向任意方向。如
2011年,Yu等[93]将
2.3 超构表面的正向设计理论
在之前的讨论中,都是采用周期性边界条件来求解超构原子的电磁响应,即假定任一超构原子周围所有单元上的超构原子也具有与之相同的结构。这种超构原子的设计策略并未考虑最终超构原子实际在超构表面上所处的周围环境(相邻超构原子)对其电磁响应特性的影响。在这种传统的正向设计策略中,超构表面被划分为一个个周期排布的单元,单元一般采用固定晶格常数的正方形或者正六边形(对正方形单元来说,晶格常数即其边长,也被称为单元尺寸),以铺满整个表面,在每个单元的中心根据目标设计的电磁响应要求放置一个超构原子(超构原子从预先通过遍历结构参量构建起来的超构原子数据库中选择),超构表面对入射光的电磁调控作用等价于局域的超构原子电磁响应的拼接。这一近似称为局域周期性近似(LPA)。以电介质超构表面为例对此近似的有效性进行说明:在亚波长级别的超构原子中,超构原子阵列的集群电磁响应的主要来源是单个超构原子内的米氏谐振及其相互间的干涉,而非相邻超构原子的组合或者整个晶格层次的衍射模式[97]。从模式分析的角度来看,局域周期性近似的局限性也正在于忽略了相邻超构原子之间形成跨越单元的模式的影响,而这样的模式在很多情形下是不能不考虑的。举例来说,对于高折射率电介质的超构原子的近场耦合作用的考察表明,通过改变超构原子之间的距离来增强有效的磁响应,可以用于控制电磁响应的特性[98]。此外,在局域周期性近似下,超构表面的单元大小决定了所引入的离散化电磁响应的空间采样率,当单元大小相对于目标电磁响应的空间变化来说采样不足时,就会带来严重的性能下降。因此,此近似条件会带来一定程度上的设计自由度和器件效率上的限制[99-100]。
正是由于传统正向设计策略存在的上述限制,近年来,基于优化理论或者深度学习技术逐渐发展起来超构表面的逆向设计方法,在突破器件性能限制、实现复杂功能的新颖设计等方面已经发挥起越来越重要的作用。对逆向设计方法的详细介绍可以在文献[99,101-102]中获得。
3 超构表面应用的发展方向
超构表面应用广泛,难以具述。下面不拘泥于具体器件,而是面向超构表面最主要和最新的一些发展方向,对相关的设计方法和研究进展进行简要的梳理和介绍。
3.1 偏振复用的超构表面
通过偏振敏感的超构原子设计,对以特定偏振态入射和出射的光引入独立的相位调控,从而实现偏振复用的多功能器件,是超构表面相较于传统光学元件的优势之一。
对于单波长设计,任意的偏振和相位调控都可以用一个对称的和酉的琼斯矩阵来描述。设这样一个琼斯矩阵
其可以满足出射电场的琼斯矢量
又由对称矩阵和酉矩阵的性质,即
这就是说,对任意的入射电场和出射电场之间的偏振和相位调控关系,由式(13)~
任一对称的和酉的矩阵总可以特征分解为
综上,对于工作在单一波长的超构表面器件,在超构原子设计自由度充足的理想情况下,混合相位调控机制可以实现任意的偏振和相位调控。此结论首先由Faraon课题组Arbabi等[88]在2015年提出,相关设计和分析方法在成像[88]、全息[45-46,90]、偏振光学[103]等领域均有广泛应用。
2017年,Capasso课题组Mueller等[103]利用混合相位机制实现了对任意正交偏振态(无论是线偏振、圆偏振还是椭圆偏振)的独立相位调控。设输入正交偏振态琼斯矢量为
和
由于超构原子琼斯矩阵受到
基于上述公式,利用椭圆形横截面的TiO2柱作为超构原子,设计了工作在532 nm波长的针对右旋圆偏振光和左旋圆偏振光复用的全息超构表面,其实验结果如
图 3. 偏振复用的超构表面。(a)偏振复用的全息超构表面的全息图像。当使用RCP(LCP)光照明时,分别产生狗(猫)的全息图像[103]。(b)多通道偏振复用超构表面的全息图像。当右下角有两个白色箭头时,其分别表示光的输入和输出偏振态;当右下角只有一个白色箭头时,其表示光的输入偏振态,此时不对光的输出偏振态进行选择[104]。(c)11通道偏振复用的超构表面在不同偏振态入射光下的全息图像(实验结果)[105]。(d)矩阵光栅将不同偏振态的光衍射到不同级次,再与成像透镜集成,成像到图像传感器阵列[106]。(e)全Stokes偏振相机的成像结果。第一列为未经处理的原始曝光图像;第二列为S0分量(传统灰度图像);第三列为极化椭圆的方位角,定义为 ;第四列为偏振度,定义为 [106]。(f)分区域式的超构透镜成像偏振计示意图[107]。(g)交错式的超构透镜成像偏振计示意图[108]。(h)交错式超构透镜的全Stokes偏振成像结果[108]
Fig. 3. Polarization multiplexed metasurfaces. (a) Holographic images of polarization multiplexed metasurface hologram. When illustrated by RCP (LCP) light, holographic image of dog (cat) is generated[103]. (b) Holographic images of multi-channel polarization multiplexed metasurface hologram. When there are two white arrows in the lower right corner, the arrows represent polarization states of input and output light respectively. When there is only one white arrow in the lower right corner, the arrow represents polarization state of input light, and polarization state of output light is not specified[104]. (c) Holographic images illuminated by incident light of different polarizations of 11-channel polarization multiplexed metasurface (experimental results)[105]. (d) Matrix grating diffracts light with different polarization states to different orders, and then is integrated with imaging lens to image object onto image sensor array[106]. (e) Full-Stokes polarization imagery. The first column shows unprocessed raw exposure image, the second column shows S0 (traditional grayscale image), the third column shows azimuth of polarized ellipse, defined as , and the fourth column shows degree of polarization, defined as [106]. (f) Schematic of segmented metalens imaging polarimeter[107]. (g) Schematic of interleaved metalens imaging polarimeter[108]. (h) Full-Stokes polarization imagery of interleaved metalens[108]
基于谐振或传播相位,可以实现对两正交线偏振态的复用。2018年,Zhao等[104]在此基础上引入几何相位这一新的自由度,实现了更为复杂的多通道偏振复用超构表面。令超构表面琼斯矩阵表达式为
式中:
当分别输入x方向的线偏振光、y方向的线偏振光、左旋圆偏振光和右旋圆偏振光时,输出光的琼斯矢量
从中可以找到
由
除上述全息领域外,混合相位调控机制在偏振成像领域亦有重要的应用。2019年,Capasso课题组Rubin等[106]提出矩阵傅里叶光学的概念,并利用超构表面实现了矩阵光栅,可以将固定波长下不同偏振态的入射光衍射到特定的衍射级次以相互分离,进而用于全Stokes的偏振成像,其原理如
3.2 波长复用的超构表面
彩色全息显示一直是全息超构表面领域追求的目标。为实现彩色的全息显示,首先要将目标彩色图像分解为红绿蓝三原色的分量,而后设计超构表面,对红绿蓝三种波长的入射光引入独立的相位调控,使其分别生成对应颜色分量的全息图像,最终合成为彩色的全息图像。值得注意的是,可能需要额外的算法来校正色差(衍射的波长相关特性导致)和大视场下的全息图像畸变,详见文献[109]。下面以彩色全息超构表面为例,介绍波长复用器件的设计方法。
利用空分复用的策略,如
图 4. 波长复用的超构表面。(a)空分复用的超构表面单元示意图[110];(b)超构表面前置颜色过滤器的原理示意图[112];(c)基于(a)所示原理的彩色全息显示结果(实验结果,下同)[110];(d)一种空分复用策略变体的原理示意图[111];(e)基于(d)所示原理的彩色全息显示结果[111];(f)多通道偏振复用超构表面的宽带特性[109];(g)基于(f)所示原理的彩色全息显示结果[109];(h)基于不同入射角度的彩色全息显示原理示意图[113];(i),(j)基于(h)所示原理的彩色全息显示结果[113-114]
Fig. 4. Wavelength multiplexed metasurfaces. (a) Schematic of unit of metasurface based on space division multiplexing[110]; (b) schematic of principle of metasurface integrated with color filters[112]; (c) color holographic display results based on principle shown in (a) (experimental results, the same below)[110]; (d) schematic of variant of space division multiplexing strategy[111]; (e) color holographic display results based on principle shown in (d)[111]; (f) broadband characteristic of multi-channel polarization multiplexed metasurface[109]; (g) color holographic display results based on principle shown in (f) [109]; (h) schematic of principle of color holographic display based on different incident angles[113]; (i), (j) color holographic display results based on principle shown in (h)[113-114]
利用偏振等其他复用通道对各波长的相位调控进行解耦,同样可以实现波长复用的器件设计。2020年,Hu等[109]基于3.1节介绍的多通道偏振复用的超构表面器件[104],实现了全彩色全息超构表面设计。当工作波长为532 nm时,利用计算生成全息的方法对
实际上,要实现彩色全息显示,也不一定要对各波长施加独立的相位调控。对于
3.3 宽带的超构表面
超构透镜的消色差问题一直以来都是领域内的难点问题,学术界和产业界都为之付出了大量的努力[115-116]。下面以宽带的消色差超构透镜为例,介绍宽带器件的设计方法。
理想透镜相位分布依赖于角频率
式中:
图 5. 消色差超构透镜。(a)超构透镜聚焦原理示意图;(b)消色差超构透镜设计中采用的两种超构原子示意图[89];(c)消色差超构透镜的成像结果,其中上图为原始图像,中图为成像结果,下图为颜色校正后的成像结果[89];(d)消色差超构透镜设计中采用的另一种超构原子示意图[78];(e)在 平面上测量的强度分布(颜色栏设置为对应各波长的颜色),白色虚线表示焦距的位置[78];(f)偏振不敏感的消色差超构透镜设计中的超构原子数据库[118];(g)准消色差超构透镜在延拓波长下的聚焦效果[119];(h)准消色差超构透镜在不同波长下的焦距[119];(i)准消色差超构透镜在不同波长下的绝对聚焦效率[119]
Fig. 5. Achromatic metalenses. (a) Schematic of focusing principle of metalens; (b) schematic of two types of meta-atoms used in design of achromatic metalenses[89]; (c) imaging results of achromatic metalens, where origin images are shown on the top, imaging results are given in the middle, and imaging results after color correction are shown in the bottom[89]; (d) schematic of another type of meta-atom used in design of achromatic metalenses[78]; (e) intensity distribution measured in plane (color bar is set to correspond to each wavelength), where white dashed line indicates position of focal length[78]; (f) meta-atom library in design of polarization-independent achromatic metalens[118]; (g) focusing effects of quasi-achromatic metalens at extended wavelengths[119]; (h) focal lengths of quasi-achromatic metalens at different wavelengths[119]; (i) absolute focusing efficiencies of quasi-achromatic metalens at different wavelengths[119]
对于小视场的情形,目标相位分布取为双曲相位分布,即
式中:
要得到实现完美消色差的超构透镜,须满足的条件为:1)角频率
2)群延迟分布
3)群延迟色散分布
一般地,取群延迟色散恒为0。对于群延迟色散不为0的情况下的消色差超构透镜设计,参见文献[117]。由群延迟色散为0可以推知,
混合相位调控机制被广泛用于实现消色差超构透镜。通过调整超构原子形状和尺寸参量,构建超构原子数据库,以覆盖目标群延迟的范围,并且保证群延迟色散接近0。由于
这一相位补偿将通过几何相位来实现,故此超构原子绕z方向中心轴沿逆时针方向的旋转角度
2017年和2018年,Tsai课题组Wang等[60,89]分别实现了工作在近红外波段和可见光波段的消色差超构透镜。其中,可见光波段的消色差超构透镜焦距为235
上述超构透镜设计是偏振敏感的。要实现偏振不敏感的消色差超构透镜设计,最直接的方法,就是只采用谐振或传播相位调控机制,利用各向同性超构原子,以产生偏振不敏感的响应。在设计方法上,角频率为
近年来,消色差超构透镜设计理论也有新的发展。2023年,浙江大学马耀光课题组Chen等[119]提出准消色差超构透镜的概念,仿照相位的
3.4 入射角度复用和大视场的超构表面
2017年,Faraon课题组Kamali等[120]对入射角度复用的超构表面器件进行了初步的探索。利用正向设计的策略,采用U形超构原子,以覆盖不同入射角度下的完整相位调控。基于此,实现了对入射角为0°和30°的入射光分别引入独立的相位分布进而生成不同全息图像的全息超构表面。事实上,这种入射角度相关的响应与非局域作用相关(见3.6节),因此正向设计方法会面临一定的限制。2018年,Lin等[121]利用拓扑优化,针对角度依赖的目标相位,实现了数值孔径0.35,在0°、7.5°、15°和20°入射角度下像差校正的柱透镜设计。但其五层级联的超构表面结构对于现有加工工艺来说难以实现。
从上面的例子可以看出,以入射角度复用的思路实现大视场超构表面器件会比较困难。下面以大视场超构透镜为例,介绍大视场的超构表面器件设计的方法和研究进展。
限制视场角的核心因素是各种轴外像差,尤其是彗差(彗差会导致成像的不对称,对成像质量有严重影响)。尽管
基于光线追迹等方法,根据具体设计通过优化获得目标相位分布,是大视场超构透镜设计中一种常见的做法[125-126]。目标相位分布的一种通常的形式由Capasso课题组Groever等[126]提出,通过引入一些可供优化的多项式项,对双曲相位分布进行修正:
式中:
优化后的相位分布之所以可以实现彗差的消除,核心在于引入随入射角度横向移动的有效光圈[124]。有效光圈可以在透镜上划定角度依赖的作用区域,使不同入射角度的入射光与透镜的不同区域作用。作为代价,有效光圈也会限制成像系统的数值孔径,且有效光圈之外的区域可能会产生杂散光,造成图像信噪比的降低。因此最好额外前置光阑进行限制[124],如
图 6. 入射角度复用和大视场的超构表面。(a)单片超构透镜前置光阑的大视场成像系统示意图[127];(b)双片超构透镜式大视场成像系统示意图[126];(c)一个双片超构透镜式成像系统在不同视场下x方向的MTF曲线[126];(d)一个单片超构透镜加光阑的成像系统在不同视场下的成像结果[127];(e),(f)不同二次透镜的成像结果[130-131]
Fig. 6. Incident angle multiplexed and wide field-of-view (FOV) metasurfaces. (a) Schematic of wide FOV imaging system composed of single metalens and front aperture[127]; (b) schematic of wide FOV imaging system composed of two metalenses[126]; (c) MTF curves along x direction at different incident angles of imaging system composed of two metalenses[126]; (d) imaging results at different incident angles of imaging system composed of metalens and aperture[127]; (e),(f) imaging results of single quadratic metalenses[130-131]
2017年,Groever等[126]采用
二次相位分布由Luo课题组Pu等[129]于2017年首次提出,其数学形式如下:
符合
式中:
由
2020年,Martins等[130]实现了工作波长为532 nm、直径为2 mm、焦距为750
除上述方法外,还有一些特殊的方法可以实现大视场的成像,例如非平面超构表面[122]和基于计算成像的超构透镜阵列[132-133]。限于篇幅,这里不再详述。
3.5 多层级联的超构表面
上面的讨论大多基于单片超构表面。类比传统光学设计,不难想到,通过级联多层超构表面相互配合,有望实现单片超构表面难以完成的设计任务,例如超构透镜的像差校正[126,134]、高纯度涡旋光束的生成[135],或者光学神经网络[136]、秘密共享[137]等新颖功能。级联超构表面中层与层之间的距离决定了相邻层超构表面的关系,从而对应不同的理论模型和设计方法。
当超构表面层间距足够远时,相邻层超构表面之间不存在耦合关系,此时通过光线追迹等传统光学设计方法预先考虑整个系统,优化设计每层超构表面的目标相位和层间距,而每层超构表面的设计根据目标相位要求独立进行,其理论和方法与单片超构表面完全一致[125-126,138]。2016年,Arbabi等[125]基于此方法,利用层间距为1 mm、超构原子材料为非晶硅的双层超构表面,实现了F数为0.9、视场角超过60°、工作波长为850 nm、绝对聚焦效率为70%(有效聚焦圆形区域直径为15
图 7. 多层级联的超构表面。(a)用双层超构表面拍摄的图像,比例尺为100 。插图为矩形所指示位置的图像的放大视图,通过相同的轮廓颜色分别对应0°、15°和30°的视场角,比例尺均为10 [125]。(b)双层超构透镜在两种波长下的成像结果[139]。(c)三层超构透镜的消色差效果,波长为450 nm、550 nm和650 nm的光聚焦在设定焦距处[140]。(d)波长复用的全息超构表面在1180 nm和1680 nm下的全息图案,上图为仿真结果,下图为实验结果[141]。(e)双层超构表面横断面的SEM照片[142]。(f)在焦距位置处沿着横截面y方向的归一化的光强分布,不同波长的光聚焦在不同的焦点上[142]
Fig. 7. Cascaded metasurfaces. (a) Image taken with bilayer metasurface, with scale bar representing 100 . Insets show enlarged view of image at locations indicated by rectangles that have the same outline color and correspond to viewing angles of 0°, 15° and 30°, with scale bar representing 10 [125]. (b) Imaging results of metalens doublet at two wavelengths[139]. (c) Achromatic effect of three-layer metalens: light with wavelength of 450 nm, 550 nm, and 650 nm is focused at preset focal lengths[140]. (d) Holographic image of multi-wavelength metasurface hologram at 1180 nm and 1680 nm. Top: simulation results; bottom: experimental results[141]. (e) SEM pictures of bilayer metasurface from cross-sectional view[142]. (f) Normalized light intensity distribution along y direction of cross-section at focal length: light of different wavelengths is focused at different focuses[142]
但是,数百微米级别的层间距离带来的限制也非常明显:一是抵消了超构透镜厚度超薄的优势,二是带来新的设计和性能上的限制,不能完全发挥出多层超构表面的优势[139]。考虑将多层超构表面紧密排列的情形。此时希望总透过率为每层超构表面的透过率之积,总相位改变量为每层超构表面的相位改变量之和。要满足上面的关系,层间距不能太大,因为由广义折射定律可知,相位梯度会导致一定程度的波前发散,波前发散会随着层间距的增加越来越严重;层间距也不能太小,以避免层间超构原子发生耦合[140]。层间距的合理范围可以通过仿真确定[139]。此类架构已用于实现数值孔径为0.42、在1180 nm和1680 nm波长下绝对聚焦效率分别为38%和52%的多波长双层超构透镜[其在两种波长下的成像结果如
在上面的设计中,多层超构表面的层间耦合一直是需要避免的因素。但从另一个角度看,超构原子复杂的层间耦合作用也是新的设计自由度,只是传统的设计方法无法将之加以利用。2020年,Mansouree等[142]基于伴随方法提出了一套针对多层超构表面的逆向设计算法,利用层间耦合来扩展传统正向设计的自由度,实验上实现了绝对聚焦效率(取有效聚焦圆形区域的直径为3.6
3.6 非局域超构表面
近年来,超构原子之间的耦合作用开始逐渐受到关注,非局域超构表面被提出和发展起来[143-145],由此衍生出多种功能新颖的器件设计,在光学模拟计算与图像处理[146-148]、空间压缩[149-150]、成像[151]、热调控[152]等领域均有广泛应用。非局域性是指超构表面上某一单元的电磁响应不只与此单元有关(像LPA所近似的那样),而是同时依赖于相邻区域的所有单元(相邻区域的大小与非局域性的强度呈正相关)。非局域效应的直接表现是电磁响应对入射光入射角度的依赖性。这一特性也被称为空间色散,在传统的正向设计中恰恰是需要避免甚至想方设法消除的[127]。非局域超构表面则反其道而行之,将超构表面的空间色散特性发挥到极致。
当光以一定角度倾斜入射时,入射光会具有在超构表面所在平面上的一定大小和方向的横向波矢或者说空间动量[153]。记横向波矢为
2020年,Zhou等[146]从实验上利用非局域超构表面实现了二维图像微分的功能。使用二氧化硅基板上的聚甲基丙烯酸甲酯(PMMA)包围的圆柱形硅超构原子阵列[超构原子结构和参量如
图 8. 非局域超构表面。(a)微分超构表面中超构原子结构示意图[146];(b)上图为无微分超构表面时系统的成像结果,下图为加入微分超构表面后系统的成像结果[146];(c)利用超构表面在普通眼镜上实现眼球追踪功能的系统示意图[156];(d)近红外相机拍摄到的不同旋转角度下的眼球成像结果[156]
Fig. 8. Nonlocal metasurfaces. (a) Schematic of meta-atom structure of differentiator metasurface[146]; (b) images of systems without (top) and with (bottom) differentiator metasurface[146]; (c) system schematic of utilizing metasurface to realize eye tracking on ordinary glasses[156]; (d) images of eye at different rotation angles taken by near-infrared camera[156]
2021年,Song等[156]在实验上证明,与高度局域化和低光学品质因数的传统超构表面相比,非局域和高光学品质因数的超构表面可以显著增强光与物质的相互作用,实现在不同波长下完全解耦的光学功能。如
自由空间也可以视为一种光学元器件,并通过非局域超构表面来代替,从而实现自由空间的压缩。自由空间的变换函数
式中:
2020年,Guo等[149]从理论上提出可以利用非局域器件来压缩自由空间,并使用光子晶体板实现器件设计。此器件适应不同的数值孔径要求进行设计,可放置在光路中任何位置以根据需要减小自由空间。数值仿真表明,压缩率(压缩前后的自由空间长度比值)可高达144,但器件工作的角度范围比较有限[150]。目前,在实验上利用非局域超构表面实现高效的自由空间压缩仍然是一个开放的问题。
4 未来展望
相较于传统光学元件,超构表面具有超轻和超薄的平面架构,其强大的电磁调控特性支持灵活的设计,以实现高性能或者在波长[157]、偏振[45]、入射角度[120]等维度多种功能复用的光学器件,易于集成和实现光学系统的小型化[158],且有望实现低成本的大规模制造。然而,在设计和加工制造等方面,超构表面依然面临着来自科学与工程上的多种挑战。
先讨论器件设计上的挑战。如何实现更高的器件性能是超构表面设计中普遍存在的一个问题,尤其体现在效率、数值孔径、视场、消色差带宽、功能复用等方面。一方面,明晰超构表面理论上的性能极限对于指导设计未来的走向具有重要意义,目前已经有一些工作从理论上指出各项指标之间的限制关系,例如:Presutti等[76]指出了消色差带宽与数值孔径之间的基本限制关系;Levy课题组Engelberg等[48]引入菲涅耳数的概念对超构透镜在实现消色差成像上的限制做了进一步的理论分析;Li等[159]指出了超构透镜厚度受到数值孔径、视场角与透镜大小的基本限制;Miller[160]指出了一定的厚度与光学器件功能之间的关系;Xiong等[105]在重申偏振复用通道数量极限的同时,给出了利用噪声突破这一极限的新设计理念。但研究领域内目前对于机理本身的理解依然是不充分的[161]。另一方面,当前正向设计方法被普遍采用,逆向设计方法开始兴起不过仍存在诸多限制[99],但设计方法对于器件性能的影响尚未被系统地阐明,导致对其基本局限理解不足。尽管有一些初步的工作,例如Chung等[100]已经指出正向设计方法在实现高效率和高数值孔径的超构透镜设计上的无力,Liu课题组Ma等[162]通过设计实例说明了正向设计方法在实现多功能复用上存在的劣势和逆向设计方法的机会,Arbabi课题组Mansouree等[163]通过实验对比初步验证了逆向设计相较于正向设计方法在实现高数值孔径的超构透镜方面的优势,但相关工作(尤其是在理论方面)依然很缺乏。
实现更大尺寸的超构表面器件是领域内一直追求的目标,除版图文件体积过大、大规模制造等加工方面的挑战之外[164],同样面临理论极限和设计方法两方面的问题。理论上,举例来说,Yu课题组Shrestha等[73]揭示了数值孔径对消色差超构透镜尺寸的限制。设计方法上,如何借助逆向设计等方法突破上述极限,让器件在具有大面积的同时仍然保持高的性能[34,165],依然是一个有待探索的问题。此外,电磁仿真的计算复杂度与仿真面积之间近似满足高次多项式的关系[166],如何准确、高效地实现大面积超构表面器件的仿真计算一直是个难题。近来,图形处理单元(GPU)并行计算[167]、区域分割[166]、分布式计算[165]等方法已经提出,但距推广使用仍有距离。
要想实现更好性能和更大尺寸的超构表面设计,离不开设计方法上的突破。目前,逆向设计方法尚无法真正获得普遍的应用。一方面,算法本身仍然面临一些长期存在的问题:常用的电磁仿真软件对逆向设计方法缺乏完善的支持,算法的实现难度往往比正向设计方法更高,其通用性也有待改善,这导致逆向设计算法的推广一直是个问题。近年来,已经有研究人员注意到这一点,并尝试加强领域内的分享与交流[168]。此外,当前普遍采用基于多核中央处理器(CPU)的电磁仿真,单次仿真时间就已经很长,进行迭代优化的时间成本和计算成本对于较大面积的超构表面器件来说更加难以承受,导致逆向设计往往局限于小面积的器件[169-170]。另一方面,领域内对逆向设计算法特性的理解仍然不够充分。逆向设计方法不可能完全取代正向设计,最重要的是,逆向设计必须明确自身在超构表面设计中的定位。逆向设计方法应该尤其关注那些正向设计难以解决的设计问题,例如,考虑单元间耦合作用以提高器件性能[171],对于高维设计空间(例如包含多个设计自由度的复杂超构单元结构)的探索[162],入射角度复用的光学器件(例如大视场的超构透镜)[120-121],考虑层间耦合的多层超构表面设计[142],等等。
对于传统的基于局域周期性近似的单层超构表面,目前的设计理论和方法已经相对比较成熟;但对于非局域超构表面、多层级联的超构表面、时空超构表面[172]、动态可调谐超构表面[173-177]等领域,目前尚有许多空间有待探索。例如,非局域超构表面在实现具有窄带响应[151]、横向动量(入射角度)依赖的响应[144,146]等特性的超构表面器件中的应用,多层级联的超构表面在非互易的光学器件设计中的应用[178],等等。
加工制造上也存在诸多挑战。目前主要有三类超构表面加工方法:刻蚀方法、直写方法和模板转移方法[179]。在加工制造上,微纳结构的形状控制和尺寸精度问题、超构表面的粗糙度误差、大面积加工的对准问题、级联超构表面的层间距离控制和层间对准问题、高深宽比的超构表面加工问题[180]、当前工艺与CMOS工艺的兼容性问题[158],以及如何实现低成本的大规模生产,都是目前主要存在的问题。近年来,围绕工艺改进,研究人员做出了一些代表性的工作,例如Rho课题组Yoon等[67]发展的适合于大规模制造的纳米压印技术,深宽比高达50的超构表面的加工技术[181],等等。截至目前,虽然已有一些初创公司聚焦于超构表面的工业化与商业化,但由于加工成本、器件封装与集成以及测试技术等方面的挑战,距离真正实现产品落地仍有很长的路要走。
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Article Outline
马耀光, 高宇斌. 超构表面:设计原理与应用挑战(特邀)[J]. 中国激光, 2024, 51(1): 0103001. Yaoguang Ma, Yubin Gao. Metasurfaces: Design Principles and Application Challenges (Invited)[J]. Chinese Journal of Lasers, 2024, 51(1): 0103001.