基于超构表面的多维光信息加密 
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Optical encryption is a technique that uses light as a multidimensional carrier of information to encode and decode plaintext images through optical transformations. It has advantages over traditional encryption methods in terms of complexity, security, robustness, and reliability. However, conventional optical encryption schemes often rely on complex and bulky optical components that limit their efficiency and portability. Metasurfaces are artificial structures that can manipulate light at subwavelength scales and control its amplitude, phase, and polarization. They provide a flexible and efficient platform for optical encryption by using different metasurface structures to modulate the incident light and generate encrypted images. The basic principle of metasurface optical encryption is to use the structure to control the input and output keys of the light, the optical parameters modulating the incident light and encrypted image respectively. Only by knowing the correct input and output keys can one decrypt the image and recover the original information. The metasurface structures can utilize different dimensions of light at the input and output ports, such as wavelength, polarization, incident angle, and distance, to achieve single- or dual-port encryption. This study summarizes and discusses three types of metasurface optical encryption schemes, namely, single-input port, single-output port, and input-output port combination, as shown in Fig. 1.
Metasurface-based optical encryption can utilize the multiple dimensions of light at the input and output ports. For any light beam, all of its parameter dimensions at the input and output ports have definite values, and identifying the dimensions that are used for encryption when information for only one image exists is difficult. Therefore, we focus on the optical encryption that changes at least one or more dimensions to encrypt multiple image signals. The optical encryption based on a single-input port is first discussed, where the analyzed parameters at the output port are fixed. For optical encryption at an input port, we discuss the use of only one parameter dimension, such as wavelength, polarization, and incident angles, to encrypt image signals (Fig. 2). The multiple optical parameter dimensions at the input port can be combined to encrypt different image signals to provide more independent encryption information channels (Fig. 3). At the output port, the dimensions of light can be used for optical encryption, whereas those at the input port are fixed (Fig. 4). Finally, input-output port joint optical encryption schemes are discussed, where different combinations of optical parameter dimensions at the input and output ports are used to encrypt and decrypt the image signals. These include polarization dimension input-polarization dimension output (Fig. 5), polarization dimension input-multiple dimension output (Fig. 6), wavelength dimension input-other dimension output (Fig. 7), incidence angle dimension input-diffraction distance dimension output (Fig. 8), and multiple dimension input-other dimension output (Fig. 9).
We discuss the recent progress and challenges of metasurface optical encryption. Various optical-field manipulation mechanisms have been previously proposed based on metasurfaces, which can achieve different degrees of freedom of the Jones matrix from one to eight, the highest possible in nature. This multiple-degree-of-freedom optical-field manipulation and new mechanisms lay the foundation for enhancing the complexity and security of optical information encryption. However, challenges remain in the field of metasurface optical encryption, such as the crosstalk phenomenon, limited utilization of light dimensions, lack of integration with other physical signals, and absence of dynamic control capabilities. We suggest that further research can be conducted to optimize and improve the performance and reliability of metasurface optical encryption and storage.
1 引言
近年来，信息技术和互联网技术飞速发展，信息安全面临着巨大挑战，因此开发出免受恶意攻击和不易篡改的加密技术显得尤为重要。信息加密技术的核心是利用一定的算法和密钥，对原始信息进行变换和编码，使其只能在输入正确密钥的情况下才能被还原。为了提高信息加密技术的安全性，密钥的维度应该尽可能多，从而增加破解的难度和成本。光作为日常生活中常见的一种媒介，具有振幅、相位、偏振、角度、波长、空间坐标、衍射成像距离等多重维度。利用其作为多维的信息载体，通过干涉、衍射、成像等光学变换过程，对明文图像进行扰乱编码［1-5］，设计的光学加密方案和密钥空间具有多维、大容量、高设计自由度等突出优势。光学加密这一优势在全息存储［6-7］、数字水印［8-10］、身份验证［11-14］等领域中有着广阔的应用前景。
传统的光学加密方案主要通过光学变换（例如干涉、衍射、成像等过程）对明文的图像等信息进行扰乱编码，从而达到加密的效果。这一过程通常依赖一些复杂和笨重的光学元件，如空间光调制器、透镜、光子晶体［15-17］，而且还需要对图像进行多个步骤的光学变换和数字处理，导致加密效率低下。超构表面是人工设计的具有特殊电磁响应的二维平面结构，能够在亚波长尺度对光场的振幅、相位、偏振态等多重光参量进行灵活的调控［18-35］，实现全息、涡旋光、超透镜等光学功能，这一结构为光学加密提供了一个灵活和高效的平台。近年来，人们提出各种基于超构表面的光学加密方法，例如偏振编码［36-41］、轨道角动量编码［42-46］等，来提升加密的复杂度和安全性。同时，利用超构表面对光场的多维操控可以实现多功能的光学加密，例如同时实现图像加密和水印的功能，增强了加密的鲁棒性和可靠性。
超构表面光学加密的基本原理是将加密信息通过算法隐藏到结构的复振幅中，然后通过入射和探测光的特定维度，实现图像信息的加密和解密。在这个过程中，光场有两个关键的端口，即输入端和输出端，分别承载着输入密钥和输出密钥。输入密钥是指入射光场的光参量，如波长、相位、偏振态等，它们决定了超构表面对光场的响应特性。输出密钥是指输出端在特定参数下接收到的光场，这些参量包含偏振、观测角度、衍射距离等信息。只有在知道正确输入密钥和输出密钥的情况下，才能够对输出端的光场进行解密，从而恢复原始的图像信息。在这些基于超构表面结构的光学加密方案中，光在输入和输入端的维度各有不同，有些方案只利用了一端，有些方案则同时利用了两端。因此，本文将以输入和输出端为出发点，分别从单一输入端、单一输出端以及输入-输出端联合三个方面对基于超构表面结构的光学加密进行总结和探讨，如
图 1. 基于超构表面结构的多维光信息加密示意图
Fig. 1. Schematic of metasurface-based multi-dimensional optical information encryption
2 单一输入端光学加密
在输入端，光具有多重参量维度，例如振幅、相位、偏振、入射角度、波长以及水平空间坐标等。通过超构表面结构的设计，可以对特定光参量的图像信号实现加密。需要指出的是，对于任意一束光，其在输入和输出端的这些维度都有确定的参量值。对于只存在单一图像信号的情况，难以识别采用了哪些维度进行加密。因此，在本文中，我们关注的光学加密是通过改变至少一个或多个维度，实现多个图像信号的加密。这不仅有助于分析光学加密的机制，而且多个图像信号可以提高加密效果和安全性，它们既可以作为真实解密的信号，也可以作为伪图进行干扰。对于单一输入端的光学加密来说，在输出端，此时光的各种参量维度保持不变。
2.1 单一维度信息加密
在输入端，光学加密的一种简单方法是通过改变光的某个单一参量维度，实现不同图像信号的生成和加密。在本文中，我们不讨论非线性的光学加密［47-49］，只考虑线性的光学加密，此时超构表面对输入光的振幅变化不敏感，也不依赖于输入光的初始相位，因此振幅和相位不能作为单一参量维度进行加密。只有振幅和相位与其他参量维度结合，如与水平空间坐标维度结合，形成空间上变化的振幅分布或相位分布，才能引起超构表面的不同光学响应。因此，我们重点探讨其他光参量作为单一维度进行信号加密的情况［
图 2. 纯输入端单一维度超构表面结构光学信息加密。（a）基于结构空间复用的波长维度光学加密［50］；（b）入射角度维度复用的光学加密［53］；（c）基于入射角度维度的四通道加密［54］；（d）左右旋圆偏振光学加密方案［36］；（e）通过在琼斯矩阵中引入噪声，实现11个偏振复用通道［37］
Fig. 2. Metasurface-based optical information encryption with single dimensional for single pure input. (a) Wavelength-dimensional optical encryption based on spatial multiplexing[50]; (b) optical encryption based on angle-of-incidence dimensional multiplexing[53]; (c) four-channel optical encryption based on angle-of-incidence dimension[54]; (d) optical encryption scheme with left and right circular polarization[36]; (e) realizing 11 polarization multiplexing channels by introducing noise into Jones matrix[37]
波长（频率）作为光的重要参量，在信息加密中起着关键作用。要实现超构表面波长光学加密，关键是超构表面结构需满足多个波长下特定的光响应。受限于结构尺寸，超构表面有效光调控的波长一般控制在一定范围内。传统的超构表面结构设计往往只针对单一波长，无法满足多个波长的要求。一种常用的设计方式是采用空间复用方式，即在一个像素单元中，将多套在不同波长下响应的结构交错复用排列，并降低不同波长之间结构的串扰，从而实现多个波长下的光学加密［50-51］。
光的入射角度，即入射波矢方向，也能用于光学加密。对于常见的结构，它们对入射光的角度依赖性很低，因此在不同角度下观察到的物体图像变化不大。为了提高光学加密系统的安全性和鲁棒性，需要设计具有强角度依赖性的超构表面结构。2017年，Kamali等［53］提出了一种利用超构表面实现角度复用全息图像显示的方法，该结构能够在0°和30°两个不同入射角下激发不同共振模式，并产生两幅具有独立相位分布的全息图像［
偏振具有两个独立的自由度，常可以分解为独立的x偏振和y偏振。基于此，通过设计纳米结构的长宽尺寸，容易实现正交线偏振入射下独立的图像加密［57-58］。对于其他正交偏振态，例如左旋光和右旋光，要实现图像变化，可以利用高的圆二色性结构实现。例如
2.2 多维度信息加密
与单一维度的光信号操控相比，将光的偏振、相位、波长、角度等多个维度组合进行光学加密可以提供更多独立的编码信息通道。
相位作为独立维度无法实现不同光响应，但与水平空间坐标维度结合后，可以产生具有空间相位分布的光场，能够引起超构表面不同的光响应。其中一类具有特殊相位空间分布的光是涡旋光，其在信息加密中具有广泛应用。涡旋光束具有环形强度分布，其相位因子具有螺旋波前分布exp（ilφ），其中φ为方位角，l为整数，代表拓扑荷数。显然，将不同拓扑荷数的涡旋光输入结构中，其光响应是不同的。如何精确调控不同光响应以进行光学加密是一个难题。2019年，基于超构表面的涡旋光角动量加密被提出［42-43］。2020年，Fang等［43］基于空间频域的概念，实现了无理论数量限制的角动量涡旋光独立全息图，并实验验证了当入射涡旋光的拓扑电荷数为-50~50之间10个均等数值时，可生成10个不同阿拉伯数字0~9的复用全息图［
图 3. 多重维度输入的超构表面结构光学信息加密。（a）基于空间与相位维度组合而成的涡旋光，实现轨道角动量全息图［43］；（b）波长和偏振维度组合输入实现两幅独立全息图［59］；（c）基于相干像素设计实现输入端波长、偏振、入射角度维度组合的光学加密［55］
Fig. 3. Metasurface-based multidimensional optical information encryption at pure input. (a) Achieving orbital angular momentum hologram based on vortex light combined with space and phase dimensions[43]; (b) two independent holographic images with input combining wavelength and polarization dimensions[59]; (c) optical encryption based on coherent pixel design realized by combining wavelength, polarization, and incident angle dimensions at input[55]
利用偏振和波长两个维度的组合实现双维度光加密的一个例子［59］如
本课题组在2018年提出的一种称为“相干像素”的设计方法［55］可以实现三种输入光参量的组合加密。在该设计方法中，我们将多个亚纳米结构组成一个像素，并考虑其整体相干作用对光的响应，其输出响应是入射光的角度、波长以及偏振的函数。通过改变纳米结构的位置和旋转角度，可以精确调控不同光参量组合下的光响应，实现多幅纳米打印图像的复用和切换。如
3 单一输出端光学加密
在这一节，我们讨论单一的输出端光学加密，即在输入端光维度保持恒定不变，而在输出端通过改变光的参量来实现图像加密与读取。在输出端，由于信号的振幅和相位信息总是以探测的强度空间分布形式体现的，因此振幅、相位和空间坐标无法作为一个维度进行调控加密。对于波长维度，其在线性光学系统的输入和输出端必然相同，因此该维度只在输入端考虑。据此，在输出端，我们从偏振、观测角度及衍射距离这三个维度探讨光学加密［
图 4. 单一输出端超构表面光学信息加密。（a）信息隐藏在特定的单个线偏振光中［60］；（b）两幅图像信息隐藏在正交偏振态中［61］；（c）两幅图像信息隐藏在非正交线偏振态中［62］；（d）基于大尺寸光栅像素结构的多观测角度图像加密［65］；（e）基于超构表面结构的大规模观测角度复用的光学加密［66］；（f）衍射距离维度光学加密［67］；（g）立体琼斯矩阵全息术［68］
Fig. 4. Metasurface-based optical information encryption with pure single output. (a) Information hidden in specific single linearly polarized light[60]; (b) two images hidden in orthogonal polarization states[61]; (c) two images hidden in non-orthogonal linearly polarized states[62]; (d) optical encryption of multiple images with different observation angles based on large-scale grating pixel structures[65]; (e) optical encryption with large-scale observation angle multiplexing based on metasurface[66]; (f) optical encryption with diffraction distance dimension[67]; (g) stereoscopic Jones matrix holography [68]
在探测端，通过选取不同偏振态的输出可以得到不同的图像信号，从而将特定信号加密到特定偏振态中。通常选取的偏振态为线偏振态，其偏振角度可作为一个自由度提供加密维度。根据Malus定律，当强度为
除此之外，Zhao等［63］和Song等［64］也先后通过将偏振与衍射级（观测角度）相结合，设计并实现了不同衍射级具有不同偏振态分布的超构表面光学全息加密。从设计角度来看，这些不同衍射级的图像位于同一平面，可看成一张视角很大的全息图，这可由亚波长尺度像素单元结构构造而成。另一方面，从衍射角度考虑，由于存在多个衍射级数，结构单元像素尺寸往往远大于波长。这一大尺寸像素也可看成是由多个亚波长尺度的小像素组合而成的（整体考虑全息图时），因此这两种思路是等价的。
与全息图像可以在空间上分开不同，平面打印图像在不同观测角度下的位置重合。当在不同观测角下观测一个平面图像时，相当于进行了角谱滤波，这会导致图像的改变，从而可实现光学加密。一种方案是通过设计多套结构分别将光衍射到不同角度，从而产生不同的图像观测效果。例如，在一个大像素中设计3×3共9个子像素［
在输出端，光在传播的过程中会发生衍射，从而在不同的距离处具有不同的光响应，因此衍射距离也可以作为一个维度进行加密。如
4 输入-输出端联合光学加密
相比于单一的输入端和输出端加密，将两者结合起来实现光学加密显然具有更高的安全性。在恢复原始图像信号的过程中，必须在输入密钥和输出密钥都正确的情况下，输出端的光场才能得到解密，这大大增加了破解的难度。由于输入和输出两端都具有多种维度，两两组合会有多种情形，因此在以下分析中我们从输入端口的维度进行分类探讨。
4.1 偏振维度输入
几何相位［70-73］依赖于超构表面结构单元的转角，这提供了一个非常便捷的自由度来调控相位，并被广泛用于超构表面结构的构建。为了产生几何相位，需要在输入端入射圆偏振光，同时在输出端探测相反旋度的圆偏振态，因此这是一个典型的偏振输入-偏振输出联合的光学加密范例。然而，几何相位在相反圆偏振态下互为相反，导致不同圆偏振态下的光响应相互共轭，无法独立成像。
为了在输入端改变圆偏振态以输出独立图像，最直接的方法是设计两套结构，分别在左右旋光下产生独立的全息图，然后交错放置，形成新的结构。如
图 5. 偏振维度输入-偏振维度输出的超构表面光学信息加密。（a）基于几何相位和结构空间复用的全息加密［74］；（b）将入射光两个圆偏振态之间的相位差作为额外自由度，实现三通道的全息加密［38］；（c）基于几何相位和传输相位，实现任意正交偏振态下的独立相位控制［39］；（d）基于各向异性单元结构线偏振态下的连续和简并输出，实现灰度图像和二元图像的光学加密［41］；（e）基于不同入射和出射线偏振态角度下形成的第三个杂化通道图像实现光学加密［76］
Fig. 5. Metasurface-based optical information encryption with polarization dimension at both input and output terminals. (a) Holographic encryption based on geometric phase and spatial multiplexing[74]; (b) three-channel holographic encryption realized by introducing phase difference between two circular polarization states of incident light as additional degree of freedom[38]; (c) independent phase control achieved under arbitrary orthogonal polarization states based on geometric and propagation phases[39]; (d) optical encryption of grayscale and binary images based on continuous and degenerate output under linear polarization states of anisotropic unit structure[41]; (e) optical encryption based on third hybrid channel image formed under different incident and outgoing linear polarization angles[76]
上述方案仅仅利用了几何相位，因此只能针对特殊的左右旋光入射偏振态，如何推广到任意的正交偏振态是一个难题。2017年，哈佛大学Capasso课题组提出了几何相位与传输相位相结合的方案［39］，此方案需要考虑像素中纳米棒的长宽和转角三个自由度。研究者实现了对任意正交偏振态的独立相位调控，并验证了独立全息图像［
如果考虑线偏振态输入和线偏振态输出，对于各向异性单元的超构表面结构，其输出强度同时依赖输入和输出线偏振态的方向，因此可以通过调控输入和输出的偏振方向来实现光学加密［40-41，75］。容易证明，对于一个转角为θ、长轴和短轴的透射系数分别为Α和Β的结构，其透射强度［41］为
式中：α1和α2分别为起偏器和检偏器的旋转角度，表征入射和探测线偏振态的方向。当α2=-α1=π/4时，可以利用结构的转角实现连续的灰度图像。此时旋转结构π/8角度，并保持这一角度不变，改变输入和输出的线偏振态方向，单元结构转角可以在保持前一个灰度图像不变的情况下，实现强或弱的二元图像［41］，即实现了线偏振输入输出的图像加密［
在上述线偏振态双通道加密的基础上，改变入射和出射的线偏振方向（与前两个通道完全不同），可形成第三个杂化通道图像，如
上述图像加密中，在输出端只考虑了偏振的单一通道，通过引入更多维度，例如衍射距离、观测角度等，可以丰富光学加密的维度，提升加密的安全性。
结构平面和全息平面与超构表面的距离是不同的，为了引入衍射距离的维度，通常在结构平面和全息平面上同时产生图像信息。平面打印图像和全息图像通常分别通过振幅和相位调控来实现。平面图像是点对点成像的，因此对光源的相干度要求不高，从而可以在非相干光源（例如白光）下成像。而全息图像则是整个结构的相干效果，因此要求光源具有良好的相干性，一般仅在激光条件下实现。2021年，Liu等［77］在Capasso课题组工作［39］的基础上，设计了包含2个纳米结构的像素单元，证明了对于两个纯相位因子，其相干叠加后可以得到任意的振幅和相位。因此，这样的结构设计可以实现任意正交偏振态下振幅和相位的独立调控。对于振幅来说，利用其分布可以在结构平面处得到纳米打印图像，而利用相位分布则可以在远场平面处实现全息图像［
图 6. 偏振维度输入-多重维度输出的超构表面光学信息加密。（a）双通道左右旋偏振加密［77］；（b）基于平面结构最高六自由度琼斯矩阵的三通道线偏振加密［78］；（c）基于双层结构最高八自由度琼斯矩阵的四通道线偏振加密［79］；（d）输出端结合偏振、衍射距离、观测角度三种维度的全息图像信息加密［80］
Fig. 6. Metasurface-based optical information encryption with polarization dimension at input terminal and multi-dimension at output terminal. (a) Two-channel encryption with left and right rotation polarization[77]; (b) three-channel linear polarization encryption based on highest six degree-of-freedom Jones matrix of planar structure[78]; (c) four-channel linear polarization encryption based on highest eight degree-of-freedom Jones matrix of double-layer structure[79]; (d) optical information encryption of holographic images combining with three dimensions of polarization, diffraction distance, and observation angle at output terminal[80]
我们课题组从超构表面调控光场琼斯矩阵的角度出发，证明了这样的琼斯矩阵必须满足6个自由度［78］，即xx、xy、yy三个分量的振幅和相位须独立任意可调。我们通过设计包含4个纳米结构的像素单元［78］，实现了具有6个自由度的琼斯矩阵构造，这也是平面结构最大上限自由度的光场调控。基于此演示了在不同衍射距离处形成纳米打印和全息图像的三通道线偏振加密［
在输出端，将偏振、衍射距离、观测角度三个维度结合的方案如
4.2 波长维度输入
在单色纳米打印和全息图像集成的基础上［81］，将单色纳米打印扩展到全彩图像，可以使图像颜色更丰富，这可以看成是波长维度输入、衍射距离维度输出的双端口图像加密。为了实现波长维度的独立调控，常见的方案是采用多套结构的复合交错设计。如
图 7. 波长维度输入-其他维度输出的超构表面光学信息加密。（a）基于纳米结构滤色片机制［82］；（b）基于不同波长下不同尺寸纳米块具有不同共振衍射的机制［83］；（c）基于三基色混合实现任意亮度、饱和度和色度的全彩颜色显示［84］；（d）三波长通道下的线偏振输出随空间变化的全息图像光学加密［85］；（e）双波长通道下不同线偏振输出纳米打印图像的光学加密［86］
Fig. 7. Metasurface-based optical information encryption with wavelength dimension at input terminal and other dimensions at output terminal. (a) Based on nanostructure color filter mechanism[82]; (b) based on mechanism that nanostructures with different sizes have different resonance diffraction under different wavelengths[83]; (c) full-color display with arbitrary brightness, saturation, and hue based on three primary colors mixing theory[84]; (d) three-wavelength channel holographic optical encryption with linearly polarized output varying in space[85]; (e) two-wavelength channel optical encryption of nanoprinting images with different linearly polarized output[86]
本课题组根据颜色的三基色混合理论，即任意一个具有强度、色度、饱和度的颜色都可由不同强度的三基色混合而成。通过相干像素的设计，在一个像素中设计两个纳米结构，利用其几何相位的干涉可以实现振幅和相位的独立调控，并将针对三基色的三种共振尺寸集成在一个大像素里［
上述衍射距离维度加密虽然利用了几何相位，但输出端的偏振恒定，没有变化，不能作为一个加密维度。将偏振方向不同的线偏振光看成是具有不同相位的左右旋光叠加，可利用几何相位和线偏振态输入实现该设计。如
4.3 入射角度维度输入
入射角度这一维度往往容易被人忽略，因为大部分结构对角度不敏感。精心设计结构，使其在不同入射角下具体不同光响应，同时结合上述打印与全息图像的集成，实现入射角度维度输入-衍射距离维度输出的联合光学加密。Wan等［87-88］基于金属-电介质-金属三明治反射层结构，通过构建不同尺寸下的振幅和相位调控数据库，实现了四通道的多路复用，即在两个不同入射角度下分别实现了纳米打印和全息图像（
图 8. 入射角度维度输入-衍射距离维度输出的超构表面光学信息加密［87-88］。（a）通过建立角度编码响应的结构数据库实现角度多路复用加密；（b）利用角度照明改变表面等离子体共振和法布里-珀罗纳米腔共振，针对不同的入射角进行编码加密
Fig. 8. Metasurface-based optical information encryption with incident-angle dimension at input terminal and diffraction-distance dimension at output terminal[87-88]. (a) Angle-multiplexed encryption by building structured database of angle-encoded responses; (b) encoding encryption for different incident angles by using angular illumination to change surface plasma resonance and Fabry-Perot nanocavity resonance
4.4 多维光参量输入
在输入端，不同维度之间的组合导致多种多样的光学加密方案，同时再结合输出端的维度变化，其带来的可能变化更是丰富。
图 9. 多维度输入-其他维度输出的超构表面光学信息加密。（a）入射角度和偏振双维度输入、偏振维度输出的光学信息加密［89］；（b）基于结构空间复用设计和圆偏振态的光学加密［90］；（c）基于单个纳米结构像素构造非复用基本单元下圆偏振态的光学加密［52］；（d）基于神经网络实现线偏振态的光学加密［91］；（e）涡旋光（相位+空间）和偏振三维度输入、线偏振态维度输出的光学加密［92］；（f）涡旋光（相位+空间）和偏振三维度输入、衍射距离维度输出的光学加密［46］
Fig. 9. Metasurface-based optical information encryption with multi-dimension at input terminal and other dimensions at output terminal. (a) Optical information encryption with polarization dimension at output terminal and dual dimensions of incident angle and polarization at input terminal[89]; (b) optical encryption based on structural spatial multiplexing design and circular polarization state[90]; (c) optical encryption of circular polarization state under non-multiplexing basic unit constructed based on single nanostructured pixel[52]; (d) optical encryption of linear polarization state based on neural network[91]. (e) optical encryption with three dimensions of vortex light (phase and spatial) and polarization at input terminal and linear polarization state dimension at output terminal[92]; (f) optical encryption with three dimensions of vortex light (phase and spatial) and polarization at input terminal and diffraction distance dimension at output terminal[46]
在输入端，入射角度与偏振组合加密的一种方案如
对于偏振，其有2个自由度，结合波长的维度（N），可得到共2N个通道。
如前所述，涡旋光是一种多维输入光场，包含了相位和空间坐标变化的维度。在此基础上，在输入和输出端同时考虑偏振维度进行光学加密的方案如
5 总结与展望
近年来，随着超构表面光学领域的蓬勃发展，各种光场调控机理被提出，超构表面对光场调控能力也越来越强大。例如，基于琼斯矩阵，单自由度调控已逐步发展至双自由度、四自由度和平面结构最高的六自由度，并最终实现了自然界结构所能达到的八自由度。这些多自由度光场调控和新机理为提升光学信息加密的复杂度和安全性打下了基础。
另一方面，基于超构表面的光学信息加密仍面临着诸多挑战。首先，目前超构表面的制备仍主要依赖于电子束曝光、离子束刻蚀等加工工艺，导致成本高，无法进行大面积的制备。其次，由于微纳结构的性质，超构表面容易受到损坏，且在光学环境不理想的情况下加密效果会受到影响。第三，由于加工误差和机理的限制，多通道光信息加密不可避免地存在串扰现象，导致加密和读取的误差，影响实际应用的可靠性。此外，为了增加主动调控性，人们将光与其他物理信号如电、化学反应等相结合来实现动态调控。例如，通过引入液晶实现对超构表面器件电调谐的动态调制［93-97］，利用镁的氢化和脱氢等改变纳米结构的材料属性以实现动态光响应变化［98-100］。然而这些方案也带来了结构单元尺寸增大、响应速度变慢等问题。因此，研究具有高响应速度、大容量的主动型超构表面器件具有重要意义。
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Article Outline
魏睿, 包燕军. 基于超构表面的多维光信息加密[J]. 中国激光, 2023, 50(18): 1813004. Rui Wei, Yanjun Bao. Metasurface-Based Multidimensional Optical Information Encryption[J]. Chinese Journal of Lasers, 2023, 50(18): 1813004.
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