Correlated triple hybrid amplitude and phase holographic encryption based on metasurface
Figure.1 Schematic illustration of a hybrid quantitative correlation amplitude and phase holographic display based on an all-dielectric metasurface. Based on the wavelength and polarization selectivity of nanoantennas, the correlated holograms are encrypted by the combination of discrete wavelengths and same/opposite handedness circular polarization channels.
Fig. 2 (a) Scanning electron microscope (SEM) images with top view and 45° tilt view, scale bar: 4 μm. (b-c) Simulations and experimental results of triple amplitude phase holography using different wavelength and polarization combinations.
Metasurfaces has provided a brand new nano-platform for controlling wavefront and intergrating traditional optical device. Metasurfaces have successfully applied in miniaturised optics, including wavefront shaping, asymmetric transmission, holographic displays, optical encryption, nonlinear optics, optical cloaking and so on. Especially, metasurface holography assisted by smart algorithms can conquer the challenges to realize large field of view, target-only diffraction orders and enhancement of information capacity.
In traditional metasurface holography, phase-only studies occupy mainstream applications. Usually, the amplitude distributions are uniform in phase-only meta-holograms. However, phase only metasurface holography has ignored another important modulation freedom. Because amplitude can also generate a hologram and reconstruct a target image through optimized nano-antennas array, called as amplitude holography. Amplitude holography can be realized by binary or discrete multi-order modulation.
As a typical binary amplitude modulation example, photon sieves could be applied effectively to achieve beam shaping, vortex beam and so on. However, since photon sieves usually compose of circular holes, the polarization sensitive property is lost. Nevertheless, hybrid dielectric amplitude filters and anisotropic nano-antennas can break the limitation of amplitude-only or phase-only modulation, leading to collaborative amplitude-phase tailoring within one single metasurface.
Recently, the research group led by Professor Huang Lingling from the Beijing Engineering Research Center of Mixed Reality and Advanced Display, School of Optoelectronics, Beijing Institute of Technology propose and experimentally demonstrate triple amplitude-phase holographic encryption strategy which integrates two binary amplitude holograms and one PB phase hologram assisted by quantitatively correlation. The research results are published in Photonics Research, Volume 10, No. 3, 2022 (Hongqiang Zhou, Xin Li, Zhentao Xu, Xiaowei Li, Guangzhou Geng, Junjie Li, Yongtian Wang, Lingling Huang. Correlated triple hybrid amplitude and phase holographic encryption based on a metasurface[J]. Photonics Research, 2022, 10(3): 03000678).
To fully utilize the space-bandwidth product of metasurface, we obtain rigorous relation in mathematics between the two binary amplitude hologram with A1⊃B1, and for the phase hologram we have the relationship A1⊃C. Actually, we achieve A1=B1∪C for the three holograms. Intriguingly, we develop a Correlated Gerchberg-Saxton (CGS) algorithm, by optimizing the "static" and "dynamic" nano-antennas functioning as spectral filter as well as phase contributor to fulfil the above scheme.
Three overlapping regions containing those switchable "dynamic" pixels are built on the metasurface. For the "static" pixels, we choose two kinds of isotropic square nanofins as amplitude "0" and "1" at both working wavelengths. While another kind of anisotropic rectangular nanofins are picked as optical amplitude switch buttons ("dynamic" pixel) based on wavelength selectivity. Simultaneously, those anisotropic antennas can function as phase contributors to reconstruct phase holography in cross-polarization channel. Hence quantitatively correlate triple holograms are formed by controlling wavelength and polarization combination.
Different from the traditional metal photon sieve structure, we provide a method that uses all-dielectric structure to achieve light transmission and block. We set two kinds of "static" pixels for (0, 0) and (1, 1) combination at two working wavelengths (λ1, λ2) in the same polarization. And we set another kind of "dynamic" pixels for (0, 1), that is, transparent at λ2 but opaque at λ1. While another degree of phase can be added for such "dynamic" pixels since one can apply the PB phase principle with anisotropic structures in cross-polarization channel.
They experimentally verified this scheme by generating two different amplitude holographic images (bees and butterflies) in the visible and near-infrared wavelength range in the co-polarization channel (LCP-LCP, λ1=510nm, λ2=720nm). And a phase hologram with blooming tangerine peony can be reconstructed in cross-polarization (LCP-RCP, λ2=720nm). Another sample with the reconstructed images (swan, hummingbird, and auspicious cloud) showes good holographic reconstruction quality as well (Fig.2).
Such metasurface can achieve amplitude and phase holography without sacrificing the space-bandwidth product. The experimental results successfully meet theoretical expectations. With the help of the selectivity of wavelength and polarization, we can dynamically switch on and off the holography. Furthermore, with elaborate design, the developed algorithm can be extended to realize the dynamic hybrid amplitude-phase holography within one device by integrating active materials. It enables high-capacity, high-speed holographic encryption, optical communication and optical manipulation in the case of incident structured light and polarization changes.
基于全介质超表面的三重关联的混合振幅和相位全息
图1 三重关联超表面全息实验结果。（a）样品的俯视和45度斜视电镜图(SEM)；（b-c）样品1和样品2在不同偏振和波长下的实验全息重建结果。
超表面能够自由调控波前，为集成和变革传统光学器件提供了一个全新的纳米操作平台。近年来，超表面得到快速的发展，已成功应用于小型化光学器件，包括波前整形、非对称传输、全息显示、光学加密、非线性光学、光学隐形等。特别是近几年在智能算法和深度学习算法的助力下，超表面全息技术可以克服实现大视场、独立可选择衍射产生和增强信息容量的挑战，并能够实现更多功能性的应用。
在传统的超表面全息术中，纯相位全息研究占据了主流应用。通常，振幅分布在纯相位超全息算法的设计中都是均匀的。因此，纯相位超表面全息忽略了另一个重要的调制自由度——振幅。利用振幅调控同样可以通过优化的纳米天线阵列生成全息分布并重建所需要的目标图像，称为振幅全息术。振幅全息一般可以通过二值或离散多阶振幅来调控波前。
作为典型的二值调控振幅，光子筛可以通过优化尺寸和空间分布来有效地实现光束整形、涡旋光束等。然而，由于光子筛通常由圆形孔阵列组成，因此失去了偏振敏感特性。然而，我们将混合的介质振幅滤波器和各向异性纳米天线进行有机结合，可以打破纯振幅或纯相位调制的限制，在单一超表面内实现协同振幅-相位调制。
近日，北京理工大学光电学院黄玲玲教授课题组提出并实验验证了两个二值振幅全息图和一幅纯相位全息定量关联算法，首次将振幅和相位全息融合集成到同一片超表面，而不是通过简单的空间复用。实验结果呈现出很好的图像质量和信噪比。研究成果发表于Photonics Research 2022年第3期。
为了充分利用超表面的空间带宽积，该团队计算并得到了两个二进制振幅全息图之间的严格定量数学关系，A1⊃B1，对于相位全息图满足A1⊃C。实际上，三个全息图同步被计算关联，并符合A1=B1∪C。该团队开发了一种全息图定量关联算法，通过优化“静态”和“动态”纳米天线作为光谱滤波器以及相位调制器来构建全介质超表面以匹配三重关联的全息分布。这些可切换“动态”像素被排布在三幅全息图共用的重叠区域上。
对于“静态”像素，两种各向同性的方形纳米天线被作为两个工作波长下的振幅遮挡和透光像素，即“0”和“1”。而另一种各向异性矩形纳米天线则根据波长选择性被作为光学振幅可调开关按钮（即“动态”像素）。同时，这些各向异性天线可以作为相位贡献者在交叉极化信道中重建相位全息图。因此，通过控制入射波长和输出偏振组合来重建定量关联的三重全息图。
不同于传统的金属光子筛结构，该团队提供了利用全介质超表面实现透光、滤光和相位调控。具体在超表面编码实现方法中，利用波长和偏振通道选择性，设置了两种“静态”纳米天线，用于在同旋但不同工作波长（λ1，λ2）通道，且同时符合两幅独立振幅全息图的像素点组合（0, 0）和（1, 1）。
此外，他们还设置了“动态”像素 (0, 1)，即在 λ2处透明但在λ1处不透明，用于实现两幅振幅全息图的差集。有意思的是，该“动态”像素在反旋偏振通道中，由于具有各向异性构型，能够实现基于贝里相位原理的纯相位全息调制。
在实验中，该团队在同旋通道和可见光、近红外波长（LCP-LCP，λ1=510 nm，λ2=720 nm）分别重建出两个不同的振幅全息图像（蜜蜂和蝴蝶），并且在交叉偏振通道（LCP-RCP，λ2=720 nm）中重建具有盛开的牡丹的相位全息图，从而验证了该方案的可行性。另一个样品（天鹅、蜂鸟和祥云）也同样表现出很好的全息重建质量（图1）。
综上，该超表面可以在不牺牲空间带宽积的情况下实现三重振幅和相位全息的定量关联。实验结果成功地验证了理论方案。借助波长和偏振的选择性，该超表面可以动态地显示和隐藏全息像。此外，通过精心设计，该团队所开发的定量关联算法可以扩展为集成主动可调的材料，利用单片超表面实现动态、混合振幅相位全息术。同时，该方法可用于入射结构光和偏振选择的大容量、高速全息加密、显示及光操纵、光通信等相关领域。