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Highdimensional Poincaré beams generated through cascaded metasurfaces for highsecurity optical encryption
PhotoniX volume 5, Article number: 13 (2024)
Abstract
Optical encryption plays an increasingly important role in the field of information security owing to its parallel processing capability and low power consumption. Employing the ultrathin metasurfaces in optical encryption has promoted the miniaturization and multifunctionality of encryption systems. Nevertheless, with the few number of degrees of freedom (DoFs) multiplexed by single metasurface, both key space and encoding space are limited. To address this issue, we propose a highsecurity and largecapacity optical encryption scheme based on perfect highdimensional Poincaré beams with expanded DoFs. By cascading two arrayed metasurfaces, more beam properties can be independently engineered, which gives rise to the extensively expanded key and encoding spaces. Our work provides a promising strategy for optical encryption with high security level and large information capacity and might facilitate the applications of Poincaré beams in optical communications and quantum information.
Introduction
With the rapid development of information technology, information security is becoming of vital significance and so do the derived encryption techniques. Optical encryption possesses the advantages of parallel processing, large capacity and low power consumption, and offers an ideal platform for information protection owing to abundant degrees of freedom (DoFs) of the photon [1,2,3,4,5]. However, conventional optical encryption system commonly involves in a series of complicated optical elements and results in a bulky volume. In addition, due to the limited optical field manipulation capability of traditional optical elements, the multidimensional DoFs of light have not been fully exploited.
As an ultrathin planar optical element composed of subwavelength nanostructures, metasurface has shown powerful capability of multidimensional optical field manipulation and emerges as a promising candidate for optical encryption in a compact form [6,7,8,9,10,11,12,13]. For metasurfaceempowered optical encryption system, the key space could be defined as the total number of keys and attributed to both incident and output states. While the encoding space refers to the information capacity of the output images or beams through metasurfaces. So far, various DoFs of light, including incident angle [14,15,16], wavelength [17], polarization [18, 19], orbital angular momentum (OAM) mode [20,21,22,23] and so on [24, 25], have been explored to construct key space for optical information security. The combination of multiple DoFs has been demonstrated the capability to enhance the complexity of keys [26,27,28,29,30]. Besides, through encoding information into optical images in the form of nanoprinting or holography, encoding space has also been established and depends on the number of multiplexing channels of metasurface [31, 32]. To further expand the key and encoding spaces, encryption algorithms and dynamic encryption schemes were aroused for high security and large capacity performance [33,34,35,36,37,38]. Nevertheless, the above two strategies usually suffer from timeconsuming decryption process and the lack of pixelated realtime modulation. Featured with spatial variant polarization states and phase distributions, Poincaré beams gain a great deal of attentions in many applications [39,40,41,42,43,44], especially in optical encryption and encoding owing to versatile independent DoFs [45,46,47,48,49]. In the recent works, optical information was encoded into the polarization order and ellipticity of perfect hybridorder Poincaré beams (HyOPBs) [45]. It presents a new scheme of optical encryption to enlarge the encoding space, which is distinguished from conventional nanoprinting or holography encryption. However, such Poincaré beams encryption strategy has constraints due to limited key space (with only one incident state in essence) and stays a low security level. With the advantages of subwavelength modulation capability and inherent ultrathin size, metasurface also allows spatial multiplexing frameworks such as arrayed metasurface [45] and cascaded metasurfaces [25, 50,51,52]. Therefore, the combination of cascaded and arrayed metasurfaces boasts great potentials for enhancement of key and encoding spaces towards highsecurity and largecapacity features.
In this work, we propose a highsecurity and largecapacity optical encryption strategy based on multichannel perfect highdimensional Poincaré beams (HDPBs) generated by cascaded metasurfaces. Benefiting from the infinite modes of HDPBs and the scalability of arrayed metasurface, both key space and encoding space have been considerably expanded. Accordingly, by cascading two arrayed metasurfaces composed of 16 × 10 cells, an optical encryption platform is implemented by encoding information into five independent parameters of HDPBs. Our work provides a promising solution to extensively enlarge the key and encoding spaces and may open an avenue towards advanced optical encryption systems.
Results
Concept and principle of highdimensional Poincaré beams encryption
Figure 1 schematically illustrates the HDPBs optical encryption scheme using cascaded metasurfaces, which is capable of generating multichannel HDPBs with diverse DoFs to encode optical information. In principle, HyOPBs can be described as a linear superposition of righthanded circular polarized (RCP) and lefthanded circular polarized (LCP) bases with different topological charges [39]. Here, we generalize a more complex vector vortex beam superposed by two HyOPBs as HDPBs, which can be represented by highdimensional Poincaré sphere indicated by the magenta or blue sphere in Fig. 1. Taking the blue sphere for instance, the north (south) pole is a linear superposition of RCP and LCP optical vortices with topological charges of l_{1} + n_{2} (n_{1} + l_{2}) and l_{1} + l_{2} (n_{1} + m_{2}), namely \(\left {\psi _{R}^{{{l_1}+{n_2}}}} \right\rangle +\left {\psi _{L}^{{{l_1}+{l_2}}}} \right\rangle\) (\(\left {\psi _{L}^{{{n_1}+{m_2}}}} \right\rangle +\left {\psi _{R}^{{{n_1}+{l_2}}}} \right\rangle\)). Arbitrary state \(\left \psi \right\rangle\) on the surface of highdimensional Poincaré sphere can take the form as follows
where
Here, \(\sin (\frac{\chi }{2}+\frac{\pi }{4})\) and \(\cos (\frac{\chi }{2}+\frac{\pi }{4})\) denote the relative amplitude while Φ is the phase difference of two poles. Also, l_{1}, m_{1}, n_{1}, l_{2}, m_{2} and n_{2} are the topological charges and the corresponding numbers 1 and 2 refer to the contributions by two cascaded metasurfaces. R and L are abbreviations of RCP and LCP states. \({\hat {e}_x}\) and \({\hat {e}_y}\) represent the unit vectors along x and y axis and ϕ is the azimuth coordinate. For instance, \(\left {{}^{\Phi }\psi _{L}^{{{n_1}+{m_2}}}} \right\rangle\) corresponds to the LCP state carried with topological charge of n_{1} + m_{2} and phase of Φ. To acquire such HDPBs, two metasurfaces made up of planar chiral metaatoms are required to be aligned to generate incident HyOPBs and perfect HDPBs. With the spindecoupled modulation channels, the generated perfect HDPBs can lie on two different highdimensional Poincaré spheres (that is the magenta and blue ones) according to the circular polarization states of incident light. In order to encrypt information with higher security and larger capacity, two arrayed metasurfaces are established so as to generate a variety of perfect HDPBs. Once the authentic coordinates (x_{1}, y_{1}, x_{2}, y_{2}) of two arrayed metasurfaces are obtained, the desired states of HDPBs could be achieved through alignment of two specific metasurfaces. The plaintext can be subsequently decoded by characterizing the properties of HDPBs based on the annular intensity distributions through RCP/LCP analyzers for RCP/LCP incidences. Otherwise, the misalignment of coordinates (a counterfeit key) would lead to generation of wrong HDPBs and make the plaintext unavailable. It should be mentioned that the scale of the arrayed metasurfaces, could be extremely expanded and contributes to a high security level. In addition, the encoding space with dependence on the states of HDPBs can also be enlarged through plenty of combinations of two cascaded metasurfaces.
Generation of multichannel perfect hybridorder Poincaré beams
As a precondition for HDPBs encryption, generation of multichannel perfect HyOPBs should be realized at the first stage. To this end, a singlelayer metasurface based on planar chiral metaatoms is employed for spindecoupled phase manipulation through breaking the mirror symmetry and higherorder rotational symmetry [53, 54]. As depicted in Fig. 2(a), the transmitted copolarized φ_{co} and two crosspolarized channels φ_{RL} and φ_{LR} enable three independent phase modulation channels under RCP and LCP incidences (Supplementary Note 1). By incorporating chiral metaatoms with geometric phase, the designed metasurface can function as a combination of four optical elements, namely a quarterwave plate, a spiral phase plate, an axicon and a Fourier lens, for generation of multichannel perfect vortex beams with controllable topological charges of l_{0}, m_{0} and n_{0} (see Supplementary Note 2 for detailed phase distributions of chiral metaatoms). Therefore, through coherent superposition of the copolarized and crosspolarized perfect vortex beams, two different perfect HyOPBs (\(\left {\psi _{L}^{{{m_0}}}} \right\rangle +\left {\psi _{R}^{{{l_0}}}} \right\rangle\) and \(\left {\psi _{R}^{{{n_0}}}} \right\rangle +\left {\psi _{L}^{{{l_0}}}} \right\rangle\)) can be accessed according to the incident circular polarization states (Supplementary Note 3).
For experimental demonstration, a metasurface made of silicon nitride chiral metaatoms with height of 1.2 μm on fused silica substrate was prepared (See Methods for fabrication process). Figure 2(b) shows the optical microscope image of the fabricated metasurface with radius of 50 μm and topological charges l_{0}, m_{0} and n_{0} of 3, 4 and 1, respectively. Through illuminating 470 nm light, the transmitted beams through metasurface were collected as exhibited in Fig. 2(c) (optical characterization can be referred to Methods). The first to fourth columns list the generated beams under RCP, LCP, horizontal linearly polarized (Hpolarized) and vertical linearly polarized (Vpolarized) incidences. It is clear that the intensities of the generated beams are split into seven and four bright lobes after passing through linear polarization analyzer under RCP and LCP incidences, which correspond to the polarization orders of \(\left {\psi _{L}^{4}} \right\rangle +\left {\psi _{R}^{{  3}}} \right\rangle\) and \(\left {\psi _{R}^{1}} \right\rangle +\left {\psi _{L}^{{  3}}} \right\rangle\). Meanwhile, the annular intensity distributions present almost identical radiuses regardless of the number of topological charges. The above experimental results are coincident with the theoretically calculated ones listed in Fig. S2(b), validating the generation of multichannel perfect HyOPBs. Additionally, these two HyOPBs can be further linearly superposed into HDPBs under linearpolarized incidences, as shown in the third and fourth column in Fig. 2(c). By changing the incident states from Hpolarization to Vpolarization, the generated perfect HDPBs evolves from point I to II on the equator of highdimensional Poincaré sphere displayed in Fig. 2(d). Characterized by nonuniformly distributed polarization states with spacevariant phase distribution, HDPBs can serve as information carriers to establish an enormous key and encoding spaces for optical encryption.
Manipulation of perfect highdimensional Poincaré beams
By virtue of the multichannel phase modulation of planar chiral metasurface, generation of HDPBs has been demonstrated above. Nonetheless, the states of HDPBs are limited within a single metasurface because of the identical copolarized phase modulation channels. In terms of HDPBs encryption, to achieve larger key and encoding spaces, another metasurface (meta_1) is adopted to generate multichannel HyOPBs as incidences for the following metasurface (meta_2) (see Supplementary Note 4 for detailed phase modulation design). As illustrated in Fig. 3(a), the incident RCP and LCP light are transformed into two HyOPBs \(\left {\psi _{R}^{{{l_1}}}} \right\rangle +\left {{}^{{{\Phi _{11}}}}\psi _{L}^{{{m_1}}}} \right\rangle\) and \(\left {\psi _{L}^{{{l_1}}}} \right\rangle +\left {{}^{{{\Phi _{12}}}}\psi _{R}^{{{n_1}}}} \right\rangle\) through meta_1. Cascaded by meta_2, the HyOPBs are subsequently modulated into multichannel perfect HDPBs. In this work, HDPBs are designed to lie on the equator of two highdimensional Poincaré spheres and can be expressed as (referred to equations S9ab)
and
for RCP and LCP incidences. Φ_{12} and Φ_{11} (Φ_{22} and Φ_{21}) denote the phase differences between copolarized and crosspolarized channels of meta_1 (meta_2), respectively. After passing through RCP/LCP analyzers, the output beams turn into \(\left {\psi _{R}^{{{l_1}+{l_2}}}} \right\rangle +\left {{}^{{{\Phi _{11}}+{\Phi _{22}}}}\psi _{R}^{{{m_1}+{n_2}}}} \right\rangle\) and \(\left {\psi _{L}^{{{l_1}+{l_2}}}} \right\rangle +\left {{}^{{{\Phi _{12}}+{\Phi _{21}}}}\psi _{L}^{{{n_1}+{m_2}}}} \right\rangle\) for RCP and LCP incidences and appear as annularly distributed bright lobes. Hence, polarization orders of two HDPBs, defined as P_{R}=(l_{1} + l_{2}m_{1}n_{2})/2 and P_{L}=(l_{1} + l_{2}n_{1}m_{2})/2, can be flexibly manipulated by designing six topological charges and emerged as the number of bright lobes. Figure 3(b) and (c) display the top and side view of the scanning electron microscope images of the fabricated chiral metasurface, respectively. The experimental setup for generating HDPBs through alignment of two cascaded metasurfaces is illustrated in Supplementary Note 5. Endowed with topological charges of l_{1} = 7, m_{1}=5, n_{1} = 7, l_{2} = 8, m_{2} = 1 and n_{2} = 4 (l_{1} = 7, m_{1} = 4, n_{1}=5, l_{2} = 8, m_{2} = 6 and n_{2} = 8), the generated HDPBs with independent polarization orders P_{R} and P_{L} of 8 and 7/2 (3/2 and 7) demonstrates 16 and 7 (3 and 14) bright lobes through RCP and LCP analyzers, as shown in the left (right) part of Fig. 3(d). Besides, due to the axicon and Fourier lens phase modulation provided by meta_2, HDPBs possess almost identical radiuses, exhibiting perfect characteristics. In this regard, the outline of the HDPBs could also be adjustable according to the designed ellipticities γ (defined as the ratio of horizontal and vertical radiuses). Figure 3(e) shows the intensity profiles of the perfect HDPBs with ellipticities of 0.6, 0.8, 1.0 and 1.2 (with topological charges of l_{1} = 7, m_{1} = 7, n_{1} = 7, l_{2} = 8, m_{2} = 8 and n_{2} = 8). The normalized intensities along horizontal and vertical directions indicated by white solid and dashed lines are plotted in Fig. S4. The corresponding ellipticities are measured to be 0.62, 0.77, 0.99 and 1.24, which match well with the theoretical values and demonstrate the capability of shaping the outlines of perfect HDPBs (Supplementary Note 6). By the way, the alignment accuracy of two cascaded metasurfaces is required to be about 5 μm (see Supplementary Note 7), which can be well accessible in experiments.
In addition, the states of HDPBs on the equators of highdimensional Poincaré spheres shown in Fig. 3(f), which are represented by azimuth angles Φ_{R} = Φ_{11} + Φ_{22} and Φ_{L} = Φ_{12} + Φ_{21} and reflect in the rotation angles θ_{L} and θ_{R} of bright lobes, is accessible to be manipulated by adjusting Φ_{12}, Φ_{11}, Φ_{22} and Φ_{21}. It is worth noting that the influence of Gouy phase on azimuth angles should be taken into careful consideration (see Supplementary Note 8 for detailed analysis). The rotation angles θ_{L} and θ_{R} of bright lobes (indicated by the white dashed lines in Fig. 3(f)), which are defined as the minimum positive angle between the center of bright lobes and the xcoordinate axis, can be employed to retrieve the azimuth angles Φ_{R} and Φ_{L} of HDPBs (see details in Supplementary equations S9ef and Supplementary Note 9). As depicted in the four corners of Fig. 3(f), the HDPBs with different azimuth angles Φ_{R} and Φ_{L} (with l_{1} = 7, m_{1}=8, n_{1}=9, l_{2} = 8, m_{2}=7 and n_{2}=8), which can be expressed as \(\left {\psi _{R}^{{15}}} \right\rangle +\left {{}^{{{\Phi _{21}}}}\psi _{L}^{0}} \right\rangle +\left {{}^{{{\Phi _{11}}}}\psi _{L}^{0}} \right\rangle +\left {{}^{{{\Phi _{11}}+{\Phi _{22}}}}\psi _{R}^{{  16}}} \right\rangle\) and \(\left {\psi _{L}^{{15}}} \right\rangle +\left {{}^{{{\Phi _{22}}}}\psi _{R}^{{  1}}} \right\rangle +\left {{}^{{{\Phi _{12}}}}\psi _{R}^{{  1}}} \right\rangle +\left {{}^{{{\Phi _{12}}+{\Phi _{21}}}}\psi _{L}^{{  16}}} \right\rangle\), are characterized by RCP and LCP analyzers. For both RCP and LCP incidences, the generated beams via four sets of cascaded metasurfaces all present 31 bright lobes determined by polarization orders P_{R} and P_{L} of 31/2 but with different rotation angles θ_{R} and θ_{L}, corresponding to the states marked by Greek numerals I, II, III and IV featured with azimuth angles Φ_{R} of 270°, 0°, 90°, 180° and Φ_{L} of 0°, 90°, 180°, 270°. Therefore, flexible and independent manipulation of polarization orders P_{L} and P_{R}, ellipticities γ along with azimuth angles Φ_{R} and Φ_{L} of perfect HDPBs have been demonstrated in virtue of two cascaded multichannel chiral metasurfaces.
Optical encryption based on cascaded metasurfaces
After investigating the manipulation capability of both the outline and states of HDPBs via cascaded metasurfaces, five explored independent parameters, namely γ, Φ_{R}, Φ_{L}, P_{R} and P_{L}, can be employed for optical information encoding. Furthermore, in order to construct an optical encryption system on the basis of HDPBs, two arrayed metasurfaces are implemented to enable a highsecurity platform with enlarged encoding capacity, as presented in Fig. 4(a). The first arrayed metasurfaces (denoted as arrayed meta_1) is composed of 16 × 10 meta_1 cells for generating multichannel HyOPBs as incidences for the second arrayed metasurfaces (denoted as arrayed meta_2) consisting of 16 × 10 meta_2 cells (see Tables S2 and S3 in Supplementary Note 10). Through combination of different cells in two arrayed metasurfaces, an abundant number of perfect HDPBs featured with different parameters are available. As a demonstration, the plaintext messages of four Chinese words “南京”, “金陵”, “建邺” and “秦淮” (four names of Nanjing in Chinese), are encrypted into two metasurfaces (ciphertext) through the Unicode encoding in the form of five parameters of perfect HDPBs, accompanied with the customized keys in the form of coordinates (x_{1}, y_{1}, x_{2}, y_{2}). Once the ciphertext and customized keys are transferred into four users, the decryption process begins with the alignment of two arrayed metasurfaces. In accordance with the received coordinates (x_{1}, y_{1}, x_{2}, y_{2}), the target cells are subsequently illuminated by 470 nm RCP and LCP light for generation of perfect HDPBs, respectively. As a consequence, each user who owns two keys could obtain two sets of HDPBs, depicted in Fig. 4(b). Then, the parameters of HDPBs, including γ, Φ_{R} and Φ_{L}, P_{R} and P_{L}, are retrieved and transformed into digital forms, as listed in Fig. 4(c). With reference to the selfdefined lookup table in Supplementary Note 11 each user could translate the obtained messages into two fourbit hexadecimal digits in Fig. 4(d). As indicated in Fig. 4(e), the ciphertext would eventually be decoded through Unicode encoding as “南京”, “金陵”, “建邺” and “秦淮”, respectively. So far, the optical encryption platform has been established via two cascaded metasurfaces based on multichannel perfect HDPBs.
Discussion and conclusion
Compared with other optical encryption schemes based on metasurface [21, 26, 30, 31, 45], the proposed optical encryption platform utilizes the combination of two arrayed metasurfaces as keys to achieve an enlarged key space. Meanwhile, the encoding space has been greatly expanded to be adaptive with Unicode encoding thanks to sufficient DoFs carried by HDPBs and multichannel light field manipulation provided by chiral metasurfaces (see Supplementary Note 12 for evaluation of key and encoding spaces). It should be emphasized that, benefiting from the compactness of metasurface and extended DoFs of HDPBs, the arrayed metasurfaces could easily be scaled up to establish larger key and encoding spaces for highcapacity optical information encryption with unprecedented level of security.
To conclude, we have proposed and experimentally demonstrated perfect HDPBs for optical encryption with large capacity and high security through cascaded metasurfaces. Attributed to the spindecoupled wavefront tailoring capability of chiral metaatoms, a singlelayer metasurface is applied to function as the combination of quarter wave plate, spiral phase plate, axicon and Fourier lens to produce multichannel perfect HyOPBs by linear superposition of transmitted copolarized and crosspolarized perfect vortex beams. By introducing another chiral metasurface to generate HyOPBs as the secondlevel input beam, multichannel HDPBs are constructed under RCP and LCP incidences through two cascaded metasurface. Particularly, five parameters of perfect HDPBs, including ellipticities, polarization orders and azimuth angles for RCP and LCP incidences, can be independently manipulated at will for optical information encoding. By virtue of two cascaded metasurfaces containing 16 × 10 cells, an optical encryption scheme with enhanced encoding capacity and security level has been constructed by encrypting information into perfect HDPBs which can only be obtained through alignment of specific cells in two arrayed metasurfaces. Overall, this work for optical information encryption and encoding via multichannel perfect HDPBs may promote the development of miniaturization and integration of optical encryption system with high security and inspire intriguing applications of Poincaré beams for highcapacity optical communications and quantum information.
Methods
Numerical simulations
Numerical simulations were performed to investigate the phase shifts of both copolarized and crosspolarized channels of chiral metaatoms through finitedifference time domain (FDTD) methods. The refractive index of SiN_{x} used in simulations was n = 2.032 + 0.0013i, which was obtained from experimental samples measured by spectroscopic ellipsometer. A 470 nm planewave source was employed to illuminate chiral metaatoms from substrate. Perfectly matched layer (PML) was utilized as boundary condition along the propagation direction of light source while periodic boundary conditions are applied along all the inplane directions.
Device fabrication
The samples were prepared on a fused silica substrate through deposition of SiN_{x} layer with 1.2 μm height using plasmaenhanced chemical vapor deposition (PECVD). Then, an electron beam resist (PMMAA4) with the thickness of 200 nm was spincoated on top of the SiN_{x} layer. The patterns of chiral metaatoms were subsequently defined on PMMA resist by Electronbeam lithography (EBL) system (ELSF125, Elionix). After development, the generated pattern was transferring to an electron beam evaporated chromium layer, which served as a hard mask for the following dry etching process of SiN_{x} layer in a mixture of CHF_{3} and SF_{6} plasma (Oxford Instruments, PlasmaPro100 Cobra300). At last, the remaining chromium mask was removed by a solution of ammonium cerium nitrate.
Optical characterization
A 470 nm laser was utilized for optical measurement and focused onto the fabricated metasurfaces through an objective (20×, NA = 0.40). The polarization states of the incident light were controlled by the combination of linear polarizer and quarterwave plate. After illuminating the metasurface/cascaded metasurface, the transmitted light was subsequently collected by an objective (20×, NA = 0.40) and analyzed by polarizers. Subsequently, the intensity profiles of the generated Poincaré beams were recorded using a CMOS camera. The alignment of two cascaded metasurfaces is detailed in Supplementary Note 5.
Availability of data and materials
The source data are available from the corresponding author upon reasonable request. All data needed to evaluate the conclusion are present in the manuscript and/or the Supplementary Information.
Abbreviations
 DOFs:

Degrees of freedom
 HDPBs:

Highdimensional Poincaré beams
 OAM:

Orbital angular momentum
 HyOPBs:

Hybridorder Poincaré beams
 RCP:

Righthanded circular polarized
 LCP:

Lefthanded circular polarized
 Hpolarized:

Horizontal linearly polarized
 Vpolarized:

Vertical linearly polarized
 FDTD:

Finitedifference time domain
 PML:

Perfectly matched layer
 PECVD:

Plasmaenhanced chemical vapor deposition
 EBL:

Electronbeam lithography
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The authors acknowledge the funding provided by National Key Research and Development Program of China (2022YFA1404301), National Natural Science Foundation of China (Nos. 62325504, 62305149, 92250304, 62288101), and Dengfeng Project B of Nanjing University. The authors acknowledge the microfabrication center of the National Laboratory of Solid State Microstructures (NLSSM) for technique support.
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C.C., J.J. and T.L. conceived the concept. C.C. and J.J. proposed the metasurface design and performed the numerical simulations; J.S. and J.L. fabricated the samples with the help of C.H. and K.Q.; J.J. and C.C. performed the optical measurements with the help of X.Y. and J.W.; J.J., C.C., Z.W., W.S., T.L. and S.Z. discussed the results; J.J., and C.C. wrote the manuscript with the help of Z.W. and W.S.; T.L. supervised the project.
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Ji, J., Chen, C., Sun, J. et al. Highdimensional Poincaré beams generated through cascaded metasurfaces for highsecurity optical encryption. PhotoniX 5, 13 (2024). https://doi.org/10.1186/s43074024001258
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DOI: https://doi.org/10.1186/s43074024001258