Creating Wavelength‐Selective Polarization Digital Numbers

Polarization and wavelength are two important properties of light for understanding optics. Engineered polarization and wavelength profiles have received considerable interest due to their unusual optical features and more degrees of freedom. However, to simultaneously control polarization and wavelengths, conventional methods suffer from big pixel size, complicated fabrication process, and limited levels in phase control. The unprecedented capability of metasurfaces in the light control has shown much promise to tackle these challenges. Polarization digital numbers with ten different wavelengths are proposed and experimentally realized. A geometric metasurface is used to simultaneously realize wavelength multiplexing, phase multiplexing, and polarization rotation, creating wavelength‐selective polarization digital numbers. A deep learning approach is used to increase the identification accuracy of the digital numbers. The approach can simultaneously control wavelength and polarization, providing more design flexibility. This work may find applications in many fields such as virtual reality, image steganography, and anti‐counterfeiting.


Introduction
Polarization plays a fundamental role in our understanding of optics.Versatile manipulation and precise characterization of polarization are two important sought-after-goals due to their practical applicability in sensing, [1,2] quantum optics, [3] optical displays, [4,5] and novel light-matter interactions. [6][15][16][17] The polarization manipulation is typically achieved using schemes that involve anisotropic resonators, which can effectively and independently change two orthogonal polarizations into a desired output. [7,18]These techniques have been effectively exploited to demonstrate polarization imaging, [19] holography, [20][21][22][23][24] vector vortex beams, [25,26] and polarization structure generation. [27,28]n the other hand, the wavelength multiplexing provides extra degrees of freedom for polarization manipulation.31][32] Wavelength-dependent manipulation of optical wavefronts is expanded by using multiple resonators within a unit cell to realize structural colors with arbitrary values of hue-saturationbrightness. [33][36] Moreover, a sub-regional approach of metasurfaces is also helpful to filter out the wavelengths of an incident light beam.Therefore, such a design can perform independent control of the dispersion at three operation wavelengths. [37]However, the quality of the beam convergence is decreased due to the sub-regional approach as it suffers from the limited pixels for each operation wavelength.Therefore, it restricts a metasurface to control dispersion for a greater number of wavelengths.Although the folded design comprised of three or more reflective metasurfaces can provide the desired degree of freedom, it suffers from the complex experimental setup, challenging alignment, and increased volume. [38,39]ost metasurface designs based on single-sized nanostructures are typically focused on either the local wavelength or polarization, limiting the practical applications.For example, metasurfaces based on the propagation phase are mostly limited to a very narrow range of wavelengths. [40,41]On the other hand, geometric phase metasurfaces that consist of rectangular nanobars with spatially varying orientation angles can operate over a broadband wavelength range, but they are limited to orthogonal circular polarizations only. [20,42]Few experimental demonstrations show that the number of polarization channels can be increased up to eight and eleven using pixelated vectorial metasurface and metasurface with engineered noise, respectively. [43,44]owever, the design involves the optimization of complex supercells for each polarization channel under a single operation wavelength.The number of polarization channels were significantly increased by employing the combination of geometric phase and detour phase to achieve a continuous polarization distribution at a single operation wavelength. [45]To include three basic wavelength information, a tri-polarization channel design was reported to encode three different phase profiles through a non-interleaved metasurface. [46]However, the existing polarization and wavelength-dependent metasurfaces typically suffer from the limited number of encrypted information channels.Furthermore, each channel has a uniform polarization profile.To increase the functionalities of metasurfaces for a wider range of applications, simultaneous and independent control of polarization profiles and on-demand wavelengths in an individual channel is highly desired.
To tackle the above challenges, we propose a metasurface approach to experimentally realize polarization digital numbers with ten different wavelengths.Inspired by the multi-foci characteristics of our metalens design, [28] we develop a geometric metasurface to simultaneously realize wavelength multiplexing, phase multiplexing, and polarization rotation, which can realize wavelength-selective polarization digital numbers.Furthermore, to increase the perception capability of the proposed metasurface and automatically recognize the numbers, a deep learning approach is implemented with an accuracy reaching up to 100%.
Simultaneous control wavelength and polarization with a singlenanostructured metasurface renders this approach very promising for immense information encoding such as color display, virtual reality, image steganography, and anti-counterfeiting.

Design and Methods
Figure 1 shows the schematic of the proposed approach for the realization of wavelength-selective digital numbers with a single metasurface.The operating wavelengths range from 500 to 680 nm, which are generated with a Supercontinuum laser source.Each wavelength corresponds to an individual digital number with a predesigned polarization structure, which consists of 7 polarization segments.With an interval wavelength of 20 nm, 10 digital numbers (0-9) are encoded into the corresponding polarization digital numbers with predesigned different polarization profiles and wavelengths.Each polarization digital number includes seven focal lines with linear polarization states along the vertical or horizontal directions.The ON and OFF states of the focal lines are controlled by the predesigned polarization directions (90°and 0°), which are realized based on the polarization rotation upon the illumination of the linearly polarized (LP) incident light.Without a linear polarizer (analyzer), all segments (focal lines) appear simultaneously, leading to the same displayed number with different wavelengths.The encoded number is revealed with the aid of an analyzer.Due to the low conversion efficiency of the plasmonic metasurface, the convolutional neural network is used to improve the identification accuracy of the displayed digital numbers on the observation plane after passing through the analyzer.
Inspired by our recent work on polarization engineering with optical metasurfaces to create predesigned polarization structures, [27,28] the metasurface is designed based on the combination of multi-foci design and polarization rotation.The phase distribution of the geometric metadevice is given by Here, (x, y) n is the phase distribution for a lens that can generate the nth focal point, which is governed by where N is the total number of the designed focal points, ϕ n is the polarization rotation for each focal point,  is the working wavelength, and f is the focal length.u and v represent the locations of a focal point along the x and y directions, respectively.(u, v, f) are the coordinates of the focal point, which can be on the optical axis or off-axis.
To create wavelength-multiplexing polarization structures of the digital numbers from 0 to 9 in the two-dimensional (2D) space, we introduce the phase profile of the metasurface as follows. where , n, q, and m represent the nth focal point, the qth focal line and the mth polarization digital number, respectively. m represents the wavelength for the mth digital number.N, Q, and M are the total numbers of the focal points, focal lines, and digital numbers, respectively.(u m,q, n , v m,q, n , f m,q, n ) are the free-space coordinates of a given focal point with a polarization rotation angle of ϕ m,q, n on the generated display numbers.
A 7-segment digital number consists of seven focal lines with an arrangement of each line depicted in Figure 2a.Each segment is 20 μm long (L) and includes 200 focal spots (N = 200).For an analyzer with a transmission axis along the vertical axis, a 7segment-based digital number can be revealed as an example of the number 5 shown in Figure 2b,c.The segments along vertical and horizontal directions are created with different parametric equations as follows.
For q = 1, 4, 7 (focal lines along the horizontal direction), the equation is given by For q = 2, 3, 5, 6 (focal lines along the vertical direction), the equation is given by )) where rcos Λ m and rsin Λ m are the coordinates of the digital number m in the xy-plane.r is the radius of the circle with its center in the focal plane.Λ m is the central angle formed between an arbitrary radius and the radius along the x-axis (Figure 2d).f 0 is the focal length of the metalens.
The idea of the wavelength-selective design is motivated by the dispersion effect of a metalens, whose focal length changes with the incident wavelengths.To explain the proposed idea, two different metasurfaces are designed and compared.First, a metadevice is designed to simultaneously create 10-polarization digital numbers in the same observation plane as expressed in Equation (3) at only one operation wavelength ( m ) of 650 nm.Then the wavelengths ranging from 500 to 680 nm with an interval wavelength of 20 nm ( 1 −  10 ) are combined to the polarization profiles in order to realize the wavelength-selective functionality for the second metadevice.The observation plane in the 2D space is located at z = 300 μm.Upon the illumination of LP light at  = 500 nm, 10 polarization digital numbers are created, but only number "0" is in the observation plane and the other numbers are not located in this plane (Figure 2e, top).When the incident wavelength is changed to 520 nm, the number "1" appears in the observation plane, while other numbers are away from this area (Figure 2e, middle).Correspondingly, only number "9" is in the observation plane at  = 680 nm (Figure 2e, bottom).Therefore, various polarization digital numbers can be achieved by controlling the wavelengths of the incident light beam.Based on Equation (3), we calculate the phase profiles of the first and second metadevices, which are shown in Figure 2f,g, respectively.
The designed metadevices are realized by using identical gold nanobars with spatially variant orientations on top of an ITOcoated glass substrate to produce Pancharatnam-Berry phases (geometric phases) ranging from 0 to 2.The generated phase Φ(x, y) is two times of the orientation angles (x, y) of the nanobars.Each nanobar is 40 nm high, 200 nm long, and 80 nm wide.Each pixel has an area of 300 × 300 nm 2 and its response spectrum can be found in Section S2 (Supporting Information).The standard electron-beam lithography, the electron-beam deposition, and the lift-off process are respectively used to fabricate the designed metadevices (see Experimental Section).The fabricated sample has a circular shape with a diameter of 360 μm. Figure 2h,i shows the scanning electron microscope (SEM) images of the fabricated metadevices for generating 10-polarization numbers and wavelength-selective polarization numbers in the same observation plane, respectively.The experimental setup numbers ("0"-"9") are given upon the illumination of the incident light from 500-680 nm for  1 to  10 nm.The observation region is defined by the plane z = 300 μm.Only one 2D polarization number is obtained for a single incident wavelength; thus, the wavelength-selective functionality is realized.f,g) The phase profiles and h,i) SEM images of the metadevices to generate the 10-polarization numbers and the 10-wavelength-selective polarization numbers, respectively.
shown in Figure 3a is then built up to characterize the fabricated metadevices and the details are in the Experimental Section.To confirm the obtained results from the experiment, the simulated 2D digital numbers are performed based on the Fresnel-Kirchhoff diffraction integration, [47] the calculation details can be found in Section S6 (Supporting

Results
We initially characterize the first metadevice at a fixed wavelength of 650 nm.Under the incident right circularly polarized (RCP) light, the intensity distributions of the ON and OFF states in each number are similar due to the uniform intensity.This means that all created numbers on the observation plane look like the number "8" as shown in Figure 3b.With the incident linearly polarized light along the x-axis and the analyzer with a transmission axis along the y-axis, only the segments that have a predesigned polarization rotation of 90°can be observed (Figure 3c).
To characterize the second metadevice, the incident wavelengths we use range from 500 to 680 nm with an interval wavelength of 20 nm. Figure 4 shows the wavelength-selective digital numbers when the polarization state of the incident light beam is LP.When the incident wavelength is 500 nm, the number "0" can be seen from the observation plane at z = 300 μm while the other numbers are blurred and unrecognizable.Similarly, the other numbers from "1" to "9" can be seen at the same observation plane when the corresponding wavelengths are selected.The experiment versus the simulated results under the incident RCP can be found in Section S3 (Supporting Information).Due to the low conversion efficiency of the fabricated metadevice across the visible region, there is a background noise arising from the non-converted part, which disturbs the number visibility when the intensity of the incident light is increased.The image fidelity values of design, simulation, and experimental results are calculated to demonstrate the quantitative comparison and to show robustness of our proposed technique, the details can be found in Section S7 (Supporting Information).
The visibility of polarization numbers is affected by the background noise, which can be suppressed by the optimization of metasurface design and the improvement of sample quality and optical setup.To address this issue, we perform simulations with different factors that affect the background noise as shown in Figure S4 in Section S8 (Supporting Information).The background noise increases with the increase of digital numbers (Figure S4a, Supporting Information), focal points (Figure S4b, Supporting Information), and focal lengths (Figure S4c, Supporting Information).However, the background noise can be significantly reduced by using the larger sample area as shown in Figure S4d (Supporting Information).The crosstalk between the neighboring numbers can be eliminated by increasing the interval wavelength (Figure S4e, Supporting Information).The created structures have the same patterns of the numbers "0" to "9," which are distinguishable with image fidelity of 0.9915, and 0.9237 for the simulation and experiment, respectively.Further details on image fidelity are provided in Section S7 (Supporting Information).To increase perception capability and automatically recognize the numbers, we introduce a built-in deep learning approach in MATLAB to identify the revealed numbers (the generated number when the incident light is LP as shown in Figures 4 and 5a) on the observation plane.The learning approach is based on a convolutional neural network (CNN), which learns directly from data rather than extracted features.CNNs are supervised learning so that inputs and correct outputs are needed for training.The CNNs are particularly useful for the recognition of objects, faces, and scenes in images. [48,49]The typical configuration of the CNNs includes an input layer, an output layer, and many hidden layers between those input and output layers.In this design, totally 7 layers with the built-in functions in MATLAB are used for training and validating the dataset.The details of CNN can be found in Section S4 (Supporting Information).
In this case, 20 captured images of each incident wavelength are used for training.Other 20 captured images are used for validation and 100% accuracy has been found.We further evaluate the performance of the learning method by developing an application program embedded with the trained data set to recognize the revealed numbers in real-time (Figure 5b).The captured im-ages for different wavelengths have their own unique patterns.In other word, the focused number, blurred numbers as well as the background noise on the observation plane of each image make the captured images different from each other.This difference provides an advantage for the CNN to identify the generated number correctly.As a result, the generated numbers are 100% correctly identified in the real-time recognition when the incident wavelength is either sequentially or randomly changed between 500 and 680 nm as demonstrated in Movie S1 (Supporting Information).

Discussion
Multispectral polarization manipulation can add more degrees of freedom.The encoded polarization information at different wavelengths is revealed by using a polarization key, which can realize different digital numbers (0-9) encoded in the same digital number (8) at various wavelengths.More digital numbers can be encoded in a metasurface by increasing its size, which is discussed in Section S8 (Supporting Information) (Figure S4, Supporting Information).The numbers of the focal points (N), focal lines (Q), digital number (M), wavelength interval, and focal length collectively put a limit on the polarization rotation and wavelength multiplexing.For example, our current design requires a combination of 10 wavelengths and 2 polarization rotations to generate digital numbers from "0" to "9."More numbers can be generated for the same size metasurface with the optimized design, which is shown in Section S8 (Supporting Information) (Figure S5, Supporting Information).As a proof-of-concept, we use a plasmonic metasurface consisting of metallic nanobars with a low efficiency (see Section S2, Supporting Information), which can be increased with a dielectric metasurface. [50,51]he displacement of the optical elements in the setup and the incident power of the laser are two factors that affect the identification accuracy.In the event of displacement of the optical elements, the generated numbers must be acquired and trained with the CNN again.If the power of the laser is dropped or increased by 50%, the accuracy is reduced to 80%.This performance has been artificially investigated by increasing and decreasing the brightness of the captured images by 50% and then used them as the validation samples.The flexible and controllable generation of multiple polarization distributions with multiple wavelengths may be of interest to many potential applications, including high-density information storage, vector beam generation, anti-counterfeiting, virtual reality, information security, and color displays.

Conclusion
In a word, we experimentally demonstrate a geometric metasurface to simultaneously control wavelength and polarization, creating wavelength-selective polarization digital numbers.The Adv. Optical Mater.2024, 12, 2203097 uniqueness of this technique lies in the metasurface approach for the realization of wavelength multiplexing, phase multiplexing, and polarization rotation.The combination of wavelength information and polarization manipulation offers more degrees of freedom for polarization control, which can promote both fundamental physics and practical applications such as color displays, virtual reality, image steganography, and anti-counterfeiting.

Experimental Section
Experimental Setup: Figure 3a illustrates the diagram of the optical setup used to characterize the fabricated metasurface devices.A supercontinuum laser source (NKT Photonics SuperK EXTREME) with tunable wavelengths can cover the broad wavelength range of the incident light.A linear polarizer (P1) and a quarter wave plate (QWP1) were utilized to control polarization states of the incident light beams.The light beam was weakly focused onto the device with a convex lens (L1).The 2D digital numbers were visualized by using an objective with a magnification of 20×, a convex lens (L2), and a monochrome charge-coupled device (CCD).The unconverted part of the transmitted light was filtered out by using a second pair of a quarter wave plate (QWP2) and a linear polarizer (P2), which were located behind the objective lens.The characterization process can be performed with an incident LP beam by removing QWP1 and QWP2 and keeping the inclined angles of the transmission axes of both P1 and P2 to be 90°.More details about the experimental setup can be found in Section S5 (Supporting Information).
Sample Fabrication: The transmissive metadevices consist of identical gold nanobars with various rotation angles on a glass substrate.The length, width, and height of each individual nanobar were 200, 80, and 40 nm, respectively.The size of each unit cell was 300 nm along both x and y directions.The ITO-coated glass substrate was initially cleaned in acetone, and then in isopropyl alcohol (IPA).Next, the substrate was rinsed in deionized water and dried with a nitrogen gun.After that, a 100-nmthick polymethyl methacrylate (PMMA) 950 A2 film was spin-coated on the glass substrate and baked on a hotplate.An electron beam from EBL (Raith PIONEER, 30 kV) was used to expose the PMMA film.The PMMA nanostructures were defined after the development process in MIBK:IPA (1:3).An electron beam evaporator was used to deposit a gold film with a thickness of 40 nm.Finally, the metasurface samples were ready for characterization after the lift-off process in acetone.The SEM images are shown in Figure 2h,i.

Figure 1 .
Figure1.Schematic of the proposed metasurface approach for the realization of wavelength-selective polarization digital numbers.10 images with different wavelengths are located at different positions along a circle in the same focal plane.Each image has a predesigned polarization profile and a given wavelength.Polarization images with the same digital number "8" are revealed with a linear polarizer (analyzer).The decoded numbers include 10 digital numbers ranging from 0 to 9. To improve the identification accuracy of digital numbers, a convolution neural network approach is used for the image identification.

Figure 2 .
Figure 2. Mechanism, design and fabrication.a) A digital number with seven focal lines.b) An example of the predesigned polarization rotation states along two different directions, which correspond to the ON and OFF states.c) The intensity distribution of the revealed number in (b) when an analyzer is used.d) The arrangement of the polarization digital numbers in the 2D space.e) Wavelength-selective mechanism.The locations of 10 different 2Dnumbers ("0"-"9") are given upon the illumination of the incident light from 500-680 nm for  1 to  10 nm.The observation region is defined by the plane z = 300 μm.Only one 2D polarization number is obtained for a single incident wavelength; thus, the wavelength-selective functionality is realized.f,g) The phase profiles and h,i) SEM images of the metadevices to generate the 10-polarization numbers and the 10-wavelength-selective polarization numbers, respectively.

Figure 3 .
Figure 3. Experimental setup and device characterization.a) Diagram of the experimental setup.b) Simulation and c) experimental results of the metadevice for creating 10-polarization numbers under the illumination of the RCP light at  = 650 nm.d) Simulation and e) experimental results of such metadevice under the illumination of the LP light when an analyzer is used.The scale bar is 50 μm.

Figure 4 .
Figure 4. Simulation and experimental measurement.Simulation and experimental results of the intensity distribution on the observation plane under the illumination of LP light with 10 wavelengths.

Figure 5 .
Figure 5. Deep learning approach to improve the identification accuracy.a) The intensity distributions on the observation plane under the illumination of LP light with 10 wavelengths (the cropped and expanded images from Figure 4).b) The developed application program for real-time recognition of the numbers on the observation plane.