1. Introduction

Metasurface is a two-dimensional array of metal /dielectric antennas with spatially varying phase response and subwavelength separation [1]. Through delicate design of the antennas, the metasurface can imprint arbitrary phase distributions on propagating light by introducing specific abrupt phase changes on each pixel. Compared to conventional optical components which rely on gradual phase shifts accumulated during light propagation to shape light beams, the metasurface possess the advantages of ultra-thin size and great flexibility [2–4]. Owing to the ability to manipulate fundamental properties of optical waves, metasurfaces have been used to demonstrate a series of intriguing phenomena, such as anomalous reflection and refraction [5], vector and structural beam generation [6,7], holographic display [8–11] and metalensing effects [12,13], to name a few. In the case of the metasurface holograms so far, the phase mask recorded in the metasurface cannot be changed into other information once it has been fabricated. To address these limitations, dynamic metaholograms using various methods have attracted widespread interests [14]. The methods include spatial interleave multiplexing [15] or multiplexing the polarization state [16], wavelength [17] and incident angle of the incident light [18], using the micro electro mechanical system (MEMS) [19,20] or some reconfigurable materials under external excitation [21].

In the optical frequency domain, the well-known tunable materials such as GeSbTe (GST), vanadium oxide (VO₂) and liquid crystal (LC) have been employed as the material of the dynamic nanophotonic devices so far [22–27]. Among these, the nematic liquid crystal (NLC) is a material whose phase change depends on several factors, including the chemical composition of its constituent molecules, its temperature and the local electric/magnetic conditions. The anisotropy geometry of NLC molecule results in the birefringent nature under electrical distributions and thus changes the local refractive index in the material. This makes NLC an attractive tuning medium to integrate with optical metasurface. Two common NLC based tuning effects are continuous resonance modulation and phase modification by integrating with the Mie-resonant dielectric metasurface [28–34] or the plasmonic metal metasurface [35–37]. However, among the related studies, the NLC tends to only act as a polarizer or a light valve, which means the NLC is usually applied with whole-layer voltage and all the NLC molecules deflect to the same direction [38–40]. Alternatively, through applying the voltage over the strip [41,42], tunable anomalous refraction and holography have been achieved by using the NLC integrated with metasurface. Through substituting the large pixels of traditional spatial light modulators (SLMs) with subwavelength antennas, the resolution and field of view (FOV) of traditional SLM can be greatly enhanced, while the thickness of LC layer can be reduced. Nevertheless, for metasurface-integrated LC device, there is still room for improvement in terms of the challenge to realize the two-dimensional dynamic modulation of NLC through different voltages.

Here, we propose and demonstrate a reconfigurable metadevice integrated with NLC. Combining with a binary holographic algorithm and applying two-dimensional electrical modulation patterns on the NLC, the ultra-thin metadevice can display any number of holograms as traditional SLM but with smaller feature size, higher resolution and wider FOV, which can be used for dynamic image display in specific places. Besides, we develop a modified Gerchberg-Saxton (GS) algorithm to realize the generation of three computer-generated holograms (CGH) with quantitative correlation based on the dynamic metadevice. Based on the new algorithm, we further propose a new optical encryption method with certain security and large information coverage. As shown in Fig. 1, there are four elements that the receiver Bob needs to decrypt the message [DANGER!] sent from Alice, namely, one unique metadevice, one set of the electrical modulation patterns as the key, one ciphertext and one ciphertext table. It should be noted that none of these four elements can be dispensed with. Meanwhile, this encryption method fully meets the requirements of the various encrypted content. We believe such metadevice may pave the way for enlightenment of a new generation of micro-optical display and optical encryption devices.

 

Fig. 1. The structure of reconfigurable metadevice and the proposed applications. The metasurface made of TiO₂ is directly embedded in the NLC. The three electrical modulation patterns A, B, C are keys to reconstruct the corresponding three basic graphs shown blow. The distribution of the NLC can be locally changed by the voltage applied in each pixel, which means more electrical modulation patterns, more reconstructed graphs. The metadevice can also be used in optical encryption, which needs one unique metadevice, one set of the electrical modulation patterns as the key, one ciphertext and one ciphertext table to decrypt. Hence, it can load arbitrary 26 letters, 10 numbers and commonly used punctuations, e.g. After using all correct decryption elements listed in the right side, Bob successfully obtained the plaintext “DANGER!” from Alice.

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2. Results and discussion

In this section, we discuss the realization of the reconfigurable metadevice, including the concrete design of the integrated metadevice, the two applications of dynamic holographic display and optical encryption. The latter is derived from the first application and based on our new holographic algorithm. We give a comprehensive explanation from the specific design parameters to the final simulation effect.

2.1. Design of the metadevice

The overall structure of the metadevice is similar to that of the traditional transmissible LC-SLM, in which the LC is sandwiched between the upper and lower substrates. The NLC molecules are initially pre-oriented along the x axis by the non-contact photo-alignment method [43], paralleling to the polarization direction of the incident light when no voltage is applied. The NLC’s type is E7 which is a kind of positive LC. When applied with voltage, it tends to rotate until the molecule’s long axis lines up with the electric field. The tilt angle depends on the value of the voltage. Unlike the LC cells of traditional SLM, there is a metasurface layer on the lower substrate, so that the subwavelength antennas directly act as the main contributor to the phase accumulation rather than the LC layer with a certain thickness. A single period of the metasurface and the metadevice is shown in Figs. 2(a)–2(c). The period is 360nm and the thickness of the LC-E7 is 1500nm. We choose the radius and the height of the TiO₂ cylindrical antennas as 135nm and 205nm, respectively. The ITO electrode layers on the upper and lower substrates can apply specific voltage value on each pixel of the metadevice so that the LC’s orientation varies locally. While due to the ultrathin thickness of ITO electrode layer, we ignored it in the simulation because we have compared the simulation results with or without ITO layer and found it does not affect the final results. We take the structure settings shown in Figs. 2(b) and 2(c) as a periodic unit in the simulation. The sweeping results of the nanoantenna’s geometric parameters are shown in Figs. 2(d) and 2(e), which are calculated when the LC orientation is 0 degree and by means of finite-difference time-domain (FDTD) method.

 

Fig. 2. Design details of the metadevice. A single period of the metasurface (a) and the metadevice (b and c). P=360nm, R=135nm, h=205nm, and the thickness of the LC-E7 is 1500nm. The cylindrical antennas arranged on the SiO₂ substrate is made of TiO₂. The LC orientation in (b) is 0 degrees and in (c) is 45 degrees, resulting in the different scattering fields ψ1 and ψ2. The sweeping transmission (d) and phase (e) results of the nanoantenna’s geometric parameters, which are calculated by means of finite-difference time-domain (FDTD) method. (f) Calculated relative phase retardation experienced by a normally incident wave passing through the unit cell of the metadevice as a function of the LC director rotation. The colorbar changes from blue to red, indicating that the angle between the LC director and the x axis changes from 0 to 90 degrees.

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The metasurface is embedded in NLC so that each nanoantenna’s surrounding refractive index changes with the LC molecules’ orientation under specific voltage values. Here, the nanoantennas act as the main contributor of phase accumulation modulate the transmitted light field into corresponding scattering fields, making it carry specific complex amplitude information. For example, as shown in Figs. 2(b) and 2(c), the x-polarized incident light is modulated to carry different complex amplitude information ψ1 and ψ2 after transmitting through two different single-period LC cells, inside which the LC orientation is 0 degree and 45 degrees, respectively. Here we swept the orientation angle q of LC from 0 to 90 degrees with an interval of 5 degrees and obtained the spectrum of the relationship between the q and the transmitted phase. As shown in Fig. 2(f), for an arbitrary orientation angle of LC, the transmitted phase can cover 2π in the spectral range of 630nm-670nm. But if the working wavelength is fixed, it is difficult to satisfy the full 2π coverage of the phase, so the LC’s orientation needs to be selected carefully in this situation. In order to simplify the design, we use the binary holographic algorithm to encode the phase so that only a pair of LC orientations need to be selected under which the transmitted amplitudes are uniform, while the phase difference is around π at a fixed wavelength. According to Figs. 2(d) and 2(f), we finally determine the working wavelength to be 665 nm and the pair of LC orientations to be 0 and 90 degrees. Moreover, the voltage control becomes more convenient because the 0 degree represents the regions without voltages and the 90 degrees represents the regions applied with the voltages that is high enough to make the LC molecules arranging along the electric field but not exceeding the breakdown voltage. Therefore, the above settings can achieve high transmittance and binary phase change for the metadevice.

2.2. Application of the dynamic holographic display

Here we adopt binary phase Gerchberg-Saxton (GS) diffraction algorithm to generate the holographic phase distribution and then reconstructed the holograms in the Fraunhofer field region. The diffraction propagation of light in the iterative process can be expressed as:

Under the working wavelength and the pair of LC’s orientation we chose in the previous section, the phase value is 1.9776 rad for 0 degrees and −2.0258 rad for 90 degrees. Note that the phase difference here is not π strictly, but close to π. We can still reconstruct the hologram well due to the strong robustness of the binary phase algorithm. Also, the binary phase algorithm can ensure the metadevice work in the broadband. It can be seen in Fig. 2(f) that if the working wavelength shifts, the phase difference under the LC orientation 0 and 90 degrees is still enough to reconstruct the hologram stably.

To further verify the feasibility of the above design method and the flexibility of two-dimensional electrical addressable modulation of such integrated metadevice, we use the GS diffraction algorithm and FDTD method to reconstruct the holograms encoded in the metadevice. Figure 3 is a set of the holographic reconstruction images, which shows the whole growth process of a plant from a seed to a flower, demonstrating that the metadevice has the same function of displaying arbitrary images as the traditional SLM. In FDTD simulations, we set the metasurface array surrounded in NLC environment. By applying the voltage according to the binary CGH, one can obtain the field distribution after near to far field propagation. The images used in the GS diffraction reconstruction algorithm and the FDTD method are both 60×60 pixels, by considering the limited calculation capacities of the full wave simulations. Note that if the number of pixels is increased, the reconstruction quality will be greatly improved.

 

Fig. 3. The application of dynamic holographic display based on the metadevice. The set of holographic reconstruction images show the whole growth process of a plant from a seed to a flower. The two rows are the corresponding far-field reconstruction results calculated by Fourier transformation and full wave simulation based on such NLC and metasurface structure array integrated metadevice, respectively. The images used in two simulation methods are both 60×60 pixels by considering the calculation capacity.

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Overall, for the application of dynamic holographic display, we firstly apply the Huygens ‘s metasurface [44] made of low-loss dielectric material to achieve higher efficiency in visible band. Second, for achieving larger resolution, the size of a pixel in the metasurface is usually minimized to accommodate as more pixels as possible in a region with a fixed area. Downsizing the pixel size for traditional LC-SLM can increase the angle of FOV, however, it will cause mutual crosstalk due to near field coupling if the unit size is too small. Thus, we introduce the subwavelength-size metasurface as the main contributor of the phase accumulation to resolve the above conflict. Third, the NLC with high birefringence is the most commonly used LC display material and has been already combined with metasurfaces. Here we renew the electrical modulation patterns to two-dimensional and load more tunable holograms, achieving better performance than traditional SLMs. Such reconfigurable metadevices are promising for achieving augmented reality (AR) display or holographic animation display. Besides, it can be further proved to achieve better display quality by redesigning of the metasurface or switching to a more flexible algorithm. And it can be easier for the metadevice to integrate into the traditional optical system if combined with the existing electronic addressable silicon chips.

2.3. Application of the optical encryption

The essence of the optical encryption is coding the plaintext through the optical transformation process. The optical properties such as wavelength, focal length and the diffraction distance can be used as the multidimensional keys to the encryption system [45–51]. Several optical encryption methods based on fractional Fourier transform or joint transform correlator have been proposed. However, the existing optical encryption system still has some disadvantages in terms of its feasibility, flexibility and stability. Here a new optical encryption method is proposed on the basis of the metadevice designed above and a new algorithm which can generate three quantitatively correlated holograms. This method enhances the difficulty of the decryption, and significantly improves the capacity of the encryption. The new algorithm is also based on binary phase holography algorithm.

Figure 4 shows the flow chart of this algorithm, in which five holograms are calculated firstly, including holograms of three target images (Holo A, Holo B, Holo C) and holograms of two blank scatter images (G1 and G2). The Holo A has already carried partial information of Holo B and Holo C. In the intermediate process, the neutralization in step 1 and step 3 are increasing or decreasing phase information of the two initial holograms within a controllable ratio and to get Holo A1, mask 1, and Holo B2, mask 2, respectively. In step 2 and step 4, Holo B and Holo C are superposed with the mask 1 and mask 2 to perform a bitwise AND operation between them, in order to obtain a subset pattern of the masks, then we get Holo B1 and Holo C1 as the preliminary hologram for the third correlation with Holo C and for the step 5, respectively. Step 5 is the final neutralization, after this step, three desired binary phase holograms with quantitative correlation can be obtained. The quantitative correlation means the phase distributions of these three holograms satisfy A${\supseteq} $B${\supseteq} $C mathematically, that is, they have the inclusion relation between each other mathematically. In fact, these three holograms directly determine the electrical modulation patterns shown in Fig. 5(a) while our integrated metadevice can easily realize this kind of gradual increment of the electrical modulation area. As shown in Figs. 5(a) and 5(b), electrical modulation pattern C has the least number of electrical pixels and can reconstruct the basic graph 3 correspondingly. If added new electrical pixels on the basis of C, the electrical modulation pattern will switch to B and generate the corresponding reconstruction graph, namely, the basic graph 2. If we keep adding other new electrical pixels, similarly, it will switch to pattern A and reconstruct basic graph 1. Due to the redundancy of hologram, that is, the hologram usually shows good robustness toward added or diminished phase and amplitude noise. Thus, Holo An, Holo Bn, Holo Cn can also reconstruct clear holographic image the same as Holo A, Holo B, Holo C.

 

Fig. 4. Flowchart to generate three binary phase holograms with quantitative correlation. Holo A, Holo B and Holo C represent the holograms of three target images, namely, the three basic graphs’ holograms. G1 and G2 represent holograms of two blank scatter images that cannot distinguished. Holo An, Holo Bn and Holo Cn represent the three desired holograms, which determines the three binary hologram patterns.

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Fig. 5. The application of the optical encryption. (a) Three electrical modulation patterns calculated by the new binary algorithm with quantitative correlation. From electrical modulation pattern A to C, the electrical pixels become less, which satisfy A${\supseteq} $B${\supseteq} $C mathematically. (b) Three reconstructed basic graphs under different electrical modulation patterns generated by commercial transmissive SLM. (c) The possible combinations of the basic graphs. ‘1’ represents selected, ‘0’ represents not selected. (d) Ciphertext table for decryption. It contains 26 letters, 10 numbers and commonly used punctuations at the same time. (e) Examples of the ciphertext ‘BIT 80’, ‘MISS U!’ and ‘AGE: 24’.

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We use these three electrical modulation patterns as the key needed for the first step in decryption. If all the electrical modulation patterns are correctly obtained, three corresponding basic graphs can be reconstructed in turn. The basic graphs in Fig. 5(b) are obtained by the commercial transmissive SLM by loading the corresponding phase distribution on it. This is to show that the three phases calculated by the quantitatively correlated algorithm can successfully reconstruct the corresponding three basic graphs with high quality. Here, the three basic graphs can be combined in any pair to produce a new pattern for subsequent decryption. The idea of this design is inspired by the braille and Morse code. Hence, the three basic graphs act as the basic symbols as that mentioned in the two methods above and their possible combinations are listed in Fig. 5(c). Using the combinations of the three basic graphs helps to increase the difficulty of the decryption and provide more possibilities for encryption. Besides, at the key setting stage, we can also use the newly added electrical positions compared to the other electrical modulation patterns as the key, rather than all the electrical modulation positions.

Then, the receiver needs to use the ciphertext from Alice. The ciphertext should be deciphered in eight-bit intervals and every eight bits represent one letter, one number or one punctuation of the plaintext and it can be further separated into three parts where each part only consists of the number 0 and 1 (0 stands for non-selected and 1 stands for selected). The first part contains 3 bits where each bit represents with or without the corresponding basic graph 1, 2, and 3. For example, 110 represents the superposition result of basic graph 1 and 2; and 001 represents only the basic graph 3 itself. More examples can be seen in Figs. 5(a)–5(c). After such a combination, the derived images all have two columns, as shown in Fig. 5(c). Then we defined that the second part contains 2 bits where contains three cases of 10,01 and 00, representing the left column is selected, the right column is selected or no selected column, respectively. The third part contains 3 bits where each bit represents the corresponding symbol listed in a box of the ciphertext table. For instance, in the box located in row 2 and column 2, 010 represents the letter Q and 001 represents the letter R. Therefore, the length of the ciphertext depends on the amount of information in the plaintext. After decrypting all 8-bit intervals of the ciphertext with the help of the ciphertext table, the receiver Bob can finally obtain the information [DANGER!] sent from Alice.

It should also be emphasized that our encrypted content can cover a wide range, including 26 English letters, 10 numbers and commonly used punctuations such as’ space’, ‘comma’ and ‘period’, which are sufficient to express the information of the plaintext. Figure 5(e) shows three examples of the ciphertext (‘BIT 80’, ‘NICE!’, ‘AGE: 24’), in which the third example contains letters, numbers and punctuation simultaneously. It should be noted that all of the decryption processes above are carried out under the condition that the receiver has obtained the particular metadevice, the ciphertext, the ciphertext table, and used the correct electrical modulation patterns to reconstruct the three basic graphs. None of these four elements can be dispensed with if the receiver wants to decrypt successfully. In addition, if Alice is aware in advance that the encryption information is leaked halfway or the metadevice is stolen, she can use the metadevice’s dynamic characteristics as mentioned in the first application to renew the three basic graphs through adjusting their sizes or altering their reconstruction orders to obtain completely different corresponding electrical modulation patterns. This approach can make the encryption truncated and reset in the start stage.

2.4. Discussion

Here we discuss the working principle of such metadevice, as shown in Fig. 6. The electric field can be controlled, pixel by pixel, through two addressable ITO subplates and a digital video interface (DVI) signal via a personal computer (PC), resulting in the locally modulation of the orientation angle of LC molecules and the environmental refractive index around nanoantennas. The alignment of the LC orientation can be controlled by applying the electrical field. The biggest challenge of the metadevice mainly comes from the tiny unit cells of the metasurface. However, our proposed idea can be realized by developing the electrode processing in nanoscale, as well as by expanding the super-pixel to adapt to the mature circuit technique. For example, we can contain 10×10 nanoantennas within each super-pixel, with the lattice constant of 3.6 µm. The size of such super-pixel is comparable to commertial SLM (HOLOEYE GAEA-2, with pixel size of 3.74 µm). While the metasurface can work as the main contributor to the phase modulation, which can significantly reduce the thickness of the device. The metadevice is used to realize holographic display in the two applications demonstrated above. Such metadevice can increase the security because it has the uniqueness of antenna arrays, which makes it difficult to duplicate. And it can function as an indispensable part for encryption. Such metadevice can add great flexibilities for various reconfigurable photonics.

 

Fig. 6. The schematic diagram of LC metadevice’s working principle.

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3. Methods

Numerical simulation. Numerical simulations were done by using a finite-difference time-domain (FDTD) based commercial solver, Lumerical Inc. In the simulations, we consider one single unit-cell containing a disk of TiO₂ and applied periodic boundary conditions. The lattice size is P = 360 nm in both the x- and y-directions. The top and bottom glasses were modelled as semi-infinite media and the ITO layer was ignored in the simulations. The E7 LC was modelled as an anisotropic medium with the material parameters taken from the Ref. [41]. The thickness of LC layer is fixed as 1500nm. The LC orientation is defined by the in-plane azimuthal angle φ and the polar angle θ, where θ = 90° represents the case without voltage and θ = 0°represents the case when the LC is fully switched by the external voltage. By using anisotropic materials to describe the birefringent properties of the liquid crystal as well as the orientation angle, one can set the background index accordingly. The refractive index of each pixel needs to be modeled according to the spatially variant orientation of LC. That is, we modify the permittivity tensor through multiplying the rotation matrix to the original diagonal matrix according to the corresponding LC orientation angle. Afterwards, the amplitude and phase information of antennas embedded in LC can be retrieved through full wave simulation.

4. Conclusion

In summary, we improve the existing electrically addressing SLM and propose a new reconfigurable metadevice by directly embedding the metasurface into the NLC layer and combining with the binary holographic algorithm. We discuss the whole process of the design and demonstrate two applications of dynamic holographic display and optical encryption based on this metadevice. The first application possesses the spatial modulation functionality as existing commercial SLM but has the advantages of smaller size, higher resolution, and larger FOV. The second application is based on the CGH algorithm with quantitative correlation. By using the unique metadevice, one set of electrical modulation patterns as the key, one ciphertext and one ciphertext table, the receiver can successfully decrypt and get the plaintext. This encryption method can load 26 letters, 10 numbers and commonly used punctuations simultaneously, fully meeting the requirements of the various encrypted content. We expect that by combining with the mature silicon-based processing technology, such metadevices can be practically applied for the next generation of micro-optical display and optical encryption. It also paves the way for the combination of the metasurface and the conventional optical elements.