1. Introduction

Metasurfaces are two-dimensional (2D) artificial nanostructures composed of metal or dielectric resonators at subwavelength scale with spatially varying phase response [1–3], which offer an unusual way to realize anomalous light propagation of abrupt phase changes instead of gradual phase shifts in conventional optical components. The advantage of flexible control propagation parameters (such as amplitude, phase and polarization) of incident beam through a thin monolayer of array provides a versatile platform to implement information encoding and optical encryption [4–6]. Different from metasurface composed of metal nanopillars with great ohmic loss, dielectric metasurface supports the broader spectral response with the high diffraction efficiency and low crosstalk in visible spectrum [7], which has been used to realize phase-encoding information authentication [8], polarization-multiplexed encryption [9], polarization and wavelength multi-channel metasurface to construct multiplex target information [10]. In addition, the nonlinear plasmonic metasurface also has been used in the information encryption [1]. The metrics of easy-tuning, high diffraction efficiency and low loss make dielectric metasurface holograms the promising candidates for the information encoding technology.

One of the most intriguing applications for metasurfaces is information encryption [11,12], which can be designed to form an unrecognizable but authenticable holographic images as the security keys to make the secret information more difficult to be attacked. Compared with other encryption methods, the visual cryptography [13,14] provides an effective and simple way to realize encryption, in which the secret (target) image is randomly expanded into a set of encrypted visual keys (VKs) by the pixel expansion rule [11] and can be decrypted directly by superimposing all VKs without any cryptographic computations, different from the complex and bulky holographic exposure facilities in traditional optical VC process [15]. In this work, we proposed a new encryption scheme integrating the VC encryption and holography with the phase-encoding technique [16] for all-dielectric metasurface to realize image hiding. The structural parameters of metasurface unit-cells were derived by the Finite-Difference Time-Domain (FDTD) simulation software to enable 0∼2π phase modulation. This metasurface holograms inherited from the VC and phase-encoding technique provide a more secure and effective way to implement image hiding.

2. Encryption principle

The process of image encryption includes three steps as shown in Fig. 1: visual cryptography, phase hiding and imprinting metasurface. First, the target image is encoded into a set of random pure-amplitude binary ciphertext keys; then the random-like pure-amplitude keys are transformed to random phase-only keys; finally, the calculated phase maps are imprinted onto the metasurfaces to get a group of unrecognized and unrelated meta-holograms.

 

Fig. 1 Schematic for image hiding process.

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The target image of “META” as Fig. 2(f) shows is converted into 30 × 30 binary distributions by pixel expansion according to the regular VC algorithm. The simplest 2 × 2 conditions with four possible choices are shown in Fig. 2(a). Each pixel is expanded randomly according to the expansion schemes illustrated in Fig. 2(b), with white pixel converted into two identical shared VKs, while black pixel converted into two complementary shared VKs. Because the selected expansion scheme of each pixel is random and independent, the secret image is transformed into two unrelated VKs with mosaic-like grayscale distributions as shown in Figs. 2(c) and 2(d) to ensure the hidden image unrecognized. When the shared pure-amplitude VKs are superimposed and aligned with each other, as shown in Fig. 2(e), the secret message can be extracted and identified directly by the human visual system. However, the small diffraction angles of pure-amplitude VKs may weaken the resistance for occlusion attack.

 

Fig. 2 VC encryption principle: (a) four possible expansions; (b) different expanded pixel pairs for white and black pixels; c) encoded VK1 and (d)VK2; (e) recovered image; (f) target image.

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Optical holography technique provides a way to convert the visible pure-amplitude image to the invisible phase-only image which greatly improves the VC security. In this work the typical Gerchberg-Saxton (GS) algorithm [17] with iteration loops of Fourier transformation is employed to transform the two pure-amplitude VKs to the digital phase-only Fourier holograms (POFHs) without any clues of pure-amplitude VKs. According to the Bragg diffraction law, as the lights illuminating on the POFHs satisfy some preconcerted conditions, such as interference angle, wavelength and polarization, the pure-amplitude VKs can be recovered, which means the more factors can be considered as the new keys to further enhance the system security. All the above image hiding procedures are calculated numerically by combining the computer technology and holography.

3. Phase-encoding technique of metasurface

The generated POFH maps hiding the secret image are composed of continuous phase information from 0 to 2π. In order to imprint the POFH maps on the metasurfaces, the discrete phases should be designed properly according to the phase-encoding technique to alleviate the fabrication complexity of metasurface holograms and guarantee their recoverability simultaneously. Titanium dioxide (TiO₂) cylinders are chosen as the unit elements due to its low absorption loss and high-efficiency transmission for visible spectrum. The metasurface is a monolayer of array composed of TiO₂ cylinders with different radii and the same height of h = 600nm, resting on the silicon dioxide (SiO₂) substrate with the thickness of t = 100nm. The inset of Fig. 3(a) gives the square unit-cell with a cylinder at the center with the unit constant of p = 200 nm. Under the illumination of normally incident light at 632.8 nm, strong Mie-type electric and magnetic dipole resonances [18] are excited and confined in the nanopillars with the negligible coupled resonance between the adjacent unit-cells. The excited phase shift depends on the radius of TiO₂ cylinder and the wavelength. Each unit-cell can be regarded as a pixel and impose a constant phase shift on the transmitted wave. FDTD software has been used to derive the cylinder radii r of unit-cells to enable the 0∼2π continuous phase modulations. Considering the diffraction efficiency and fabrication complexity, the optimal design of metasurface consists of eight gradient unit-cells respectively corresponding to r = 20, 42, 58, 65, 74, 82, 88 and 95 nm with an increment of π/4 to cover the phase shift from 0 to 2π. Figure 3(a) gives the simulation results of normalized transmittances and phases as a function of cylnder radius with the uniform phase variation from 0 to 2π as well as the high transmittances about 90%.

 

Fig. 3 (a) Transmittance and phase shift vs. radius of TiO2 nanopillar. (b) Super-cell and corresponding phase shift. (c) Spatial phase distribution in the x-z profile. (d) Phase shift vs. radius r from 20 nm to 95 nm covering the wavelength from 620nm to 680nm.

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Figure 3(b) shows a super-cell composed of eight gradient unit-cells with different radii to cover the phase shift from 0 to 2π with the increment of π/4, whose phase gradient along the x-axis is expressed as (∇ϕ)_x = 2π/T with the period of T = 1600nm, keeping with the tangential wavevector component of k_x = (∇ϕ)_x. When the beam normally incidents on the x-y plane of the super-cell at the wavelength of 632.8 nm, according to the generalized Huygens principle [19], the transmitted beam is modulated by the multi-resonance of the gradient unit-cells to radiate at an emergent angle of θ_t = arcsin(k_x/k₀) = 23.3°, where k₀ denotes the wavevector in air. The phase distribution in the transmission space of x-z plane is simulated and shown in Fig. 3(c) with an emergent angle of 23.21° agreeing well with the theoretical result, which demonstrates the predefined eight unit-cells are definitely qualified for the accurate phase control. Different from the broad band requirement of general meta-hologram for imaging with high tolerance and practicality [20,21], the optical encryption system prefers a narrowband response for the security reason. In Fig. 3(d), the phase shift of the super-cell covering from 0 to 2π can be achieved within a relative narrower band from 620nm to 680nm [18,22], which offers an appropriate flexibility and guarantee the security of encryption system simultaneously. The simulation results demonstrate the design of eight unit-cells is suitable to imprint the POFH maps on the metasurfaces to obtain two unrelated and invisible TiO₂-based mete-holograms as the shared phase-only VK1 and VK2 images with a high security.

4. Decryption

The optical extraction system for the decryption of hidden image is shown in Fig. 4(a). Two collimated incoherent laser beams are used to normally illuminate on the two mete-holograms at the wavelength of 632.8nm to avoid the interference between them, which may disturb the decryption quality. The diffractive beams carrying modulated phase information pass through the Fourier lens and image on the back focal planes. Through the Fourier transform, the invisible phase-only keys are recovered to pure-amplitude VK-patterns just like the original pure-amplitude VK₁ and VK₂. When all extracted diffraction patterns are superimposed and aligned with each other by a beam splitter, the extracted secret information “META” can be identified directly by human visual system without any additional decryption computation.

 

Fig. 4 (a) Optical setup for the VC decryption. (b) Schematic diagram of meta-hologramic imaging; (c) Recovered pure-amplitude VKs and extracted secret image.

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Due to the microstructure of meta-hologram with the dimension of 120μm × 120μm, so long as the image plane is placed few centimeters behind the meta-holograms, the condition of far-field diffraction can be satisfied, the hidden pure-amplitude VK images can be recovered easily as shown in Fig. 4(b). Indeed, the decrypted images can be magnified by increasing the imaging distance from the meta-holograms to 1m or farther. Notably, the meta-holograms composed of circle cylinders are polarization insensitive. Figure 4(c) shows the extracted pure-amplitude VK patterns in the case of y-polarized illuminations which coincide with the calculated VKs shown in Figs. 2(c) and 2(d), which keep identical for different polarization directions. By superimposing and aligning them, the hidden secret image is decrypted even with some random-like spotted noise on it due to the phase discreteness. The contrasts of the decrypted image are still high enough for us to recognize the secret image clearly without any lens or other optical components.

The proposed metasurface-based image hiding method integrate the advantage of phase-encoding technique with the classical visual cryptography. The image fidelity and diffraction efficiency of decrypted image can be further improved by increasing the steps of phase discrete and reducing the pixel dimension. However, considering the improvements are asymptotic [23] and become negligible after some phase steps, eight phase degrees are enough to satisfy the requirement of VC encryption. Due to the high transmittance property of TiO₂ for visible spectrum, as shown in Fig. 5(a), a high transmittance of 90% can be achieved in a wide wavelength band, which ensures the decryption quality of the secret image. Compared with the broad band spanning at least several hundred nanometers of common meta-holograms for imaging, the span from 620nm to 680nm can offer an appropriate flexibility and guarantee the security of VC system simultaneously. Since eight nanopillar unit-cells can keep covering the phase shift of 0~2π perfectly within the 60nm span as shown in Fig. 3(d), even if the wavelength deviates from the optimum wavelength of 632.8nm to 650nm, the positive decryption result can still be extracted clearly, as shown in Fig. 5(c). As the contrast, the negative results of extracted secret images at 600nm and 700nm are shown in Figs. 5(b) and 5(d). Because the excited discrete phase shifts cannot cover 0~2π equably and completely out of the 60nm wavelength span, the POFH maps contain all phase information cannot be imprinted on the meta-holograms precisely which lead to the dramatic decrease of decryption quality.

 

Fig. 5 (a) Transmission of TiO₂ meta-holograms over a wide band. The extracted secret images at different wavelengths of (b) 600nm, (c) 650nm, and (d) 700nm.

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In the decryption procedure, the polarization-independent meta-holograms composed of dielectric circle cylinders do not need polarizer or other polarization devices to excite holographic images. In fact, the polarization can also serve as a new key to improve the security of optical encryption system by using the polarization-sensitive asymmetric unit-cells, such as ellipse, rectangular, L-shaped, V-shaped nanopillars. The resonant polarizations of exposure lights can be modulated by rotating the asymmetric orientations of nanopillars on the meta-holograms, which provide more freedom degrees to further improve the security of encryption system.

5. Conclusions

In summary, we have proposed an optical encryption scheme based on the dielectric metasurfaces integrating the Visual Cryptography with the phase-encoding technique. In the encryption process, the VC and GS algorithms are used to generate POFH maps and the phase-code technique is employed to fabricate a group of mutually-unrelated and unrecognized TiO₂-based meta-holograms according to the generated POFH maps, whose subwavelength structure makes it easy to be hidden and difficult to be damaged and counterfeited. In the decryption process, the hidden image can be decrypted readily by two incoherent laser beams normally illuminating on the dielectric meta-holograms due to the characteristics of miniature and high diffraction efficiency, instead of complicated optical implementations and any additional holography computation. The narrow coverage of working wavelength from 620nm to 680nm provides an appropriate flexibility and guarantees the system security at the same time. The research results demonstrate the advantages of this proposed VC encryption strategy based on dielectric metasuface, such as the high security, efficiency, adjustability and visuality, making it attractive for practical applications.