Terahertz metasurface polarization coding encryption method based on angular spectrum modulation

Abstract

The invention discloses a terahertz metasurface polarization coding encryption method based on angular spectrum modulation, and belongs to the technical field of information encryption. In the encryption method, to-be-encrypted information is mapped to an optical transfer function of a metasurface, so that an angular spectrum of an input plaintext image is modulated under specific linearly polarized light, and then a ciphertext image is generated through inverse Fourier transform. During decryption, Fourier transform is carried out on a ciphertext image obtained under a correct polarization condition, and information is recovered through angular spectrum difference analysis. According to the method, an optical 4f system can be used as a framework, a terahertz metasurface composed of rotating rectangular hole structure units is used as an angular spectrum modulator, and 2-bit information coding is achieved through different arrangement strategies of the metasurface. According to the method, a direct mapping strategy is adopted, the method does not need to depend on a complex iterative optimization algorithm like traditional metasurface holography, the design process is simplified, decoupling of encrypted data and physical hardware is achieved, and system flexibility and digital compatibility are improved. Meanwhile, the method is combined with a specific polarization observation and coding mechanism, so that the information security is further enhanced. The invention provides an effective solution for information encryption and anti-counterfeiting of the terahertz wave band.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of information encryption, and particularly relates to a terahertz super surface polarization encoding encryption method based on angular spectrum modulation. BACKGROUND

[0002] The rapid popularization of information technology and the Internet has brought severe challenges to data security. Therefore, it is particularly urgent to develop encryption technology that can resist malicious attacks and has tamper-proofing capability. Traditional encryption schemes mainly rely on electronic signal processing technology, but its performance is severely restricted by two aspects: one is the inherent speed bottleneck of von Neumann architecture, and the other is the large amount of Joule heat generated in the process of electronic signal processing. Therefore, optical encryption has become a promising solution with its inherent parallelism and ultra-high-speed computing capability, and has attracted widespread attention from researchers.

[0003] Since Refregier and Javidi proposed the pioneering double random phase encoding technology in 1995, optical encryption has attracted much attention. Subsequently, in order to improve security and flexibility, researchers have extended this architecture to the fractional Fourier domain and the Fresnel domain. However, these traditional implementations mainly rely on bulky optical elements such as spatial light modulators (SLMs), lenses and prisms. In view of the growing demand for system miniaturization and integration, this encryption scheme based on bulky optical elements is becoming unsuitable.

[0004] Super surface is a two-dimensional planar structure with special electromagnetic response designed artificially, which can precisely manipulate wavefront at subwavelength scale. After successfully realizing holographic imaging, vortex light generation and superlens, super surface has developed into a highly potential multifunctional platform in the field of optical encryption. In recent years, super surface-based optical encryption schemes have emerged. These schemes use the multi-degree-of-freedom characteristics of electromagnetic waves, such as amplitude, phase, polarization, orbital angular momentum and their combinations, to realize information encryption. In addition to using a single super surface, researchers have also adopted a cascaded super surface architecture; in such a system, information can only be recovered when all super surfaces are combined in the correct way, thereby enhancing the security and anti-cracking ability of the system.

[0005] Although significant progress has been made in super surface-based encryption technology, there are still three key problems to be solved. First, in most existing schemes, the encrypted information is inherently bound to the physical structure of the super surface. Without the super surface, decryption cannot be performed; while this helps to improve security, it also severely restricts information sharing. Second, although the degrees of freedom such as polarization and wavelength have been fully utilized, encryption design mainly focuses on the spatial domain, and exploration of the angular spectrum domain is still insufficient. Finally, most of the super surfaces reported so far work in the visible or near-infrared waveband, while research in the terahertz (THz) waveband is relatively scarce. SUMMARY

[0006] In order to overcome these limitations, the present application proposes a terahertz super surface polarization encoding encryption method based on angular spectrum modulation, which aims to realize an information encryption scheme with high security, good flexibility, compatibility with digital systems, and suitable for terahertz band.

[0007] The terahertz super surface polarization encoding encryption method based on angular spectrum modulation proposed by the present application includes two processes of information encryption and decryption. In the encryption process, the information to be encrypted is mapped to an optical transfer function realized by a super surface. In the terahertz band, a linearly polarized light in a specific direction is used to irradiate an object to obtain a plaintext image as an information carrier. After the image is Fourier transformed into the angular spectrum domain, it is modulated by the super surface with a specific optical transfer function, and then inverse Fourier transformed to output a ciphertext image carrying encrypted information. In the decryption process, the received ciphertext image is Fourier transformed to obtain its angular spectrum, which is compared and analyzed with the angular spectrum of the original plaintext image, and according to the pre-established mapping rule, the hidden encrypted information can be decoded.

[0008] Unlike traditional direct modulation in the spatial domain, the present application shifts the encryption operation to the angular spectrum domain of the image. The angular spectrum G(u,v) of the image g(x,y) is defined by its two-dimensional Fourier transform as follows:

[0009]

[0010] In the formula, j represents the imaginary unit, and (u,v) is the spatial frequency coordinate.

[0011] The key of the encryption method is to construct an optical transfer function h(u,v) corresponding to the information to be encrypted, and the function is physically realized by a super surface. The principle of realizing encryption in the image angular spectrum domain is as follows:

[0012]

[0013] wherein, and denote the Fourier transform and inverse Fourier transform, g P (x,y) represents the plaintext image used to carry information, g C (x,y) represents the ciphertext image that has completed angular spectrum modulation, i.e., information encryption, h(u,v) is an optical transfer function constructed by a super surface in the angular spectrum domain. The information to be encrypted is directly represented by the super surface in the form of the optical transfer function, and then transferred to the angular spectrum modulation process of the optical image.

[0014] Therefore, it is almost impossible to retrieve information by only observing the encrypted image, and only by correctly processing and analyzing the angular spectrum of the encrypted image, the correct encrypted information can be decoded.

[0015] The encoding process of the encryption method is realized by different arrangement strategies of the super surface physical design. The core is to map different encrypted information into different optical transfer functions determined by the super surface structure. Specifically, by changing the distribution of the unit structure on the two-dimensional plane, the response of the super surface to the incident terahertz wave in the angular spectrum domain can be accurately controlled, thereby constructing the optical transfer function corresponding to different transmission information, thereby completing the encoding of information to physical structure.

[0016] In the encryption process, when the polarization direction of the electromagnetic wave and the preset polarization direction have an included angle, an incorrect ciphertext image will be obtained, which will also prevent the receiver from decrypting the correct information.

[0017] The information decryption process includes two key steps of comparison and analysis and decoding. Firstly, the angular spectrum intensity difference between the plaintext image and the ciphertext image is calculated, and the function relationship of the average angular spectrum intensity difference with the spatial frequency is analyzed. Finally, the encrypted information decoding is based on the predetermined mapping rule, that is, different encrypted information corresponds to different angular spectrum difference distribution characteristics.

[0018] The beneficial technical effects of the present application are:

[0019] The present application provides a terahertz super surface polarization encoding encryption method based on angular spectrum modulation. The method takes the angular spectrum domain as the core encryption channel, maps the encrypted information directly to the optical transfer function of the super surface, and sets a specific polarization direction as a necessary condition for encryption, so that the correct information cannot be decoded when the encrypted image is analyzed from the spatial domain, the angular spectrum or the polarization state is incorrect, forming a double security barrier of "angular spectrum domain + polarization". The method realizes the decoupling of encrypted information and super surface physical hardware, so that the encrypted information can be flexibly transmitted, shared and processed. On this basis, the encryption scheme is extended to the terahertz wave band, which has the advantages of high speed and large bandwidth of photonics and strong penetration of electronics. Moreover, since the encrypted information can be directly mapped to the super surface, the complex iterative optimization algorithm required in traditional computer holography or super surface holography is avoided, greatly simplifying the design process of the super surface. Therefore, the method provides a new solution for the field of secure communication, anti-counterfeiting and other related fields in the terahertz wave band, which has high security, high flexibility and strong compatibility. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 It is a whole flow chart of the terahertz super surface polarization encoding encryption method based on angular spectrum modulation proposed by the present application.

[0021] Figure 2 is a schematic diagram of a rectangular hole unit structure etched on a molybdenum plate with a thickness of 100 μm, which is employed in an embodiment of the present application.

[0022] Figure 3 is a schematic diagram of a partitioned aperiodic metasurface arrangement, which is employed in an embodiment of the present application.

[0023] Figure 4 is a schematic diagram of three different arrangement strategies of metasurfaces prepared on a molybdenum sheet by laser etching, plus one without a metasurface, which can constitute a 2-bit code in an embodiment of the present application.

[0024] Figure 5 is an analog and experimental result of encryption under a correct polarization according to an embodiment of the present application. Each row corresponds to a specific information, and from top to bottom, they represent "00", "01", "10" and "11", respectively. Columns 1, 3 and 5 show simulated ciphertext images, angular spectra and angular spectrum differences, respectively. Correspondingly, columns 2, 4 and 6 show experimental test results.

[0025] Figure 6 is an intensity distribution of angular spectrum differences of different information under a correct polarization channel according to an embodiment of the present application. Sim. and Exp. represent simulation and experimental results, respectively. For example, the legend "Exp. 10" represents the experimental test intensity curve of information "10".

[0026] Figure 7 is an analog and experimental encryption result of ciphertext, ciphertext angular spectrum and angular spectrum difference of information "01" under different polarization deviation angles β according to an embodiment of the present application. DETAILED DESCRIPTION

[0027] The present application will be described in detail below with reference to the embodiments and drawings, and it should be understood that the following embodiments are only to enable those skilled in the art to better understand and implement the present application, and do not limit the scope of the present application in any way.

[0028] The present application proposes a terahertz metasurface polarization encoding encryption method based on angular spectrum modulation, as shown in Figure 1 , which includes two processes of information encryption and decryption. In the encryption process, the information to be encrypted is mapped to an optical transfer function realized by a metasurface. In the terahertz waveband, a linearly polarized light in a specific direction is used to irradiate an object to obtain a plaintext image as an information carrier. After the image is Fourier transformed into the angular spectrum domain, it is modulated by the metasurface, and then inverse Fourier transformed to output a ciphertext image carrying encrypted information. In the decryption process, the angular spectrum of the ciphertext image obtained under the correct polarization condition is obtained by Fourier transform, and then compared and analyzed with the angular spectrum of the original plaintext image. According to the pre-established mapping rule, the hidden encrypted information can be decoded.

[0029] Different from the traditional spatial domain direct modulation, the present application transfers the encryption operation to the angular spectrum domain of the image. The angular spectrum G(u,v) of the image g(x,y) is defined by its two-dimensional Fourier transform as:

[0030]

[0031] In the formula, j represents the imaginary unit, and (u,v) is the spatial frequency coordinate.

[0032] The key of the encryption method is to construct an optical transfer function h(u,v) corresponding to the information to be encrypted uniquely, and the function is physically realized by the metasurface. The principle of realizing encryption in the angular spectrum domain of the image is as follows:

[0033]

[0034] Wherein, and represent the Fourier transform and inverse Fourier transform, g P (x,y) represents the plaintext image used to carry information, g C (x,y) represents the ciphertext image which has completed angular spectrum modulation, i.e., information encryption, h(u,v) is the optical transfer function constructed by the metasurface in the angular spectrum domain. The information to be encrypted is directly represented by the metasurface in the form of the optical transfer function, and then transferred to the angular spectrum modulation process of the optical image.

[0035] Therefore, it is almost impossible to retrieve the information by observing the encrypted image, and only by correctly processing and analyzing the angular spectrum of the encrypted image, the correct encrypted information can be decoded.

[0036] In the embodiment, to realize the encryption method, first, the information to be encrypted is 2-bit coded, i.e., “00”, “01”, “10” and “11”. Then the four different information to be encrypted is mapped to the metasurfaces with different optical transfer functions.

[0037] As a preferred embodiment of the present application, the unit structure of the metasurface is selected as a rectangular hole structure etched on a molybdenum plate with a thickness of 100 μm, the unit period P = 250 μm, the rectangular hole length a = 215 μm, the rectangular hole width b = 50 μm, and the thickness t = 100 μm, as shown in Figure 2 The metasurface can realize the above-mentioned coding by using a partitioned aperiodic arrangement structure. As shown in Figure 3 The entire metasurface is divided into a central circular region with a radius R1 and a peripheral annular region with an inner diameter R1 and an outer diameter R2, and the long axis orientations of the rectangular hole structure units in the two regions are orthogonal to each other.

[0038] According to waveguide theory, when the polarization direction of an electromagnetic wave is perpendicular to a and the wavelength is between a and 2a, the electromagnetic wave can pass through a rectangular aperture.

[0039] According to Malus's law, horizontally polarized electromagnetic waves pass through... Figure 2 When the metasurface is composed of a single-unit structure, the relationship between the transmission intensity of the common-polarized wave and the deflection angle θ is as follows:

[0040] I = I0sin 2 (θ)

[0041] In the formula, I0 represents the intensity of the incident electromagnetic wave. Therefore, by adjusting the angle θ between a and the polarization of the electromagnetic wave, the intensity of the transmitted electromagnetic wave can be flexibly adjusted. Thus, by arranging elements with different θ in the plane as needed, a specific h(u,v) can be achieved.

[0042] In this embodiment, unit structures with θ = 0° and 90° are selected for the central circular region and the outer annular region of the metasurface, respectively. Then, by changing the radius R1 of the central circular region, the optical transfer function h(u,v) of the entire metasurface is changed. Three metasurfaces, MS1, MS2, and MS3, are fabricated, each corresponding to a different h(u,v). All three metasurfaces have the same R2 = 25 mm, and R1s of 2.5 mm, 5 mm, and 7.5 mm, respectively. Figure 4 As shown.

[0043] Assuming the angle between the polarization direction of a linearly polarized electromagnetic wave and the horizontal direction is α, then the OTF applied to the metasurface... h (u,v) are as follows:

[0044]

[0045] It should be noted that the above-described orthogonal partitioning structure is merely one example of achieving the purpose of this invention.

[0046] In this embodiment, three metasurfaces are prepared to correspond to the information "01", "10", and "11" respectively. When the metasurface is not used to modulate the angular spectrum, it corresponds to the information "00", such as... Figure 4 As shown.

[0047] During encryption, the ciphertext image is obtained using the angular spectrum of the metasurface modulation image. The message "00" does not use metasurface modulation, so its ciphertext image is the same as its plaintext image.

[0048] The information decryption process includes two key steps: comparative analysis and decoding. The first step is to calculate the difference in angular spectral intensity between the plaintext image and the ciphertext image. The final decoding of the encrypted information is based on a predetermined mapping rule, that is, different encrypted information uniquely corresponds to different angular spectral difference characteristics.

[0049] The technical effects of the present invention were further verified through simulation and testing.

[0050] Figure 5 The ciphertext image obtained under the correct polarization channel, the corresponding angular spectrum, and the angular spectrum difference are shown. The angular spectrum difference is the difference between the angular spectrum intensity of the ciphertext image and the plaintext image. Figure 5 Each row in the figure represents different information, namely 00, 01, 10, and 11 as indicated in the leftmost column of the figure. Among them, columns 1, 3, and 5 represent the simulated ciphertext image, angular spectrum, and angular spectrum difference, respectively, while columns 2, 4, and 6 represent the actual tested ciphertext image, the angular spectrum obtained by Fourier transforming the test results, and the angular spectrum difference, respectively.

[0051] Because "00" does not use metasurface modulation angular spectrum, the spectral difference is 0. Figure 5 Therefore, the encrypted ciphertext image and the plaintext image are different, but it is virtually impossible to decrypt the information directly from these differences. Similarly, it is impossible to directly decrypt the information from the image's spectrum, because the spectral intensity similarity of information is very high, such as... Figure 5 As shown in columns 3 and 4, the information can only be decrypted by subtracting the angular spectrum of the ciphertext image from that of the plaintext image.

[0052] Figure 5 Columns 5 and 6 show the angular spectral difference distribution. The angular spectral difference for "00" information is 0, while the angular spectral differences for "01", "10", and "11" information exhibit a ring-shaped band pattern. Although Figure 5 The obvious features of the information “00” and “01” can be observed, but the difference between “10” and “11” is not visually distinguishable.

[0053] further, Figure 6 Quantified from Figure 5 The average intensity of the angular spectral difference was derived, and the function of this difference intensity versus spatial frequency was plotted. As expected, the "00" case shows zero difference due to the lack of modulation. In contrast, "01", "10", and "11" share consistent spectral characteristics: a rapid rise from zero to a low-frequency main peak, followed by high-frequency oscillations. Crucially, these signals can be distinguished by their peak characteristics. As the encoded information progresses from "11" to "10" and then to "01", the peak amplitude gradually decreases, while the peak frequency increases slightly. Although there are slight differences between the simulation and experimental results, these deviations do not affect the overall decryption process. Figure 5 and Figure 6 It successfully demonstrated the mapping relationship between the encrypted information and the angular spectral difference required in the encryption and decryption process under correct polarization, which the receiver can use to decode the information.

[0054] Furthermore, during the encryption process, when the polarization direction of the electromagnetic wave and the preset polarization direction have an angle β, a correct ciphertext image cannot be obtained, causing the decryptor to be unable to decrypt the correct information. To characterize this sensitivity, Figure 7 The results of tracking the ciphertext, angular spectrum, and angular spectrum difference of the message "01" as a function of β were investigated. At the correct polarization channel, a clear spectral difference feature was observed in both simulation and experiments, i.e., β = 0°. As β increases from 0° to 90°, the ciphertext image transforms from a single hexagram into a circular Gaussian point, and the angular spectrum result also distorts accordingly. Therefore, from... Figure 7 The results confirm that only under the correct polarization channel can the correct ciphertext image be obtained, enabling effective information decryption. This strict dependence on polarization alignment significantly enhances the security of the proposed encryption scheme.

Claims

1. A terahertz metasurface polarization coding encryption method based on angular spectrum modulation, characterized in that, Includes the encryption and decryption processes: Information encryption process: In the terahertz band, after the plaintext image is Fourier transformed to the angular spectrum domain, its angular spectrum is modulated using a metasurface as a modulator under specific polarization conditions. An inverse Fourier transform is performed on the modulated angular spectrum to generate a ciphertext image carrying encrypted information. Information decryption process: Perform Fourier transform on the received ciphertext image to obtain its angular spectrum distribution; The angular spectrum of the encrypted image is compared and analyzed with the angular spectrum of the received plaintext image, and the encrypted information is decoded according to a predetermined mapping relationship.

2. The terahertz metasurface information encryption method based on angular spectrum modulation according to claim 1, characterized in that, The encryption process uses the angular spectral domain as the channel for information encryption. The encrypted information is mapped to a specific optical transfer function (OTF) implemented by the metasurface, and encryption is accomplished by applying this function to the angular spectrum of the plaintext image.

3. The metasurface as an angular spectrum modulator according to claims 1 and 2, characterized in that, By changing the arrangement of basic structural units in different metasurfaces, the modulation of the angular spectrum of the input plaintext image can be altered, enabling the metasurface to possess an optical transfer function uniquely corresponding to different encrypted information, thereby achieving information encryption.

4. The comparative analysis in the information decryption process according to claim 1, characterized in that, By calculating the angular spectral intensity difference between the plaintext and ciphertext images, the functional relationship between the mean of the angular spectral intensity difference and the spatial frequency is analyzed.

5. The information decoding according to claim 1, characterized in that, The encoding rules followed in the encryption process and the corresponding decryption mapping rules are such that different encrypted information uniquely corresponds to different angular spectral difference distribution characteristics.

6. The encryption process according to claim 1 must be performed under specific polarization conditions, characterized in that, During the encryption process, when there is an angle between the polarization direction of the electromagnetic wave and the preset polarization direction, an incorrect ciphertext image will be obtained, and the receiver will not be able to decrypt the correct information.

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