Torsional metasurface frequency reconfigurable holographic method and device based on dispersion regulation and control

Abstract

The invention provides a torsion metasurface frequency reconfigurable holographic method and device based on dispersion regulation and control, and belongs to the field of optical imaging. The problem that an existing mechanical rotary cascade metasurface mainly works at a single fixed frequency and lacks a cross-spectrum function switching capability is solved. The method comprises the following steps: constructing a cascaded double-layer metasurface system which comprises a radiation type metasurface and a pure phase metasurface; the relative torsion angle between the pure phase metasurface and the radiation type metasurface is changed by rotating the pure phase metasurface in a plane, so that the phase distribution of the pure phase metasurface interacts with the output wavefront of the radiation type metasurface; according to the dispersion characteristics of the target holographic image in the three-dimensional space position and frequency, the phase distribution of the radiation type metasurface and the pure phase metasurface is collaboratively optimized through a reverse design frame, and the dynamic switching of the holograms is realized. The method is mainly used in the fields of near-field calculation imaging / detection, high-speed large-data-capacity near-field wireless communication and the like.

Description

Technical Field

[0001] The present invention belongs to the field of optical imaging, and in particular relates to a twisted metasurface frequency reconfigurable holographic method based on dispersion control. Background Art

[0002] Holography, a technique that uses the principles of optical interference and diffraction to reconstruct three-dimensional (3D) objects, has garnered widespread attention in advanced photonics research. A significant advantage of holographic technology is the ability to flexibly manipulate the dispersion properties of the reconstructed light field. For example, near-eye display systems require the elimination of chromatic aberration to improve imaging quality, while color holographic displays require flexible control of dispersion properties to achieve dynamic spectral tuning. Traditional methods rely on cascaded optical elements (such as lenses and stacked polarizers) to achieve holographic dispersion control, but these methods typically increase structural complexity and are difficult to miniaturize in compact optoelectronic platforms.

[0003] In recent years, metasurface-based holography has emerged as a revolutionary alternative. This technique utilizes ultracompact optical elements on a two-dimensional surface to precisely manipulate electromagnetic wave properties point by point. Advances in metasurface platforms are particularly evident in their unprecedented ability to control dispersion properties. Most research focuses on eliminating the negative chromatic aberration of typical meta-atoms, employing methods such as sub-elements, staggered element arrangements, and multi-layered element structures. These techniques primarily utilize structural design and theoretical methods to construct meta-atoms with dispersion control capabilities. By constructing a library of meta-atoms with rich dispersion responses, ideal holographic dispersion control has been achieved at various frequencies. Furthermore, linear phase compensation methods are used to approximate the dispersion curve, eliminating chromatic aberration within a specific operating band, thereby improving imaging quality. Furthermore, the freedom to design the structural dispersion of subwavelength meta-atoms has enabled dispersion control at discrete wavelengths, making wavelength-multiplexed holography possible. This multidimensional multiplexing design has driven the development of a variety of emerging applications, such as full-color holography, which increases information display and storage capacity. Overall, the metasurface platform offers remarkable flexibility for holographic dispersion engineering.

[0004] Despite significant progress in recent years, holographic designs based on metasurfaces typically exhibit fixed dispersion properties. While this is beneficial for specific, single-use applications such as security surveillance, reconfigurable dispersion control is crucial for multifunctional applications such as optical encryption and dynamic displays, where greater flexibility can enhance channel capacity. Current reconfiguration strategies primarily focus on input wavefront modulation or tunable meta-atoms. The former employs spatial light modulators (SLMs) or other optical elements to achieve dynamic holographic imaging through intensity or polarization modulation. The latter utilizes dynamic materials to construct meta-atoms and implements switching functionality through external control devices. However, existing meta-devices often overlook the reconfigurability of their dispersion. This is because dispersion is related to the group delay characteristics of the meta-atom, which is typically determined by its structural design. Common building blocks, such as active components, liquid crystals, and phase-change materials, primarily control phase, amplitude, and polarization rather than dispersion properties. Therefore, achieving simple and effective reconfigurable meta-atom dispersion control remains a challenge.

[0005] Multi-layer cascaded metasurfaces, with their multi-degree-of-freedom characteristics, uniquely enable dynamic functional reconfiguration for complex operational needs. By precisely manipulating complex diffraction waves through analytical or optimization-driven design methods, this cascaded metasurface platform has become a paradigm for dynamically switching functions. As a result, key technologies, including spatial beam steering, zoom lenses, large-capacity holographic devices, dynamic polarization control / detection, and multi-task diffraction neural networks, have been gradually developed in recent years. However, existing mechanically rotating cascaded metasurfaces mainly operate at a single fixed frequency and lack the ability to switch functions across the spectrum. This limitation stems from their inherent dispersion properties, which are usually fixed during the design process. Summary of the Invention

[0006] In view of this, the present invention aims to propose a frequency reconfigurable holographic method and device for torsional metasurface based on dispersion regulation to solve the problem that the existing mechanically rotating cascaded metasurface mainly operates at a single fixed frequency and lacks the ability to switch functions across the spectrum.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a frequency reconfigurable holographic method of twisted metasurface based on dispersion control, the method comprising: Construct a cascaded dual-layer metasurface system, including a radiative metasurface RA-M and a pure phase metasurface PM; By rotating the pure phase metasurface PM in the plane, the relative twist angle α between the PM and the radiative metasurface RA-M is changed, so that the phase distribution of the pure phase metasurface PM interacts with the output wavefront of the radiative metasurface RA-M. According to the dispersion characteristics of the target holographic image at the three-dimensional spatial position z and frequency f, the phase distributions of the radiative metasurface RA-M and the pure phase metasurface PM are collaboratively optimized through an inverse design framework to achieve dynamic switching of holograms.

[0008] Furthermore, a preferred method is proposed, in which the radiative metasurface RA-M is composed of broadband radiative meta-atoms, each meta-atom includes three copper layers and two layers of F4BM-2 dielectric substrates, and the two layers of F4BM-2 dielectric substrates are located between the three copper layers; the top copper layer is a radiating patch, the bottom copper layer is a feeding structure, and the middle copper layer is a shared ground layer for the radiating patch and the feeding structure, and the top copper layer and the bottom copper layer are connected by metal vias.

[0009] Furthermore, a preferred method is proposed, in which the pure phase metasurface PM is composed of pure phase modulation meta-atoms, each meta-atom includes three copper layers and two F4BM-2 dielectric substrates, and the two F4BM-2 dielectric substrates are located between the three copper layers; the top copper layer and the bottom copper layer are respectively provided with a linear polarization LP sensitive patch and a circular polarization CP sensitive patch, which are used to receive the linear polarization LP matching incident wave through the bottom copper layer patch, and transmit energy with the help of the metal vias of the middle copper layer, and finally generate a CP matching wave from the top copper layer patch.

[0010] Furthermore, a preferred embodiment is proposed, in which the distance between the radiative metasurface RA-M and the pure phase metasurface PM is 100 mm, satisfying the following conditions: In the 12-18 GHz frequency band, it corresponds to 4-6 times the wavelength; Compute the wavefront propagation using the Rayleigh-Sommerfeld diffraction model:

[0011] in, d represents the axial propagation distance, , ( x m , y m , z m ) represents the metasurface aperture, ( x , y , z ) represents the spatial coordinate on the observation plane (or target plane), j represents the imaginary unit, defined as j²=-1, c Represents the speed of light.

[0012] Furthermore, a preferred embodiment is proposed, wherein the switching range of the relative twist angle α is 0°-180°, corresponding to different holographic states: When α=0°, the multi-frequency multiplexing holographic function is activated; When α=90°, the space-frequency multiplexing function is activated; Achromatism is activated when α=180°.

[0013] Furthermore, a preferred embodiment is proposed, wherein the reverse design framework includes: Establish the output plane electric field distribution model:

[0014] in, It means that the electromagnetic field after RA-M control propagates a specific distance in the double-layer configuration. represents the electric field after RA-M regulation, Represents the impulse response function, which represents the point ( x 0, y 0) after the unit point source propagates through the distance z, at point ( x , y ) represents the electric field after PM regulation; Minimize the loss function using the gradient descent algorithm:

[0015] in, represents the number of discrete points in the output plane, is the output intensity, is the target normalized intensity, k is a normalization factor used to balance the target field and the output field strength, and m is an index variable used to traverse all discrete points on the output plane.

[0016] Furthermore, a preferred embodiment is proposed, in which the phase distributions of the radiative metasurface RA-M and the pure phase metasurface PM satisfy the linear dispersion relation:

[0017] in, is the RA-M linear dispersion modulation factor at discrete points, is the PM linear dispersion modulation factor at discrete points, b 1 represents the intercept of the RA-M phase distribution in the frequency linear relationship, b 2 represents the intercept of PM phase distribution in the linear relationship of frequency; When implementing achromatic holography, k=0 is set to eliminate propagation dispersion.

[0018] Based on the same inventive concept, the present invention also proposes a twisted metasurface frequency reconfigurable holographic device based on dispersion control, the device comprising: Double-layer metasurface system construction unit, used to construct a cascaded double-layer metasurface system, including the radiative metasurface RA-M and the pure phase metasurface PM; A rotation unit is used to change the relative twist angle α between the phase-pure metasurface PM and the radiative metasurface RA-M by rotating the phase-pure metasurface PM in a plane, so that the phase distribution of the phase-pure metasurface PM interacts with the output wavefront of the radiative metasurface RA-M; The hologram dynamic switching unit is used to realize dynamic switching of holograms by collaboratively optimizing the phase distribution of the radiative metasurface RA-M and the pure phase metasurface PM through an inverse design framework according to the dispersion characteristics of the target holographic image at the three-dimensional spatial position z and frequency f.

[0019] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a torsional metasurface frequency reconfigurable holographic method based on dispersion control as described in any one of the above items.

[0020] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium, which stores a computer program. When the computer program is run by a processor, it executes the steps of a torsional metasurface frequency reconfigurable holographic method based on dispersion control as described above.

[0021] Compared with the prior art, the present invention has the following beneficial effects: This invention pioneers a dynamically reconfigurable dispersion framework. Through a dual-layer cascaded architecture of RA-M and PM and an in-plane rotation mechanism, three types of dispersion modes can be switched in real time simply by varying the PM twist angle α: multi-frequency multiplexing mode (when α = 0°, 13GHz / 15GHz / 17GHz holograms are simultaneously displayed in a single plane); space-frequency multiplexing mode (when α = 90°, 13GHz / 15GHz / 17GHz holograms are displayed in the z1 / z2 / z3 planes, respectively); and broadband achromatic mode (when α = 180°, single-plane imaging is maintained in the 12-18GHz frequency band). This invention overcomes the limitations of conventional metasurfaces with rigid dispersion properties, achieving for the first time dynamic switching of dispersion modes under mechanical control, with a switching response time of less than 0.5 seconds (the physical limit of the rotation mechanism) and crosstalk between modes below -15dB.

[0022] The present invention solves the problem of multi-plane dispersion compensation by accurately modeling group delay based on the DIDF framework, and realizes independent control of multiple planes within a depth range of 180mm (z=50-230mm); in the space-frequency multiplexing mode, the imaging efficiency of the z2z2=200mm plane 15GHz hologram reaches 27.8% (simulation) and 22.48% (measurement), which is 1.8 times higher than the traditional GS algorithm; it overcomes the defect that the existing mechanical rotating metasurface can only work at a single frequency, and verifies the cross-band and cross-depth holographic reconstruction capability in the microwave frequency band for the first time.

[0023] Through meta-atom integration and a feed-free architecture, this invention achieves a double-layer metasurface system with a total thickness of 105.57 mm, a volume reduction of over 90% compared to traditional cascaded optical systems. The RA-M and PM spacing is optimized to 4-6λ (100 mm), ensuring wavefront transmission accuracy while avoiding near-field coupling. In achromatic mode, the average imaging efficiency in the 12-18 GHz band reaches 16.7%, a 40% improvement over similar metasurface solutions. While maintaining millimeter-level ultra-thin properties (single-layer thickness <0.15λ), this invention resolves the conflicting relationship between broadband achromatism and miniaturization.

[0024] The present invention has applications in fields such as near-field computational imaging / detection, high-speed and large-data capacity near-field wireless communications, and switchable metadevice design. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings, which constitute part of the present invention, are provided to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are provided to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings: Figure 1 Schematic diagram of the frequency-cascaded double-layer metasurface system architecture of the present invention, wherein Rotation-driven Switching of Holograms represents rotation-driven holographic switching; Figure 2 This is the reverse design framework flow chart of the present invention, where Optimized Variables represents optimized variables, Loss Function l Represents the loss function l , Gradient Descent represents gradient descent, and UpdateParameter represents update parameter; Figure 3 Schematic diagram of constructing a corresponding super surface for the meta-atom of the present invention, wherein: Figure 3 (a) 3D exploded view of the RA-M meta-atom; Figure 3 (b) Schematic diagram of the geometric structure of the RA-M meta-atom; Figure 3 (c) The radiation amplitude of RA-M atoms changes with the length of the feed line l 1 Schematic diagram of the simulation response to the change; Figure 3 (d) is the radiation phase of RA-M atomic unit with the change of feed line length l 1 Schematic diagram of the simulation response to the change; Figure 3 (e) is a three-dimensional exploded view of the PM meta-atom; Figure (f) is a schematic diagram of the geometric structure of the PM meta-atom; Figure (g) is the transmission amplitude of the PM meta-atom with the rotation angle φ 1 schematic diagram of the simulation response of the change; Figure (h) shows the PM atomic transmission phase with the rotation angle φ 1. Simulation response of the change; Top Layer represents the top layer, Bottom Layer represents the bottom layer, Frequency represents the frequency, and Amplitude represents the amplitude; Figure 4 The RA-M and PM of the present invention are in a torsion angle α Schematic diagram of matching phase distribution at =0° (state 1), 90° (state 2) and 180° (state 3); Figure 5 Schematic diagram of the simulated intensity distribution of state 1 in the frequency range of 12-18 GHz and the focal plane of z1=150 mm according to the present invention; Figure 6 The simulated intensity distribution of state 2 in the frequency range of 12-18 GHz and the focal planes of z1 = 150 mm, z2 = 200 mm, and z3 = 250 mm according to the present invention; Figure 7 This is the simulated intensity distribution of state 3 described in the present invention in the frequency range of 12-18 GHz and the focal plane of z1=150 mm; Figure 8 Schematic diagram of experimental preparation and measurement of the layered twisted metasurface system of the present invention, wherein: Figure 8 (a) Photograph of the metadevice prototype, including: i) RA-M bottom view; ii) RA-M top view; iii) PM bottom view; iv) PM top view; v) experimental setup for near-field intensity measurement in a microwave anechoic chamber. Figure 8 (b) Schematic diagram of the measured intensity distribution of state 1 in the frequency range of 12-18 GHz and the focal plane of z1 = 150 mm; Figure 8 (c) Schematic diagram of the measured intensity distribution of state 2 in the frequency range of 12-18 GHz and the focal planes of z1 = 150 mm, z2 = 200 mm, and z3 = 250 mm; Figure 8 (d) Schematic diagram of the measured intensity distribution of state 3 in the frequency range of 12-18 GHz and the focal plane of z1=150 mm. DETAILED DESCRIPTION

[0026] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely explain the technical solutions in the embodiments of the present invention. It should be noted that the embodiments of the present invention and the features therein can be combined with each other in the absence of conflict, and the embodiments described are only part of the embodiments of the present invention, not all of the embodiments.

[0027] Embodiment 1: This embodiment describes a method for frequency reconfigurable holography of a twisted metasurface based on dispersion control, the method comprising: Construct a cascaded dual-layer metasurface system, including a radiative metasurface RA-M and a pure phase metasurface PM; By rotating the pure phase metasurface PM in the plane, the relative twist angle α between the PM and the radiative metasurface RA-M is changed, so that the phase distribution of the pure phase metasurface PM interacts with the output wavefront of the radiative metasurface RA-M. According to the dispersion characteristics of the target holographic image at the three-dimensional spatial position z and frequency f, the phase distributions of the radiative metasurface RA-M and the pure phase metasurface PM are collaboratively optimized through an inverse design framework to achieve dynamic switching of holograms.

[0028] Implementation method 2. This implementation method is a further limitation of the torsional metasurface frequency reconfigurable holographic method based on dispersion control described in implementation method 1. The radiative metasurface RA-M is composed of broadband radiative meta-atoms, each meta-atom includes three copper layers and two F4BM-2 dielectric substrates, and the two F4BM-2 dielectric substrates are located between the three copper layers; the top copper layer is a radiating patch, the bottom copper layer is a feeding structure, and the middle copper layer is a shared ground layer for the radiating patch and the feeding structure, and the top copper layer and the bottom copper layer are connected by metal vias.

[0029] Implementation method three. This implementation method is a further limitation of the torsional metasurface frequency reconfigurable holographic method based on dispersion control described in implementation method one. The pure phase metasurface PM is composed of pure phase modulation meta-atoms, each meta-atom includes three copper layers and two F4BM-2 dielectric substrates, and the two F4BM-2 dielectric substrates are located between the three copper layers; the top copper layer and the bottom copper layer are respectively provided with a linear polarization LP sensitive patch and a circular polarization CP sensitive patch, which are used to receive the linear polarization LP matching incident wave through the bottom copper layer patch, and transmit energy with the help of the metal vias in the middle copper layer, and finally generate CP matching waves from the top copper layer patch.

[0030] Implementation 4: This implementation further limits the method for frequency reconfigurable holography of a twisted metasurface based on dispersion control described in Implementation 1. The spacing between the radiative metasurface RA-M and the pure phase metasurface PM is 100 mm, satisfying the following conditions: In the 12-18 GHz frequency band, it corresponds to 4-6 times the wavelength; Compute the wavefront propagation using the Rayleigh-Sommerfeld diffraction model:

[0031] Where λ is the operating wavelength, d represents the axial propagation distance, , ( x m , y m , zm ) represents the metasurface aperture, ( x , y , z ) represents the spatial coordinates on the observation plane or target plane, f Indicates frequency, j represents the imaginary unit, defined as j² = -1, c Represents the speed of light.

[0032] Implementation 5: This implementation further limits the frequency reconfigurable holographic method of twisted metasurface based on dispersion control described in Implementation 1. The switching range of the relative twist angle α is 0°-180°, corresponding to different holographic states: When α=0°, the multi-frequency multiplexing holographic function is activated; When α=90°, the space-frequency multiplexing function is activated; Achromatism is activated when α=180°.

[0033] Implementation 6: This implementation further defines the method for frequency reconfigurable holography of a twisted metasurface based on dispersion control described in Implementation 1. The inverse design framework includes: Establish the output plane electric field distribution model:

[0034] in, It means that the electromagnetic field after RA-M control propagates a specific distance in the double-layer configuration. represents the electric field after RA-M regulation, Represents the impulse response function, which represents the point ( x 0, y 0) after the unit point source propagates through the distance z, at point ( x , y ), the complex amplitude response generated at represents the electric field after PM regulation; Minimize the loss function using the gradient descent algorithm:

[0035] in, represents the number of discrete points in the output plane, is the output intensity, is the target normalized intensity, k is a normalization factor used to balance the target field and output field strength, and m is an index variable.

[0036] Implementation 7. This implementation further defines the method for frequency reconfigurable holography of a twisted metasurface based on dispersion control described in Implementation 6. The phase distributions of the radiative metasurface RA-M and the pure phase metasurface PM satisfy the linear dispersion relation:

[0037] in, is the RA-M linear dispersion modulation factor at discrete points, is the PM linear dispersion modulation factor at discrete points, b 1 represents the intercept of the RA-M phase distribution in the frequency linear relationship, b 2 represents the intercept of PM phase distribution in the linear relationship of frequency; When implementing achromatic holography, k=0 is set to eliminate propagation dispersion.

[0038] Embodiment 8: This embodiment describes a twisted metasurface frequency reconfigurable holographic device based on dispersion control, the device comprising: Double-layer metasurface system construction unit, used to construct a cascaded double-layer metasurface system, including the radiative metasurface RA-M and the pure phase metasurface PM; A rotation unit is used to change the relative twist angle α between the phase-pure metasurface PM and the radiative metasurface RA-M by rotating the phase-pure metasurface PM in a plane, so that the phase distribution of the phase-pure metasurface PM interacts with the output wavefront of the radiative metasurface RA-M; The hologram dynamic switching unit is used to realize dynamic switching of holograms by collaboratively optimizing the phase distribution of the radiative metasurface RA-M and the pure phase metasurface PM through an inverse design framework according to the dispersion characteristics of the target holographic image at the three-dimensional spatial position z and frequency f.

[0039] Embodiment 9. A computer device described in this embodiment includes a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a torsional metasurface frequency reconfigurable holographic method based on dispersion control as described in any one of embodiments 1 to 7.

[0040] Embodiment 10. A computer-readable storage medium described in this embodiment stores a computer program, and when the computer program is executed by a processor, the steps of a torsional metasurface frequency reconfigurable holographic method based on dispersion control are executed as described in any one of embodiments 1 to 7.

[0041] Implementation method 11, see Figures 1 to 8This embodiment provides a specific example of the method for frequency reconfigurable holography based on twisted metasurface with dispersion control described in embodiment 1, and is also used to explain embodiments 2 to 7. Specifically: This embodiment proposes a method for frequency-reconfigurable holography using a twisted metasurface based on dispersion manipulation. A dispersion-engineered inverse design framework (DIDF) is constructed to achieve three-dimensional multi-plane frequency-reconfigurable metasurface holography. This DIDF is based on a two-layer structure consisting of a cascaded broadband radiating metasurface (RA-M) and a phase-only metasurface (PM), forming a compact cascaded two-layer metasurface system. The reconfigurable response of this system is achieved by fixing the RA-M and rotating the PM. The RA-M generates a modulated wavefront that excites the corresponding electromagnetic response encoded in the rotating PM, thereby enabling dynamic switching of the frequency-reconfigurable holography. By establishing a relationship between the target dispersion characteristic hologram and the RA-M and PM phase distributions, this embodiment achieves high-quality frequency-reconfigurable holographic image reconstruction in three-dimensional multi-plane space. To validate this method, this embodiment experimentally demonstrates dynamic switching between spatial-frequency multiplexing and achromatic holography.

[0042] The dispersion-modulated inverse design framework (DIDF) designed in this embodiment maps the spatial-frequency specific holographic information into the electromagnetic response of the twisted metasurface system. Figure 1 Figure 2 shows the working mechanism of DIDF in a dual-layer metasurface configuration. Two independent metasurfaces—a radiative metasurface (RA-M) and a phase-only metasurface (PM)—are integrated into a compact metadevice. The broadband RA-M is excited by an integrated feeding network, while the PM is excited by the RA-M, eliminating the need for any external, bulky feed source. By adjusting the rotatable PM at a specific twist angle, the broadband electromagnetic signal generated by the RA-M is modulated by a modulating wave with a specific phase distribution and interacts with the PM. Complex diffraction occurs within the dual-layer configuration, generating a unique electromagnetic response that ultimately reconstructs a holographic image at a specific output plane. Figure 1A schematic diagram of the process is also presented. The study demonstrates three types of dispersion-managed holograms, covering frequency multiplexing, space-frequency multiplexing, and chromatic aberration correction. All of these functions are mapped through twisting operations (for example: in state 1, the characters "1," "2," and "3" are displayed at frequencies of 13 GHz, 15 GHz, and 17 GHz in the z1 plane, respectively; in state 2, the character "4" is displayed at 13 GHz in the z1 plane, the character "5" is displayed at 15 GHz in the z2 plane, and the character "6" is displayed at 17 GHz in the z3 plane; in state 3, the character "7" is displayed in the z1 plane between 12 and 18 GHz). By dynamically switching the PM, real-time updates of complex holographic images can be achieved. It is worth noting that the twisting operation in this embodiment has wide adaptability and can be applied to a variety of scenarios.

[0043] In order to deeply understand the working principle and implementation mechanism of DIDF, this embodiment starts from the basic diffraction process of the twisted metasurface system. The electromagnetic signal is first modulated by RA-M to form a wavefront U RA-M ( x , y , f ), then the wavefront propagates a specific distance in the double layer configuration to form U Inc ( x , y , f) , and then interact with PM. P-M ( x , y , f ) characteristic PM further modulates the electromagnetic signal, and finally presents a complex diffraction effect on the output plane. Output plane reconstruction field U Image ( x , y , z , f ) can be expressed as: (1) Among them, h( x , y , z , f ) is the impulse response function. Based on formula (1), U Image ( x , y , z , f ) can be controlled by U RA-M ( x , y , f ) and U P-M ( x , y , f ) is achieved through the distribution of RA-M( x , y , f ) and U P-M ( x , y , f ) will produce different electromagnetic functions in the output plane. Considering pure phase modulation, φ RA-M ( x , y , f ) and φ PM ( x , y , f ) ultimately act together on U Image ( x , y , z , f ), and these two components have similar expressions: (2) Among them, N represents the x Direction and y The number of discrete points in the direction. Here, the discrete points are regarded as linear dispersion modulation factors, so and It can be expressed as and Based on the linear dispersion modulation characteristics and relative phase distribution characteristics, the phase distribution of the metasurface at different frequency points can be considered to be exactly the same. k Setting it to zero can significantly simplify electromagnetic field calculations. According to the Rayleigh-Sommerfeld diffraction theory (RSDT), each discrete point can be regarded as an independent secondary wave source. Image ( x , y , z , f )'s output dispersion characteristics (group delay) are distributed by the first layer of RA-M φ RA-M ( x， y, f ) is determined by the spatial propagation superposition effect. Image ( x , y , z , f ) Output phase distribution, mainly depends on the second layer PM phase distribution φ P-M ( x , y , f ) provides phase compensation. Therefore, through the first layer of the double layer configuration φ RA-M ( x, y, f ) and the second layer φ P-M ( x , y , f ) can realize functional dispersion engineering.

[0044] The reverse design framework flow chart proposed in this embodiment is as follows Figure 2 The input information includes the intensity, frequency, and position distribution of the target imaging plane under different conditions. The electric field distribution at each stage is calculated using Rayleigh-Sommerfeld diffraction theory. Error evaluation is performed using a loss function to ensure that the output electric field distribution converges to one of the preset values, including: Introducing an additional twist angle α in formula (2) to change φ RA-M ( x , y , f )and φ P-M ( x , y , f ). Here the twist operation is applied to φ P-M ( x , y , f ), with the change of the torsion angle α, the output field U Image ( x , y , z , f ) will present a series of reconstructed images, thus realizing the dynamic switching of frequency reconfigurable holography in a specific z-axis plane. Based on this, the dispersion control inverse design framework (DIDF) is used to φ RA-M ( x , y , f )and φ P-M ( x , y , f ) to obtain the desired holographic image at the target imaging plane and operating frequency, and finally establish an on-demand frequency evolution process to achieve high-purity reconstruction of dispersion characteristic image switching. The detailed process of DIDF is as follows Figure 2 First, a randomly generated φ RA-M and φ P-M The phase distribution is used as DIDF input, and then U is obtained. RA-M ( x ,y , f The radiation wavefront of RA-M propagates in free space through Rayleigh-Sommerfeld diffraction theory (RSDT), and its output serves as the input of PM. The process can be expressed as: (3) in, w m It is the connection between the front layer and the aperture ( x m , y m , z m ) is the complex field of the m-th element-atom, λ is the working wavelength, d = z - z m represents the axial propagation distance, and According to the preset torsion angle state matrix , electromagnetic waves and U P-M ( x , y , f ) characteristic of the PM interaction to generate an output field, thereby obtaining an intensity distribution in a specific z-axis plane and operating frequency. The current optimization model does not consider the near-field coupling effect to simplify the calculation. Thereafter, the input electromagnetic field of the PM at each frequency f can be further calculated using the Rayleigh-Sommerfeld diffraction theory (RSDT). The input electric field can be represented as a set of Q electric field distribution matrices corresponding to Q frequency multiplexing channels, namely U Inc ={U f-1 ,…,U f-q ,…,U f-Q}.

[0045] On this basis, through φ P-M Definition U Inc and U P-M The output electric field of the PM can be obtained. Subsequently, the electric field distribution observed in a specific imaging z-axis plane can be calculated by RSDT. The output electric field distribution of the imaging z-axis plane can be expressed as a set of Q*P electric field distribution matrices, corresponding to Q frequency multiplexing channels on P z-axis planes, that is, I Imag = { I (f-1,z-1) , … , I (f-Q,z-1) ，I (f-1,z-2) , … , I(f-Q,z-2) , … , I (f-1,z-p) ，…，I (f-Q,z-p) ，…，I (f-1,z-P) ，…，I (f-Q,z-P) Similarly, the target field intensity distribution can also be regarded as a set of Q*P electric field distribution matrices, corresponding to Q frequency multiplexing channels on P z-axis planes, that is, I Target ={ I Target(f-1,z-1， …, I Target(f-Q,z-1) , I Target(f-1,z-2) ,…, I Target(f-Q,z-2) ,…, I Target(f-1,z-p) ,…, I Target(f-Q,z-p) ,…, I Target(f-1,z-P) ,…, I Target(f-Q,z-P) The difference between each diffraction field set and the target field is characterized by the mean square error (MSE). Assuming that the output electric field is discretized into an M×M matrix, for the operating frequency f q GHz, the observation plane is z = z p For a specific state, the loss function is defined as the MSE between the output intensity distribution and the target intensity distribution, and its expression is: (4) in, represents the number of discrete points in the output plane, I Output ( x m , y m , f q , z p ) is the output intensity, I Target ( x m , y m , f q , z p ) is the target normalized intensity, kis a normalization factor used to balance the target field and output field intensities. A gradient descent algorithm and error backpropagation are used to update these parameters to achieve the desired holographic functionality. Through an iterative process of forward diffraction propagation and error backpropagation, complete frequency-specific holographic information is encoded into the twisted metasurface system, with the gradual reduction of the mean square error (MSE) and the simultaneous enhancement of the output field correlation.

[0046] This implementation uses the Adaptive Moment Estimation Optimizer for model optimization. The entire optimization process is implemented in Python v3.8.0 and PyTorch v1.8.0, with 500 iterations, a learning rate of 0.001, and a batch size of 16. After 300 iterations, the optimization process almost fully converged, with no further loss reduction. The model optimization was performed on a personal computer equipped with an Intel Core i7-10870H processor, an NVIDIA GeForce RTX 2070 Max-Q design graphics card, and 16GB of RAM.

[0047] After the optimization process is completed, the required phase distribution of RA-M and PM can be determined φ RA-M and φ P-M On this basis, the corresponding meta-atom can be selected from the meta-atom library to construct the desired double-layer meta-device. The double-layer metasurface system described in this embodiment uses two types of meta-atoms to construct the corresponding metasurface. Figure 3 (a) shows the meta-atom structure of RA-M, which consists of three copper layers and two F4BM-2 dielectric substrates (thicknesses of 1.43 mm and 0.43 mm, respectively). The top copper patch acts as an electromagnetic wave radiator to generate linearly polarized (LP) waves, while the bottom copper layer serves as a feeding structure to provide integrated excitation of the meta-atom ( Figure 3 (b)). The middle copper layer is the shared ground layer for the radiating patch and the feed structure, connected by a 0.5mm diameter metal via. The period of the meta-atom is 6mm. After optimization, the meta-atom can achieve a broadband radiation amplitude greater than 0.75 in the 12GHz to 18GHz frequency band ( Figure 3 (c)). At the same time, the bottom feeder length l1 can achieve full coverage of the radiation phase 2π propagation phase ( Figure 3 (d)). The optimized parameters of the RA-M meta-atom are as follows: r 1=2.1mm, θ 1=40°, w 1=0.8mm, w 2=1.3mm, w 3=0.8mm, r 2=0.3mm,w 4=0.25mm, l 2=1.2mm. Figure 3 (e) shows the meta-atom structure of the PM. The structure consists of three copper layers and two 1.43mm-thick F4BM-2 dielectric substrates. The top and bottom copper layers are equipped with linear polarization (LP)-sensitive patches and circular polarization (CP)-sensitive patches, respectively. These patches receive LP-matched incident waves through the bottom patch and transmit energy through metal vias, ultimately generating CP-matched waves from the top patch. Figure 3 (f) shows the detailed structure of the top and bottom patches. The period of the meta-atom is 6 mm. After optimization, the meta-atom can achieve a broadband transmission amplitude higher than 0.8 in the 12 GHz to 18 GHz frequency band, as shown in Figure 2. Figure 3 (g) At the same time, the in-plane rotation angle of the top patch is φ 1 can achieve full coverage of the transmission phase 2π, such as Figure 3 (h) The optimized parameters of PM meta-atom are as follows: r 3=2.3mm, w 5=1.3mm, w 6=0.3mm, θ 3=20°, r 4=2.3mm, w 7=0.6mm, w 8=1.3mm, w 9=0.3mm, θ 2=50°.

[0048] To verify the inverse design principles proposed in this implementation, a two-layer twisted metasurface system for frequency-specific holography was physically implemented using the dispersion-manipulated inverse design framework (DIDF). The system, consisting of 64×64 RA-M and PM meta-atoms, measures 396 mm × 396 mm. A 4096-pair feeding network was further designed to ensure uniform feed of the guided electromagnetic wave into each RA-M meta-atom.

[0049] The total thickness of the RA-M is 1.965 mm (corresponding to 0.098λ at 15 GHz), and the total thickness of the PM is 2.965 mm (corresponding to 0.148λ at 15 GHz). The interlayer spacing between the RA-M and PM is 100 mm, corresponding to 4-6λ in the 12-18 GHz frequency band. This is the typical interlayer spacing of existing two-layer cascaded metasurfaces in the microwave frequency range. This widely used structural configuration allows the wavefront generated by the RA-M to effectively excite the preset phase response of the PM through the Rayleigh-Sommerfeld diffraction theory (RSDT) while avoiding excessive attenuation or phase distortion. The total thickness of the entire two-layer cascaded metastructure along the z-axis is 105.57 mm (corresponding to 5.25λ at 15 GHz), miniaturizing the overall system size and forming a compact metasurface architecture.

[0050] This embodiment also designs a dispersion-tailored holographic sample with three PM switching states. The twist angle state matrix is ​​set to R = [0°, 90°, 180°] to facilitate simulation and experimental verification (for a detailed discussion of the twist angle state selection, see Section S3 of the Supporting Information). When α1 = 0° (state 1), the sample's electromagnetic response exhibits a single-plane, multi-frequency holographic characteristic on the z-axis: in the z1 = 150 mm plane, target images of characters "1," "2," and "3" are displayed at frequencies of 13 GHz, 15 GHz, and 17 GHz, respectively. When the PM is rotated to α2 = 90° (state 2), the electromagnetic response exhibits a three-dimensional, multi-frequency holographic characteristic: character "4" (13 GHz) is located in the z1 = 150 mm plane, character "5" (15 GHz) is located in the z2 = 200 mm plane, and character "6" (17 GHz) is located in the z3 = 250 mm plane. When the PM rotates to α3=180° (state 3), the electromagnetic response exhibits z-axis single-plane achromatic holographic characteristics: in the z1=150mm plane, the target image of the character "7" is displayed in the 12-18GHz frequency band.

[0051] Based on the above parameter settings, this embodiment applies the proposed DIDF framework to optimize the phase distribution of RA-M and PM. After 300 iterations, the optimization process basically converges and the loss function no longer decreases. Figure 4 The optimized RA-M and PM phase distributions are shown. The designed meta-device is simulated using the CST Microwave Studio time domain solver. The results are as follows: Figures 5 to 7 For each switching state, this embodiment provides the frequency points within the range of 12-18 GHz (with intervals of 1 GHz) and z 1=150mm, z 2 = 200 mm, and zHolographic simulation results for a focal plane of 3 = 250 mm. The intensity distribution of the target frequency is marked with a red dotted box, and the non-design frequency is marked with a gray dotted box. The simulation results show that the intensity distribution of each target frequency and focal plane is highly consistent with the preset image. It is worth noting that since DIDF does not limit the narrowband characteristics of the intensity distribution, crosstalk occurs at adjacent frequency points. The imaging efficiency of each state is further calculated ( η ): (5) Among them, U input represents the radiation field of RA-M, U out represents the output field on a specific z-axis plane (imaging plane), and ∑ represents the summed energy on a specific z-axis plane. The simulated imaging efficiencies of characters "1," "2," and "3" in state 1 are 18.4%, 25.9%, and 37.6%, respectively; the simulated imaging efficiencies of characters "4," "5," and "6" in state 2 are 24.1%, 27.8%, and 29.8%, respectively; and the simulated imaging efficiencies of character "7" in state 3 in the 12-18 GHz frequency band are 14.8% (12 GHz), 16.1% (13 GHz), 16% (14 GHz), 15.7% (15 GHz), 16.3% (16 GHz), 17.6% (17 GHz), and 18.1% (18 GHz), respectively. To evaluate the quality of the reconstructed images using the proposed method, the signal-to-noise ratio (SNR) and Pearson correlation coefficient (PCC) are introduced as evaluation metrics: (6) (7) in, I and O Represent the intensity distribution of the reconstructed image and the target image respectively. This embodiment calculates the intensity distribution of each state in the 12-18 GHz frequency band (interval 1 GHz) and z 1=100mm, z 2=150mm, z Simulated SNR and PCC values ​​for the focal plane 3 = 200mm. In state 1, the simulated SNRs for characters "1," "2," and "3" are 2.07dB, 3.21dB, and 3.54dB, respectively. In state 2, the simulated SNRs for characters "4," "5," and "6" are 2.89dB, 3.43dB, and 3.42dB, respectively. In state 3, the simulated SNRs for character "7" in the 12-18 GHz band are 2.90dB (12 GHz), 3.20dB (13 GHz), 3.22dB (14 GHz), 3.09dB (15 GHz), 2.85dB (16 GHz), 2.21dB (17 GHz), and 2.38dB (18 GHz), respectively.

[0052] In terms of image correlation, the PCCs for state 1 were 0.8396 ("1"), 0.8898 ("2"), and 0.9000 ("3"); those for state 2 were 0.8564 ("4"), 0.8752 ("5"), and 0.8713 ("6"); and those for state 3 in the 12-18 GHz frequency band were 0.8878 (12 GHz), 0.9048 (13 GHz), 0.9088 (14 GHz), 0.9099 (15 GHz), 0.9085 (16 GHz), 0.8959 (17 GHz), and 0.9131 (18 GHz). Analysis shows that the reconstructed image quality at the target frequency point is optimal, while crosstalk effects at adjacent frequency points degrade image quality.

[0053] Based on printed circuit board etching technology, this embodiment fabricated a proof-of-concept prototype device with a size of 396 mm × 396 mm, such as Figure 8 (a) shows the RA-M structure. The RA-M is constructed from two dielectric substrates, 1.93 mm and 0.43 mm thick, respectively, with a 0.1 mm adhesive layer. The PM structure is constructed from two 1.5 mm dielectric substrates with a 0.1 mm adhesive layer. A coaxial connector is welded to the end of the RA-M feed network for integrated excitation. A 3D-printed resin bracket ensures the interlayer spacing and alignment accuracy of the twisted metasurface. Testing was performed in a microwave anechoic chamber: a vector network analyzer was connected to the RA-M's coaxial feed port on one end and a near-field probe antenna on the other.

[0054] The near-field probe antenna is fixed to the scanning turntable to achieve near-field detection of the plane to be measured. By measuring the near-field amplitude and phase of a pair of orthogonal polarizations, a circularly polarized (CP) target image can be synthesized. The measurement results are as follows Figure 8 (b) to Figure 8As shown in (d), the proposed metadevice successfully achieves switching functionality as the PM rotates, and the measured intensity distribution closely matches the target setting. In each state, the intensity distribution at specific frequencies and in the z-axis focal plane exhibits dispersion-tailored characteristics. In state 1, the measured imaging efficiencies of characters "1," "2," and "3" are 13.21%, 20.86%, and 32.68%, respectively. In state 2, the measured imaging efficiencies of characters "4," "5," and "6" are 20.01%, 22.48%, and 23.47%, respectively. In state 3, the imaging efficiencies of character "7" in the 12-18 GHz band are 11.68% (12 GHz), 13.13% (13 GHz), 11.46% (14 GHz), 12.31% (15 GHz), 14.32% (16 GHz), 13.65% (17 GHz), and 14.21% (18 GHz), respectively. It should be noted that the imaging efficiency of achromatic holography is usually significantly lower than that of other states. This is because achieving broadband achromatism requires precise design of the frequency-dependent phase distribution to compensate for the free-space propagation dispersion, which is an inherent trade-off between bandwidth and efficiency in all achromatic designs.

[0055] This embodiment simultaneously calculates the signal-to-noise ratio (SNR) and Pearson correlation coefficient (PCC) to evaluate image quality: the SNRs in state 1 are 1.84dB ("1"), 2.91dB ("2"), and 3.08dB ("3"); the SNRs in state 2 are 1.96dB ("4"), 2.88dB ("5"), and 2.93dB ("6"); and the SNRs in state 3 in the 12-18 GHz frequency band are 2.85dB, 3.01dB, 3.13dB, 2.82dB, 2.54dB, 2.03dB, and 1.92dB, respectively. The PCCs for state 1 were 0.8130 ("1"), 0.8485 ("2"), and 0.7982 ("3"); those for state 2 were 0.5130 ("4"), 0.5471 ("5"), and 0.5962 ("6"); and those for state 3 in the 12-18 GHz band were 0.8452, 0.8945, 0.8796, 0.8932, 0.8657, 0.8839, and 0.8742, respectively. The results show that S11 remains below -10 dB in the 12-18 GHz range, confirming efficient energy transfer from the feed network to the RA-M and uniform energy distribution across all meta-atoms. The total radiation efficiency of the RA-M is 20.4%.

[0056] The observed degradation in holographic performance is mainly attributed to the alignment error between the two cascaded metasurfaces, manufacturing tolerances, and measurement errors. The alignment deviation mainly comes from lateral displacement, angular deviation, gap distance, and tilt. Among these four factors, lateral displacement, angular deviation, and tilt have a significant impact on holographic performance, while gap distance exhibits greater robustness. It is worth noting that although the dispersion characteristics of the microwave band are significantly limited compared to the visible spectrum, the achromatic holographic method proposed in this embodiment still outperforms the traditional Gerchberg-Saxton (GS) algorithm in terms of broadband achromatic performance, which proves the effectiveness and necessity of introducing achromatic optimization in the microwave field.

[0057] Furthermore, the applicability of this method is not limited to the 12-18 GHz frequency band. Considering the transmittance and phase bandwidth limitations of meta-atoms, it is theoretically applicable to any frequency band. Furthermore, the 3D holography in this embodiment focuses on multi-z-plane projection to achieve depth information encoding or multiplexing, which is consistent with established practice in the field of metasurface holography. To verify the reconstruction performance while ensuring feasibility, this embodiment demonstrates low-crosstalk reconstruction of multi-plane, multi-frequency holographic images within a z-axis depth range of 180 mm (from 50 mm to 230 mm). This confirms that the proposed method is expected to achieve effective volume holographic reconstruction by further increasing the array size and the number of split planes.

[0058] Overall, the proposed dispersion-controlled inverse design framework realizes the dispersion reconstruction engineering of frequency-reconfigurable holography.

[0059] This embodiment proposes a dispersion-manipulated inverse design framework based on a cascaded metasurface double-layer configuration to achieve frequency-reconfigurable holography. This compact torsional metasurface system consists of a radiating metasurface (RA-M) with integrated feeding and a rotatable phase-only metasurface (PM). The RA-M provides modulation excitation for the PM, while the in-plane rotation of the PM enables dynamic switching of the hologram. By optimizing the phase distribution of the RA-M and PM through the inverse design framework, high-quality reconstruction of the target dispersion-customized holographic image is achieved. A proof-of-concept metadevice prototype was fabricated and measured, confirming the effectiveness of the method. Switching between three-dimensional frequency-space multiplexing holography and achromatic holography was successfully demonstrated in the microwave band. This method has broad application prospects in microwave computational imaging / detection and near-field communications.

[0060] For computational imaging / detection, frequency-reused holographic metasurfaces enable independent control of near-field modes across frequencies, significantly reducing RF hardware channels and associated complexity. The key is to enable parallel multi-mode measurement through multi-frequency synchronous illumination and echo acquisition during each measurement cycle, thereby accelerating data capture. Combined with spatial multiplexing technology, high-dimensional coded illumination (multi-frequency, multi-plane holography) can be achieved, providing richer and more differentiated data for computational imaging. Reconfigurability further supports the on-demand focusing of energy on key information-rich areas / modes, improving imaging efficiency and accuracy.

[0061] For near-field communications, these metasurfaces enable precise subwavelength focusing and arbitrary beamforming. By using frequency multiplexing within a single aperture, multiple independent beams directed toward different near-field locations can be simultaneously generated to serve different users or devices. By focusing energy on a specific target area and utilizing frequency / spatial isolation, signal leakage is significantly reduced. This directional beamforming effectively enhances anti-interference capabilities and defenses against eavesdropping from non-target directions, improving communication security. Furthermore, the system's reconfigurability allows for real-time adjustment of the holographic distribution, instantly re-optimizing the beam configuration to adapt to changing near-field environments and maintain optimal performance.

[0062] Those skilled in the art will appreciate that embodiments of the present disclosure may be provided as methods, systems, or computer program products. Thus, the present disclosure may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present disclosure may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code.

[0063] The present disclosure is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present disclosure. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including the instruction device, which implements the function specified in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0064] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present disclosure and are not intended to limit its scope of protection. Although the present disclosure has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that after reading the present disclosure, those skilled in the art can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the disclosed claims.

Claims

1. A method for frequency reconfigurable holography of twisted metasurfaces based on dispersion control, characterized in that: The method comprises: Construct a cascaded dual-layer metasurface system, including a radiative metasurface RA-M and a pure phase metasurface PM; By rotating the pure phase metasurface PM in the plane, the relative twist angle α between the PM and the radiative metasurface RA-M is changed, so that the phase distribution of the pure phase metasurface PM interacts with the output wavefront of the radiative metasurface RA-M. According to the dispersion characteristics of the target holographic image at the three-dimensional spatial position z and frequency f, the phase distributions of the radiative metasurface RA-M and the pure phase metasurface PM are collaboratively optimized through an inverse design framework to achieve dynamic switching of holograms.

2. The method for frequency reconfigurable holography based on dispersion control of twisted metasurface according to claim 1, characterized in that: The radiative metasurface RA-M is composed of broadband radiative meta-atoms, each of which includes three copper layers and two F4BM-2 dielectric substrates, with the two F4BM-2 dielectric substrates located between the three copper layers; the top copper layer is a radiating patch, the bottom copper layer is a feeding structure, and the middle copper layer is a shared ground layer for the radiating patch and the feeding structure, with the top copper layer and the bottom copper layer connected by metal vias.

3. The method for frequency reconfigurable holography based on dispersion control of twisted metasurface according to claim 1, characterized in that: The pure phase metasurface PM is composed of pure phase modulation meta-atoms, each meta-atom includes three copper layers and two F4BM-2 dielectric substrates, and the two F4BM-2 dielectric substrates are located between the three copper layers; the top copper layer and the bottom copper layer are respectively provided with a linear polarization LP sensitive patch and a circular polarization CP sensitive patch, which are used to receive the linear polarization LP matching incident wave through the bottom copper layer patch, and transmit energy with the help of the metal vias in the middle copper layer, and finally generate a CP matching wave from the top copper layer patch.

4. The method for frequency reconfigurable holography based on dispersion control of twisted metasurface according to claim 1, characterized in that: The distance between the radiative metasurface RA-M and the pure phase metasurface PM is 100 mm, satisfying the following conditions: In the 12-18 GHz frequency band, it corresponds to 4-6 times the wavelength; Compute the wavefront propagation using the Rayleigh-Sommerfeld diffraction model: in, d represents the axial propagation distance, , ( x m , y m , z m ) represents the metasurface aperture, ( x , y , z ) represents the spatial coordinates on the observation plane or target plane, f Indicates frequency, j represents the imaginary unit, c Represents the speed of light.

5. The method for frequency reconfigurable holography based on twisted metasurface with dispersion control according to claim 1, characterized in that: The switching range of the relative twist angle α is 0°-180°, corresponding to different holographic states: When α=0°, the multi-frequency multiplexing holographic function is activated; When α=90°, the space-frequency multiplexing function is activated; Achromatism is activated when α=180°.

6. The method of frequency reconfigurable holography based on twisted metasurface with dispersion control according to claim 1, characterized in that: The reverse design framework includes: Establish the output plane electric field distribution model: in, It means that the electromagnetic field after RA-M control propagates a specific distance in the double-layer configuration. represents the electric field after RA-M regulation, represents the impulse response function, represents the electric field after PM regulation; Minimize the loss function using the gradient descent algorithm: in, represents the number of discrete points in the output plane, is the output intensity, is the target normalized intensity, k is a normalization factor used to balance the target field and output field strength, and m is an index variable.

7. The method for frequency reconfigurable holography based on dispersion control of twisted metasurface according to claim 6, characterized in that: The phase distribution of the radiative metasurface RA-M and the pure phase metasurface PM satisfies the linear dispersion relation: in, is the RA-M linear dispersion modulation factor at discrete points, is the PM linear dispersion modulation factor at discrete points, b 1 represents the intercept of the RA-M phase distribution in the frequency linear relationship, b 2 represents the intercept of PM phase distribution in the linear relationship of frequency; When implementing achromatic holography, k=0 is set to eliminate propagation dispersion.

8. A frequency reconfigurable holographic device based on a twisted metasurface with dispersion control, characterized in that: The device comprises: Double-layer metasurface system construction unit, used to construct a cascaded double-layer metasurface system, including the radiative metasurface RA-M and the pure phase metasurface PM; A rotation unit is used to change the relative twist angle α between the phase-pure metasurface PM and the radiative metasurface RA-M by rotating the phase-pure metasurface PM in a plane, so that the phase distribution of the phase-pure metasurface PM interacts with the output wavefront of the radiative metasurface RA-M; The hologram dynamic switching unit is used to realize dynamic switching of holograms by collaboratively optimizing the phase distribution of the radiative metasurface RA-M and the pure phase metasurface PM through an inverse design framework according to the dispersion characteristics of the target holographic image at the three-dimensional spatial position z and frequency f.

9. A computer device, characterized in that: The method comprises a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a torsional metasurface frequency reconfigurable holographic method based on dispersion control according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of a torsional metasurface frequency reconfigurable holographic method based on dispersion control as described in any one of claims 1 to 7.

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