A full-space multi-domain modulation method and device based on a single-layer superstructure surface

Abstract

The application discloses a full-space multi-domain regulation method and device based on a single-layer super surface, and the method comprises the following steps: arranging a transmission type super unit and a reflection type super unit on a substrate of the single-layer super surface; establishing a relationship between geometric parameters of the super unit and wavelength efficiency and screening an optimal structure; arranging positions of two kinds of isomerism super units according to amplitude distribution of a color nano printing image in a transmission space and a reflection space; the two kinds of isomerism super units control the transmission space and the reflection space respectively; a simulated annealing algorithm is adopted to realize independent decoupling of a Fresnel domain and a Fourier domain simultaneously, realize multiplexing of a far-field holographic image, realize reflection focusing light beams and transmission Bessel light beams under the same design architecture; corresponding phase distribution is calculated on a nano structure array, and a turning angle of a nano brick is regulated. Each pixel point of the application controls two independent phases of the Fresnel domain and the Fourier domain while bearing a near-field amplitude, and the full-space near-field color nano printing and the synchronous multiplexing of the Fourier domain and the Fresnel domain holographic image in the far field are realized on the single-layer super surface for the first time.

Description

Technical Field

[0001] This invention belongs to the fields of micro-nano optics and polarization optics, and particularly relates to a method and device for full-space multi-domain control based on a single-layer metasurface. Background Technology

[0002] Metasurfaces are artificial optical materials composed of subwavelength nanostructures arranged together, possessing the ability to manipulate light waves. By designing the size and orientation angle of the nanostructures, the phase, amplitude, and polarization of light waves can be manipulated individually.

[0003] Currently, typical metasurface structures are mostly based on arrays of single nanostructures (such as nanopillars, nanobricks, or resonators) with specific electromagnetic responses built on dielectric or metallic substrates. These structures introduce phase abrupt changes through their own geometric parameters (such as diameter and height) or spatial orientation (rotation angle), thereby achieving unprecedented flexible manipulation of the light wavefront. Based on these principles, metasurfaces have shown great application potential in many fields, such as: developing metalenses that are thinner, lighter, and flatter than traditional lenses for use in high-end imaging systems; generating computational holograms that can be used for information encryption and display; and realizing arbitrary deflection and shaping of light beams.

[0004] In the field of metasurface optics, achieving high-density, low-crosstalk, and multifunctional optical field multiplexing on a single platform has always been a core objective pursued by researchers. In recent years, full-space manipulation (i.e., simultaneously utilizing transmission and reflection channels) and multi-domain imaging (i.e., generating images in the interface near-field, Fresnel diffraction domain, and Fourier diffraction domain respectively) have been considered two key paths to enhance information capacity. To further meet the demands of multifunctional integration, in addition to achieving full-space manipulation and multi-domain imaging, how to utilize a unified design architecture to generate reflected focused beams and transmitted Bessel beams in different application scenarios has become an important direction for application expansion.

[0005] Chinese patent publication CN202510587854 proposes a single-layer metasurface based on coherent pixels to generate near-field binarized nanoprinted images and far-field holographic images in full space. However, the "far-field" in this paper does not distinguish the diffraction domain and is only optimized for a single far-field hologram. It cannot handle multi-domain joint targets, and its function is still limited to the near-field interface and the far-field Fourier domain, making it difficult to meet the needs of multi-depth imaging or layered information encoding.

[0006] Furthermore, existing metasurface optical field manipulation techniques typically only function within a single space of transmission or reflection, and are often limited to a specific holographic imaging domain, making it difficult to simultaneously handle interface-printed images, Fresnel holograms, and Fourier holograms on the same platform. While some cutting-edge research has successfully achieved three-domain multiplexing in the reflection space—generating nanoprinted images at the interface and reconstructing two holograms in the Fresnel and Fourier domains respectively—this approach is entirely limited to the reflection channel, neglecting the design of a transmission channel. This prevents the utilization of the entire optical field, significantly restricting information capacity and application scenarios. Moreover, the strong coupling effect between the transmission and reflection channels makes achieving independent multiplexing and manipulation of multiple domains on the same metasurface extremely challenging.

[0007] Chinese patent publication CN115377697A proposes a full-space multifunctional coded metasurface, employing a "double-layer metal patch-dielectric substrate" structure to achieve controllable scattering beam formation in the reflection channel and multi-focal focusing in the transmission channel. However, this scheme uses a complex double-layer metasurface process and does not involve optical near-field color nanoprinting and multi-domain synchronous multiplexing of holography. Even combining the above-mentioned existing technologies, it is still impossible to achieve synchronous multiplexing of the three domains of the full-space near-field interface, far-field Fourier domain, and Fresnel domain, as well as reflection focusing and transmission Bessel beams. Achieving the above functions requires overcoming a fundamental challenge: how to forcibly separate the two channels in the structural design (each pixel can only belong to transmission or reflection), while allowing the reflection space and transmission space to independently optimize the images of two different diffraction domains, and on this basis, realize the generation of reflection focusing and transmission Bessel beams in the corresponding functional scenarios, while meeting the corresponding energy distribution requirements and effectively suppressing channel crosstalk. Summary of the Invention

[0008] To overcome the above-mentioned shortcomings of the prior art, this invention proposes a full-space multi-domain control method based on a single-layer metasurface.

[0009] This invention achieves phase decoupling of transmission and reflection channels on a single-layer metasurface, and simultaneously generates multiple independent images in different spatial domains, or generates a focused beam in the reflection channel and a Bessel beam in the transmission channel. This overcomes existing limitations and provides a new technical path for high-security optical encryption, multi-dimensional information storage, and integrated photonic systems. The invention employs two heterogeneous metaunits to construct the metasurface: one is a transmission-type metaunit with two nanobricks whose long axes are parallel to each other, and the other is a reflection-type metaunit with two nanobricks whose long axes are perpendicular to each other. Based on their distinct optical response characteristics—the transmission-type metaunit exhibits high transmittance in the transmission channel and low reflectance in the reflection channel, while the reflection-type metaunit exhibits the opposite—this design achieves decoupling of the physical channels. Therefore, the transmission-type and reflection-type metaunits on the metasurface can independently construct holographic phase distributions for the transmission and reflection channels without interfering with each other. On the one hand, this invention enables a single metasurface platform to simultaneously generate and control interface color nanoprinted images, Fresnel domain holographic images, and Fourier domain holographic images, achieving full-space multi-domain optical field multiplexing. On the other hand, by introducing a specific phase distribution on the same design architecture, this invention enables the reflection channel to generate a focused beam and the transmission channel to generate a Bessel beam. Thus, it achieves full-space multi-domain optical field multiplexing and the separate integration of beam functions in different scenarios.

[0010] The present invention provides a full-space multi-domain control method based on a single-layer metasurface, comprising the following steps: S1. Construction of a monolayer metasurface: The monolayer metasurface comprises two heterogeneous metaunits. The transmissive metaunit has two nanobricks with parallel long axes on its substrate; the reflective metaunit has two nanobricks with perpendicular long axes on its substrate. The angle between the long axis of the nanobrick and the X-axis of the coordinate system on the substrate plane is the nanobrick's turning angle. ; S2. Constructing a nanostructure array: Using electromagnetic simulation, the relationship between the geometric parameters of the supercells and the wavelength efficiency is established, and the optimal structure is selected. Based on the amplitude distribution of the color nanoprinted image in the transmission and reflection space, the positions of two heterogeneous supercells are arranged: when the target amplitude is greater than 0.5 in the transmission space, the corresponding position of the pixel is arranged with a transmissive supercell; when the target amplitude is greater than 0.5 in the reflection space, the corresponding position of the pixel is arranged with a reflective supercell. S3. Full-space multi-domain manipulation and beam generation: Two heterogeneous supercells control the transmission and reflection spaces respectively. Simulated annealing algorithm is used to simultaneously achieve independent decoupling of the Fresnel and Fourier domains, enabling far-field holographic image multiplexing. Under the same design architecture, the focused beam is reflected and the Bessel beam is transmitted. S4. Calculate the corresponding phase distribution on the nanostructure array and adjust the turning angle of the nanobricks.

[0011] Preferably, the parameters in step S2 include the length L, width W, and height H of the nanobrick, the side length CS of the square substrate, and the arrangement positions of the two heterogeneous superunits.

[0012] Preferably, in step S2, the arrangement of the two heterogeneous supercells is as follows: the transmissive supercell has varying high transmittance in the transmission channel and approaches 0 in the reflection channel, corresponding to the transmissive near-field color region; the reflective supercell has varying high transmittance in the reflection channel and approaches 0 in the transmission channel, corresponding to the reflective near-field color region; through the amplitude selective transmission of the two supercells in the dual channels, complementary display of near-field color images in the whole space is achieved.

[0013] Preferably, in the process of realizing far-field holographic image multiplexing in step S3, a simulated annealing optimization algorithm is used to optimize the phase distribution of the transmission channel. Phase distribution of the reflection channel By decoupling the algorithms, each pixel can simultaneously control two independent phases in the Fresnel and Fourier domains, and the two heterogeneous superunits can realize far-field holographic image multiplexing in the transmission and reflection space.

[0014] Preferably, in step S3, during the realization of the reflected focused beam and the transmitted Bessel beam, a phase distribution for beam focusing is designed for the reflection channel. Equal to the phase distribution of the reflection channel For the transmission channel, a phase distribution is designed to generate the Bessel beam. Equal to the phase distribution of the transmission channel The phase distribution of each channel is optimized using a simulated annealing optimization algorithm.

[0015] Furthermore, in step S3, the simulated annealing optimization algorithm optimizes the phase distribution of each channel, including: initializing the temperature and phase distribution for the transmission and reflection channels respectively; generating new solutions by performing random perturbations in the neighborhood; and calculating the distribution deviation between the hologram and the beam based on their respective evaluation functions. The optimization process follows a probabilistic acceptance mechanism, accepting inferior solutions in the cooling cycle to avoid local optimum traps, and using an exponential cooling strategy to ensure robust convergence of the search process. Finally, when the system reaches the termination temperature, the optimal transmission and reflection phases are output.

[0016] More specifically, the process of selecting the turning angle of the nanobrick in step S4 is as follows: S41. For a transmissive supercell, the difference in the turning angles of the two nanobricks is 0°. Based on the derivation of the coherent pixel Jones matrix, by keeping the turning angles of the two nanobricks consistent, the transmitted light field satisfies the condition of having a high amplitude. At this time, the transmissive supercell controls the phase distribution of the transmission channel. It is equal to twice the turning angle of the nanobrick.

[0017] S42. For a reflective supercell, the difference in the turning angles of the two nanobricks is 90°. The phase difference π generated by this difference in turning angles is used to suppress energy output in the transmission direction, thereby concentrating energy in the reflection direction. Based on the superposition of the phases of the two nanobricks and the derivation of the coherent pixel Jones matrix, the phase distribution of the reflection channel controlled by the reflective supercell is... It is equal to four times the turning angle of the nanobrick.

[0018] S43. By utilizing the aforementioned two-fold and four-fold phase relationships, and adjusting the turning angle of the nanobricks, independent and precise control of the phase distribution in the transmission and reflection spaces can be achieved.

[0019] A second aspect of the present invention relates to a method and device for full-space multi-domain manipulation based on a single-layer metasurface, comprising a single-layer metasurface containing two heterogeneous metaunits, wherein two nanobricks with parallel long axes are disposed on a substrate of a transmissive metaunit; and two nanobricks with perpendicular long axes are disposed on a substrate of a reflective metaunit; the angle between the long axis of the nanobrick and the X-axis of a coordinate system on the substrate plane is the turning angle of the nanobrick. ; The structural parameters of the nanobricks were established based on electromagnetic simulation to establish the relationship between the geometric parameters of the superunits and the wavelength efficiency, and the optimal structure was selected. Based on the amplitude distribution of the color nanoprinted image in the transmission and reflection space, the positions of two heterogeneous superunits were arranged: when the target amplitude is greater than 0.5 in the transmission space, the corresponding position of the pixel is arranged with a transmission type superunit; when the target amplitude is greater than 0.5 in the reflection space, the corresponding position of the pixel is arranged with a reflection type superunit.

[0020] Two heterogeneous supercells control the transmission space and the reflection space respectively. The simulated annealing algorithm is used to simultaneously achieve independent decoupling of the Fresnel domain and the Fourier domain, realize the reuse of far-field holographic images, and reflect and transmit Bessel beams under the same design architecture.

[0021] Furthermore, based on the relationship between phase and nanobrick orientation angle, the orientation angle of the nanobricks in each superunit is determined: For a transmissive supercell, the phase distribution of its transmission channel The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The directional angle of the nanobricks in the transmission-type superunit; For reflective supercells, the phase distribution of their reflection channels The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The θ represents the turning angle of the nanobricks in the reflective supercell.

[0022] The working principle of this invention is as follows: Transmissive and reflective superunits are integrated on a single-layer metasurface, enabling multi-domain image multiplexing and multi-functional beam output in two independent channels, avoiding crosstalk between channels. Specifically, the transmissive e-superunit exhibits high-amplitude output in the transmission channel, and its phase delay satisfies the following condition: It can be used to construct the transmission phase distribution of holographic image information and Bessel beam phase distribution information; the reflective supercell effectively suppresses transmission and directs energy to the reflection channel, and its reflection phase delay satisfies This invention enables independent control of reflected holographic images and beam focusing at specific focal lengths. Based on this, the invention successfully achieves full-space multi-domain optical field multiplexing and multifunctional beam generation in the near-field (nanoprinted image), Fresnel domain, and Fourier domain using a single-layer metasurface, significantly improving information capacity and the degree of freedom in optical integration. Based on a single-layer metasurface, the invention simultaneously realizes nanoprinting, Fresnel holography, and Fourier holography, and achieves beam focusing and Bessel beam generation on the same platform. Its core innovation lies in the introduction of two heterogeneous metaunits, achieving phase decoupling and independent control of the transmission and reflection channels. The six generated images and two beams are located on different observation planes in the transmission and reflection channels, completely separated in space with almost no crosstalk, effectively ensuring the independence and reproduction quality of each channel image and overcoming the image interference problem common in traditional multi-channel metasurfaces. This invention lays the technical foundation for full-space multi-domain multiplexing, high information density, and low crosstalk optical field control. The proposed metasurface structure is simple and easy to fabricate, providing a new path for the development of multifunctional integrated photonic devices.

[0023] The innovative aspects of this invention:

[0024] 1) A full-space decoupling mechanism for single-pixel corresponding to multiple phases is proposed:

[0025] This invention breaks through the physical spatial limitations of Fourier and Fresnel domain holographic imaging, achieving full-space control of transmission and reflection, and achieving a qualitative breakthrough in phase modulation complexity. The core of this invention is not simple phase mapping, but rather algorithmic decoupling, enabling each pixel to control two independent phases in both the Fresnel and Fourier domains while carrying near-field amplitude. This single-pixel-level "one-to-many" architecture, combined with global optimization using simulated annealing algorithms, achieves, for the first time on a single-layer metasurface, the simultaneous multiplexing of full-space near-field color nanoprinting, Fresnel holography, and Fourier holography.

[0026] 2) A full-space synchronous color nanoprinting control mechanism was proposed: it is not a simple black-and-white binary nanoprinting or single-space display, but through in-depth optimization of the relationship between the geometric parameters of nanobricks and wavelength efficiency, the amplitude efficiency of cross wavelength and cross space is precisely matched for the first time, and complementary color nanoprinting display is realized through spatial synchronization of transmission and reflection.

[0027] 3) Functional branching technology based on a unified design architecture: The core is to utilize a decoupling framework with full-space multi-domain control to independently realize the simultaneous reflection and focusing of beams and transmission of Bessel beams according to requirements, breaking through the limitations of single static holographic displays. Through the same set of phase decoupling and algorithm optimization logic, the transmission and reflection channels are forcibly separated and the energy distribution is precisely controlled, realizing cross-scene functional reuse from holographic imaging to special beam generation.

[0028] The beneficial effects of this invention include: 1) For the first time, full-space interface near-field was achieved on a single metasurface, with simultaneous multiplexing of the Fourier and Fresnel domains: By constructing independent images in the interface near field, Fresnel diffraction domain, and Fourier diffraction domain, and combining transmission and reflection dual channels, six spatially separated and functionally independent optical images are generated simultaneously. This significantly breaks through the limitation of existing technologies that can only achieve functions in a single space or a single diffraction domain, and greatly improves information capacity and optical freedom.

[0029] 2) Separate control of holographic image multiplexing and specific beam generation based on a unified design architecture: This invention is based on the same super-unit design framework, which can realize multi-domain image multiplexing or special beam generation according to application requirements. The phase distribution of Bessel beams is introduced in the transmission channel, and efficient beam focusing is achieved in the reflection channel. This unified design logic of image display and wavefront shaping enables a series of devices developed based on this invention to not only perform high-density information storage, but also possess the ability to perform precision optical manipulation (such as optical tweezers and metalenses).

[0030] 3) Employing a simulated annealing algorithm channel decoupling optimization strategy, high-quality image reconstruction across multiple domains and phase control of special beams are achieved: By introducing two types of superunits based on coherent pixel theory on a single-layer metasurface, the degree of freedom in light wave manipulation is improved. The structure used is simple, requiring only a single-layer metasurface to achieve full-space light field manipulation. For the structure where the superunit type is determined by the near-field nanoprinted image and its steering angle is adjustable, a simulated annealing optimization strategy is innovatively introduced to independently optimize the phase distribution of the transmission and reflection channels, while jointly considering the reconstruction objectives of Fresnel diffraction and Fourier transform. This method effectively overcomes the shortcomings of the traditional Gerchberg–Saxton (GS) algorithm, which is prone to getting trapped in local optima in multi-objective optimization and struggles to simultaneously meet the phase requirements of different diffraction domains. It significantly improves the overall imaging quality and inter-channel isolation of the six-channel image, while ensuring the consistency of the Bessel beam principal maxima and the focusing efficiency of the focal spot, achieving low crosstalk, high quality, and multi-domain compatible light field multiplexing.

[0031] 4) Single-layer structures combine high information density, low crosstalk, and ease of fabrication: The metasurface designed in this invention requires only a single-layer fused silica substrate and a silicon nanobrick array, without the need for multi-layer stacking or complex processes; the six images and two beams are completely separated in space (different channels, different observation planes), with extremely low crosstalk between channels and domains; the structure is compatible with standard semiconductor processes, is easy to fabricate on a large scale, and is suitable for high-security optical anti-counterfeiting, multi-level information encryption, three-dimensional imaging, and integrated photonic systems.

[0032] 5) Achieve layered storage and independent decoding of information to enhance optical security: The interface nanoprinted images serve as intuitive visual identifiers, while Fresnel and Fourier holograms act as hidden information channels. These three elements are physically isolated, requiring specific channels and distances for accurate reading, effectively preventing information forgery and illegal copying, and providing technical support for high-security applications. Furthermore, the generation of specific functional beams (such as Bessel beams) can serve as higher-dimensional encryption keys or physical anti-counterfeiting features, further enhancing the system's anti-counterfeiting capabilities. Attached Figure Description

[0033] Figure 1 This is a structural diagram of the single-layer metasurface of the present invention.

[0034] Figure 2 This is a structural diagram of the transmissive supercell of the present invention.

[0035] Figure 3 This is a structural diagram of the reflective supercell of the present invention.

[0036] Figure 4This is the transmission spectrum of the optimized nanobrick structure unit in the embodiment of the present invention.

[0037] Figure 5 This is the transmittance and reflectance spectral response curve of a single nanobrick of the present invention at the working wavelength.

[0038] Figure 6 The turning angle of the nanobricks in the transmissive superunit of this invention. The spectral response curves of the device in the transmission and reflection space as the temperature varies from 0° to 180°.

[0039] Figure 7 The turning angle of the nanobricks in the reflective supercell of this invention. The spectral response curves of the device in the transmission and reflection space as the temperature varies from 0° to 180°.

[0040] Figure 8 This is a schematic diagram showing the change of the transmission and reflection phases of the present invention with the turning angle of the first nanobrick.

[0041] Figure 9 This is a flowchart of the simulated annealing algorithm of the present invention.

[0042] Figure 10a This is a nanoprinted image of the reflective space in Embodiment 2 of the present invention.

[0043] Figure 10b This is a Fresnel hologram of the reflection space in Embodiment 2 of the present invention.

[0044] Figure 10c This is a Fourier hologram of the reflection space in Embodiment 2 of the present invention.

[0045] Figure 11a This is a nanoprinted image of the transmission space in Embodiment 2 of the present invention.

[0046] Figure 11b This is a Fresnel hologram of the transmission space in Embodiment 2 of the present invention.

[0047] Figure 11c This is a Fourier hologram of the transmission space in Embodiment 2 of the present invention.

[0048] Figure 12a It is the Bessel beam in the reflection space in Embodiment 3 of the present invention.

[0049] Figure 12b It is the focused beam of the transmission space in Embodiment 3 of the present invention. Detailed Implementation

[0050] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0051] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0052] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0053] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0054] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0055] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0056] The present invention will now be described in detail with reference to the accompanying drawings and exemplary embodiments.

[0057] Example 1

[0058] This embodiment relates to a method for full-space multi-domain control based on a single-layer metasurface, comprising the following steps:

[0059] S1. Construction of a monolayer metasurface: The monolayer metasurface comprises two heterogeneous metaunits. The transmissive metaunit has two nanobricks with parallel long axes on its substrate; the reflective metaunit has two nanobricks with perpendicular long axes on its substrate. The angle between the long axis of the nanobrick and the X-axis of the coordinate system on the substrate plane is the nanobrick's turning angle. ; S2. Constructing a nanostructure array: Using electromagnetic simulation, the relationship between the geometric parameters of the supercells and the wavelength efficiency is established, and the optimal structure is selected. Based on the amplitude distribution of the color nanoprinted image in the transmission and reflection space, the positions of two heterogeneous supercells are arranged: when the target amplitude is greater than 0.5 in the transmission space, the corresponding position of the pixel is arranged with a transmissive supercell; when the target amplitude is greater than 0.5 in the reflection space, the corresponding position of the pixel is arranged with a reflective supercell. S3. Full-space multi-domain manipulation and beam generation: Two heterogeneous superunits control the transmission and reflection spaces respectively. Simulated annealing algorithm is used to simultaneously achieve independent decoupling of the Fresnel and Fourier domains, enabling far-field holographic image multiplexing. The simulated annealing optimization algorithm process for reflecting and focusing beams and transmitting Bessel beams under the same design architecture includes: Phase 1: Optimizing the phase distribution of the transmission channel S31a. Initialization: Set the initial temperature Lower limit of temperature In the initial solution state, the number of iterations For all positions arranged as transmissive supercells, their transmission phase distribution is randomly generated. S32a: Neighborhood search: Randomly generate a new solution within the neighborhood of the initial solution; S33a: Acceptance Criterion: Calculate the difference between the evaluation function of the holographic pattern and Bessel beam intensity distribution corresponding to the new solution in the transmission space and the corresponding target distribution. ;like If the solution is correct, then accept the new solution; otherwise, use probability. Accept the new interpretation; S34a: Cooling strategy: Gradually reduce temperature; S35a: Termination condition: When the temperature drops to... When the time is up, the algorithm stops and outputs the current solution as the phase distribution of the optimal transmission channel. .

[0060] Phase 2: Optimize the phase distribution of the reflection channel; S31b. Initialization: Set initial temperature Lower limit of temperature In the initial solution state, the number of iterations For all locations arranged as reflective supercells, their reflection phase distributions are randomly generated. S32b: Neighborhood Search: Randomly generate a new solution within the neighborhood of the initial solution; S33b: Acceptance Criterion: Calculate the difference between the evaluation function of the reflection holographic pattern and the focused beam corresponding to the new solution in the reflection space and the corresponding target distribution. ;like If the solution is correct, then accept the new solution; otherwise, use probability. Accept the new interpretation; S34b: Cooling strategy: Temperature is updated using an exponential cooling method; S35b: Termination condition: When the temperature drops to... When the time is up, the algorithm stops and outputs the current solution as the phase distribution of the optimal reflection channel. .

[0061] To achieve the generation of focused beams and Bessel beams, a specific phase distribution needs to be introduced into the phase design of each channel, as follows:

[0062] S31c. Phase control of Bessel beam in transmission space ; To generate a Bessel beam in the transmission space, the transmission element needs to introduce a corresponding phase distribution, which is expressed by the following formula: (5) in, For the designed operating wavelength, These are the pixel coordinates on the metasurface plane. This is the preset cone angle.

[0063] S32c. Beam focusing and phase control in the reflection space ; To achieve wavefront focusing of incident light in the reflection space, the reflective supercell needs to introduce a focusing phase distribution, which is expressed by the formula: (6) in, For the designed operating wavelength, These are the pixel coordinates on the metasurface plane. The focal length is used for focusing. After determining the basic phase distribution, the Bessel and focusing phases are optimized using a simulated annealing optimization algorithm to obtain the optimal beam shaping quality.

[0064] S4. Calculate the corresponding phase distribution on the nanostructure array and adjust the turning angle of the nanobricks.

[0065] S4. The process of selecting the turning angle of nano-bricks is as follows: S41. Define two nanobricks arranged along the x-axis in a superunit as the first nanobrick and the second nanobrick, respectively. S42. For a transmissive supercell, the difference in the turning angle between the first nanobrick and the second nanobrick is 0°. The transmissive electric field is derived from the coherent pixel Jones matrix: (1) in, and The turning angles of the first and second nanobricks are respectively; in the transmission space, the emitted light field of the transmission superunit satisfies the condition that the amplitude is high, and the phase distribution of the transmission channel. It is twice the turning angle of the first nanobrick, that is ; S43. For a reflective supercell, the difference in the turning angle between the first and second nanobricks is 90°, resulting in a phase delay difference of π. Its transmitted electric field is: (2) Therefore, the incident light through the reflective supercell is blocked in the transmission direction, and the energy can only be output through the reflection channel. The amplitude of the emitted light field in the reflection space is high, and the reflected electric field of the reflective supercell is: (3) in, , ,and The reflection phase delay of a reflective supercell is: (4) Therefore, the phase distribution of the reflection channel The turning angle of the first nanobrick It is a four-fold relationship, that is Therefore, the reflected electric field of a reflective superunit is expressed as: .

[0066] Example 2

[0067] This embodiment relates to a full-space multi-domain control method based on a single-layer metasurface, comprising the following steps: S1. Constructing a single-layer metasurface: The structure of the single-layer metasurface is as follows... Figure 1 As shown, the substrate is divided into several rectangular unit substrates of the same size. Two nanobricks are arranged on each unit substrate to form a superunit. For transmissive superunits, two nanobricks with parallel major axes are arranged on the substrate; for reflective superunits, two nanobricks with perpendicular major axes are arranged on the substrate. The angle between the major axis of the nanobrick and the x-axis of the coordinate system on the substrate plane is the turning angle of the nanobrick. ; Figure 2 The structure of the transmissive supercell was shown. Figure 3 The structure of the reflective superunit was demonstrated; S2. Constructing a nanostructure array: Optimizing the geometric parameters of two heterogeneous superunits, and selecting a design wavelength of... =633nm. For this wavelength, the geometric parameters of the nanobrick were optimized using the electromagnetic simulation software CST. These geometric parameters include the length L, width W, and height H of the nanobrick, the side length CS of the square substrate, and the arrangement positions of the two heterogeneous superunits. After optimization, the height of the nanobrick is 148nm, and the CS of the unit substrate is 287nm. The transmittance corresponding to several optimized length-width combinations is as follows: Figure 4 As shown, a representative set of nanobrick units was selected, with a length L of 132 nm and a width W of 87 nm. Under these structural parameters, the polarization conversion efficiency of the nanobricks for circularly polarized light transmission and reflection in space is as follows: Figure 5 As shown, R-Co and R-Cross represent the common polarization conversion efficiency and cross polarization conversion rate of the reflected light, respectively, while T-Co and T-Cross represent the common polarization conversion efficiency and cross polarization conversion rate of the transmitted light, respectively.

[0068] Depend on Figure 5 It can be seen that at the working wavelength of 633 nm, the R-Cross is 0.43%, the T-Cross is as high as 95.3%, and the R-Co and T-Co are 4.6% and 0.16% respectively, indicating that the optimized nanobrick structure has good half-wave plate performance. Figure 6 It can be seen that, at an operating wavelength of 633 nm, the transmission-type supercell reflective common polarization conversion efficiency is... =4.12%, Reflection Cross-Polarization Conversion Efficiency =0.3%, transmission common polarization conversion efficiency =0.13%, transmission cross-polarization conversion efficiency =97.3%, indicating that the transmissive metaunit is mainly used for modulating transmitted light, realizing the generation of color nanoprinted images at the metasurface interface in the transmission space, through the corner To achieve modulation of transmitted light. (By...) Figure 7 It can be seen that, at an operating wavelength of 633 nm, the reflective supercell reflective common polarization conversion efficiency is... =5.2%, Reflection Cross-Polarization Conversion Efficiency =92.9%, transmission common polarization conversion efficiency =2.1%, transmission cross-polarization conversion efficiency =2.2%, indicating that the reflective metaunits are mainly used for modulating reflected light, realizing the generation of color nanoprinted images in the reflection space at the metasurface interface, through corner... This is to achieve modulation of the reflected light. Figure 8 It was confirmed that when the first nanobrick was rotated for scanning, the transmission phase delay of the transmissive supercell was twice the change in orientation angle, while the reflection phase delay of the reflective supercell was four times the change in orientation angle.

[0069] Based on the target amplitude of each pixel in the color nanoprinted image, and an amplitude threshold of 0.5, transmissive or reflective superunits are arranged for pixels whose transmission or reflection components exceed this value. Furthermore, based on the specific efficiency value required for color nanoprinting at each pixel, [the following steps are taken]. Figure 4 The corresponding geometric parameters are selected to construct a nanostructure array.

[0070] S3. Full-space multi-domain manipulation and beam generation: Two heterogeneous supercells control the transmission and reflection spaces respectively, and a simulated annealing optimization algorithm is used to optimize the phase distribution of the transmission channel. Phase distribution with the reflection channel Through algorithmic decoupling, each pixel can simultaneously control two independent phases in the Fresnel and Fourier domains, enabling full-space multi-domain manipulation of the two heterogeneous superunits in the transmission and reflection space. In the realization of reflected and focused beams and transmitted Bessel beams, a phase distribution for beam focusing is designed for the reflection channel. Equal to the phase distribution of the reflection channel For the transmission channel, a phase distribution is designed to generate the Bessel beam. Equal to the phase distribution of the transmission channel The phase distribution of each channel is optimized using a simulated annealing optimization algorithm.

[0071] When white light is incident on the nanostructure array, such as Figure 9As shown, the flowchart illustrates the optimization and design process of the metasurface array. The length and width of the nanobricks are determined based on the target nanoprinted image, thus obtaining the amplitude distribution. Based on this, a holographic image corresponding to a specific orientation angle distribution can be obtained through forward calculation of Fresnel diffraction (FrT) and Fast Fourier Transform (FFT). To reconstruct four preset target images in the Fresnel diffraction domain and Fraunhofer diffraction domain respectively for the transmission and reflection channels, this invention employs a simulated annealing algorithm to iteratively optimize the orientation angle distribution of the nanobricks. This algorithm, based on a preset loss function, continuously updates the orientation angle to gradually improve the multi-domain imaging quality, and uses a simulated annealing optimization algorithm to optimize the phase distribution of the transmission and reflection channels.

[0072] S4. Calculate the corresponding phase distribution on the nanostructure array and adjust the turning angle of the nanobricks.

[0073] Based on the relationship between phase and nanobrick orientation angle, the final orientation angle of the nanobricks in each superunit is determined: For a transmissive supercell, the phase distribution of its transmission channel The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The turning angle of the first nanobrick in the transmission-type superunit; For reflective supercells, the phase distribution of their reflection channels The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The turning angle of the first nanobrick in the reflective supercell; The phase modulation of the transmission channel and the reflection channel are independent of each other and do not interfere with each other.

[0074] Ultimately, the color nanoprinted images, Fresnel holograms, and Fourier holograms at the metasurface interface in the transmission space, such as... Figures 10a-10c As shown; reflective spatial nanoprinted images, Fresnel holograms, and Fourier holograms, such as Figures 11a-11c As shown.

[0075] Example 3

[0076] This embodiment relates to a device for implementing the full-space multi-domain multiplexing control method based on a single-layer metasurface as described in Embodiment 1. The single-layer metasurface comprises two heterogeneous metaunits: a transmissive metaunit has two nanobricks with parallel long axes disposed on its substrate; and a reflective metaunit has two nanobricks with perpendicular long axes disposed on its substrate. The angle between the long axis of the nanobrick and the X-axis of the coordinate system on the substrate plane is the turning angle of the nanobrick. ; The structural parameters of the nanobricks were established based on electromagnetic simulation to establish the relationship between the geometric parameters of the superunits and the wavelength efficiency, and the optimal structure was selected. Based on the amplitude distribution of the color nanoprinted image in the transmission and reflection space, the positions of two heterogeneous superunits were arranged: when the target amplitude is greater than 0.5 in the transmission space, the corresponding position of the pixel is arranged with a transmission type superunit; when the target amplitude is greater than 0.5 in the reflection space, the corresponding position of the pixel is arranged with a reflection type superunit.

[0077] Two heterogeneous supercells control the transmission space and the reflection space respectively. The simulated annealing algorithm is used to simultaneously achieve independent decoupling of the Fresnel domain and the Fourier domain, realize the reuse of far-field holographic images, and reflect and transmit Bessel beams under the same design architecture.

[0078] Based on the relationship between phase and nanobrick orientation angle, the orientation angle of the nanobricks in each superunit is determined, including: For a transmissive supercell, the phase distribution of its transmission channel The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The directional angle of the nanobricks in the transmission-type superunit; For reflective supercells, the phase distribution of their reflection channels The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The θ represents the turning angle of the nanobricks in the reflective supercell.

[0079] The phase distribution of the transmission channel is optimized using a simulated annealing optimization algorithm. Phase distribution of the reflection channel Through algorithmic decoupling, each pixel can simultaneously control two independent phases in the Fresnel and Fourier domains, enabling far-field holographic image multiplexing in both transmission and reflection spaces. Complementary color nanoprinted images are generated at the metasurface interface between the transmission and reflection spaces; simultaneously, independent holographic patterns are formed in the Fresnel and Fourier domains. The phases of the transmission and reflection channels are decoupled and can be continuously controlled.

[0080] For the reflection channel, a phase distribution is designed for beam focusing. Equal to the phase distribution of the reflection channel For the transmission channel, a phase distribution is designed to generate the Bessel beam. equal to the phase distribution of the transmission channel The phase distribution of each channel is optimized using a simulated annealing optimization algorithm. While maintaining channel decoupling, optimal beam shaping quality is obtained. Ultimately, a Bessel beam is generated in the transmission space as shown... Figure 12a As shown, the reflected space generates a focused beam of light, as Figure 12bAs shown.

Claims

1. A method for full-space multi-domain control based on a single-layer metasurface, comprising the following steps: S1. Construction of a monolayer metasurface: The monolayer metasurface comprises two heterogeneous metaunits. The transmissive metaunit has two nanobricks with parallel long axes on its substrate; the reflective metaunit has two nanobricks with perpendicular long axes on its substrate. The angle between the long axis of the nanobrick and the X-axis of the coordinate system on the substrate plane is the nanobrick's turning angle. ; S2. Constructing a nanostructure array: Using electromagnetic simulation, the relationship between the geometric parameters of the supercells and the wavelength efficiency is established, and the optimal structure is selected. Based on the amplitude distribution of the color nanoprinted image in the transmission and reflection space, the positions of two heterogeneous supercells are arranged: when the target amplitude is greater than 0.5 in the transmission space, the corresponding position of the pixel is arranged with a transmissive supercell; when the target amplitude is greater than 0.5 in the reflection space, the corresponding position of the pixel is arranged with a reflective supercell. S3. Full-space multi-domain manipulation and beam generation: Two heterogeneous supercells control the transmission and reflection spaces respectively. Simulated annealing algorithm is used to simultaneously achieve independent decoupling of the Fresnel and Fourier domains, enabling far-field holographic image multiplexing. Under the same design architecture, the focused beam is reflected and the Bessel beam is transmitted. S4. Calculate the corresponding phase distribution on the nanostructure array and adjust the turning angle of the nanobricks.

2. The method for full-space multi-domain control based on a single-layer metasurface according to claim 1, characterized in that, The geometric parameters mentioned in step S2 include the length L, width W, height H of the nanobrick, the side length CS of the square substrate, and the arrangement positions of the two heterogeneous superunits.

3. The method for full-space multi-domain control based on a single-layer metasurface according to claim 2, characterized in that, Transmissive supercells exhibit varying high transmittance in the transmission channel and approach zero in the reflection channel, corresponding to the transmissive near-field color region; reflective supercells exhibit varying high transmittance in the reflection channel and approach zero in the transmission channel, corresponding to the reflective near-field color region; through the amplitude-selective transmission of the two types of supercells in the dual channels, complementary display of near-field color images in the entire space is achieved.

4. The method for full-space multi-domain control based on a single-layer metasurface according to claim 1, characterized in that, Step S3, the far-field holographic image multiplexing, includes: optimizing the phase distribution of the transmission channel using a simulated annealing optimization algorithm. Phase distribution of the reflection channel By decoupling the algorithms, each pixel can simultaneously control two independent phases in the Fresnel and Fourier domains, and the two heterogeneous superunits can realize far-field holographic image multiplexing in the transmission and reflection space.

5. The full-space multi-domain control method based on a single-layer metasurface according to claim 4, characterized in that, The reflected focused beam and the transmitted Bessel beam mentioned in step S3 include: a phase distribution designed for beam focusing for the reflection channel. Equal to the phase distribution of the reflection channel For the transmission channel, a phase distribution is designed to generate the Bessel beam. Equal to the phase distribution of the transmission channel The phase distribution of each channel is optimized using a simulated annealing optimization algorithm.

6. The method for full-space multi-domain control based on a single-layer metasurface according to claim 5, characterized in that, Step S3 uses a simulated annealing optimization algorithm to optimize the phase distribution of each channel, including: initializing the temperature and phase distribution for the transmission and reflection channels respectively; generating new solutions by performing random perturbation in the neighborhood; calculating the distribution deviation between the hologram and the beam based on their respective evaluation functions; the optimization process follows a probabilistic acceptance mechanism, accepting inferior solutions in the cooling cycle to avoid local optimum traps; and using an exponential cooling strategy to make the search process robust and convergent; when the system reaches the termination temperature, the optimal transmission and reflection phases are output.

7. The method for full-space multi-domain control based on a single-layer metasurface according to claim 1, characterized in that, The process of selecting the turning angle of the nanobrick in step S4 is as follows: S41. For a transmissive supercell, based on the derivation of the coherent pixel Jones matrix, the amplitude of the transmitted light field is high, and the transmissive supercell controls the phase distribution of the transmission channel. It is equal to twice the turning angle of nanobricks; S42. For reflective supercells, the phase difference π generated by the difference in steering angle is used to suppress the energy output in the transmission direction, thereby concentrating the energy in the reflection direction; Based on the superposition of the phases of two nanobricks and the derivation of the Jones matrix of coherent pixels, the phase distribution of the reflection channel controlled by the reflective supercell is shown. It is equal to four times the turning angle of the nanobrick; S43. By adjusting the turning angle of the nanobricks, independent and precise control of the phase distribution of the transmission and reflection spaces can be achieved.

8. A device implementing the full-space multi-domain control method based on a single-layer metasurface as described in claim 1, characterized in that, This includes a monolayer metasurface, which comprises two heterogeneous metaunits. The transmissive metaunit has two nanobricks with parallel long axes on its substrate; the reflective metaunit has two nanobricks with perpendicular long axes on its substrate. The angle between the long axis of each nanobrick and the X-axis of a coordinate system on the substrate plane is the nanobrick's turning angle. ; The structural parameters of the nanobricks are established based on electromagnetic simulation to establish the relationship between the geometric parameters of the superunits and the wavelength efficiency, and the optimal structure is selected. Based on the amplitude distribution of the color nanoprinted image in the transmission and reflection space, the positions of two heterogeneous superunits are arranged: when the target amplitude is greater than 0.5 in the transmission space, the corresponding position of the pixel is arranged with a transmission type unit. When the target amplitude is greater than 0.5 in the reflection space, reflective supercells are arranged at the corresponding positions of the pixels; Two heterogeneous supercells control the transmission space and the reflection space respectively. The simulated annealing algorithm is used to simultaneously achieve independent decoupling of the Fresnel domain and the Fourier domain, realize the reuse of far-field holographic images, and reflect and transmit Bessel beams under the same design architecture.

9. The device as claimed in claim 8, characterized in that: Based on the relationship between phase and nanobrick orientation angle, the orientation angle of the nanobricks in each superunit is determined: For a transmissive supercell, the phase distribution of its transmission channel The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The directional angle of the nanobricks in the transmission-type superunit; For reflective supercells, the phase distribution of their reflection channels The phase modulation is achieved by the turning angle of its nanobricks and satisfies ,in The θ represents the turning angle of the nanobricks in the reflective supercell.

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