Aperiodic metasurface, design method and display device

Abstract

The invention belongs to the field of micro-nano optics, and discloses a non-periodic super-structure surface, a design method and a display device.Nano structures are randomly distributed above a waveguide layer and keep a certain minimum distance, improved Fraunhofer diffraction and a GS optimization algorithm are combined, phase distribution before and after diffraction angle expansion is calculated, and a super-structure is obtained. Taking an included angle between a long axis and an x axis at each position as a phase influence factor; and based on the target image, the rotation angles of a plurality of nano structures are determined in combination with the phase influence factors, and the designed aperiodic super-structure surface is obtained after arrangement. According to the invention, the design is flexible, the structure is compact, the integration level is high, and the diffraction angle can be expanded by using the aperiodic super-structure surface, so that the view field range is expanded, and the system has a relatively high potential value in holographic application.

Description

Technical Field

[0001] The present invention belongs to the field of micro-nano optics and relates to a metasurface design technology, and in particular to a non-periodic metasurface, a design method and a display device. Background Art

[0002] Amid the continuous evolution of integrated photonics technology, achieving large diffraction angle light field manipulation in free space has become a key issue hindering the development of high-performance optoelectronic devices. The diffraction angle not only directly determines the system's viewing angle range and image spatial restoration capabilities, but also significantly impacts the imaging quality and immersive experience of cutting-edge applications such as holographic displays, spatial light modulation, and naked-eye 3D imaging. Therefore, expanding the diffraction angle in free space is a core requirement for improving system display performance and enriching the dimensionality of optical information. Currently, light field manipulation in free space primarily relies on metasurface technology. Metasurfaces are two-dimensional control platforms composed of subwavelength-scale artificial structural units, capable of highly precise manipulation of parameters such as the phase, amplitude, and polarization state of incident light waves. However, traditional metasurfaces typically employ periodic or quasi-periodic structural arrangements, and their control mechanisms are often based on Bragg diffraction and grating equations, operating under specific wavelength and incident angle conditions. This structural characteristic results in their diffraction output being primarily concentrated in a specific off-axis direction, resulting in a narrow-angle diffraction distribution, making it difficult to achieve a wide-range, highly uniform wavefront spread. In response to the above challenges, the current research trend is moving towards non-periodic structural arrangements. By introducing non-periodic geometric configurations such as quasi-lattice structures, fractal structures, and random lattices, the angle limitations under traditional Bragg conditions can be effectively broken, forming a more discrete and uniform far-field diffraction pattern. Although the relevant design strategies have achieved initial results, due to the physical scale, intrinsic resonance characteristics and complexity of the preparation process of sub-wavelength structures, there are still many challenges in achieving metasurfaces while maintaining high efficiency while expanding the diffraction angle. For example: the optical response of non-periodic arranged structures is difficult to accurately predict through analytical models, and requires large-scale numerical simulation and machine learning optimization; the mutual coupling effect between structural units is more complex in irregular arrangements, which places higher demands on phase control accuracy; at the same time, how to achieve precise construction and stable reproduction at the nanoscale also poses severe challenges to current nano-fabrication technology.

[0003] In summary, for high-performance holographic displays and free-space light field manipulation applications, the narrow diffraction angle range is insufficient to meet the key driving force behind the evolution of metasurfaces from traditional wavefront shaping to intelligent, programmable light field manipulation. Structural innovations and mechanism explorations in this area will play a significant role in novel photonic applications such as glasses-free 3D displays, augmented reality, and intelligent sensing, possessing significant scientific research value and engineering application prospects. Summary of the Invention

[0004] One of the purposes of the present invention is to provide a design method for non-periodic metasurfaces, which combines an improved Fraunhofer diffraction with a GS optimization algorithm to calculate the phase distribution before and after the diffraction angle expansion, thereby solving the problem that the diffraction angle range achieved by metasurfaces in the prior art needs to be improved.

[0005] Another object of the present invention is to provide a non-periodic metasurface, which is obtained by utilizing the above method to obtain a metasurface with a larger diffraction angle display.

[0006] Another object of the present invention is to provide a display device that utilizes the above-mentioned non-periodic metasurface for display, thereby performing naked-eye 3D display.

[0007] In order to solve the above technical problems, the solution adopted by the present invention is as follows: In a first aspect, the present invention provides a method for designing a non-periodic metasurface, comprising the following steps: Determine the design area of the metasurface as the near field; Randomly filling the nanostructures in the design area to a maximum value, and making the distance between any two nanostructures greater than a first threshold; Select the target image, working wavelength and diffraction distance of the target image; The diffraction angle expansion coefficient is introduced into the mapping relationship between spatial frequency and far-field coordinates to calculate the far-field coordinates used to display the target image; According to the selected target image and working wavelength, combined with the mapping relationship between spatial frequency and far-field coordinates, the inverse optimization algorithm and optical diffraction calculation method are used to calculate the geometric phase distribution of the nanostructure to complete the design of the non-periodic metasurface.

[0008] Furthermore, the method of randomly filling the nanostructures within the design area to a maximum value and making the distance between any two nanostructures greater than a first threshold includes: Any one of the random sequential adsorption method, Poisson disk sampling method, simulated annealing optimization, and molecular dynamics simulation method, or a combination of several of these methods.

[0009] Furthermore, the inverse optimization algorithm adopts a simulated GS algorithm or a gradient descent algorithm, and the optical diffraction calculation method adopts a Fraunhofer diffraction integral method.

[0010] Furthermore, the diffraction angle expansion coefficient is introduced to determine the mapping relationship between spatial frequency and far-field coordinates as follows:

[0011]

[0012] in, is the horizontal coordinate of the far-field pixel point of the target image, is the far-field pixel ordinate of the target image, z is the diffraction distance, is the working wavelength, F is the diffraction angle expansion coefficient, 、 are the horizontal spatial frequency and the vertical spatial frequency, respectively.

[0013] Furthermore, the method for calculating the geometric phase distribution of the nanostructure using the inverse optimization algorithm and the optical diffraction calculation method is as follows: Model definition, defining the design area of the metasurface as the near field plane, defining the display area of the target image as the far field flat; Determine the target light intensity distribution based on the target image ; Initialize the phase distribution of the near field ; Forward propagation, calculate the far-field complex amplitude distribution based on the current phase of the near field ; Apply far-field constraints and distribute the far-field complex amplitude The amplitude in is replaced by , the phase remains unchanged, and the updated far-field complex amplitude distribution is obtained ; Backward propagation, using the updated far-field complex amplitude distribution Inverse calculation of the new near-field complex amplitude distribution ; Updated near-field phase distribution ; Repeat far-field propagation and reverse propagation until convergence, and output the final phase distribution Phase distribution of nanostructures as metasurfaces.

[0014] Furthermore, during the forward propagation process, the calculation formula for the far-field complex amplitude distribution is as follows:

[0015] During the reverse propagation process, the calculation formula for the near-field complex amplitude distribution is as follows:

[0016] In the above formula, is the far-field complex amplitude distribution, is the near-field complex amplitude distribution, e is the natural base, k is the wave number, which represents the phase change per unit length, j is the imaginary unit, are the coordinates of the near-field nanostructure, are the coordinates of the far field of the holographic image, and z is the diffraction distance.

[0017] Further, the far-field propagation and reverse propagation are repeated until the convergence condition is that the phase distribution of the updated near field is used Calculate the far-field complex amplitude distribution , calculate the far-field complex amplitude distribution The error E between the amplitude and the target light intensity distribution. When the error E is less than the second threshold, the iteration is terminated and the phase distribution at this time is output. .

[0018] On the other hand, the present invention provides a non-periodic metasurface structure designed using the above-mentioned non-periodic metasurface design method.

[0019] On the other hand, the present invention provides a light field display device, comprising a substrate, a waveguide layer formed on the substrate, and a nanostructure formed on the waveguide layer, wherein the distribution of the nanostructure is designed using the above-mentioned design method of the non-periodic metasurface.

[0020] Furthermore, the projection of the nanostructure on the waveguide layer includes a long axis and a short axis, and the size ratio of the long axis to the short axis is greater than 2.

[0021] One or more technical solutions provided in the present invention have at least the following technical effects or advantages: The present invention first constructs a unit structure forming an aperiodic metasurface. The unit structure includes a planar substrate, a waveguide layer located above the planar substrate, and nanostructures disposed on the working surface of the waveguide layer. All nanostructures contained in the aperiodic metasurface have the same size. A target image that satisfies the design is then selected. The rotation angles of the nanostructures within their respective unit structures are then used as phase influencing factors. Based on the three-dimensional target image and in combination with the phase influencing factors, the positions of the nanostructures within the unit structures are determined, and the designed aperiodic metasurface is obtained after arrangement. Specifically, the nanostructures in the present invention have a distribution of nanostructures that can be randomly arranged in a certain aperiodic region while ensuring a minimum distance between any two nanostructures. The rotation angle variation of the nanostructures provides geometric phase modulation of light waves in free space. The present invention utilizes the geometric phase modulation of light waves at the working wavelength at any nanostructure position to optimize the design of the holographic image projected by the aperiodic metasurface at the working wavelength. Furthermore, the characteristics of optical Fraunhofer diffraction are utilized to realize a metaphotonic device characterized by a changing diffraction angle.

[0022] In summary, the present invention has the characteristics of flexible design, compact structure, and high integration. It can use non-periodic metasurfaces to expand the diffraction angle range and can be applied to naked-eye 3D display, augmented reality, intelligent perception and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1This is a flow chart of the design method for the non-periodic metasurface provided in Example 1.

[0024] Figure 2 This is a schematic diagram of the local structure of the non-periodic metasurface provided in Example 1.

[0025] Figure 3 : is a schematic diagram of holographic projection observation using a non-periodic metasurface in the application of the non-periodic metasurface provided in Example 2. Figure 4 It is a schematic diagram of the expanded diffraction angle of the non-periodic metasurface of the present invention.

[0026] Figure 5 This is a schematic diagram of the process of calculating the geometric phase distribution of a nanostructure using an inverse optimization algorithm and an optical diffraction calculation method in Example 1 of the present invention.

[0027] Figure 6 This is the simulation result of the extended diffraction of the non-periodic metasurface, where Figure 6 Figure a in the middle is the far-field simulated image of phase optimization when the diffraction angle is not expanded; Figure 6 Figure b is the far-field simulation image of phase optimization when the diffraction angle is expanded (the diffraction angle expansion coefficient is 2).

[0028] Figure 7 This is the FDTD simulation result of the expanded diffraction angle of the non-periodic metasurface, where Figure 7 Figure a in the middle is the far-field simulation (FDTD) image of phase optimization when the diffraction angle is not expanded; Figure 7 (b) is the far-field simulation (FDTD) image of phase optimization when the diffraction angle is expanded (the diffraction angle expansion coefficient is 2).

[0029] 100-substrate, 200-waveguide layer, 300-nanostructure. DETAILED DESCRIPTION

[0030] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0031] In the description of the present invention, it should be noted that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "back," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer" and the like, indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0032] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "connected" and "connection" should be understood in a broad sense. For example, they can refer to fixed connection, detachable connection, or integral connection; mechanical connection, electrical connection; direct connection, or indirect connection through an intermediary. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0033] Example 1, as Figure 1 As shown, the present invention provides a method for designing a non-periodic metasurface, comprising the following steps: S100, determining the metasurface as a design area of the near field; S200, randomly filling the nanostructures in the design area to a maximum value, and making the distance between any two nanostructures greater than a first threshold; S300, selecting a target image, an operating wavelength, and a diffraction distance of the target image; S400, introducing a diffraction angle expansion coefficient into a mapping relationship between spatial frequency and far-field coordinates to calculate far-field coordinates for displaying a target image; S500. Based on the selected target image and working wavelength, combined with the mapping relationship between spatial frequency and far-field coordinates, the inverse optimization algorithm and optical diffraction calculation method are used to calculate the geometric phase distribution of the nanostructure and complete the design of the non-periodic metasurface.

[0034] In step S100, the metasurface of the present invention is designed on a substrate, such as Figure 2 As shown, a waveguide layer 200 is provided on a substrate 100, on which a large number of nanostructures 300 are distributed. The nanostructures have identical dimensions, and the length, width, and height of the nanostructures are denoted as L, W, and H, respectively. The design of the metasurface of the present invention is actually the position and phase design of the nanostructures. An XOY coordinate system is established with the directions of the two sides parallel to the working surface of the waveguide layer being set as the X-axis and the Y-axis, respectively. The long axis of the nanostructure is the length direction, and the short axis is the width direction, that is, the long axis length is L, and the short axis length is W. The spacing between the nanostructures is defined as the distance between the centers of the two nanostructures, and the position of the nanostructure 300 is defined as the coordinates at the center of the nanostructure, denoted as , that is, when only the position is considered, the nanostructure can be regarded as a particle; the phase of the nanostructure is defined as the angle between the long axis and the X axis ; For example, Figure 3 As shown in the figure, the present invention establishes a Cartesian coordinate system XYZ with the center of the design area as the origin, the Z axis is the incident light direction of the metasurface, and the diffraction angle of the outgoing light field is divided into the diffraction angle in the XOZ plane and the diffraction angle in the YOZ plane , the range of the outgoing light field is , .

[0035] Common substrates include silicon-based materials, optically transparent materials, flexible polymer materials and high refractive index materials; silicon-based materials include silicon (Si), silicon dioxide (SiO2) and silicon nitride (Si3N4); optically transparent materials include quartz, sapphire and calcium fluoride; flexible polymer materials include polyimide, PDMS and PET / PC films; high refractive index materials include titanium dioxide (TiO2), gallium arsenide (GaAs) and the like; illustratively, the present invention may preferably use silicon dioxide.

[0036] Common materials for the waveguide layer include dielectric materials, semiconductor materials, and metal materials. Dielectric materials include TiO2 (titanium dioxide), Si (silicon), and Si3N4 (silicon nitride). Exemplarily, silicon nitride is preferred in the present invention.

[0037] Materials for the nanostructure include high-refractive-index dielectric materials, metal materials, and semiconductor materials. High-refractive-index dielectric materials include titanium dioxide, silicon nitride, and gallium arsenide; metal materials include gold (Au), silver (Ag), and aluminum (Al); and semiconductor materials include silicon (Si) and indium phosphide (InP). Exemplarily, silicon is preferred in the present invention.

[0038] It should be noted that the selection of the above-mentioned functional structural materials needs to ensure not only the continuity and compatibility of the preparation process, but also the refractive index matching and loss selection of the nanostructure and waveguide layer. Generally speaking, the refractive index of the nanostructure and the waveguide layer need to be designed in a coordinated manner, such as high-refractive-index nanocolumns with low-refractive-index waveguides to enhance light field coupling; for low loss: material absorption (k value) and scattering losses need to be minimized, especially for high-efficiency devices (such as super lenses requiring total loss <10%).

[0039] In step S100, Figure 3 As shown, the size of the design area depends on the target image and molding accuracy requirements. Generally speaking, the design can be considered as a rectangular area or a square area, with the side lengths recorded as 、 , when designed as a square area .

[0040] In step S200, the method of randomly filling the nanostructures in the design area to a maximum number and making the distance between any two nanostructures greater than a first threshold includes: Any one of the random sequential adsorption method, Poisson disk sampling method, simulated annealing optimization, and molecular dynamics simulation method, or a combination of several of these methods.

[0041] Random Sequential Adsorption (RSA) can be combined with spatial segmentation to accelerate infill. Specifically, candidate locations are randomly generated one by one and retained if their distance to existing structures is greater than a threshold. Using a quadtree or grid to accelerate proximity queries reduces the time complexity of each check. Its advantages are simplicity and ease of implementation, making it suitable for low-density infill.

[0042] Poisson disk sampling (Bridson algorithm) uses a uniform grid to accelerate the process. Each time, a random point is selected from the active list and a new point is generated in a circular area around it, ensuring minimum spacing. This process is repeated until no more points can be added. The advantage is that the generated distribution is uniform and random, and it is more efficient than pure RSA.

[0043] The iterative filling method based on the Voronoi diagram dynamically constructs the Voronoi diagram of the current structure and attempts to insert new points at the Voronoi vertices (centers of the largest gaps), adding them only after the distance constraints are met. This process is repeated until there are no gaps large enough.

[0044] Simulated annealing optimization involves initializing a random distribution and then gradually optimizing the infill quantity by randomly moving or adding or removing structures, accepting degraded solutions with a certain probability. The objective function is to maximize the number of points, with the constraint being the spacing. Its advantage is that it can break through local optima and approach the global optimum.

[0045] The molecular dynamics simulation method treats nanostructures as particles with repulsive forces. By simulating the equilibrium state of motion, the particles are allowed to diffuse naturally and fill the area, maintaining a minimum spacing. The advantage is that it generates a natural random distribution and is suitable for complex boundaries.

[0046] Hybrid methods can be combined in various ways, such as first generating a base distribution using Poisson disk sampling, then inserting additional points through Voronoi gap detection or local optimization. For example, after Poisson sampling, the remaining area can be scanned and small gaps filled using RSA. Advantages: Combining the strengths of multiple methods to improve filling density.

[0047] The first threshold value is also related to the diffraction angle. Without introducing the expansion coefficient, the first threshold value determines the diffraction angle. Taking the first threshold value as the distance d as an example, when the diffraction angle expansion coefficient is not introduced, the diffraction angle range is ,Right now .

[0048] In step S300, the target image is the image to be displayed, the working wavelength is the wavelength selected based on the metasurface and the display image, and the diffraction distance is the distance between the target image display area and the metasurface. All of these are prior arts and will not be described in detail in the present invention.

[0049] In step S400, the diffraction angle expansion coefficient is introduced to determine the mapping relationship between spatial frequency and far-field coordinates as follows:

[0050]

[0051] in, is the horizontal coordinate of the far-field pixel point of the target image, is the far-field pixel ordinate of the target image, z is the diffraction distance, is the working wavelength, F is the diffraction angle expansion coefficient, and the diffraction angle expansion coefficient ranges from 1 to 3. When F=1, the diffraction angle is not expanded. When F=2, the diffraction angle expands by about one time. , ; 、 are the transverse spatial frequency and the longitudinal spatial frequency, respectively, which are calculated using the frequency domain array of the periodic metasurface array, and the period P is assumed to be the first threshold.

[0052] Figure 4 As shown, the XYZ coordinate system of the metasurface is called Cartesian space, and the far-field space is defined as K space. Then the schematic diagram of introducing the diffraction angle expansion coefficient to expand the display space is as follows Figure 4 As shown, it can be seen that before expansion , after expansion , the display area is significantly increased.

[0053] like Figure 5 As shown, in step S500, the method for calculating the geometric phase distribution of the nanostructure using the inverse optimization algorithm and the optical diffraction calculation method is as follows: S510, model definition, define the design area of the metasurface as the near field Plane, that is, establish an XOY coordinate system with the two adjacent sides of the design area as the horizontal and vertical coordinate axes; define the display area of the target image as the far field flat; S520: Determine target light intensity distribution based on target image ; S530, initializing the phase distribution of the near field ; S540, forward propagation, calculate the far-field complex amplitude distribution based on the current phase of the near field ; S550, apply far-field constraints and distribute the far-field complex amplitude The amplitude in is replaced by , the phase remains unchanged, and the updated far-field complex amplitude distribution is obtained ; S560, back propagation, using the updated far-field complex amplitude distribution Inverse calculation of the new near-field complex amplitude distribution ; S570, update the phase distribution of the near field ; S580, repeat the reverse propagation from step S540 to step S570 until convergence, and output the final phase distribution Phase distribution of nanostructures as metasurfaces.

[0054] In step S520, the target image is binarized to obtain the intensity distribution as the target light intensity distribution. .

[0055] In step S530, the phase distribution of the initialization near field is initialized by using a random function, for example, a uniform distribution random function can be used, in the interval Generates uniformly distributed random phase angles within the cycle, ensuring that the phase is completely randomized within the cycle.

[0056] In step S540, during the forward propagation process, the calculation formula for the far-field complex amplitude distribution is the Fraunhofer diffraction integral formula, which is as follows:

[0057] In step S550, the far-field complex amplitude distribution contains phase and amplitude information, so the target light intensity distribution , Represents the target far-field complex amplitude distribution, which can be recorded as , j is the imaginary unit, is the far-field light intensity distribution, is the far-field phase distribution; when applying far-field constraints, Replace with That's it.

[0058] In step S560, during the reverse propagation process, the calculation formula for the near-field complex amplitude distribution is as follows:

[0059] In the above formula, is the far-field complex amplitude distribution, is the near-field complex amplitude distribution, e is the natural base, k is the wave number, which represents the phase change per unit length, j is the imaginary unit, are the coordinates of the near-field nanostructure, are the coordinates of the far field of the holographic image, and z is the diffraction distance; In step S570, the near-field complex amplitude distribution , is the near-field amplitude distribution. The present invention only modulates the phase, so the near-field amplitude distribution is a fixed value and can be expressed as , is the near-field phase distribution. By using the above formula, the near-field phase distribution can be calculated when the near-field complex amplitude distribution is known; keeping the amplitude Unchanged, updated , we can get the new near-field complex amplitude distribution , so that the next cycle calculation can be carried out until convergence, and in the process of calculating the phase, the phase needs to be constrained to .

[0060] In step S580, the convergence condition is: using the updated near-field phase distribution Calculate the far-field complex amplitude distribution , calculate the far-field complex amplitude distribution The error E between the amplitude and the target light intensity distribution. When the error E is less than the second threshold, the iteration is terminated and the phase distribution at this time is output. , n represents the nth iteration calculation.

[0061] For example, , it converges when E is less than the second threshold. The size of the second threshold is determined by the target image accuracy that needs to be displayed. If high accuracy is required, a smaller second threshold can be set, and vice versa. The specific decision is based on experience and requirements.

[0062] Example 2: Figure 2 and Figure 3 As shown, the present invention provides a light field display device, including a substrate 100, a waveguide layer 200 formed on the substrate 100, and a nanostructure 300 formed on the waveguide layer 200. The distribution of the nanostructure 300 is designed using the above-mentioned design method of the non-periodic metasurface.

[0063] The projection of the nanostructure 300 on the waveguide layer 200 includes a long axis and a short axis, and the size ratio of the long axis to the short axis is greater than 2.

[0064] For example, the material of the nanostructure 300 is silicon, the waveguide layer 200 is silicon nitride, and the substrate 100 is a planar silicon dioxide substrate; the thickness of the planar silicon dioxide substrate is 500 μm, the thickness of the waveguide layer is 190 nm, the height of all nanostructures in the square design area is H = 360 nm, the top surface length is L = 280 nm, the top surface width is W = 90 nm, and the lengths of the design area in the X and Y directions are respectively set to =80 μm and =80 μm.

[0065] The invention's technical principle for achieving diffraction angle expansion holographic display is as follows: When a free-space light wave propagates normally incident on a metasurface, it is affected by the nanostructures on the waveguide layer, causing scattering and outcoupling. This outcoupling carries a geometric phase φPB determined by the nanostructure's current position, which can be reverse-calculated using an optimization algorithm. Diffraction angle expansion displays utilize the Fraunhofer diffraction integral method to calculate the diffraction field distribution in the spatial domain. The diffraction angle is related to the spatial coordinates of the diffraction field, so changing the spatial coordinates of the diffraction field will also change the corresponding diffraction angle.

[0066] A laser light source with a specific wavelength that meets the design requirements is coupled vertically and incident on the metasurface for transmission. The designed holographic image can be observed in the projection area of the non-periodic metasurface.

[0067] In order to observe the holographic image, the Figure 3 The conceptual diagram shown. The light waves required for holographic reconstruction can be incident vertically by laser coupling in free space. Then a hologram is formed on the right side of the metasurface. Based on the provided Fraunhofer diffraction integral method and the GS algorithm, the diffraction angle expansion is achieved. The simulation results of the holographic image diffraction angle expansion are shown in Figure 6 As shown; Figure 6 Figure a is the phase-optimized far-field simulation (computer-generated holographic) image when the diffraction angle is not expanded (the diffraction angle expansion coefficient is 1); Figure b is the phase-optimized far-field simulation (computer-generated holographic) image when the diffraction angle is expanded (the diffraction angle expansion coefficient is 2); it can be seen that when the diffraction angle expansion coefficient becomes larger, the diffraction angle in the X and Y directions increases, and at the same time, according to the corresponding diffraction angle formula 、 In order to verify the feasibility of the simulation results, the optimal phase distribution simulated was imported into the FDTD simulation, the relevant simulation was built, and the actual simulation effect was measured. The final simulation results are as follows: Figure 7 As shown, Figure 7 Middle a: When the diffraction angle is not expanded (the diffraction angle expansion coefficient is 1), the phase-optimized far-field simulation (FDTD) image; Figure 7 Figure b shows a far-field FDTD simulation of phase optimization when the diffraction angle is extended (diffraction angle extension factor is 2). As can be seen, when the diffraction angle extension factor increases, the phase distribution of the optimized nanostructure is simulated using FDTD software, and the resulting pattern is similar to that of the computer-generated hologram simulation, demonstrating the feasibility of this approach. This demonstrates the feasibility of combining the Fraunhofer diffraction integral and the GS optimization algorithm to achieve an extended diffraction angle range. The simulation results exhibit significant background noise, likely due to the random placement of the nanostructures, which results in noise in the K-space of the diffraction field.

[0068] The above embodiments are intended to illustrate the present invention only and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that various combinations, modifications, or equivalent substitutions of the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention and should be encompassed by the scope of the claims of the present invention.

Claims

1. A method for designing a non-periodic metasurface, characterized in that: The following steps are involved: Determine the design area of the metasurface as the near field; Randomly filling the nanostructures in the design area to a maximum value, and making the distance between any two nanostructures greater than a first threshold; Select the target image, working wavelength and diffraction distance of the target image; The diffraction angle expansion coefficient is introduced into the mapping relationship between spatial frequency and far-field coordinates to calculate the far-field coordinates used to display the target image; According to the selected target image and working wavelength, combined with the mapping relationship between spatial frequency and far-field coordinates, the inverse optimization algorithm and optical diffraction calculation method are used to calculate the geometric phase distribution of the nanostructure to complete the design of the non-periodic metasurface.

2. The method for designing a non-periodic metasurface according to claim 1, characterized in that: The method of randomly filling nanostructures in a design area to a maximum extent and making the distance between any two nanostructures greater than a first threshold includes: Any one of the random sequential adsorption method, Poisson disk sampling method, simulated annealing optimization, and molecular dynamics simulation method, or a combination of several of these methods.

3. The method for designing a non-periodic metasurface according to claim 1, characterized in that: The reverse optimization algorithm adopts a simulated GS algorithm or a gradient descent algorithm, and the optical diffraction calculation method adopts a Fraunhofer diffraction integral method.

4. The method for designing a non-periodic metasurface according to claim 1, characterized in that: The formula for determining the mapping relationship between spatial frequency and far-field coordinates by introducing the diffraction angle expansion coefficient is as follows: in, is the horizontal coordinate of the far-field pixel point of the target image, is the far-field pixel ordinate of the target image, z is the diffraction distance, is the working wavelength, F is the diffraction angle expansion coefficient, 、 are the horizontal spatial frequency and the vertical spatial frequency, respectively.

5. The method for designing a non-periodic metasurface according to claim 4, characterized in that: The method for calculating the geometric phase distribution of nanostructures using the inverse optimization algorithm and optical diffraction calculation method is as follows: Model definition, defining the design area of the metasurface as the near field plane, defining the display area of the target image as the far field flat; Determine the target light intensity distribution based on the target image ; Initialize the phase distribution of the near field ; Forward propagation, calculate the far-field complex amplitude distribution based on the current phase of the near field ; Apply far-field constraints and distribute the far-field complex amplitude The amplitude in is replaced by , the phase remains unchanged, and the updated far-field complex amplitude distribution is obtained ; Backward propagation, using the updated far-field complex amplitude distribution Inverse calculation of the new near-field complex amplitude distribution ; Updated near-field phase distribution ; Repeat far-field propagation and reverse propagation until convergence, and output the final phase distribution Phase distribution of nanostructures as metasurfaces.

6. The method for designing a non-periodic metasurface according to claim 5, characterized in that: During forward propagation, the calculation formula for the far-field complex amplitude distribution is as follows: During the reverse propagation process, the calculation formula for the near-field complex amplitude distribution is as follows: In the above formula, is the far-field complex amplitude distribution, is the near-field complex amplitude distribution, e is the natural base, k is the wave number, which represents the phase change per unit length, j is the imaginary unit, are the coordinates of the near-field nanostructure, are the coordinates of the far field of the holographic image, and z is the diffraction distance.

7. The method for designing a non-periodic metasurface according to claim 5, characterized in that: Repeat the far-field propagation and reverse propagation until the convergence condition is to use the updated near-field phase distribution Calculate the far-field complex amplitude distribution , calculate the far-field complex amplitude distribution The error E between the amplitude and the target light intensity distribution. When the error E is less than the second threshold, the iteration is terminated and the phase distribution at this time is output. .

8. A non-periodic metasurface structure, characterized in that: The non-periodic metasurface is designed by the design method of any one of claims 1 to 7.

9. A light field display device, characterized in that: The invention comprises a substrate, a waveguide layer formed on the substrate and a nanostructure formed on the waveguide layer, wherein the distribution of the nanostructure is designed by the design method of the non-periodic metasurface according to any one of claims 1 to 7.

10. The light field display device according to claim 9, characterized in that: The projection of the nanostructure on the waveguide layer includes a long axis and a short axis, and the size ratio of the long axis to the short axis is greater than 2.

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