Four-channel image display design method based on spin-angle multiplexing metasurface

Abstract

The invention discloses a four-channel image display design method based on a spin-angle multiplexing metasurface, and belongs to the technical field of micro-nano optics. Under the irradiation of left-hand circularly polarized light and right-hand circularly polarized light, the emergent light of the metasurface device can generate a binary grayscale image 1 and a binary grayscale image 2 at an angle 1 and generate a continuous grayscale image 1 and a continuous grayscale image 2 at an angle 2 respectively. By using the angle multiplexing characteristic of the cosine type hologram after the phase Bessel expansion and the spin multiplexing characteristic of the combination of the transmission phase and the geometric phase of the unit structure, the spin-angle multiplexing image display can be realized, and the switching of the nano printing image can be realized only by changing the observation angle and the rotation direction of the circular polarization incident light. The limitation of complex observation conditions and cumbersome switching conditions of a traditional nano printing image is overcome, the observation conditions and the switching conditions of the nano printing image are greatly simplified, and the information capacity of image display is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of micro-nano optics, and more specifically, relates to a design method for four-channel image display based on a spin-angle multiplexing metasurface. Background Art

[0002] Regarding the method of expanding the information capacity by combining spin multiplexing for the current display capacity of nano-printed images, this method usually combines the geometric phase and transmission phase of sub-wavelength unit structures to achieve different phase modulations of incident left-handed circularly polarized light and incident right-handed circularly polarized light, thereby achieving the effect of switching the circular polarization state of the incident light and then switching the nano-printed image. In addition, the sub-wavelength unit structure is optimized into a half-wave plate, combined with a polarizer and an analyzer, so as to achieve the effect of rotating the metasurface to adjust the intensity distribution of the outgoing light to realize the switching of the nano-printed image. These schemes are limited by the degree of freedom of regulation and can encode at most two nano-printed images, making it difficult to improve the display capacity of nano-printed images. Summary of the Invention

[0003] Aiming at the deficiencies of the existing schemes, the present invention proposes a design method for four-channel image display based on a spin-angle multiplexing metasurface based on the Bessel expansion characteristics of the cosine-type phase and the geometric phase and transmission phase characteristics of the sub-wavelength unit structure. This method uses the angle multiplexing characteristics of the outgoing light after Bessel expansion and the spin multiplexing characteristics of the sub-wavelength unit structure to theoretically prove the feasibility of realizing four holographic nano-printed images, and encodes two continuous grayscale holographic nano-printed images and two binary grayscale holographic nano-printed images into a single hologram, and conducts simulation verification. This method improves the display capacity of nano-printed images and promotes the application of metasurfaces in the fields of data storage, image display, information encryption, etc.

[0004] According to one aspect of the specification of the present invention, there is provided a design method for four-channel image display based on a spin-angle multiplexing metasurface, including: Deriving the initial hologram phase distributions for left-handed circularly polarized light and right-handed circularly polarized light respectively according to the target continuous grayscale image and the principle of angle multiplexing of the outgoing light, and then adjusting the phase according to the one-to-two mapping relationship and the gray values of the corresponding pixel points of the binary grayscale image to obtain the final hologram phase distributions for left-handed circularly polarized light and right-handed circularly polarized light respectively; Designing a unit structure for constructing a spin-angle multiplexing metasurface device, the unit structure including a substrate and nano-bricks on the working surface of the substrate; establishing an xoy coordinate system with the directions of two sides parallel to the working surface of the substrate as the x-axis and the y-axis; the nano-bricks are rectangular structures, the major axis and the minor axis of the nano-bricks are both parallel to the working surface of the substrate, and the rotation angle of the nano-bricks is the included angle between the major axis of the nano-bricks and the x-axis; Through an electromagnetic simulation software, the optimized unit structure enables the nano-bricks with different geometric parameters to achieve 16-step quantization of 2 phases, and each unit structure is equivalent to a half-wave plate. The unit structure adds a geometric phase and a transmission phase to the incident circularly polarized light. According to the transmission phase distribution of each pixel point on the hologram, arrange the unit structures with corresponding geometric parameters whose phase delay amounts are closest to the transmission phase. Then, according to the geometric phase distribution of each pixel point on the hologram, rotate each unit structure by an angle equal to half of the phase value to construct a spin-angle multiplexed metasurface device for realizing four-channel image holographic nano-printed image display.

[0005] As a further technical solution, the method further includes: When the incident left-handed circularly polarized light irradiates the hologram, at the outgoing light angle 1, a binary gray-scale image holographic nano-printed image 1 is decoded on the surface of the metasurface device; at the outgoing light angle 2, a continuous gray-scale image holographic nano-printed image 1 is decoded on the surface of the metasurface device; when the incident right-handed circularly polarized light irradiates the hologram, at the outgoing light angle 1, a binary gray-scale image holographic nano-printed image 2 is decoded on the surface of the metasurface device; at the outgoing light angle 2, a continuous gray-scale image holographic nano-printed image 2 is decoded on the surface of the metasurface device.

[0006] As a further technical solution, when the unit structure adds a geometric phase and a transmission phase to the incident circularly polarized light, it further includes: The geometric phase is related to the rotation angle of the unit structure and has a two-fold relationship with the rotation angle; the transmission phase is related to the geometric parameters of the unit structure.

[0007] As a further technical solution, the intensity distributions of the outgoing light at different angles are as follows: , where, represents the phase distribution of the hologram, represents the periodic phase, which divides the outgoing light into different angles, so as to encode different target gray-scale images on the outgoing light at different angles, represents the m-th order Bessel function of the first kind, , respectively represent the intensity distributions of the binary gray-scale image and the continuous gray-scale image.

[0008] As a further technical solution, when obtaining the final hologram phase distribution, it further includes: According to the mapping relationship in the outgoing light intensity distribution and the hologram phase formula, deduce the value corresponding to each pixel point of the continuous gray-scale image, so as to obtain the initial phase distribution. Then, according to the one-to-two mapping relationship and the gray-scale value of the corresponding pixel point of the binary gray-scale image, perform phase adjustment to obtain the final hologram phase distribution; According to the derived final holographic phase distribution and the relationship between the rotation angle of the unit structure and the phase modulation amount, determine the rotation angle of the nanobricks in the unit structure corresponding to each pixel point, and then arrange the optimized unit structures to construct a metasurface device capable of achieving angular multiplexing; Based on this angular multiplexing principle, further introduce the geometric phase and transmission phase of the unit structure to endow the spin multiplexing characteristics, and obtain the final holographic phase distributions for left-handed circularly polarized light and right-handed circularly polarized light respectively, so as to increase the information capacity of a single metasurface device to four images.

[0009] As a further technical solution, when optimizing the design of the unit structure, it further includes: Determine the height of the nanobricks and the distance between the centers of adjacent nanobricks according to the processing conditions; Use electromagnetic simulation software to perform parametric scanning on the major axis and minor axis dimensions of the nanobricks at the working wavelength, and simulate the reflectivity diagrams of the major axis and minor axis of the nanobricks at different dimensions, the phase and phase difference diagrams between the major axis and the minor axis, the transmission phase of the nanobricks, and the co-polarization and cross-polarization conversion efficiencies of the nanobricks; Select different-sized unit structures with 16-step transmission phase and high circular polarization conversion efficiency in the working band according to the scanning results.

[0010] As a further technical solution, the reflectivities of the major axis and minor axis of the selected unit structure are higher than 60%, and the phase difference between the major axis and the minor axis is close to and the transmission phase of the nanobricks is 16-step.

[0011] According to one aspect of the specification of the present invention, there is also provided a spin-angle multiplexing metasurface for realizing four-channel image display, which is constructed by using the four-channel image display design method based on the spin-angle multiplexing metasurface.

[0012] One or more technical solutions provided in the present invention have at least the following technical effects or advantages: The present invention selects the outgoing light angle 1, the outgoing light angle 2, the left-handed circularly polarized incident light, and the right-handed circularly polarized incident light as encoding channels respectively. Under the left-handed circularly polarized incident light, the binary gray-scale image 1 is encoded into the outgoing light angle 1 and the continuous gray-scale image 1 is encoded into the outgoing light angle 2. Under the right-handed circularly polarized incident light, the binary gray-scale image 2 is encoded into the outgoing light angle 1 and the continuous gray-scale image 2 is encoded into the outgoing light angle 2. Under the left-handed circularly polarized incident light and the right-handed circularly polarized incident light respectively, according to the angular multiplexing characteristic of the cosine-type phase Bessel expansion, the continuous gray-scale image is encoded into the initial hologram phase distribution, and then combined with the one-to-two mapping relationship and the gray-scale value of each pixel point on the binary gray-scale image, the phase of each pixel point on the hologram is adjusted, so as to obtain the final phase distributions respectively for the left-handed circularly polarized incident light and the right-handed circularly polarized incident light, improving the current display capacity of the nano-printed image.

[0013] The metasurface device provided by the present invention has a compact structure, and at the same time has the advantages of miniaturization and light weight. It can directly observe the image holographic nano-printed image without the assistance of a polarizer and an analyzer, and is expected to promote the practical application of nano-printed images in the fields of information multiplexing, information encryption, optical anti-counterfeiting, etc. Description of the Drawings

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings used in the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0015] Figure 1 It is a conceptual diagram of a spin-angle multiplexing metasurface device for realizing four-channel image display provided by an embodiment of the present invention.

[0016] Figure 2 It is a schematic diagram of the design principle for realizing the angular multiplexing of the metasurface device and the design flow of the angular multiplexing metasurface device provided by an embodiment of the present invention.

[0017] Figure 3 It is a schematic diagram of the spin multiplexing design principle of the angular multiplexing metasurface device provided by an embodiment of the present invention.

[0018] Figure 4 It is a simulation result diagram of four-channel image holographic nano-printed image display provided by an embodiment of the present invention. Detailed Embodiments

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. In addition, the technical features in each embodiment or individual embodiment provided by the present invention can be arbitrarily combined with each other to form a new technical solution. This combination is not restricted by the order of steps and / or the structural composition mode, but must be based on the ability of those of ordinary skill in the art to implement. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present invention. Embodiment 1

[0020] Embodiment 1 provides a four-channel image display design method based on a spin-angle multiplexing metasurface, including the following steps: Step 1: According to the target continuous grayscale image and the principle of outgoing light angle multiplexing, the initial hologram phase distributions for left-handed circularly polarized light and right-handed circularly polarized light are derived, and then the phase is adjusted according to the one-to-two mapping relationship and the grayscale values of the corresponding pixel points of the binary grayscale image to obtain the final hologram phase distributions for left-handed circularly polarized light and right-handed circularly polarized light and , where the geometric phase distribution is , and the transmission phase distribution is . When the incident left-handed circularly polarized light irradiates the hologram, at the outgoing light angle 1, a binary grayscale image holographic nanoprinting image 1 can be decoded on the surface of the metasurface device; at the outgoing light angle 2, a continuous grayscale image holographic nanoprinting image 1 can be decoded on the surface of the metasurface device; when the incident right-handed circularly polarized light irradiates the hologram, at the outgoing light angle 1, a binary grayscale image holographic nanoprinting image 2 can be decoded on the surface of the metasurface device; at the outgoing light angle 2, a continuous grayscale image holographic nanoprinting image 2 can be decoded on the surface of the metasurface device.

[0021] Step 2: Design a unit structure for constructing a spin-angle multiplexing metasurface device. The unit structure includes a substrate and nanobricks on the working surface of the substrate; an xoy coordinate system is established with the directions of two sides parallel to the working surface of the substrate as the x-axis and the y-axis; the nanobricks are rectangular structures, the major axis and minor axis of the nanobricks are both parallel to the working surface of the substrate, and the rotation angle of the nanobricks is the angle between the major axis of the nanobricks and the x-axis.

[0022] Step 3: Use electromagnetic simulation software to optimize the designed unit structure so that nanobricks with different geometric parameters achieve 16-step quantization of 2π phase, and each unit structure is equivalent to a half-wave plate. The reflectivities of the major axis and minor axis of the unit structure are higher than 60%, and the phase difference between the major axis and the minor axis is close to , and the unit structure adds geometric phase and transmission phase to the incident circularly polarized light. The geometric phase is related to the rotation angle of the unit structure and is twice the rotation angle; the transmission phase is related to the geometric parameters of the unit structure.

[0023] Step 4: According to the transmission phase distribution of each pixel point on the hologram, arrange the unit structures with corresponding geometric parameters whose phase delay is closest to the transmission phase. Then, according to the geometric phase distribution of each pixel point on the hologram, rotate each unit structure by an angle equal to half of the phase value to construct a spin-angle multiplexing metasurface device capable of realizing four-channel image holographic nanoprinting image display: When left-handed circularly polarized light is incident on the hologram, at the output light angle 1, a binary gray-scale image holographic nanoprinting image 1 can be decoded on the surface of the metasurface device; at the output light angle 2, a continuous gray-scale image holographic nanoprinting image 1 can be decoded on the surface of the metasurface device; when right-handed circularly polarized light is incident on the hologram, at the output light angle 1, a binary gray-scale image holographic nanoprinting image 2 can be decoded on the surface of the metasurface device; at the output light angle 2, a continuous gray-scale image holographic nanoprinting image 2 can be decoded on the surface of the metasurface device.

[0024] In the said Step 1, the intensity distributions of the output light at different angles are as follows: , wherein, represents the phase distribution of the hologram, represents the periodic phase, which divides the output light into different angles, so as to encode different target gray-scale images on the output light at different angles, represents the Bessel function of the first kind of order m, , represent the intensity distributions of the binary gray-scale image and the continuous gray-scale image respectively.

[0025] When obtaining the final hologram phase distribution, first, according to the mapping relationship between the output light intensity distribution and A in the hologram phase formula, deduce the value of A corresponding to each pixel point of the continuous gray-scale image, so as to obtain the initial phase distribution , and then perform phase adjustment according to the one-to-two mapping relationship and the gray-scale value of the corresponding pixel point of the binary gray-scale image to obtain the final hologram phase distribution According to the derived final holographic phase distribution and the relationship between the rotation angle of the unit structure and the phase modulation amount, determine the rotation angle of the nanobricks in the unit structure corresponding to each pixel point, and then arrange the optimized unit structures to construct a metasurface device capable of achieving angular multiplexing. Based on this angular multiplexing principle, by introducing the geometric phase and transmission phase of the unit structure to endow the spin multiplexing characteristics, the final holographic phase distributions for left-handed circularly polarized light and right-handed circularly polarized light can be obtained, expanding the information capacity of a single metasurface device to four images.

[0026] In step 3, when optimizing the design of the unit structure, first determine the height of the nanobricks and the distance between the centers of adjacent nanobricks according to the processing conditions, and then use electromagnetic simulation software to perform parametric scanning on the major and minor axis dimensions of the nanobricks at the working wavelength. The simulation obtains the schematic diagrams of the reflectivities of the major and minor axes of the nanobricks at different sizes, the schematic diagrams of the phase and phase difference between the major and minor axes, the transmission phase of the nanobricks, and the co-polarization and cross-polarization conversion efficiencies of the nanobricks. Finally, select different-sized unit structures with a 16-step transmission phase and high circular polarization conversion efficiency in the working band according to the scanning results.

[0027] The reflectivities of the major and minor axes of the selected unit structures are higher than 60%, the phase difference between the major and minor axes is close to π, and the transmission phase of the nanobricks is 16-step.

[0028] When parametrically scanning the unit structure, the major axis of the nanobricks is parallel to the x-axis, and periodic boundary conditions are used. Embodiment 2

[0029] Embodiment 2 provides a spin-angle multiplexing metasurface for realizing four-channel image display, which is obtained by using the construction method of four-channel image display based on the spin-angle multiplexing metasurface provided in Embodiment 1.

[0030] The following further describes this embodiment.

[0031] The metasurface device includes a substrate and nanobricks periodically arranged above the substrate, where both the substrate and the nanobricks are sub-wavelength in size. The substrate material is silicon-on-insulator, and the nanobrick material is single-crystalline silicon. The substrate is divided into square units of the same size, and a nanobrick is placed above the center of each unit. The side length of the square unit is equal to the distance between the centers of adjacent nanobricks. The designed working band of the metasurface device is red light (wavelength 630 nm). The following takes the working wavelength of 630 nm as an example for illustration.

[0032] Each of the nanobricks corresponds to an imaging pixel. Nanobricks with different sizes and different rotation angles add different geometric phases and transmission phase delays to incident light with a wavelength of 630 nm. By reasonably arranging the size and rotation angle distribution of the nanobricks, two independent holographic nano-printed images can be generated respectively under the irradiation of left-handed circularly polarized incident light and right-handed circularly polarized incident light without the assistance of any polarizer and analyzer.

[0033] Principle of different-sized nanobricks adding different transmission phase delays to 630-nm incident circularly polarized light: When incident circularly polarized light irradiates nanobricks with different sizes but the same rotation angle, the transmission phase delays added by different-sized nanobricks to 630-nm incident circularly polarized light can be calculated using the equivalent refractive index theory and electromagnetic simulation software. Then, the size of the nanobricks can be determined according to the requirements of the transmission phase delay.

[0034] Principle of different-rotation-angle nanobricks adding different geometric phase delays to 630-nm incident circularly polarized light: When incident circularly polarized light irradiates nanobricks with the same size but different rotation angles, by combining the Jones matrix of the incident circularly polarized light, the Jones matrix of the nanobricks, and the rotation matrix using the Jones matrix method, it can be deduced that the outgoing light contains circularly polarized light with the same polarization direction and circularly polarized light with the opposite polarization direction. Among them, the circularly polarized light with the same polarization direction has no additional phase, while the circularly polarized light with the opposite polarization direction has an additional phase, and the additional phase is twice the rotation angle of the nanobricks. Therefore, the rotation angle of the nanobricks can be determined only according to the requirements of the geometric phase delay.

[0035] When designing the size of the nanobricks, make the long axis of the nanobricks parallel to the x-axis. Parametric scanning is used to obtain the phases added by different-sized nanobricks to polarized light in the long-axis direction and short-axis direction, and the phase difference between the long axis and short axis of different-sized nanobricks under the irradiation of red light with a wavelength of 630 nm is obtained. At the same time, parametric scanning is used to obtain the transmission phase delay of red light with a wavelength of 630 nm and the co-polarization and cross-polarization conversion efficiencies for different-sized nanobricks. Finally, select different-sized nanobrick structures with a phase difference between the long axis and short axis of the nanobricks close to , with reflectivities of both the long axis and short axis of the nanobricks exceeding 60% and a 16-step transmission phase.

[0036] When obtaining the phase distribution of the hologram, first, according to the mapping relationship between the outgoing light intensity distribution and A in the hologram phase formula, the value of A corresponding to each pixel point of the continuous grayscale image is deduced to obtain the initial phase distribution , and then the phase is adjusted according to the one-to-two mapping relationship and the gray value of the corresponding pixel point of the binary grayscale image to obtain the final hologram phase distribution , so that a continuous grayscale image and a binary grayscale image are encoded into the hologram phase. Based on this principle, the final hologram phase distributions for left-handed circularly polarized light and right-handed circularly polarized light are obtained and , where the geometric phase distribution is , and the transmission phase distribution is .

[0037] Each nanobrick in the metasurface corresponds to a pixel. First, according to the transmission phase distribution of the hologram obtained from the above derivation as , determine the size of the nanobrick, and then according to the geometric phase distribution of the hologram as and the relationship between the rotation angle of the unit structure and the phase modulation amount, determine the rotation angle distribution of the nanobrick . When a 630 nm circularly polarized incident light irradiates the metasurface device, the intensity distributions of the outgoing light at angle 1 and the outgoing light at angle 2 are:

[0038] where, , respectively represent the phase distributions of the hologram under left-handed circularly polarized incident light and right-handed circularly polarized incident light, represents the periodic phase, which divides the outgoing light into different angles, so as to encode different target grayscale images on the outgoing light at different angles, represents the m-th order Bessel function of the first kind. , and , respectively represent the intensity distributions of the binary grayscale image and the continuous grayscale image under left-handed circularly polarized incident light and right-handed circularly polarized incident light.

[0039] Without the assistance of any polarizer and analyzer, irradiate the metasurface device with left-handed circularly polarized light and right-handed circularly polarized light with a wavelength of 630 nm, and binary grayscale image 1 and binary grayscale image 2 can be generated at angle 1 respectively, and continuous grayscale image 1 and continuous grayscale image 2 can be generated at angle 2.

[0040] A construction method for a spin-angle multiplexing metasurface device for realizing four-channel image display includes the following steps: (1) Determine the materials and basic structures of the substrate and the nanobrick. The two mutually perpendicular sides of the substrate are the x-axis and the y-axis. Determine the height H of the nanobrick and the side length of the square substrate unit according to the processing conditions.

[0041] (2) Optimize the designed unit structure size: Under the incidence of x - polarized light and y - polarized light, the major and minor axis dimensions of the parametrically scanned nanobricks are measured, and the reflectivities of the major and minor axes of nanobricks with different dimensions and the phase difference between the major and minor axes of nanobricks with different dimensions are simulated. Under the incidence of circularly polarized light, the transmission phase and the co - polarized and cross - polarized conversion efficiencies of nanobricks with different dimensions are simulated. Finally, different - sized unit structures with a 16 - step transmission phase and high circular - polarization conversion efficiency in the working band are selected according to the scanning results.

[0042] (3) Determine the hologram phase distribution that acts simultaneously on left - hand circularly polarized incident light and right - hand circularly polarized incident light according to the mapping relationship between the intensity distribution of the target binary gray - scale image, the intensity distribution of the target continuous gray - scale image, and the angular multiplexing characteristics after the cosine - type phase Bessel expansion. First, determine the size of the nanobricks according to the transmission phase distribution of the hologram, and then determine the angular distribution of the nanobricks according to the geometric phase distribution of the hologram and the relationship between the rotation angle of the unit structure and the phase modulation amount.

[0043] The following further explains the present invention with reference to the accompanying drawings.

[0044] Figure 1 It is a conceptual diagram of a spin - angle multiplexing metasurface device for realizing four - channel image display. The metasurface device is composed of silicon - on - insulator, including single - crystal silicon nanobricks with different sizes and different rotation angles. When left - hand circularly polarized incident light and right - hand circularly polarized light are respectively irradiated on the metasurface device, a binary gray - scale image 1 and a binary gray - scale image 2 are respectively generated at angle 1, and a continuous gray - scale image 1 and a continuous gray - scale image 2 are generated at angle 2.

[0045] The design principle for realizing the angle multiplexing of the metasurface device is as shown in Figure 2 the left - hand part. When the phase distribution of the metasurface device is , when the incident light irradiates on the metasurface, the outgoing light can be divided into outgoing lights at different angles. Among them, the light - field intensity distribution of the outgoing light at angle 1 is:

[0046] The light - field intensity distribution of the outgoing light at angle 2 is:

[0047] According to the mapping relationship between the intensity of the outgoing light at angle 2 and A in the hologram phase, it can be known that one intensity value of the continuous gray - scale image can correspond to two A values. In the mapping relationship between the intensity of the outgoing light at angle 1 and the hologram phase, the two A values can respectively correspond to two states of "black" and "white". Combining with the gray - scale values of the binary gray - scale image, the A values that meet the design requirements are selected, so as to realize the simultaneous encoding of a binary gray - scale image and a continuous gray - scale image by a metasurface device. Figure 2The right part is the design flow chart of the angle multiplexing metasurface device. First, based on the intensity distribution of the continuous grayscale image and the mapping relationship between the intensity of the light emitted at angle 2 and the hologram phase, the initial phase distribution is deduced. , and then the phase is adjusted according to the one-to-two mapping relationship and the grayscale values of the corresponding pixels of the binarized grayscale image to obtain the final hologram phase distribution. , thereby realizing the simultaneous encoding of two grayscale images.

[0048] Figure 3 The spin multiplexing design principle of the angle multiplexing metasurface device. First, the phase distributions are obtained from the binarized grayscale image 1, the continuous grayscale image 1, the binarized grayscale image 2, and the continuous grayscale image 2 respectively. and , based on which the transmission phase distribution and the geometric phase distribution can be obtained. According to the transmission phase distribution, the size of the nanobricks on each pixel can be determined, and according to the geometric phase distribution, the rotation angle of the nanobricks on each pixel can be determined, and thus the final morphology of the metasurface device can be determined.

[0049] In this embodiment, the number of pixels of the metasurface device is 1000*1000, which is the same as the number of pixels of the target image. The working wavelength is 630 nm. The period CS of the selected nanobricks is 400 nm, and the height H is 220 nm. The CST electromagnetic simulation software is used to perform parametric scanning on the length and width dimensions of the nanobricks at the working wavelength, and the periodic boundary condition is used. The scanning range of the short axis is 60 nm - 140 nm, the scanning range of the long axis is 180 nm - 320 nm, and the step size is 5 nm. The reflectivity of the length and width and the phase difference between the length and the width of the nanobricks with different sizes under the incidence of x-polarized light and y-polarized light are obtained by simulation; the transmission phase and the co-polarization and cross-polarization conversion efficiencies of the nanobricks with different sizes under the incidence of circularly polarized light are obtained by simulation. Finally, according to the goal of high circular polarization conversion efficiency and 16-step transmission phase in the working band, the following 16 types of nanobricks are selected, as shown in Table 1.

[0050] Table 1 Structural parameters corresponding to sixteen groups of nanobricks

[0051]

[0052] According to the transmission phase distribution the size of the nanobricks on each pixel can be determined, and according to the geometric phase distribution Then, the rotation angles of the nano-bricks at each pixel number can be determined. Then, when the left-handed circularly polarized incident light with a wavelength of 630 nm is irradiated onto the metasurface device, a binary gray-scale image 1 that highly conforms to the target image will be generated at angle 1 and a continuous gray-scale image 1 that highly conforms to the target image will be generated at angle 2, as shown in Figure 4 the left half; when the right-handed circularly polarized incident light with a wavelength of 630 nm is irradiated onto the metasurface device, a binary gray-scale image 2 that highly conforms to the target image will be generated at angle 1 and a continuous gray-scale image 2 that highly conforms to the target image will be generated at angle 2, as shown in Figure 4 the right half.

[0053] In summary of the above embodiments, a four-channel image display design method based on spin-angle multiplexing metasurface provided by the present invention has at least the following technical effects: (1) Under the irradiation of left-handed circularly polarized light and right-handed circularly polarized light, the outgoing light of the metasurface device will generate a binary gray-scale image 1 and a binary gray-scale image 2 at angle 1, and a continuous gray-scale image 1 and a continuous gray-scale image 2 at angle 2, respectively. By utilizing the angle multiplexing characteristic after the cosine-type hologram phase Bessel expansion and the spin multiplexing characteristic combining the transmission phase and geometric phase of the unit structure, spin-angle multiplexing image display can be realized. The switching of the nano-printed image can be achieved only by changing the observation angle and the handedness of the circularly polarized incident light, overcoming the limitations of the complex observation conditions and cumbersome switching conditions of the traditional nano-printed image, greatly simplifying the observation conditions and switching conditions of the nano-printed image, and enhancing the information capacity of the image display.

[0054] (2) The metasurface device provided by the present invention has a compact structure, and at the same time has the advantages of miniaturization and light weight, and has a large information capacity. It can directly observe holographic nano-printed images without the assistance of a polarizer and an analyzer, and is expected to promote the practical applications of nano-printed images in the fields of information multiplexing, information encryption, optical anti-counterfeiting, etc.

[0055] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A four-channel image display design method based on spin-angle multiplexing metasurface, characterized in that: include: The initial hologram phase distributions for left-handed circularly polarized light and right-handed circularly polarized light are derived according to the target continuous grayscale image and the principle of multiplexing of the outgoing light angle, and then the phases are adjusted according to the one-to-two mapping relationship and the grayscale values ​​of the corresponding pixels of the binary grayscale image to obtain the final hologram phase distributions for left-handed circularly polarized light and right-handed circularly polarized light; A unit structure for constructing a spin-angle multiplexing metasurface device is designed, wherein the unit structure includes a substrate and a nanobrick on a working surface of the substrate; an xoy coordinate system is established with the directions of two sides parallel to the working surface of the substrate as the x-axis and the y-axis; the nanobrick is a rectangular structure, the major axis and the minor axis of the nanobrick are both parallel to the working surface of the substrate, and the rotation angle of the nanobrick is the angle between the major axis of the nanobrick and the x-axis; Through electromagnetic simulation software, the unit structure is optimized to enable nanobricks with different geometric parameters to achieve 16 steps of 2p phase, and each unit structure is equivalent to a half-wave plate, and the unit structure adds geometric phase and transmission phase to the incident circularly polarized light; According to the transmission phase distribution of each pixel point on the hologram, the unit structure with the phase delay closest to the corresponding geometric parameters of the transmission phase is arranged. Then, according to the geometric phase distribution of each pixel point on the hologram, each unit structure is rotated with an angle equal to half of the phase value, thereby constructing a spin-angle multiplexing metasurface device for realizing four-channel holographic nano-printed image display.

2. According to claim 1, a four-channel image display design method based on spin-angle multiplexing metasurface is characterized in that: The method further comprises: When incident left-handed circularly polarized light is irradiated onto the hologram, at the exit light angle 1, the surface of the metasurface device decodes a binary grayscale image holographic nano-printed image 1; at the exit light angle 2, the surface of the metasurface device decodes a continuous grayscale image holographic nano-printed image 1; when incident right-handed circularly polarized light is irradiated onto the hologram, at the exit light angle 1, the surface of the metasurface device decodes a binary grayscale image holographic nano-printed image 2; at the exit light angle 2, the surface of the metasurface device decodes a continuous grayscale image holographic nano-printed image 2.

3. According to claim 1, a four-channel image display design method based on spin-angle multiplexing metasurface is characterized in that: The unit structure adds a geometric phase and a transmission phase to the incident circularly polarized light, and further includes: The geometric phase is related to the rotation angle of the unit structure and is twice the rotation angle; the transmission phase is related to the geometric parameters of the unit structure.

4. According to claim 2, a four-channel image display design method based on spin-angle multiplexing metasurface is characterized in that: The intensity distribution of light emitted at different angles is as follows: ， in, represents the phase distribution of the hologram, Represents a periodic phase, which divides the outgoing light into different angles, thereby encoding different target grayscale images on the outgoing light at different angles. represents the m-th order Bessel function of the first kind, , Represent the intensity distribution of binary grayscale image and continuous grayscale image respectively.

5. The four-channel image display design method based on spin-angle multiplexing metasurface according to claim 4, characterized in that: When obtaining the final hologram phase distribution, it also includes: According to the mapping relationship between the intensity distribution of the emitted light and the phase formula of the hologram, the value corresponding to each pixel of the continuous grayscale image is derived to obtain the initial phase distribution, and then the phase is adjusted according to the one-to-two mapping relationship and the grayscale value of the corresponding pixel of the binary grayscale image to obtain the final hologram phase distribution; According to the derived final hologram phase distribution and the relationship between the rotation angle of the unit structure and the phase control amount, the rotation angle of the nanobricks in the unit structure corresponding to each pixel is determined, and then the optimized unit structure is arranged to construct a metasurface device that can achieve angle multiplexing; Based on this angle multiplexing principle, the spin multiplexing characteristics imparted by the geometric phase and transmission phase of the unit structure are introduced to obtain the final hologram phase distribution for left-handed circularly polarized light and right-handed circularly polarized light respectively, thereby expanding the information capacity of a single metasurface device to four images.

6. The four-channel image display design method based on spin-angle multiplexing metasurface according to claim 1, characterized in that: When optimizing the design of the unit structure, it also includes: Determine the height of the nanobricks and the distance between the center points of adjacent nanobricks according to the processing conditions; The electromagnetic simulation software was used to perform parametric scanning of the long axis and short axis dimensions of the nanobrick at the working wavelength, and the simulation obtained the schematic diagram of the long axis and short axis reflectivity of the nanobrick at different sizes, the schematic diagram of the phase and phase difference between the long axis and the short axis, the transmission phase of the nanobrick, and the co-directional and reverse polarization conversion efficiency of the nanobrick; According to the scanning results, unit structures of different sizes with 16-step transmission phase and high circular polarization conversion efficiency in the working band are selected.

7. The four-channel image display design method based on spin-angle multiplexing metasurface according to claim 6, characterized in that: The long-axis and short-axis reflectivity of the selected unit structure is higher than 60%, and the phase difference between the long axis and the short axis is close to And the transmission phase of the nanobrick is 16 steps.

8. A spin-angle multiplexing metasurface for realizing four-channel image display, which is constructed using the four-channel image display design method based on the spin-angle multiplexing metasurface described in any one of claims 1 to 7.

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