Three-Dimensional Vector Holographic Imaging Method Based on Metasurface

Abstract

The three-dimensional vector holographic imaging method based on metasurface disclosed by the present invention belongs to the technical fields of micro-nano optics, diffractive optics and holographic imaging applications. The implementation method of the present invention is as follows: the manipulation of the polarization state of the holographic reconstruction image is introduced into the hologram calculation process, the required polarization response constraints are applied in different reconstruction image planes, and the polarization state of the three-dimensional holographic reconstruction image is arbitrarily manipulated. Using the matrix polar decomposition method, a hologram in the form of a unitary matrix is generated according to the electric field distribution obtained by backpropagation. By combining the polarization rotation matrix with the birefringence characteristics of the metasurface, the Jones matrix of each unit is customized, and the hologram in the form of a unitary matrix is encoded in the metasurface. According to the size and azimuth angle of each unit nanorod of the metasurface, a processing file for the corresponding dielectric metasurface structure is generated. When incident light with an arbitrary polarization state irradiates the metasurface, the holographic reconstruction images at different planes can present different polarization information, realizing the reconstruction of three-dimensional vector holographic images.

Description

Technical Field

[0001] The present invention relates to a holographic imaging method, in particular to a three-dimensional vector holographic imaging method based on metasurface, belonging to the technical fields of micro-nano optics, diffractive optics and holographic imaging applications. Background Art

[0002] Arbitrarily manipulating physical quantities such as the amplitude, phase, and polarization of the outgoing light in three-dimensional space has very important research value. The polarization characteristics related to the propagation process can provide new design freedoms for the generation of high-dimensional structured light. Usually, for a light beam propagating in free space (without any interference), its polarization state generally does not change with the propagation of light. By utilizing the optical activity of birefringent materials, the polarization direction of the light beam can be continuously rotated as it propagates by inserting a birefringent material into the optical path. However, the optical activity of birefringent materials in nature is relatively low, and a relatively large volume of birefringent material usually needs to be inserted into the optical path to achieve a 180° rotation of the polarization direction of the light beam. To solve this problem, researchers have proposed various methods for realizing the polarization control of the light field along the propagation direction. For example, encoding the phase distribution of a conical lens in a spatial light modulator, based on the simultaneous control of the polarization and phase of the outgoing light beam, and using the transverse-longitudinal mapping relationship when generating a Bessel beam with a conical lens to achieve the control of the polarization state at different propagation distances. At the same time, for the orthogonal polarization components in the outgoing light beam, by introducing an amplitude or phase change related to the propagation distance, the polarization control of the light field along the propagation direction can also be achieved. However, such methods have disadvantages such as a relatively complex experimental optical path and a relatively large volume of the optical elements used. This limits the realization of polarization control along the propagation direction in a miniaturized optical system.

[0003] With the continuous advancement of micro-nano processing technology, metasurfaces have demonstrated powerful wavefront control capabilities, and can arbitrarily control the amplitude, phase, polarization state and other physical properties of the outgoing light beam with sub-wavelength resolution. It has been widely used in the fields of beam shaping, superlenses, holographic imaging, nonlinear optics, and the generation and detection of polarization states. By utilizing the anisotropy of metaatoms and carefully designing the azimuth angles of each metaatom in the plane, the polarization direction of each point on the cross section of the outgoing light beam can be controlled, thereby realizing the generation of cylindrical vector beams, vector vortex beams and Poincare beams. In addition, the unique sub-wavelength pixel resolution of metasurfaces makes the holographic reconstruction image generated by metasurfaces have the advantages of high resolution, large field of view, and no multi-order diffraction crosstalk, which makes up for the shortcomings of traditional holographic imaging based on spatial light modulators. At the same time, metasurfaces can also manipulate the polarization information of the generated holographic reconstruction image, so that the generated holographic reconstruction image has uneven polarization state distribution characteristics. However, previous metasurface-based vector holographic methods have all manipulated the polarization state distribution within a specific reconstructed image plane, and no solution has yet been able to achieve the reconstruction of a three-dimensional vector holographic image. Summary of the invention

[0004] The purpose of the present invention is to provide a three-dimensional vector holographic imaging method based on a metasurface, which combines the hologram calculation method of a three-dimensional image with the Jones matrix method to generate a hologram in a matrix form, and manipulates the polarization response of holographic reconstruction images in different planes so that the holographic reconstruction images at different planes have different polarization information. That is, the present invention can realize the manipulation of the polarization dimension along the z direction while retaining the three-dimensional holographic imaging function, thereby realizing three-dimensional vector holographic imaging.

[0005] The object of the present invention is achieved through the following technical solutions.

[0006] The three-dimensional vector holographic imaging method based on metasurface disclosed in the present invention combines the three-dimensional image hologram calculation method with the Jones matrix method, that is, the manipulation of the polarization state of the holographic reconstruction image is introduced into the hologram calculation process, and the required polarization response restrictions are imposed on different reconstruction image planes along the z direction, so as to arbitrarily manipulate the polarization state of the three-dimensional holographic reconstruction image. Using the matrix polar decomposition method, a unitary matrix hologram is generated on the hologram plane according to the electric field distribution obtained by back propagation. The metasurface for realizing three-dimensional vector holographic imaging is composed of an array of dielectric nanocolumns with different geometric sizes and different azimuth angles having a rectangular cross-section. By combining the polarization rotation matrix with the birefringence characteristics of the dielectric metasurface, the Jones matrix of each unit is customized, and the generated hologram in the form of a unitary matrix is encoded in the metasurface. According to the size and azimuth angle of each unit nanocolumn of the metasurface, a processing file for the corresponding dielectric metasurface structure is generated. The transmissive dielectric metasurface is processed by the micro-nano processing technology of electron beam lithography. When incident light with any polarization state irradiates the metasurface, the holographic reconstructed images at different planes can present different polarization information, thus realizing the reconstruction of three-dimensional vector holographic images.

[0007] The three-dimensional vector holographic imaging method based on a metasurface disclosed in the present invention includes the following steps:

[0008] Step 1: Select a three-dimensional image with a contrast meeting the preset standard requirements as the original image for realizing three-dimensional vector holographic imaging. By combining the hologram calculation method of the three-dimensional image with the Jones matrix method, that is, introducing the manipulation of the polarization state of the holographic reconstructed image into the hologram calculation process, applying the required polarization response constraints along the z direction at different reconstructed image planes, and arbitrarily manipulating the polarization state of the three-dimensional holographic reconstructed image. Using the matrix polar decomposition method, a hologram in the form of a unitary matrix is generated in the hologram plane according to the electric field distribution obtained by backpropagation.

[0009] Select a three-dimensional image with a contrast meeting the preset standard requirements as the original image for realizing three-dimensional vector holographic imaging. Sample the selected three-dimensional image and slice the three-dimensional image into N mutually parallel planes. For the nth reconstructed image plane (n = 1, 2, 3,..., N), its amplitude and phase distributions are represented by A n and Simultaneously, specific polarization response constraints are applied at different reconstructed image planes such that the holographic reconstructed images at different planes are equivalent to polarization elements with specific polarization responses. The polarization elements are polarizers with arbitrary transmission axis directions or wave plates with arbitrary fast axis directions. Limited by a single-layer metasurface, the polarization response should be a symmetric 2×2 matrix. In addition, the propagation process between the hologram plane and the reconstructed image planes at different reconstruction distances is realized by the backpropagation method. The backpropagation method is realized based on the backpropagation formula shown in formula (1).

[0010]

[0011] Formula (1) describes the propagation process from different reconstructed images to the hologram plane. Among them, represents the backpropagation method. The coordinates of the hologram plane and the reconstructed image plane are respectively represented by (x h, y h ), and (x o , y o ) is represented. Using the matrix polar decomposition method, the complex amplitude distribution in matrix form is decomposed into the form of the product of a Hermitian matrix and a unitary matrix . Discarding the Hermitian matrix part, the hologram in the form of a unitary matrix

[0012] The hologram calculation method of the three-dimensional image described in Step 1 includes the Fresnel algorithm, the point source method, and the angular spectrum method.

[0013] When the hologram calculation method of the three-dimensional image selects the Fresnel algorithm or the angular spectrum method to calculate the hologram in the form of a unitary matrix It is necessary to use the forward and backward propagation methods to iteratively calculate the electric field distributions in the hologram plane and the reconstructed image plane, and generate the hologram in the form of a unitary matrix according to the electric field distributions obtained by the iterative calculation

[0014] The forward propagation method is implemented based on the forward propagation formula shown in Equation (2).

[0015]

[0016] Among them, represents the forward propagation method. The specific forward formulas based on the Fresnel algorithm and the angular spectrum method are shown in Equations (3) and (4).

[0017]

[0018]

[0019] In the formula, represents the complex amplitude distribution in matrix form of the nth reconstructed image plane, λ is the wavelength of the incident light, k is the wave vector of the incident light, f x and f y are spatial frequencies, and z is the propagation distance. And F and F -1 represent the Fourier transform and the inverse Fourier transform.

[0020] Step 2: The metasurface for realizing three-dimensional vector holographic imaging is composed of a medium nanocylinder array with different geometric sizes and different azimuth angles having a rectangular cross-section. By combining the polarization rotation matrix with the birefringence characteristics of the dielectric metasurface, the Jones matrix of each unit is customized, and the hologram in the form of a unitary matrix generated in Step 1 is encoded in the metasurface, and a processing file for the corresponding dielectric metasurface structure is generated according to the size and azimuth angle of each unit nanocylinder of the metasurface. The geometric sizes include the major axis length L, minor axis length W, height H of the nanocylinder, and the period length P of the metasurface unit.

[0021] The metasurface for realizing three-dimensional vector holographic imaging is composed of a medium nanocylinder array with different geometric sizes and different azimuth angles having a rectangular cross-section. The Jones vectors of the outgoing and incoming light beams corresponding to each unit of the metasurface are associated using the Jones matrix method.

[0022] The Jones vector E of the outgoing light beam out is calculated by formula (5) as:

[0023]

[0024] where t ij (i = x or y) is the transmission coefficient, and j and i represent the polarization directions of the incoming and outgoing light beams respectively. When the dielectric nanocylinder structure in the metasurface unit has a high transmittance, the Jones matrix T corresponding to this unit is equivalent to a symmetric unitary matrix. The Jones matrix T satisfying the unitary matrix condition is decomposed according to its eigenvectors and eigenvalue matrix (Δ) as:

[0025]

[0026] In the formula, the matrix V represents a two-dimensional rotation matrix in the plane, and the rotation angle is θ. According to formula (6), when the incident light (E in ) is incident on the dielectric nanocylinder, the electric field vector E of the incident light in first rotates -θ degrees in the plane. The dielectric nanocylinder introduces phase shifts φ x and φ y to the x and y components of the rotated electric field vector respectively. Then the electric field vector with the introduced phase shift is rotated by θ degrees and converted back to the initial coordinate system. According to the propagation phase principle, different-sized nanocylinder arrays can be used to realize the corresponding phase shifts φ x and φ y , and the hologram in the form of a unitary matrix calculated by formula (1) is encoded in the metasurface.

[0027] When the nanocylinder height H and period P are fixed, by changing the major axis length L and minor axis length W of the nanocylinder, the transmission coefficient t corresponding to different-sized nanocylinders is obtained through two-dimensional scanning using simulation softwarexx and t yy During simulation, the wavelength of the incident light, the type of material constituting the nanocolumns, the height H and the period P of the nanocolumns should be selected so that the phase of the transmission coefficient and can cover 0 to 2π. At the same time, the amplitudes abs(t xx ) and abs(t yy ) should be as close as possible to 1, so that the Jones matrix T of each unit of the metasurface satisfies the unitary matrix condition. By changing the geometric dimensions and azimuth angles of the nanocolumn units, that is, encoding the hologram in the form of the calculated unitary matrix into the metasurface, a processing file for the corresponding dielectric metasurface structure is generated.

[0028] The simulation software described in step two uses RCWA based on the rigorous coupled wave analysis method, FDTD based on the finite difference time domain method, or COMSOL based on the finite element method.

[0029] Step three: Using the processing file of the dielectric metasurface structure obtained in step two, a transmissive dielectric metasurface is prepared. By manipulating the polarization response of different planar holographic reconstruction images, the holographic reconstruction images at different planes along the z direction can present different polarization information under the illumination of incident light in any polarization state, thereby realizing three-dimensional vector holographic imaging.

[0030] It also includes step four: According to steps one to three to realize three-dimensional vector holographic imaging, on the basis of retaining the three-dimensional holographic imaging function, it can also realize the manipulation of the polarization dimension along the z direction. Applying the three-dimensional vector holographic imaging method to the fields of beam shaping, particle manipulation, and information encryption to solve related engineering and technical problems.

[0031] In the field of beam shaping, the three-dimensional vector holographic imaging method can simultaneously manipulate the amplitude, phase, and polarization of any point in the three-dimensional light field, which is beneficial to generating complex three-dimensional structured beams.

[0032] In the field of particle manipulation, the three-dimensional vector holographic imaging method can generate multiple polarization-controllable foci in three-dimensional space, which is beneficial to simultaneously manipulating multiple particles in three-dimensional space.

[0033] In the field of information encryption, the three-dimensional vector holographic imaging method can realize a three-dimensional light field with complex polarization characteristics, and can store the information to be encrypted in the polarization dimension of the light field.

[0034] Beneficial effects:

[0035] 1. The three-dimensional vector holographic imaging method based on metasurface disclosed by the present invention combines the hologram calculation method of three-dimensional images with the Jones matrix method, generates a hologram in the form of a unitary matrix by using the polar decomposition method of the matrix, and encodes it in the dielectric metasurface. By manipulating the polarization response of the holographic reproduction images on different planes, the holographic reproduction images on different planes can present different polarization information under the illumination of incident light in any polarization state, thereby realizing three-dimensional vector holographic imaging.

[0036] 2. The three-dimensional vector holographic imaging method based on metasurface disclosed by the present invention applies polarization response restrictions on different reproduction image planes along the z direction such that the holographic reproduction images on different planes are equivalent to polarization elements (polarizers with arbitrary transmission axis directions or wave plates with arbitrary fast axis directions) with corresponding polarization responses.

[0037] 3. The three-dimensional vector holographic imaging method based on metasurface disclosed by the present invention realizes the manipulation of the polarization state of the three-dimensional holographic reproduction image by applying different polarization response restrictions at different reproduction distances along the z direction, and has no strict requirements on the polarization state of the incident light beam. Under the illumination of incident light in any polarization state, the reproduction of three-dimensional vector holographic images can be realized. The polarization state of the reproduction image at different reproduction distances is calculated according to the Jones vector of the incident light and the applied polarization response restrictions and the polarization state of the reproduction image is quantitatively manipulated by changing the polarization state of the incident light.

[0038] 4. The three-dimensional vector holographic imaging method based on metasurface disclosed by the present invention, on the basis of realizing the above beneficial effects 1, 2, and 3, while retaining the advantages of three-dimensional holographic imaging, can also perform manipulation in the polarization dimension along the z direction, that is, can arbitrarily manipulate physical quantities such as the amplitude, phase, and polarization of the three-dimensional light field, and apply the three-dimensional vector holographic imaging method to the fields of beam shaping, particle manipulation, and information encryption to solve related engineering and technical problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of a three-dimensional vector holographic imaging method based on metasurface of the present invention;

[0040] Figure 2 is a schematic diagram of a three-dimensional vector holographic imaging method based on metasurface in an embodiment of the present invention;

[0041] Figure 3 is a two-dimensional scanning result of the transmission coefficients of nanocolumns of different sizes in an embodiment of the present invention;

[0042] where: (a) - schematic diagram of a rectangular nanocolumn structure, (b) - amplitude scanning result of the transmission coefficient t xx amplitude scanning result, (c) - transmission coefficient t yyAmplitude scan results, (d) - Transmission coefficient t xx Phase scan results, (e) - Transmission coefficient t yy Phase scan results;

[0043] Figure 4 is the experimental optical path diagram used in the embodiments of the present invention;

[0044] where: 1 - Linear polarizer LP1, 2 - Half-wave plate HWP, 3 - Dielectric metasurface, 4 - Microscope objective, 5 - Linear polarizer LP2, 6 - CCD;

[0045] Figure 5 are the theoretical and experimental results of the three-dimensional vector holographic imaging method in the embodiments of the present invention. Detailed implementation manners

[0046] The present invention will be described in detail below in conjunction with the drawings and embodiments. At the same time, the technical problems solved by the technical solution of the present invention and the beneficial effects are also described. It should be noted that the described embodiments are only for facilitating the understanding of the present invention and do not impose any limitations on it.

[0047] As Figure 1 shown, the multi-plane vector holographic imaging method based on metasurface disclosed in this embodiment is specifically implemented as follows:

[0048] Step 1: Select a three-dimensional image with a contrast meeting the preset standard requirements as the original image for realizing three-dimensional vector holographic imaging. By combining the hologram calculation method of the three-dimensional image with the Jones matrix method, that is, introducing the manipulation of the polarization state of the holographic reconstructed image into the hologram calculation process, applying the required polarization response constraints in different reconstructed image planes along the z direction, and arbitrarily manipulating the polarization state of the three-dimensional holographic reconstructed image. Using the matrix polar decomposition method, generate a hologram in the form of a unitary matrix according to the electric field distribution obtained by backpropagation in the hologram plane

[0049] First, select a hollow spiral pattern along the z direction for three-dimensional vector holographic imaging. As Figure 2 shown, the spiral has 3 pitches, each pitch length is 500 μm, and the spiral diameter is 150 μm. Then, sample the spiral and divide it into 200 point sources located in different reconstructed image planes. These point sources are evenly distributed in the range from 500 μm to 2000 μm away from the metasurface. For the point source n located in the nth reconstructed image plane, apply a specific polarization response constraint to make it exhibit the polarization characteristics of a half-wave plate with the fast axis along the θ f,,n direction. This polarization response constraint is represented by formula (7):

[0050]

[0051] In the process of generating a hologram in the form of a unitary matrix each corresponding θ of the point source f,,n is uniformly increased from 0° to 90°. Therefore, this helix is regarded as a half-wave plate with a gradually changing fast-axis direction along the z direction. The point-source method is usually used to calculate the hologram of a three-dimensional image. It splits the three-dimensional image into many point sources, and each point source radiates spherical waves outward. By accumulating the electric field distributions radiated by all point sources in the hologram plane, the corresponding hologram is obtained. Combining the point-source method with the Jones matrix method can effectively control the polarization response of each point source to achieve three-dimensional vector holography. The backward propagation process of the vector point-source method is represented by formula (8):

[0052]

[0053] where N represents the total number of point sources included in the three-dimensional image, A n is the amplitude of each point source, represents a certain point source (x n , y n , z n ) in three-dimensional space and a certain point (x h , y h , z h ) in the hologram plane. is a random phase used to obtain a hologram with a relatively uniform amplitude distribution. Using the matrix polar decomposition method, the complex amplitude distribution in matrix form is decomposed into the product form of a Hermitian matrix and a unitary matrix . Discarding the Hermitian matrix part, the hologram in the form of a unitary matrix is obtained. This decomposition process is similar to obtaining a pure-phase hologram from the complex amplitude distribution in the traditional holographic method.

[0054] Step 2: The metasurface for realizing three-dimensional vector holographic imaging is composed of a dielectric nanocylinder array with different geometric sizes and different azimuth angles having a rectangular cross-section. By combining the polarization rotation matrix with the birefringence characteristics of the dielectric metasurface, the Jones matrix of each unit is customized, and the hologram in the form of a unitary matrix generated in Step 1 is encoded into the metasurface. According to the size and azimuth angle of each unit nanocylinder of the metasurface, a processing file for the corresponding dielectric metasurface structure is generated. The said geometric sizes include the major-axis length L, minor-axis length W, height H of the nanocylinder, and the period length P of the metasurface unit.

[0055] The designed metasurface is composed of amorphous silicon nanocolumns with different sizes and azimuth angles. The working wavelength is 800 nm. With the height H and period P of the nanocolumns fixed, a two-dimensional scan (L: 60 nm to 280 nm, W: 60 nm to 280 nm) of the geometric dimensions of the nanocolumns is performed using the Rigorous Coupled-Wave Analysis (RCWA) method, and the transmission coefficients t corresponding to different-sized nanocolumns as shown in Figure 3 are obtained. xx And t yy . During the simulation, the refractive indices of the amorphous silicon nanocolumns and the fused silica substrate are set to n Si = 3.802 and n sub = 1.5 respectively. When linearly polarized light in the x-direction passes through nanocolumns of different sizes, the amplitude abs(t xx ) and the phase xx of the transmission coefficient t are calculated from the simulated electric field data. Similarly, when the polarization direction of the incident light is changed to the y-direction, the amplitude abs(t yy ) and the phase yy of the corresponding transmission coefficient t are obtained. During the simulation, the wavelength of the incident light, the type of material forming the nanocolumns, the height H and period P of the nanocolumns should be reasonably selected so that the phases and of the transmission coefficients can cover 0 to 2π. At the same time, the amplitudes abs(t xx ) and abs(t yy ) of the transmission coefficients should be as close to 1 as possible, so that the Jones matrix T of each unit of the metasurface satisfies the unitary matrix condition. During the process of determining the geometric dimensions of the nanocolumns, it is necessary to ensure that the error ε shown in formula (9) is as small as possible, so that the Jones matrix corresponding to the designed nanocolumns is as close as possible to the expected unitary matrix.

[0056] ε = abs(t xx - exp(iφ x )) + abs(t yy - exp(iφ y )) (9)

[0057] Finally, the height H of the nanocolumns is determined to be 600 nm, the period P is 400 nm, and both the major axis length L and the minor axis length W are in the range of 60 nm to 280 nm. Using the unitary matrix form hologram The phase changes φ x and φ y required for the metasurface unit and the rotation angle θ are obtained according to formulas (5) and (6). From the transmission coefficients t xx and t yy of the metasurface unit obtained in step twoThe two-dimensional scanning results are used to determine the geometric dimensions of the nanocolumns within each unit of the metasurface. Thereby, a processing file for the corresponding dielectric metasurface structure is generated.

[0058] Step 3: Using the processing file of the dielectric metasurface structure obtained in Step 2, a transmissive dielectric metasurface is fabricated. By manipulating the polarization response of different planar holographic reconstruction images, the holographic reconstruction images at different planes along the z-direction can present different polarization information under the illumination of incident light in any polarization state, thereby realizing three-dimensional vector holographic imaging.

[0059] Figure 4 is the optical path diagram used in the experiment of the embodiment of the present invention. By rotating the polarizer LP1 and the half-wave plate HWP, linearly polarized light in the x-direction is irradiated onto the metasurface. A microscope objective is used to receive the outgoing beam from the metasurface and appropriately magnify it. By adjusting the distance between the microscope objective and the metasurface sample, the reconstruction images at different distances can be imaged and recorded by a CCD. A polarizer LP2 is placed between the microscope objective and the CCD to verify the polarization information of the three-dimensional vector holographic image.

[0060] Figure 5 are the three-dimensional vector holographic images obtained under different polarization analysis conditions during the experiment of the embodiment of the present invention.

[0061] By imposing specific polarization response restrictions on the point sources located in different reconstruction image planes, the helix is equivalent to a half-wave plate with a gradually changing fast-axis direction along the z-direction, and the fast-axis direction θ f,,n uniformly increases from 0° to 90°. Therefore, when linearly polarized light in the x-direction is irradiated onto the processed metasurface sample, the entire helix remains in a linearly polarized state, but the polarization direction will gradually rotate from 0° to 180° as the reconstruction distance z increases. Figure 5 shows the reconstruction images of different z-positions of the first half of the helix under different polarization analysis conditions. When no polarizer is added, the point sources at different z-positions will rotate clockwise as the z-distance increases. At the same time, the intensities of the point sources at different planes are relatively uniform, and the intensity of the point sources does not change significantly in intensity as the reconstruction distance z increases. When a polarizer LP2 with a transmission axis along the horizontal direction is placed in front of the CCD, the intensity of the point source will decrease as the reconstruction distance z increases and finally almost disappear at z 10 = 1273 μm. This phenomenon indicates that the polarization direction of the first half of the helix gradually rotates from 0° to 90° as the reconstruction distance z increases. When the transmission axis direction of LP2 is rotated to the vertical direction, the intensity of the point source changes from almost disappearing to the strongest intensity state as the z-distance increases. The above phenomenon further verifies that the generated helix pattern has a non-uniform polarization state along the z-direction.

[0062] The three-dimensional vector holographic imaging method based on metasurface disclosed in this embodiment combines the hologram calculation method of three-dimensional images with the Jones matrix method to generate a hologram in matrix form, and manipulates the polarization responses of holographic reconstruction images on different planes, so that the holographic reconstruction images at different planes have different polarization information. Applying the three-dimensional vector holographic imaging method to the fields of beam shaping, particle manipulation, and information encryption to solve related engineering and technical problems. In the field of beam shaping, the three-dimensional vector holographic imaging method can simultaneously manipulate the amplitude, phase, and polarization of any point in a three-dimensional light field to generate a complex three-dimensional structured beam. In the field of particle manipulation, the three-dimensional vector holographic imaging method can generate multiple polarization-controllable focal points in three-dimensional space, which is beneficial to simultaneously manipulate multiple particles in three-dimensional space. In the field of information encryption, the three-dimensional vector holographic imaging method can realize a three-dimensional light field with complex polarization characteristics, and can store the information to be encrypted in the polarization dimension of the light field.

[0063] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A three-dimensional vector holographic imaging method based on a metasurface, characterized in that: The method includes the following steps: Step 1: Select a 3D image with a contrast meeting the preset standard requirements as the original image for realizing 3D vector holographic imaging; combine the hologram calculation method of the 3D image with the Jones matrix method, that is, introduce the manipulation of the polarization state of the holographic reconstructed image into the hologram calculation process, apply the required polarization response constraints in different reconstructed image planes along the z direction, and arbitrarily manipulate the polarization state of the 3D holographic reconstructed image; use the matrix polar decomposition method to generate a hologram in the form of a unitary matrix according to the electric field distribution obtained by backpropagation in the hologram plane Step 2: The metasurface for realizing three-dimensional vector holographic imaging is composed of an array of dielectric nanocolumns with different geometric sizes and different azimuth angles having a rectangular cross-section; by combining the polarization rotation matrix with the birefringence characteristics of the dielectric metasurface, the Jones matrix of each unit is customized, and the hologram in the form of a unitary matrix generated in Step 1 is encoded in the metasurface, and a processing file for the corresponding dielectric metasurface structure is generated according to the size and azimuth angle of each unit nanocolumn of the metasurface; the geometric sizes include the major axis length L, minor axis length W, height H of the nanocolumn, and the period length P of the metasurface unit. Step 3: Using the processing file of the dielectric metasurface structure obtained in Step 2, a transmissive dielectric metasurface is prepared; by manipulating the polarization response of different planar holographic reconstructed images, the holographic reconstructed images at different planes along the z direction can present different polarization information under the illumination of incident light in any polarization state, so as to realize three-dimensional vector holographic imaging.

2. The three-dimensional vector holographic imaging method based on a metasurface according to claim 1, characterized in that: It further includes Step 4: According to Steps 1 to 3 to realize three-dimensional vector holographic imaging, on the basis of retaining the three-dimensional holographic imaging function, the manipulation of the polarization dimension along the z direction can also be realized; applying the three-dimensional vector holographic imaging method to the fields of beam shaping, particle manipulation, and information encryption to solve related engineering and technical problems.

3. The three-dimensional vector holographic imaging method based on a metasurface according to claim 2, characterized in that: In the field of beam shaping, the three-dimensional vector holographic imaging method can simultaneously manipulate the amplitude, phase, and polarization of any point in the three-dimensional light field, which is beneficial to generating complex three-dimensional structured beams. In the field of particle manipulation, the three-dimensional vector holographic imaging method can generate multiple polarization-controllable focal points in three-dimensional space, which is beneficial to simultaneously manipulating multiple particles in three-dimensional space. In the field of information encryption, the three-dimensional vector holographic imaging method can realize a three-dimensional light field with complex polarization characteristics, and the information to be encrypted can be stored in the polarization dimension of the light field.

4. The three-dimensional vector holographic imaging method based on a metasurface according to claim 1, 2 or 3, characterized in that: The implementation method of Step 1 is as follows: Select a three-dimensional image with a contrast meeting the preset standard requirements as the original image for realizing three-dimensional vector holographic imaging; sample the selected three-dimensional image and divide the three-dimensional image into N mutually parallel planes; for the nth reconstructed image plane (n = 1, 2, 3, …, N), its amplitude and phase distributions are represented by A n and denote; Meanwhile, specific polarization response restrictions are imposed on different reconstructed image planes. The holographic reconstructed images on different planes are equivalent to polarization elements with specific polarization responses. The polarization elements are polarizers with arbitrary transmission axis directions or wave plates with arbitrary fast axis directions. Limited by a single-layer metasurface, the polarization response should be a symmetric 2×2 matrix. In addition, the propagation process between the hologram plane and the reconstructed image planes at different reconstruction distances is realized by the backpropagation method. The backpropagation method is implemented based on the backpropagation formula shown in Equation (1). Equation (1) describes the propagation process of different reconstructed images to the hologram plane; among them, represents the backpropagation method; the coordinates of the hologram plane and the reconstructed image plane are represented by (x h , y h ) and (x o , y o ), respectively; using the matrix polar decomposition method, the complex amplitude distribution in matrix form is decomposed into the form of the product of a Hermitian matrix and a unitary matrix ; by discarding the Hermitian matrix part, the hologram in the form of a unitary matrix 5. The three-dimensional vector holographic imaging method based on a metasurface according to claim 4, characterized in that: The hologram calculation methods for the three-dimensional image described in Step 1 include the Fresnel algorithm, the point source method, and the angular spectrum method. When the Fresnel algorithm or the angular spectrum method is used to calculate the hologram of a three-dimensional image in the form of a unitary matrix The forward and backward propagation methods are required to perform iterative calculations on the electric field distributions in the hologram plane and the reconstructed image plane, and a hologram in the form of a unitary matrix is generated based on the electric field distributions obtained from the iterative calculations The forward propagation method is implemented based on the forward propagation formula shown in Equation (2); Among them, represents the forward propagation method; the specific forward formulas based on the Fresnel algorithm and the angular spectrum method are shown in Formulas (3) and (4); In the formula, represents the complex amplitude distribution in the form of a matrix of the nth reproduced image plane, λ is the wavelength of the incident light, k is the wave vector of the incident light, f x and f y are spatial frequencies, and z is the propagation distance; while F and F -1 represent Fourier transform and inverse Fourier transform.

6. The three-dimensional vector holographic imaging method based on a metasurface according to claim 5, characterized in that: In Step 2, The metasurface for realizing three-dimensional vector holographic imaging is composed of an array of dielectric nanocolumns with different geometric sizes and different azimuth angles having a rectangular cross-section; the Jones matrix method is used to associate the Jones vectors of the outgoing and incident beams corresponding to each unit of the metasurface. The Jones vector E of the output beam out Calculated by formula (5): where t ij (i = x or y) is the transmission coefficient, and j and i respectively represent the polarization directions of the incident beam and the outgoing beam; when the dielectric nanorod structure in the metasurface unit has a high transmittance, the Jones matrix T corresponding to this unit is equivalent to a symmetric unitary matrix; the Jones matrix T that satisfies the unitary matrix condition is decomposed according to its eigenvectors and eigenvalue matrix (Δ) as follows: In the formula, the matrix V represents a two-dimensional rotation matrix in the plane, and the rotation angle is θ; according to Equation (6), when the incident light (E in ) is incident on the dielectric nanorod, the electric field vector E in of the incident light first rotates by -θ degrees in the plane; the dielectric nanorod introduces phase shifts φ x and φ y to the x and y components of the rotated electric field vector respectively; then rotate the electric field vector with the introduced phase shift by θ degrees to convert it back to the initial coordinate system; According to the propagation phase principle, corresponding phase shifts φ x and φ y can be achieved using nanocolumn arrays of different sizes, and the hologram in the form of a unitary matrix calculated by formula (1) is encoded in the metasurface; With the height H and period P of the nanorods fixed, the major axis length L and minor axis length W of the nanorods are changed, and two-dimensional scanning is performed using simulation software to obtain the transmission coefficients t corresponding to different-sized nanorods. xx and t yy ; When simulating, the wavelength of the incident light, the type of material constituting the nanorods, the height H and period P of the nanorods should be selected so that the phase of the transmission coefficient and can cover 0 to 2π; At the same time, the amplitudes abs(t xx ) and abs(t yy ) should be as close to 1 as possible, so that the Jones matrix T of each unit of the metasurface satisfies the unitary matrix condition; By changing the geometric size and azimuth angle of the nanorod unit, that is, encoding the hologram in the form of the calculated unitary matrix into the metasurface, a processing file for the corresponding dielectric metasurface structure is generated.

7. The three-dimensional vector holographic imaging method based on a metasurface according to claim 6, characterized in that: The simulation software described in Step 2 adopts RCWA based on the rigorous coupled wave analysis method, FDTD based on the finite difference time domain method, or COMSOL based on the finite element method.

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