A large-depth metasurface polarization holographic 3D display method

Abstract

This invention proposes a method for large-depth metasurface polarization holographic 3D display, which includes the following four steps: First, for two different 3D objects I and II, large-depth metasurface holograms I and II are calculated based on angular spectrum diffraction theory to obtain them respectively; Second, metasurface holograms I and II are interleaved row-by-row to encode a synthetic hologram, and then the phase of the synthetic hologram is optimized using an error diffusion algorithm to obtain the metasurface structure's required elementary phase information; Third, based on the elementary phase information obtained in step two... The metasurface structure is designed such that the odd-numbered rows of the metasurface structure are sensitive to left-handed circularly polarized light, and the even-numbered rows are sensitive to right-handed circularly polarized light, thus achieving independent control of different polarization states. In the fourth step, the metasurface structure is irradiated with a laser to perform holographic 3D reconstruction. When left-handed circularly polarized light irradiates the metasurface structure, a large-depth holographic reconstruction image of 3D object I is seen. When right-handed circularly polarized light irradiates the metasurface structure, a large-depth holographic reconstruction image of 3D object II is seen. When both left-handed and right-handed circularly polarized light irradiate the metasurface structure, large-depth holographic reconstruction images of 3D object I and 3D object II are seen simultaneously.

Description

I. Technical Field

[0001] This invention relates to holographic display technology, and more specifically, to a method for deep metasurface polarization holographic 3D display. II. Background Technology

[0002] Holographic 3D display technology can completely record and reconstruct wavefront information, making it one of the most ideal 3D display technologies. However, limited by the pixel size of spatial light modulators, the viewing angle of holographic 3D displays is narrow, restricting their application range. With the development of micro-nano technology, metasurface devices, due to their advantages such as small pixel size and light weight, have provided new ideas for the development of holographic 3D display technology. Metasurface devices are composed of subwavelength unit structures, which can control the amplitude, phase, and polarization state of incident light. Some researchers have achieved metasurface holographic 3D reconstruction using the traditional Gerchberg-Saxton algorithm; however, as the propagation distance increases, the spatial frequency of the object will alias, thus limiting the reconstruction depth. Some researchers have achieved holographic 3D reconstruction in the visible and near-infrared ranges by using subwavelength pixelated plasmonic metasurface structures, expanding the depth to 1.3 mm, but this still cannot meet the requirements for large-depth holographic 3D displays. Currently, how to achieve large-depth holographic 3D displays is an urgent problem to be solved, and how to achieve independent control of the polarization state while achieving large-depth holographic 3D displays, thereby increasing the amount of information, is an even greater challenge. III. Summary of the Invention

[0003] This invention proposes a method for large-depth metasurface polarization holographic 3D display. (See attached diagram) Figure 1As shown, the method includes the following four steps: First, for two different 3D objects I and II, large-depth metasurface holograms I and II are calculated based on angular spectrum diffraction theory. Metasurface holograms I and II are used for left-handed circular polarization holographic reconstruction and right-handed circular polarization holographic reconstruction, respectively. Second, metasurface holograms I and II are interleaved row-by-row to encode a synthetic hologram. Then, the phase of the synthetic hologram is optimized using an error diffusion algorithm to obtain the meta-phase information required for the metasurface structure. Third, based on the meta-phase information in step two, a metasurface structure is designed so that the odd-numbered rows of the metasurface structure are sensitive to left-handed circular polarization, while the even-numbered rows are sensitive to right-handed circular polarization. The method is sensitive to right-hand circularly polarized light, thus enabling independent control of different polarization states. Furthermore, adjacent rows of metasurface structures do not experience crosstalk due to mutual diffraction during the diffraction process. In the fourth step, laser light is used to irradiate the metasurface structure for holographic 3D reconstruction. When left-hand circularly polarized light irradiates the metasurface structure, only the odd-numbered rows are sensitive to the incident light, thereby modulating the phase of the light field. At this point, a deep-depth holographic reconstruction image of 3D object I is seen. When right-hand circularly polarized light irradiates the metasurface structure, only the even-numbered rows are sensitive to the incident light, thus modulating the phase of the light field. At this point, a deep-depth holographic reconstruction image of 3D object II is seen. When both left-hand and right-hand circularly polarized light irradiate the metasurface structure, deep-depth holographic reconstruction images of both 3D object I and 3D object II are seen simultaneously. The method proposed in this invention achieves deep-depth holographic 3D display while simultaneously controlling the polarization state, and there is no diffraction crosstalk between the reconstructed images of different polarization states.

[0004] In step one, for any 3D object, the complex amplitude distributions on the 3D object and the hologram plane are respectively represented as:

[0005]

[0006]

[0007] Where T0 and T are the complex amplitude distributions of the 3D object and the hologram plane, respectively; x0 and y0 are the position coordinates of the object; x and y are the position coordinates of the hologram plane; and f x and f y These are the spatial frequencies of the light field in the x and y directions, respectively; j is the imaginary unit; z is the distance between the 3D object and the holographic plane; A0(f x ,f y ;0) and A(f x ,f y z) represent the spatial spectra of the 3D object and the hologram plane, respectively. This is obtained by solving the Helmholtz equation:

[0008] A(fx ,f y ;z)=A0(f x ,f y ;0)H(f x ,f y ;z), (3)

[0009]

[0010] Wherein, H(f) x ,f y z) is the transfer function. λ is the phase of the transfer function, and λ is the wavelength.

[0011] Therefore, for two different 3D objects I and II, the complex amplitude distribution of the corresponding holographic plane can be directly obtained by solving formula (3):

[0012]

[0013]

[0014] Among them, T LCP It is the complex amplitude distribution of the holographic plane of 3D object I, T RCP It is the complex amplitude distribution of the holographic plane of the 3D object II. and Let T1(x,y;0) and T2(x,y;0) represent the Fourier transform and inverse Fourier transform, respectively, and let H represent the complex amplitude distributions of 3D object I and 3D object II, respectively. LCP (f x ,f y ;z) and H RCP (f x ,f y ;z) represent the transfer functions of 3D object I and 3D object II, respectively.

[0015] In hologram computation, the operations performed during the discrete sampling process can introduce errors, leading to aliasing of the light field. To avoid aliasing errors, the local signal frequency M of the transfer function is... f and sampling frequency Δf x The following conditions must be met:

[0016]

[0017] Δf x ≥2|M f |. (8)

[0018] When calculating metasurface holograms, the sampling frequency is determined by the following formula:

[0019] Δfx =(2Np) -1 (9)

[0020] Where N is the number of pixels in the metasurface hologram in the x-direction, and p is the pixel pitch. Therefore, in order to achieve a deep metasurface holographic display, the transfer function can only be a band-limited function. According to formula (8), the transfer function in the x-direction should be constrained within the range shown in the following formula:

[0021]

[0022]

[0023] Among them, f xlimit It is the maximum frequency of the transfer function in the x-direction. From equation (10), it can be seen that the bandwidth limitation of the transfer function in the x-direction is an ellipse with the y-axis as the major axis, and similarly, the bandwidth limitation of the transfer function in the y-direction is an ellipse with the x-axis as the major axis. The overlapping region of the two is the band-limited region of the transfer function. The method proposed in this invention expands the depth of the metasurface holographic 3D display by limiting the high-frequency information of the transfer function, and finally generates a large-depth metasurface hologram I and a metasurface hologram II to realize the function of large-depth holographic 3D display. The pixel spacing of the two holograms along the x and y directions is p and 2p, respectively.

[0024] The method proposed in this invention can independently realize the functions of deep holographic 3D display and polarization holographic 3D display. To achieve independent control of the polarization state, in step two, the complex amplitude information of metasurface hologram I and metasurface hologram II is synthesized using a row-by-row alternating insertion method to obtain the complex amplitude distribution of the synthesized hologram. The pixel spacing along the x and y directions of the synthesized hologram is p. Along the y direction, odd-numbered rows correspond to the complex amplitude of metasurface hologram I, and even-numbered rows correspond to the complex amplitude of metasurface hologram II. Since the designed metasurface is phase-modulated, the complex amplitude information needs to be converted into phase information. An error diffusion algorithm is used to scan and optimize each pixel of the synthesized hologram to obtain the metaphase information required for the metasurface structure.

[0025] As attached Figure 2 As shown, in step three, the metasurface structure, based on the principle of geometric phase control, independently modulates the phase of each unit structure. Each structural unit of the metasurface consists of rectangular amorphous silicon nanorods fabricated on a quartz substrate. The length, width, and height of the rectangular amorphous silicon nanorods are L, W, and H, respectively, with a period of p and a rotation angle of θ about the x-axis. Phase modulation is achieved by rotating the rectangular amorphous silicon nanorods, with the phase shift amount... The polarization state of the incident light is positive when it is left-handed circularly polarized and negative when it is right-handed circularly polarized. Based on the elementary phase information generated in step two, the metasurface structure is designed. The metasurface structure in the odd-numbered rows is sensitive to left-handed circularly polarized light, and the metasurface structure in the even-numbered rows is sensitive to right-handed circularly polarized light, thus achieving independent control of different polarization states. IV. Description of the attached drawings

[0026] Appendix Figure 1 This is a schematic diagram of the process of a deep metasurface polarization holographic 3D display method according to the present invention.

[0027] Appendix Figure 2 This is a schematic diagram of the metasurface structure of a deep metasurface polarization holographic 3D display method according to the present invention.

[0028] Appendix Figure 3 This is a top view schematic diagram of the metasurface structure of a deep metasurface polarization holographic 3D display method according to the present invention.

[0029] Appendix Figure 4 This is a schematic diagram illustrating the reconstruction effect of a deep metasurface polarization holographic 3D display method according to the present invention. Figure 4 (a)-(b) show the deep reconstruction effect of 3D object I; Figure 4 (c)-(d) show the deep reconstruction effect of 3D object II.

[0030] It should be understood that the above figures are only schematic and are not drawn to scale. V. Detailed Implementation Methods

[0031] The following detailed embodiments of the deep metasurface polarization holographic 3D display method proposed in this invention further illustrate the invention. It is important to note that the following embodiments are for illustrative purposes only and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made to this invention by those skilled in the art based on the above description are still within the scope of protection of this invention.

[0032] One embodiment of the present invention involves selecting two letters, "N" and "U," as the 3D object I corresponding to a left-handed circular polarization state, and two other letters, "O" and "C," as the 3D object II corresponding to a right-handed circular polarization state. The reconstruction distance for both letters "N" and "O" is 3 mm; the reconstruction distance for both letters "C" and "U" is 70 mm. Based on angular spectral diffraction theory, the light field distributions of 3D object I and 3D object II are calculated, generating corresponding metasurface holograms I and II. A composite hologram is generated using a row-by-row alternating insertion method, and the phase is optimized using an error diffusion algorithm to obtain the elementary phase information. Based on this elementary phase information, a metasurface structure is designed and fabricated using electron beam lithography, as shown in the attached figure. Figure 3 The image shown is a top-view view of the metasurface structure captured by a scanning electron microscope. The amorphous silicon nanorods have a length, width, and height of 210 nm, 400 nm, and 90 nm, respectively, with a period of 300 nm. The metasurface structure has a resolution of 5000 × 5000 pixels and a pixel pitch of 0.3 μm. Holographic reconstruction was performed using a 671 nm laser, with polarizers and quarter-wave plates of the corresponding wavelengths used to convert the polarization state of the incident light. The reconstructed image is shown in the attached image when the incident beam is left-handed circularly polarized. Figure 4 As shown in (a)-(b), the letters "N" and "U" are focused at diffraction distances of 3 mm and 70 mm, respectively. The reconstructed images are shown below when the incident beam is right-handed circularly polarized. Figure 4 As shown in (c)-(d), the letters "O" and "C" are focused at diffraction distances of 3 mm and 70 mm, respectively. The experiments verify that the method of this invention can achieve deep metasurface polarization holographic 3D display.

Claims

1. A large-depth metasurface polarization holographic 3D display method, characterized in that, The method comprises the following four steps: in the first step, for two different 3D objects I and 3D object II, based on the angular spectrum diffraction theory, a large-depth metasurface hologram I and a metasurface hologram II are respectively calculated, the metasurface hologram I and the metasurface hologram II are respectively used for left circularly polarized holographic reconstruction and right circularly polarized holographic reconstruction; in the second step, the metasurface hologram I and the metasurface hologram II are alternately inserted row by row, so as to be encoded into a synthetic hologram, and then the phase of the synthetic hologram is optimized by using an error diffusion algorithm, so as to obtain the required meta-phase information of the metasurface structure; in the third step, based on the meta-phase information in the second step, the metasurface structure is designed, so that the metasurface structure in the odd rows is sensitive to the left circularly polarized light, and the metasurface structure in the even rows is sensitive to the right circularly polarized light, thereby realizing independent control of different polarization states, and the metasurface structures in adjacent two rows will not cause crosstalk in the diffraction process; in the fourth step, the metasurface structure is irradiated by using a laser to perform holographic 3D reconstruction, when the left circularly polarized light irradiates the metasurface structure, only the metasurface structure in the odd rows is sensitive to the incident light, and then the phase of the light field is regulated, at this time, a large-depth holographic reconstruction image of the 3D object I is seen, when the right circularly polarized light irradiates the metasurface structure, only the metasurface structure in the even rows is sensitive to the incident light, and then the phase of the light field is regulated, at this time, a large-depth holographic reconstruction image of the 3D object II is seen, when the left circularly polarized light and the right circularly polarized light irradiate the metasurface structure at the same time, the large-depth holographic reconstruction images of the 3D object I and the 3D object II are simultaneously seen; In the first step, for any 3D object, the complex amplitude distribution on the hologram plane is represented as: where T0and T are the complex amplitude distributions of the 3D object and the hologram plane, respectively, x0and y0are the position coordinates of the object, x and y are the position coordinates of the hologram plane, f x and f y are the spatial frequencies of the optical field in x and y directions, respectively, j is the imaginary unit, z is the distance between the 3D object and the hologram plane, A0(f x ,f y ; 0) and A(f x ,f y ; z) are the spatial spectra of the 3D object and the hologram plane, respectively, which are obtained by solving the Helmholtz equation: A(f x ,f y ;0) = A0(f x ,f y ;0)H(f x ,f y ;0) A(f x ,f y ;z) = A0(f x ,f y ;z)H(f x ,f y ;z) where H(f x ,f y ; z) is the transfer function, is the phase of the transfer function, and λ is the wavelength. For two different 3D objects I and 3D object II, the corresponding complex amplitude distribution on the hologram plane is obtained: where T LCP is the complex amplitude distribution of the hologram plane of the 3D object I, T RCP is the complex amplitude distribution of the hologram plane of the 3D object II, and denote the Fourier transform and the inverse Fourier transform, respectively, T1(x,y;0) and T2(x,y;0) denote the complex amplitude distribution of the 3D object I and the 3D object II, respectively, H LCP (f x ,f y ; z) and H RCP (f x ,f y ; z) denote the transfer function of the 3D object I and the 3D object II, respectively; In the calculation of the hologram, the operation of the hologram in the discrete sampling process will cause errors, resulting in light field aliasing. In order to avoid aliasing errors, the local signal frequency M f and the sampling frequency Δf x need to meet the following conditions: Δf x ≥2|M f | In the calculation of the metasurface hologram, the sampling frequency is determined by the following formula: Δf x = (2Np) -1 Wherein, N is the pixel number of the metasurface hologram in the x direction, and p is the pixel pitch, therefore, in order to realize large-depth metasurface holographic display, the transfer function can only be a band-limited function, and the transfer function in the x direction should be constrained in the range shown in the following formula: Wherein, f xlimit is the maximum frequency of the transfer function in the x direction, the bandwidth limitation of the transfer function in the x direction is a positive ellipse with the y axis as the long axis, similarly, the bandwidth limitation of the transfer function in the y direction is a positive ellipse with x as the long axis, and the overlapping area of the two is the band-limited area of the transfer function, the method proposed in the application limits the high-frequency information expansion of the transfer function to expand the depth of the metasurface holographic 3D display, and finally generates a large-depth metasurface hologram I and a metasurface hologram II to realize the function of large-depth holographic 3D display, and the pixel spacing of the two holograms along the x and y directions is p and 2p respectively.

2. The large-depth metasurface polarization holographic 3D display method according to claim 1, characterized in that, In the second step, the complex amplitude information of the metasurface hologram I and the metasurface hologram II is synthesized by using the row-by-row alternate insertion method, to obtain the complex amplitude distribution of the synthetic hologram, the pixel pitch of the synthetic hologram along the x and y directions is p, the odd rows along the y direction correspond to the complex amplitude of the metasurface hologram I, and the even rows correspond to the complex amplitude of the metasurface hologram II, since the designed metasurface is a phase modulation, it is necessary to convert the complex amplitude information into phase information, and all pixel points of the synthetic hologram are scanned and optimized by using the error diffusion algorithm, so as to obtain the required meta-phase information of the metasurface structure.

3. The large-depth metasurface polarization holographic 3D display method according to claim 1, characterized in that, In step three, the metasurface structure independently controls the phase of each unit structure based on the geometric phase control principle. Each structure unit of the metasurface is composed of a rectangular amorphous silicon nanorod made on a quartz substrate. The rotation angle of the rectangular amorphous silicon nanorod to the x-axis is θ. The phase is controlled by rotating the angle of the rectangular amorphous silicon nanorod. The phase shift is where the sign is positive when the polarization state of the incident light is left-handed circularly polarized and negative when the polarization state of the incident light is right-handed circularly polarized. The metasurface structure is designed based on the meta-phase information generated in step two. The odd-numbered row of metasurface structures is sensitive to left-handed circularly polarized light, and the even-numbered row of metasurface structures is sensitive to right-handed circularly polarized light, thereby achieving independent control of different polarization states.

Images