A zoom microprojector based on metasurface holography

Abstract

This invention proposes a zoom microprojector based on metasurface holography, comprising a laser, a transmissive metasurface, and an electrowetting liquid lens. To achieve system miniaturization, the transmissive metasurface and the electrowetting liquid lens are integrated into a single cavity, with the electrowetting liquid lens located behind the transmissive metasurface. During the metasurface fabrication process, a 3D Fourier transform algorithm is proposed to generate a 3D metasurface hologram, thereby fabricating the transmissive metasurface. The liquid lens is a small-aperture liquid lens designed based on the electrowetting principle to cooperate with the transmissive metasurface to achieve zoom microprojection. When the laser emitted from the laser illuminates the transmissive metasurface, the 3D image diffracted by the metasurface passes through the electrowetting liquid lens. The position and size of the 3D image can be adjusted according to the voltage of the liquid lens, thus achieving a 3D zoom projection effect.

Description

I. Technical Field

[0001] This invention relates to micro-projection technology, and more specifically, to a zoom micro-projector based on metasurface holography. II. Background Technology

[0002] Metasurface structures, due to their advantages such as small pixel size, light weight, and flexible light field manipulation, have significant application value in fields such as optical storage, holographic projection, display, and super-resolution imaging. In metasurface holographic projection, achieving large-size, deep, and zoomable 3D projection effects using miniaturized devices has always been a goal. In 2016, researchers proposed holographic projection based on Huygens metasurfaces, projecting a 5mm image at a reconstruction distance of 10mm. In 2018, researchers used chemical methods to control the composition of metasurface structural units, achieving dual-channel controllable metasurface holographic 3D projection. However, this chemical process is slow, resulting in long response times, making it difficult to meet the rapid control requirements of holographic projection. In 2024, researchers proposed a multi-channel metasurface holographic projection method based on a polarization multiplexing mechanism, projecting two different holographic images at distances of 0.4mm and 0.6mm respectively, but the projected image size using this method is less than 1mm. In recent years, although metasurface holographic projection technology has made significant progress, existing methods mainly achieve 3D projection through multiplexing, and the number of 3D projection layers is determined by the number of channels designed in the metasurface structure. In addition, existing methods also suffer from problems such as large projection system size, small projected image size, and fixed and non-adjustable projection distance, which limit the further development of metasurface holographic projection technology. III. Summary of the Invention

[0003] This invention proposes a zoom microprojector based on metasurface holography. (See attached image.) Figure 1 As shown, the microprojector includes a laser, a transmissive metasurface, and an electrowetting liquid lens. To achieve system miniaturization, the transmissive metasurface and the electrowetting liquid lens are integrated into a single cavity, with the electrowetting liquid lens located behind the transmissive metasurface. During the metasurface fabrication process, this invention proposes a 3D Fourier transform algorithm to generate a 3D metasurface hologram, which is then encoded onto a subwavelength metasurface unit structure to fabricate the transmissive metasurface. Unlike traditional liquid lenses, the proposed liquid lens is a small-aperture liquid lens designed based on the electrowetting principle, thus enabling zoom microprojection in conjunction with the transmissive metasurface. When the laser emitted by the laser illuminates the transmissive metasurface, the 3D image diffracted by the metasurface passes through the electrowetting liquid lens. By changing the driving voltage U of the liquid lens, the 3D image is projected to different depths d. The position and size of the 3D image can be adjusted according to the voltage of the liquid lens, thereby achieving a 3D zoom projection effect.

[0004] The proposed electrowetting liquid lens mainly consists of a mechanical housing, two window glass panes, a hydrophobic layer, a dielectric layer, an upper electrode, a lower electrode, an insulating ring, an insulating liquid, a conductive liquid, and a flexible electrode connected to the drive plate, as shown in the attached figure. Figure 2 As shown in (a). To ensure a large optical-to-mechanical aperture ratio for the liquid lens, this invention designs a straight cylindrical cavity structure to reduce the cavity thickness of the liquid lens, thereby ensuring the compactness of the zoom micro-projector. Furthermore, to guarantee a wide range of optical power variation and good stability for the liquid lens, a two-phase liquid composed of a conductive liquid without aqueous solution and an insulating liquid with low surface tension was developed. By adjusting the driving voltage of the liquid lens, the wetting characteristics of the conductive and insulating liquids change accordingly, resulting in changes in the curvature of the liquid-liquid interface and the optical power. The optical power Φ of the liquid lens is expressed as:

[0005]

[0006] Where, γ 12 θ0 is the interfacial tension between the conductive and insulating liquids, θ0 is the initial contact angle without applied voltage, C is the total capacitance per unit area of ​​the dielectric layer coated with a hydrophobic layer, D is the optical aperture of the liquid lens, and Δn is the refractive index difference between the conductive and insulating liquids. The focal length f of the liquid lens is... liquidlens for:

[0007]

[0008] The proposed transmissive metasurface is controlled based on the Pancharatnam-Berry geometric phase principle, precisely controlling the phase distribution without altering the physical dimensions of the metasurface structure. Each structural unit of the metasurface consists of rectangular single-crystal silicon nanorods fabricated on a sapphire substrate. (See attached image.) Figure 2 As shown in (b), L, W, and H represent the length, width, and height of the monocrystalline silicon, respectively. p is the period, and θ is the rotation angle of the monocrystalline silicon. By adjusting the rotation angle of each unit structure of the metasurface, the phase shift and control of each pixel in the 3D image are achieved. The Pancharatnam-Berry geometric phase control process is wavelength-independent; therefore, when the wavelength of the laser changes, the proposed transmissive metasurface can generate reconstructed images of various wavelengths, and the size of the image is directly related to the wavelength.

[0009] In the fabrication of metasurfaces, this invention proposes a 3D Fourier transform algorithm to generate 3D metasurface holograms. This algorithm introduces fractional Fourier transform and inverse fractional Fourier transform, and adds iterative constraints in the fractional and spatial domains respectively to obtain a convergent final phase distribution and generate the 3D metasurface hologram. Specifically, for a 3D object, the algorithm first performs layering processing on the 3D object. For each layer, a random phase distribution is introduced to generate an initial complex amplitude distribution g(x,y) in the spatial domain. Then, by designing the transform order a and using the fractional Fourier transform, the complex amplitude distribution G(u,v) in the fractional domain is obtained:

[0010]

[0011] Where F a Let f denote the fractional Fourier transform of order a, where (x, y) and (u, v) are the position coordinates of the light field in the spatial and fractional domains, respectively, j is the imaginary number, λ is the wavelength of the incident light, dx and dy are the sampling frequencies in the spatial domain, and f a It is the focal length when the transformation order is a, derived from the rotation transformation of the Wigner function. a for:

[0012]

[0013] Where f is the normalized focal length selected during the holographic calculation process.

[0014] When the transformation order a is set to 1, any focal length f a This is equivalent to the normalized focal length. Introducing the transform order changes the rotation angle of the Wigner function, making the diffraction distance related to the transform order, thus breaking the limitation in traditional Fourier coding that the diffraction distance is determined solely by the focal length. Constraints are placed on the complex amplitude distribution G(u,v) in the fractional domain, retaining only phase information:

[0015]

[0016] Where |·| represents modulo. This represents the phase distribution in the fractional domain. The inverse fractional Fourier transform is used to... Convert to g'(x,y):

[0017]

[0018] in Let represent the fractional inverse Fourier transform of order 'a', and 'du' and 'dv' represent the sampling frequencies in the fractional domain. Preserving the phase and replacing the original amplitude information A0(x,y) of the 3D object, we obtain the complex amplitude distribution g1(x,y) in the spatial domain:

[0019]

[0020] After the first iteration, g1(x,y) is used as the input for the next iteration until the phase in the fractional domain converges to the optimal value. The phase is then extracted to obtain the final 3D metasurface hologram. The final phase distribution T is:

[0021] T(u,v)=|(∑angle(G(u,v)),2π)| (8)

[0022] Here, angle(·) represents the extraction of phase from the complex amplitude distribution, and Σ represents the sum of phases across different layers of the 3D object. The phase information T of the 3D metasurface hologram is denoted as an n×n matrix, where each element corresponds to a unit structure of the metasurface. The metasurface is fabricated by encoding the 3D metasurface hologram on a subwavelength structure. IV. Description of the attached drawings

[0023] Appendix Figure 1 This is a schematic diagram of the structure of a zoom microprojector based on metasurface holography according to the present invention.

[0024] Appendix Figure 2 This invention describes the working principle of a zoom micro-projector based on metasurface holography. Figure 2 (a) shows the structure of the proposed liquid lens. Figure 2 (b) shows the calculation process of the 3D metasurface hologram.

[0025] Appendix Figure 3 This is a schematic diagram illustrating the zoom projection effect of a zoom micro-projector based on metasurface holography according to the present invention. Figure 3 (a) The reconstruction effect of the letter "N" at different depths when the driving voltage of the liquid lens is turned off and on; Figure 3 (b) shows the 3D reconstruction effect when the focal length of the liquid lens is 15cm; Figure 3 (c) shows the 3D reconstruction effect when the focal length of the liquid lens is 7cm.

[0026] The figure labels in the above figures are as follows:

[0027] (1) Zoom micro-projector, (2) Laser, (3) Transmissive metasurface, (4) Electrowetting liquid lens, (5) Mechanical housing, (6) Two window glass, (7) Hydrophobic layer, (8) Dielectric layer, (9) Upper electrode, (10) Lower electrode, (11) Insulating ring, (12) Insulating liquid, (13) Conductive liquid, (14) Flexible electrode, (15) Sapphire substrate, (16) Single crystal silicon nanorod.

[0028] It should be understood that the above figures are only schematic and are not drawn to scale. V. Detailed Implementation Methods

[0029] The following detailed description of an embodiment of a zoom microprojector based on metasurface holography proposed in this invention further illustrates 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.

[0030] One embodiment of the present invention is as follows: In the proposed zoom microprojector based on metasurface holography, a laser with a wavelength of 671 nm is used as the reproduction light to illuminate the metasurface. A liquid lens is located 2 mm behind the metasurface, with an effective optical aperture of 2 mm and a mechanical diameter of 5 mm. The metasurface and the liquid lens are integrated into a cavity with total dimensions of 6.5 mm × 6.5 mm × 4.2 mm. The letters "N" and "U" located in two different depth planes are selected as 3D objects with a resolution of 2500 × 2500. The proposed 3D Fourier transform algorithm is used to generate a 3D metasurface hologram, and the normalized focal length f is set to 10 cm. The transform orders of the letters "N" and "U" are set to 1 and 0.2, respectively. Next, the metasurface units were fabricated. The substrate for the metasurface units was sapphire, on which single-crystal silicon was etched. The pixel pitch of the metasurface was 0.35 μm, and the period, height, length, and width of the single-crystal silicon nanorods were 350 nm, 600 nm, 160 nm, and 80 nm, respectively. When a voltage from 0 V to 70 V was applied to the liquid lens, the optical power of the liquid lens increased from -47.54 m. -1 It changed to 18.31m -1 The response time of the liquid lens is 68ms.

[0031] To verify the zoom projection performance of the proposed microprojector, this invention compared the imaging results of the letter "N" at different depth planes, as shown in the attached figure. Figure 3 As shown in (a), the first row displays the results with the liquid lens applied, where the letter "N" appears blurry and cannot be clearly projected at depths of 6cm, 12cm, 18cm, and 30cm. The second row displays the results with the liquid lens applied; by adjusting the driving voltage of the liquid lens, the letter "N" can be clearly projected to different depths. Furthermore, the 3D zoom projection effect has also been verified, as shown in the attached figure. Figure 3 As shown in (b), when the focal length of the liquid lens is 15 cm, the letter "N" is projected onto a depth plane of 15 cm, while the letter "U" is focused at a depth plane of 0.9 cm. As the focal length of the liquid lens decreases, the projection distance becomes closer, as shown in the attached diagram. Figure 3As shown in (c), when the focal length of the liquid lens is 7 cm, the letter "N" is projected onto a depth plane of 7 cm, while the letter "U" is focused at a depth plane of 0.3 cm. Experimental results demonstrate that the proposed microprojector achieves a 3D zoom projection effect.

Claims

1. A metasurface holography based zoom micro-projector, characterized in that, The micro projector comprises a laser, a transmission metasurface and an electrowetting liquid lens, in order to realize system miniaturization, the transmission metasurface and the electrowetting liquid lens are integrated into a single cavity, the electrowetting liquid lens is located behind the transmission metasurface, in the preparation process of the metasurface, a 3D Fourier transform algorithm is proposed to generate a 3D metasurface hologram, and then the 3D metasurface hologram is encoded on a subwavelength metasurface unit structure, so that the transmission metasurface is prepared, the proposed liquid lens is a small-aperture liquid lens designed based on the electrowetting principle, so as to realize zoom micro projection with the transmission metasurface, when the laser emitted by the laser irradiates the transmission metasurface, the 3D image diffracted by the metasurface passes through the electrowetting liquid lens, by changing the driving voltage U of the liquid lens, the 3D image is projected at different depths d, the position and size of the 3D image can be adjusted according to the voltage of the liquid lens, so as to realize 3D zoom projection effect; The electrowetting liquid lens in the zoom micro projector mainly comprises a mechanical shell, two window glasses, a hydrophobic layer, a dielectric layer, an upper electrode, a lower electrode, an insulating ring, an insulating liquid, a conductive liquid and a flexible electrode connected to a driving board, in order to ensure that the liquid lens has a large optical and mechanical aperture ratio, a straight cylinder cavity structure is designed to reduce the cavity thickness of the liquid lens, so as to ensure the compactness of the zoom micro projector, in addition, in order to ensure that the liquid lens has a large range of optical power change and good stability, a two-phase liquid composed of a conductive liquid without water solution and an insulating liquid with low surface tension is developed, by adjusting the driving voltage of the liquid lens, the wetting characteristics of the conductive liquid and the insulating liquid change accordingly, resulting in changes in the curvature and optical power of the liquid-liquid interface, and the optical power Φ of the liquid lens is expressed as: where γ 12 is the interfacial tension between the conductive liquid and the insulating liquid, θ0is the initial contact angle when no voltage is applied, C is the total capacitance per unit area of the dielectric layer coated with a hydrophobic layer, D is the optical aperture of the liquid lens, Δn is the difference in refractive index of the conductive liquid and the insulating liquid, and the focal length f liquid lens of the liquid lens is given by: The proposed transmission metasurface is based on the Pancharatnam-Berry geometric phase principle, which accurately controls the phase distribution without changing the physical size of the metasurface structure, each structure unit of the metasurface is composed of a rectangular single-crystal silicon nanorod fabricated on a sapphire substrate, by adjusting the rotation angle of each unit structure of the metasurface, the phase shift and control of each pixel of the 3D image are realized, the control process of the Pancharatnam-Berry geometric phase is independent of the wavelength, when the wavelength of the laser changes, the proposed transmission metasurface can generate reconstructed images of various wavelengths, and the size of the image is directly related to the wavelength. A 3D metasurface hologram is generated using a 3D Fourier transform algorithm, which obtains a convergent final phase distribution and generates a 3D metasurface hologram by introducing a fractional Fourier transform and a fractional inverse Fourier transform and adding iterative constraints in the fractional domain and the spatial domain, respectively; specifically, for a 3D object, the algorithm first performs layering processing on the 3D object, for each layer, an initial complex amplitude distribution g(x, y) in the spatial domain is generated by introducing a random phase distribution, then a complex amplitude distribution G(u, v) in the fractional domain is obtained by designing a transform order a and using a fractional Fourier transform: where F a denotes the fractional Fourier transform of order a, (x, y) and (u, v) are the position coordinates in the spatial and fractional domains, respectively, j is the imaginary unit, l is the wavelength of the incident light, dxand dyare the sampling frequencies in the spatial domain, f a is the focal length for the transform order a, which is derived from the rotational transform of the Wigner function a as: Where f is a normalized focal length selected in the holographic calculation process; When the transform order a is set to 1, the arbitrary focal length f a is equal to the normalized focal length, the introduction of the transform order changes the rotation angle of the Wigner function, so that the diffraction distance is related to the transform order, thereby breaking the limitation that the diffraction distance is only determined by the focal length in the traditional Fourier coding. The fractional domain complex amplitude distribution G(u,v) is constrained, and only the phase information is retained: where | · | denotes the modulo operation, denotes the phase distribution in the fractional domain, using the inverse fractional Fourier transform to convert into g'(x, y): where F a -1 denotes the inverse fractional Fourier transform of order a, du and dv denote the sampling frequencies in the fractional domain, and the original amplitude information A0(x, y) of the 3D object is preserved and replaced to obtain the complex amplitude distribution g1(x, y) in the spatial domain: After completing the first cycle iteration, g1(x, y) is taken as the input of the next cycle, until the phase in the fractional domain converges to the best, the final 3D metasurface hologram is obtained by extracting the phase, and the final phase distribution T is: T(u, v) = |(∑angle(G(u, v)), 2π)| Where angle(·) represents the phase extracted from the complex amplitude distribution, ∑ represents the sum of the phases of different layers of the 3D object, and the phase information T of the 3D metasurface hologram is recorded as an n x n matrix, where each element corresponds to a unit structure of the metasurface, and the metasurface is prepared by encoding the 3D metasurface hologram on the subwavelength structure.

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