Zoom micro projector based on metasurface holography

Abstract

The invention provides a zoom micro-projector based on metasurface holography. The micro-projector comprises a laser, a transmission-type metasurface and an electrowetting liquid lens. In order to realize system miniaturization, the transmission-type metasurface and the electrowetting liquid lens are integrated into a single cavity, and the electrowetting liquid lens is located behind the transmission-type metasurface. In the preparation process of the metasurface, a 3D Fourier transform algorithm is provided to generate a 3D metasurface hologram, so that the transmission-type metasurface is prepared. The liquid lens is a small-aperture liquid lens designed based on an electrowetting principle so as to cooperate with the transmission-type metasurface to realize zoom micro projection. When laser emitted by the laser irradiates the transmission-type metasurface, a 3D image diffracted by the metasurface passes through the electrowetting liquid lens, the position and the size of the 3D image can be adjusted according to the voltage of the liquid lens, and therefore the 3D zoom projection effect is achieved.

Description

1. Technical Field

[0001] The present invention relates to micro - projection technology, and more specifically, to a zoom micro - projector based on metasurface holography. 2. Background Art

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

[0003] The present invention proposes a zoom micro - projector based on metasurface holography. As shown in the appendix Figure 1 The micro - projector 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, and the electrowetting liquid lens is located behind the transmissive metasurface. During the preparation process of the metasurface, the present invention proposes a 3D Fourier transform algorithm to generate a 3D metasurface hologram, and then encodes the 3D metasurface hologram onto the sub - wavelength metasurface unit structure, thereby preparing the transmissive metasurface. Different from traditional liquid lenses, the proposed liquid lens is a small - aperture liquid lens designed based on the electrowetting principle, so as to cooperate with the transmissive metasurface to achieve zoom micro - projection. When the laser emitted by the laser irradiates 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, and 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 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, as shown in Figure 2 (a). To ensure that the liquid lens has a large optical-to-mechanical aperture ratio, the present 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. In addition, to ensure that the liquid lens has a large range of optical power variation and good stability, a biphasic liquid composed of a conductive liquid without an aqueous solution and an insulating liquid with a 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. The optical power Φ of the liquid lens is expressed as:

[0005]

[0006] where γ 12 is the interfacial tension between the conductive liquid and the insulating liquid, θ0 is the initial contact angle when no voltage is applied, C is the total capacitance per unit area of the dielectric layer coated with the hydrophobic layer, D is the optical aperture of the liquid lens, and Δn is the refractive index difference between the conductive liquid and the insulating liquid. The focal length f of the liquid lens liquidlens is:

[0007]

[0008] The proposed transmissive metasurface is regulated based on the Pancharatnam-Berry geometric phase principle to precisely control the phase distribution without changing the physical size of the metasurface structure. Each structural unit of the metasurface consists of rectangular single-crystalline silicon nanorods fabricated on a sapphire substrate. As shown in Figure 2 (b), L, W, and H represent the length, width, and height of the single-crystalline silicon, respectively. p is the period, and θ is the rotation angle of the single-crystalline silicon. By adjusting the rotation angle of each unit structure of the metasurface, the phase shift and regulation of each pixel of the 3D image are achieved. The regulation process of the Pancharatnam-Berry geometric phase is independent of the wavelength. 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 process of fabricating the metasurface, the present invention proposes a 3D Fourier transform algorithm to generate 3D metasurface holograms. This algorithm obtains a converged final phase distribution and generates 3D metasurface holograms by introducing the fractional Fourier transform and the inverse fractional Fourier transform, and adding iterative constraints in the fractional domain and the spatial domain respectively. Specifically, for a 3D object, the algorithm first performs a layering process 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, the complex amplitude distribution G(u, v) in the fractional domain is obtained by designing the transform order a and using the fractional Fourier transform:

[0010]

[0011] where F a represents the fractional Fourier transform with a transform order of a, (x, y) and (u, v) are the position coordinates of the optical field in the spatial domain and the fractional domain respectively, j is the imaginary unit, λ is the wavelength of the incident light, dx and dy are the sampling frequencies in the spatial domain, and f a is the focal length when the transform order is a, and f is obtained from the rotation transformation of the Wigner function a as:

[0012]

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

[0014] When the transform order a is set to 1, any focal length f a is equal 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 encoding where the diffraction distance is only determined by the focal length. Constraining the complex amplitude distribution G(u, v) in the fractional domain and only retaining the phase information:

[0015]

[0016] where |·| represents taking the modulus, represents the phase distribution in the fractional domain. Using the inverse fractional Fourier transform to convert into g’(x, y):

[0017]

[0018] where represents the inverse fractional Fourier transform of order a, and du and dv represent the sampling frequencies in the fractional domain. Retaining the phase and replacing the original amplitude information A0(x, y) of the 3D object, the complex amplitude distribution g1(x, y) in the spatial domain is obtained:

[0019]

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

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

[0022] Where angle(·) represents extracting the phase from the complex amplitude distribution, and Σ represents the sum of the phases of different layers of the 3D object. The phase information T of the 3D metasurface hologram is recorded as an n×n matrix, where each element corresponds to a unit structure of the metasurface. By encoding the 3D metasurface hologram on the sub-wavelength structure, the metasurface is fabricated. IV. DESCRIPTION OF THE DRAWINGS

[0023] Attached Figure 1 is a schematic structural diagram of a zoom micro-projector based on metasurface holography according to the present invention.

[0024] Attached Figure 2 is the working principle of a zoom micro-projector based on metasurface holography according to the present invention. Among them, Figure 2 (a) is the structure of the proposed liquid lens, Figure 2 (b) is the calculation process of the 3D metasurface hologram.

[0025] Attached Figure 3 is a schematic diagram of the zoom projection effect of a zoom micro-projector based on metasurface holography according to the present invention. Among them, Figure 3 (a) is 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) is the 3D reconstruction effect when the focal length of the liquid lens is 15 cm; Figure 3 (c) is the 3D reconstruction effect when the focal length of the liquid lens is 7 cm.

[0026] The reference numerals in the above-mentioned drawings are as follows:

[0027] (1) Zoom micro-projector, (2) Laser, (3) Transmissive metasurface, (4) Electrowetting liquid lens, (5) Mechanical housing, (6) Two pieces of 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-crystalline silicon nanorod.

[0028] It should be understood that the above-mentioned drawings are only schematic and are not drawn to scale. V. DETAILED IMPLEMENTATION MANNER

[0029] An embodiment of the zoom micro-projector based on metasurface holography proposed by the present invention will be described in detail below to further describe the present invention. It is necessary to point out here that the following embodiments are only used to further illustrate the present invention and cannot be construed as limiting the protection scope of the present invention. Those skilled in the art make some non-essential improvements and adjustments to the present invention according to the above-mentioned invention content, which still fall within the protection scope of the present invention.

[0030] One embodiment of the present invention is as follows: In a proposed zoom micro-projector based on metasurface holography, a laser with a wavelength of 671 nm is used as the reconstruction light to irradiate the metasurface. The liquid lens is located 2 mm behind the metasurface. The effective optical aperture of the liquid lens is 2 mm, and the mechanical diameter is 5 mm. The metasurface and the liquid lens are integrated in a cavity, and the total size of the cavity is 6.5 mm × 6.5 mm × 4.2 mm. The letters "N" and "U" located on 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 transformation orders of the letters "N" and "U" are set to 1 and 0.2 respectively. Then, the metasurface unit is processed. The substrate of the metasurface unit is sapphire, and single-crystalline silicon is etched on the substrate. The pixel pitch of the metasurface is 0.35 μm, and the period, height, length, and width of the single-crystalline silicon nanorods are 350 nm, 600 nm, 160 nm, and 80 nm respectively. When a voltage of 0 V to 70 V is applied to the liquid lens, the optical power of the liquid lens changes from -47.54 m -1 to 18.31 m -1 , and the response time of the liquid lens is 68 ms.

[0031] To verify the zoom projection performance of the proposed micro-projector, the present invention compares the imaging results of the letter "N" at different depth planes, as shown in Figure 3 (a). The first row shows the results when no voltage is applied to the liquid lens, where the letter "N" appears blurred at depths of 6 cm, 12 cm, 18 cm, and 30 cm and cannot be clearly projected. The second row shows the results when a voltage is applied to the liquid lens. By adjusting the driving voltage of the liquid lens, the letter "N" can be clearly projected to different depths. In addition, the 3D zoom projection effect is also verified, as shown in Figure 3 (b). When the focal length of the liquid lens is 15 cm, the letter "N" is projected on the depth plane of 15 cm, while the letter "U" is focused on the depth plane of 0.9 cm. As the focal length of the liquid lens decreases, the projection distance becomes closer, as shown in Figure 3(c) As shown, when the focal length of the liquid lens is 7 cm, the letter "N" is projected on the depth plane of 7 cm, while the letter "U" is focused at the depth plane of 0.3 cm. The experimental results show that the proposed micro-projector achieves a 3D zoom projection effect.

Claims

1. A zoom micro-projector based on metasurface holography, characterized in that, The micro-projector 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. The electrowetting liquid lens is located behind the transmissive metasurface. During the fabrication 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 onto the sub-wavelength metasurface unit structure, thereby fabricating the transmissive metasurface. The proposed liquid lens is a small-aperture liquid lens designed based on the electrowetting principle to cooperate with the transmissive metasurface to achieve zoom micro-projection. When the laser light emitted by the laser irradiates 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.

2. The zoom micro-projector based on metasurface holography according to claim 1, wherein The electrowetting liquid lens in the zoom micro-projector mainly consists of a mechanical housing, 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 the driving board. To ensure that the liquid lens has a large optical-to-mechanical aperture ratio, a straight-cylindrical cavity structure is designed to reduce the cavity thickness of the liquid lens, thereby ensuring the compactness of the zoom micro-projector. In addition, to ensure that the liquid lens has a large range of optical power variation and good stability, a two-phase liquid composed of a conductive liquid without an aqueous solution and an insulating liquid with a 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. 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, θ0 is the initial contact angle when no voltage is applied, C is the total capacitance per unit area of the dielectric layer coated with the hydrophobic layer, D is the optical aperture of the liquid lens, Δn is the refractive index difference between the conductive liquid and the insulating liquid, and the focal length f of the liquid lens liquidlens is given by: The proposed transmissive metasurface is regulated based on the Pancharatnam-Berry geometric phase principle to precisely control the phase distribution without changing the physical size of the metasurface structure. Each structural unit of the metasurface consists of rectangular single-crystalline silicon nanorods fabricated on a sapphire substrate. By adjusting the rotation angle of each unit structure of the metasurface, the phase shift and regulation of each pixel of the 3D image are achieved. The regulation process of the Pancharatnam-Berry geometric phase is independent of the wavelength. 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.

3. The zoom micro-projector based on metasurface holography according to claim 1, wherein The 3D Fourier transform algorithm is used to generate a 3D metasurface hologram. This algorithm introduces the fractional Fourier transform and the inverse fractional Fourier transform, and adds iterative constraints in the fractional domain and the spatial domain respectively to obtain a converged final phase distribution and generate a 3D metasurface hologram. Specifically, for a 3D object, the algorithm first performs a layering process 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: where F a represents the fractional Fourier transform of order a, (x, y) and (u, v) are the position coordinates of the optical field in the spatial domain and the fractional domain respectively, j is the imaginary unit, λ is the wavelength of the incident light, dx and dy are the sampling frequencies in the spatial domain, f a is the focal length when the transform order is a, and f is obtained from the rotational transformation of the Wigner function a as follows: where f is the normalized focal length selected during the holographic calculation process; When the transformation order a is set to 1, for any focal length f a is equal to the normalized focal length. Introducing the transformation order changes the rotation angle of the Wigner function, making the diffraction distance related to the transformation order, thus breaking the limitation in traditional Fourier encoding where the diffraction distance is only determined by the focal length, constraining the complex amplitude distribution G(u, v) in the fractional domain and only retaining the phase information: where |·| represents taking the modulus, represents the phase distribution in the fractional domain, and the inverse fractional Fourier transform is used to convert it 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, retain the phase and replace the original amplitude information A0(x,y) of the 3D object to obtain the complex amplitude distribution g1(x,y) in the spatial domain: After the first loop iteration is completed, g1(x,y) is used as the input for the next loop until the phase in the fractional domain converges to the best. Then, the phase is extracted to obtain the final 3D metasurface hologram. The final phase distribution T is: T(u,v) = |(∑angle(G(u,v)), 2π)| where angle(·) represents extracting the phase from the complex amplitude distribution, Σ represents the sum of the phases of different layers of the 3D object. The phase information T of the 3D metasurface hologram is recorded as an n×n matrix, where each element corresponds to a unit structure of the metasurface. By encoding the 3D metasurface hologram on the subwavelength structure, the metasurface is fabricated.

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