Actively controlled holographic method and holographic element for free-form metasurface

Abstract

The present invention relates to a method for actively controlling holographic free-form surface metasurfaces and a holographic element, which comprises the following steps: selecting multiple free-form surfaces of a target and their corresponding multiple target holographic images; calculating the reflection phase difference caused by the optical path difference based on the free-form surfaces of the target; F 自由曲面 ; The intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to solve the phase distribution of the metasurface F 超构表面 Or the electric field distribution E on the metasurface 超构表面 Since multiple reflection phase differences caused by optical path differences can be calculated based on multiple free-form surfaces, and combined with the intensity distribution of multiple target holographic images, the metasurface phase distribution or electric field distribution can be solved through optimization algorithms, a certain metasurface can produce multiple different holographic images when combined with multiple different free-form surfaces. Different holographic images can then be presented by changing the shape of the free-form surface, and a larger number of holographic channels can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical fields of micro-nano optics and computational holography, and in particular to an active control holographic method for a free-form metasurface and a holographic element. Background Art

[0002] Metasurfaces are an emerging class of optical components. They leverage the interaction between micro- and nanostructures and light to control parameters such as amplitude, phase, and polarization. Micro- and nanostructures can then be combined into arrays to achieve functions such as beam deflection, focusing, and computational holography. Metasurfaces offer advantages not found in conventional optical components, such as ultrathinness and ease of integration, subwavelength control precision, and independent control of multiple optical parameters. Actively controlled metasurfaces are devices whose optical functions can be altered by applying external stimuli. For example, immersion-type actively controlled metasurfaces can produce two different holographic images by placing the metasurface device in air and a liquid of a specific refractive index.

[0003] In related technologies, previous methods of actively controlling metasurfaces usually include utilizing the crystal orientation change of phase change materials, utilizing chemical reactions to change materials, utilizing electrochemical effects to change the refractive index of materials, utilizing micro-electromechanical systems to change the thickness of the air layer in micro-nanostructures, utilizing immersion to change the refractive index of the environment, and utilizing stretching flexible substrates to change the period of micro-nanostructures.

[0004] However, since the above methods usually require the design of a variety of complex micro-nanostructures to achieve independent light field modulation under different working states, and the phase control capabilities of various schemes are limited, this limits the number of active control channels to no more than four.

[0005] Currently, in applications such as high-density optical information storage and multi-dimensional encryption, dynamic augmented reality display, and wearable optical devices, dynamic control of metasurface technology urgently needs new active control solutions to expand the number of channels. Summary of the Invention

[0006] The embodiments of the present invention provide a method and a holographic element for actively controlling a free-form metasurface, so as to solve the problem in the related art that the number of active control channels is limited to no more than four by common methods.

[0007] In the first aspect, a method for actively controlling holography of a free-form surface metasurface is provided, which comprises the following steps: selecting multiple free-form surfaces of a target and their corresponding multiple target holographic images; calculating the reflection phase difference caused by the optical path difference based on the free-form surfaces of the target; F 自由曲面 ; The intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to solve the phase distribution of the metasurface F超构表面 Or the electric field distribution E on the metasurface 超构表面 .

[0008] In some embodiments, the target-based free-form surface calculates the reflection phase difference caused by the optical path difference. F 自由曲面 , including: determining the incident direction of the incident light and intercepting a wavefront plane of the incident light, obtaining the distance L from each point on the free surface to the wavefront plane, and the phase difference of the point is F =4πL / λ, where λ is the wavelength of the incident light.

[0009] In some embodiments, the intensity distribution of the multiple target holographic images and the multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to solve the phase distribution of the metasurface F 超构表面 , including: randomly generating an initial metasurface phase distribution F 超构表面 ; The metasurface phase distribution F 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to calculate the phase distribution of the metasurface F 超构表面 , and iterate in sequence. When the number of iterations reaches the threshold or the holographic image quality meets the requirements, the current metasurface phase distribution is output F 超构表面 .

[0010] In some embodiments, the metasurface phase distribution F 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to calculate the phase distribution of the metasurface F 超构表面 , including: distributing the metasurface phase F 超构表面 With different reflection phase differences F 自由曲面 Combined with the above, the corresponding holographic surface electric field distribution E is calculated. 全息n Based on the holographic optimization algorithm, combined with the electric field distribution E 超构表面n , different reflection phase differences F 自由曲面 and the corresponding target holographic image, generating the next generation metasurface phase distribution F 超构表面 .

[0011] In some embodiments, the metasurface phase distribution F 超构表面 With different reflection phase differences F 自由曲面 Combined with the above, the corresponding holographic surface electric field distribution E is calculated. 全息n , including: different reflection phase differences F 自由曲面 Superimposed on the metasurface phase distribution F 超构表面 Obtain the total electric field distribution E on the metasurface 总 , and use the holographic calculation method to calculate the holographic surface electric field distribution E corresponding to the free-form surface 全息n .

[0012] In some embodiments, the holographic calculation method includes an algorithm for calculating a holographic image based on electric field distribution, including fast Fourier transform, diffraction integral, or angular spectrum diffraction.

[0013] In some embodiments, the intensity distribution of the multiple target holographic images and the multiple reflection phase differences F 自由曲面 Substitute into the holographic optimization algorithm to solve the electric field distribution E on the metasurface 超构表面 , including: randomly generating a complex amplitude metasurface electric field distribution E 超构表面 ; The electric field distribution E on the metasurface 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to calculate the electric field distribution E on the metasurface 超构表面 , and iterate in sequence. When the number of iterations reaches the threshold or the holographic image quality meets the requirements, the current metasurface electric field distribution E is output. 超构表面 .

[0014] In some embodiments, the holographic optimization algorithm includes an annealing algorithm, a genetic algorithm, or a gradient descent algorithm.

[0015] In a second aspect, a holographic element is provided, which includes: a flexible substrate, on which a micro-nanostructure array is arranged, and the phase distribution of the micro-nanostructure array is obtained according to an active control holographic method of a free-form metasurface.

[0016] In some embodiments, the array arrangement of the micro-nanostructure array utilizes the geometric phase or transmission phase principle and the metasurface phase distribution F 超构表面 get.

[0017] In some embodiments, the rotation angles of the micro-nano structures in the micro-nano structure array are different.

[0018] The beneficial effects brought about by the technical solution provided by the present invention include:

[0019] An embodiment of the present invention provides a method for actively controlling a holographic image of a free-form metasurface and a holographic element. Based on multiple free-form surfaces, multiple reflection phase differences caused by optical path differences can be calculated, and combined with the intensity distribution of multiple target holographic images, the metasurface phase distribution or electric field distribution can be calculated through an optimization algorithm. This allows a certain metasurface to generate multiple different holographic images when combined with multiple different free-form surfaces, and then different holographic images can be presented by changing the shape of the free-form surface. Therefore, the more free-form surfaces there are, the more dynamic holographic channels there are, and a larger number of holographic channels can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 A schematic diagram of the principle of the active holographic control method provided by an embodiment of the present invention;

[0022] Figure 2 A schematic structural diagram of a holographic element provided by an embodiment of the present invention;

[0023] Figure 3 A schematic diagram of the principle of calculating the reflection phase difference provided by an embodiment of the present invention;

[0024] Figure 4 An algorithm flow chart of the active holographic control method provided by an embodiment of the present invention;

[0025] Figure 5 A diagram showing calculation results of a holographic element provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0027] The embodiments of the present invention provide a method and a holographic element for actively controlling a free-form metasurface, which can solve the problem in related arts that the number of active control channels is limited to no more than four by conventional methods.

[0028] See also Figure 1 As shown, a method for actively controlling holography of a free-form metasurface provided by an embodiment of the present invention may include the following steps:

[0029] S1: Select multiple free-form surfaces of a target and their corresponding multiple target holographic images. The number of free-form surfaces can be more than four, or more than ten, or even more. The shapes of the multiple free-form surfaces are different, and the corresponding multiple target holographic images are also different.

[0030] S2: Calculate the reflection phase difference caused by the optical path difference based on the target free-form surface F 自由曲面 .

[0031] S3: Combine the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to solve the phase distribution of the metasurface F 超构表面 Or the electric field distribution E on the metasurface 超构表面 The calculated metasurface phase distribution F 超构表面 Or the electric field distribution E on the metasurface 超构表面 Reflection phase difference with different free-form surfaces F 自由曲面 When combined, the corresponding target holographic image can be displayed.

[0032] In this embodiment, multiple reflection phase differences caused by optical path differences can be calculated based on multiple free-form surfaces, and combined with the intensity distribution of multiple target holographic images, the metasurface phase distribution or the metasurface electric field distribution can be solved through an optimization algorithm. Therefore, when a certain metasurface is combined with multiple different free-form surfaces, it can produce multiple different holographic images, that is, form multiple dynamic holographic channels, and then different holographic images can be presented by changing the shape of the free-form surface. Therefore, the number of dynamic holographic channels is the same as the number of free-form surfaces. The more free-form surfaces there are, the more dynamic holographic channels there are. This embodiment can achieve a larger number of holographic channels; and different holographic images can be presented by changing the shape of the free-form surface.

[0033] Moreover, the active control holographic method provided in this embodiment utilizes the reflection phase difference of the free-form surface, and does not require decoupling the optical response of the micro-nanostructure under different working states. The geometric phase of the same structure can be used to realize active control holography, and the micro-nanostructure design is simpler.

[0034] Further, in some embodiments, see Figure 3 As shown, the free-form surface based on the target calculates the reflection phase difference caused by the optical path difference F 自由曲面 , which may include: determining the incident direction of the incident light and intercepting a wavefront plane of the incident light, obtaining the distance L from each point on the free-form surface to the wavefront plane, and the phase difference of the point is F =4πL / λ, where λ is the wavelength of the incident light.

[0035] In some optional embodiments, the intensity distribution of the multiple target holographic images and the multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to solve the phase distribution of the metasurface F 超构表面 , which may include: randomly generating an initial metasurface phase distribution F 超构表面 ; The metasurface phase distribution F 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to calculate the phase distribution of the metasurface F 超构表面 , and iterate in sequence. When the number of iterations reaches the threshold or the holographic image quality meets the requirements, the current metasurface phase distribution is output F 超构表面 In this embodiment, it is necessary to continuously adjust the phase distribution of the metasurface. F 超构表面 Perform iterative calculations and judge the number of iterations or the quality of the holographic image in real time. When the requirements are met, output the current metasurface phase distribution. F 超构表面 If the value does not meet the requirements, the iteration is repeated; eventually the metasurface phase distribution that meets the requirements can be obtained. F 超构表面 Among them, the first substitution of the metasurface phase distribution F 超构表面 is the initial value, and the metasurface phase distribution entered in each subsequent iteration is F 超构表面 These are the metasurface phase distributions calculated last time. F 超构表面In this embodiment, the threshold of the number of iterations is preferably set to 20 times. In other embodiments, the number of thresholds may also be set as needed.

[0036] Furthermore, in the above-mentioned iterative calculation process, the selected loop termination conditions, in addition to the number of iterations and the quality of the holographic image, can also be that the root mean square error of the calculated hologram is less than a certain threshold, the electric field intensity of the calculated holographic surface is uniform, etc.

[0037] Based on the above technical solution, see Figure 4 As shown, the metasurface phase distribution F 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to calculate the phase distribution of the metasurface F 超构表面 , which may include:

[0038] Step a: Phase distribution of the metasurface F 超构表面 With different reflection phase differences F 自由曲面 Combined with the above, the corresponding holographic surface electric field distribution E is calculated. 全息n .

[0039] Step b: The holographic surface electric field distribution E 全息n Combined with the target holographic image, calculate the electric field distribution E of the output surface 超构表面n .

[0040] Step c: Based on the holographic optimization algorithm, combined with the electric field distribution E of the output surface 超构表面n , different reflection phase differences F 自由曲面 and the corresponding target holographic image, generating the next generation metasurface phase distribution F 超构表面 In this embodiment, a round of calculation can be performed through steps a, b, and c to obtain a metasurface phase distribution F 超构表面 Next time, we will calculate the metasurface phase distribution obtained this time. F 超构表面 Perform a round of calculations according to steps a, b, and c to obtain the next metasurface phase distribution F 超构表面 , and the calculation is repeated iteratively.

[0041] In some embodiments, the metasurface phase distribution F 超构表面 With different reflection phase differences F 自由曲面Combined with the above, the corresponding holographic surface electric field distribution E is calculated. 全息n , which may include: different reflection phase differences F 自由曲面 Superimposed on the metasurface phase distribution F 超构表面 Obtain the total electric field distribution E on the metasurface 总 , and use the holographic calculation method to calculate the holographic surface electric field distribution E corresponding to the free-form surface 全息n In this embodiment, the holographic calculation method can be used to calculate the holographic image corresponding to the corresponding free-form surface, and obtain the corresponding holographic surface electric field distribution E 全息n Among them, the total electric field distribution E 总 = exp(i*( F 自由曲面 + F 超构表面 ), holographic surface electric field distribution , the electric field distribution of the output surface calculated according to the above steps , metasurface phase distribution .

[0042] In some optional embodiments, the holographic calculation method may include an algorithm for calculating holographic images based on electric field distribution, such as fast Fourier transform, diffraction integral, or angular spectrum diffraction. That is, the holographic calculation method may be one of fast Fourier transform, diffraction integral, or angular spectrum diffraction. In this embodiment, the holographic calculation method is preferably fast Fourier transform.

[0043] In the above, the holographic surface electric field distribution E 全息n Combined with the target holographic image, calculate the electric field distribution E of the output surface 超构表面n When , the electric field distribution on the exit surface can be calculated by inverse Fourier transform.

[0044] The above iterative calculation of the metasurface phase distribution F 超构表面 The holographic optimization algorithm used is the improved GS algorithm. Based on the above technical solution, the holographic optimization algorithm can also be an annealing algorithm, a genetic algorithm or a gradient descent algorithm.

[0045] In some optional embodiments, the intensity distribution of the multiple target holographic images and the multiple reflection phase differences F 自由曲面 Substitute into the holographic optimization algorithm to solve the electric field distribution E on the metasurface 超构表面 , which may include the following steps: randomly generating a complex amplitude metasurface electric field distribution E 超构表面 , the electric field distribution E on the surface of this metastructure 超构表面 It is also the initial value; the electric field distribution E on the metastructure surface 超构表面, the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to calculate the electric field distribution E on the metasurface 超构表面 , and iterate in sequence. When the number of iterations reaches the threshold or the holographic image quality meets the requirements, the current metasurface electric field distribution E is output. 超构表面 In this embodiment, it is necessary to continuously monitor the electric field distribution E on the metasurface. 超构表面 Perform iterative calculations and judge the number of iterations or the quality of the holographic image in real time. When the requirements are met, output the current metasurface electric field distribution E 超构表面 If the value does not meet the requirements, the iteration is repeated; eventually the surface electric field distribution E that meets the requirements can be obtained. 超构表面 Among them, the first substitution of the metasurface electric field distribution E 超构表面 is the initial value, and the electric field distribution E of the metasurface is input in each subsequent iteration. 超构表面 are all the metasurface electric field distribution E calculated last time. 超构表面 .

[0046] Furthermore, the surface electric field distribution E 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences F 自由曲面 Substitute the holographic optimization algorithm to calculate the electric field distribution E on the metasurface 超构表面 , including: distributing the electric field E on the metasurface 超构表面 With different reflection phase differences F 自由曲面 Combined with the holographic calculation method, the holographic surface electric field distribution E corresponding to the free-form surface is calculated 全息n ;Holographic surface electric field distribution E 全息n Combined with the target holographic image, calculate the electric field distribution E of the output surface 超构表面n ; Then the electric field distribution E 超构表面n Combined reflection phase difference F 自由曲面 , calculate the electric field distribution E on the next generation metasurface 超构表面 .

[0047] Among them, the holographic surface electric field distribution here is , the electric field distribution of the output surface calculated according to the above steps , the electric field distribution on the metasurface .

[0048] Furthermore, the surface electric field distribution E 超构表面 With different reflection phase differences F 自由曲面 Combined with the holographic calculation method, the holographic surface electric field distribution E corresponding to the free-form surface is calculated 全息n, including: different reflection phase differences F 自由曲面 Superimposed on the electric field distribution E of the metasurface 超构表面 Obtain the total electric field distribution E on the metasurface 总 , and use the holographic calculation method to calculate the holographic surface electric field distribution E corresponding to the free-form surface 全息n At this time, the total electric field distribution E 总 =E 超构表面 *exp(i* F 自由曲面 ).

[0049] The holographic calculation method may also be one of fast Fourier transform, diffraction integral or angular spectrum diffraction. In this embodiment, the holographic calculation method is preferably fast Fourier transform. In addition, when calculating the electric field distribution E of the output surface, 超构表面n , can be calculated by inverse Fourier transform.

[0050] See also Figure 2 As shown, an embodiment of the present invention further provides a holographic element, which may include: a flexible substrate, wherein the material of the flexible substrate may be PDMS (polydimethylsiloxane) or other flexible materials; a micro-nanostructure array disposed on the flexible substrate, preferably silicon micro-nanostructures in this embodiment, wherein the phase distribution of the micro-nanostructure array is obtained according to the active control holographic method of free-form metasurfaces. The micro-nanostructure array is a rectangular parallelepiped structure of uniform size with a reflection cross-polarization efficiency. The reflection cross-polarization efficiency is calculated by dividing the intensity of the reflected circularly polarized light of the same polarization by the intensity of the incident circularly polarized light when a single circularly polarized light is incident. The value can be obtained by modeling and calculation using methods such as finite-difference time-domain method.

[0051] Furthermore, the array arrangement of the micro-nanostructure array utilizes the geometric phase or transmission phase principle and the metasurface phase distribution F 超构表面 The rotation angles of the micro-nano structures in the micro-nano structure array are different.

[0052] The micro-nanostructure array is adhered to the flexible substrate, and the micro-nanostructure array can be micro-nanostructures with different morphologies that can obtain different reflection phases.

[0053] The characteristic dimensions of the micro-nanostructure array are: period p=400nm, micro-nanostructure height h=380nm, length l=230nm, and width w=100nm. The rotation angle of each micro-nanostructure is numerically half of the corresponding target phase.

[0054] It should be noted that the free-form surface shapes selected in this embodiment are surfaces with different bending directions and curvatures; the target image selected is the 16 spelling letters of "Metaform Hologram", and its matrix size is 1600*1600, see Figure 5 shown.

[0055] The holographic element prepared in the embodiment of the present invention can show different holographic images when bent in different directions and curvatures, which is consistent with the design scheme.

[0056] Through the solution of this embodiment, it is possible to display at least 16 independently designable reflective holographic images when the element is bent in different directions to different curvatures. The number of independently adjustable holographic channels, corresponding information capacity and encryption dimension exceed those of other control methods.

[0057] The device can be designed to be actively controlled by bending the hand or fitting the skin, and has the advantages of large area, high repeatability, and can be applied to wearable optical devices.

[0058] An embodiment of the present invention provides a method for actively controlling holography of a free-form metasurface and a holographic element. This method combines a free-form surface with a freely encodable metasurface, and uses an optimization algorithm to calculate the phase distribution of the metasurface. This allows a given metasurface to produce different holographic images when combined with different free-form surfaces. This allows the active control holography to present different holographic images by changing the shape of a metasurface with a flexible free-form substrate when incident light is irradiated.

[0059] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "upper" and "lower" is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be internal communication between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0060] It should be noted that, in the present invention, relational terms such as "first" and "second" are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0061] The foregoing description is intended only to provide specific embodiments of the present invention, which will enable those skilled in the art to understand and implement the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not intended to be limited to the embodiments shown herein, but is intended to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for actively controlling holographic free-form metasurfaces, characterized in that: It includes the following steps: multiple free-form surfaces of a selected target and multiple corresponding target holographic images thereof; Calculate the reflection phase difference caused by the optical path difference based on the target's free-form surface Φ 自由曲面 ; The intensity distribution of multiple target holographic images and multiple reflection phase differences Φ 自由曲面 Substitute the holographic optimization algorithm to solve the phase distribution of the metasurface Φ 超构表面 Or the electric field distribution E on the metasurface 超构表面 ; When a metasurface is combined with multiple different free-form surfaces, it generates multiple different holographic images, and then presents different holographic images by changing the shape of the free-form surface; the free-form surface based on the target calculates the reflection phase difference caused by the optical path difference. Φ 自由曲面 ,include: After determining the incident direction of the incident light, intercept a wavefront plane of the incident light and obtain the distance L from each point on the free surface to the wavefront plane. The phase difference of the point is Φ =4πL / λ, where λ is the wavelength of the incident light; The intensity distribution of multiple target holographic images and multiple reflection phase differences Φ 自由曲面 Substitute the holographic optimization algorithm to solve the phase distribution of the metasurface Φ 超构表面 ,include: Randomly generate an initial metasurface phase distribution Φ 超构表面 ; Phase distribution of metasurface Φ 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences Φ 自由曲面 Substitute the holographic optimization algorithm to calculate the phase distribution of the metasurface Φ 超构表面 , and iterate in sequence. When the number of iterations reaches the threshold or the holographic image quality meets the requirements, the current metasurface phase distribution is output Φ 超构表面 ; Among them, the first substitution of the metasurface phase distribution Φ 超构表面 is the initial metasurface phase distribution Φ 超构表面 , the metasurface phase distribution input in each subsequent iteration Φ 超构表面 These are the metasurface phase distributions calculated last time. Φ 超构表面 ; The metasurface phase distribution Φ 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences Φ 自由曲面 Substitute the holographic optimization algorithm to calculate the phase distribution of the metasurface Φ 超构表面 ,include: Phase distribution of metasurface Φ 超构表面 With different reflection phase differences Φ 自由曲面 Combined with the above, the corresponding holographic surface electric field distribution E is calculated. 全息n ; The holographic surface electric field distribution E 全息n Combined with the target holographic image, calculate the electric field distribution E of the output surface 超构表面n ; Based on the holographic optimization algorithm, combined with the electric field distribution E 超构表面n , different reflection phase differences Φ 自由曲面 and the corresponding target holographic image, generating the next generation metasurface phase distribution Φ 超构表面 ; The metasurface phase distribution Φ 超构表面 With different reflection phase differences Φ 自由曲面 Combined with the above, the corresponding holographic surface electric field distribution E is calculated. 全息n ,include: The different reflection phase differences Φ 自由曲面 Superimposed on the metasurface phase distribution Φ 超构表面 Obtain the total electric field distribution E on the metasurface 总 , and use the holographic calculation method to calculate the holographic surface electric field distribution E corresponding to the free-form surface 全息n ; Among them, the total electric field distribution E 总 = exp(i*( Φ 自由曲面 + Φ 超构表面 ), holographic surface electric field distribution , the electric field distribution of the output surface calculated according to the above steps , metasurface phase distribution ; The intensity distribution of multiple target holographic images and multiple reflection phase differences Φ 自由曲面 Substitute into the holographic optimization algorithm to solve the electric field distribution E on the metasurface 超构表面 ,include: Randomly generate a complex amplitude metasurface electric field distribution E 超构表面 ; The electric field distribution E on the metasurface 超构表面 , the intensity distribution of multiple target holographic images and multiple reflection phase differences Φ 自由曲面 Substitute the holographic optimization algorithm to calculate the electric field distribution E on the metasurface 超构表面 , and iterate in sequence. When the number of iterations reaches the threshold or the holographic image quality meets the requirements, the current metasurface electric field distribution E is output. 超构表面 ; The electric field distribution of the holographic surface here , the electric field distribution of the output surface calculated according to the above steps , the electric field distribution on the metasurface ; The first substitution of the metasurface electric field distribution E 超构表面 It is a metasurface electric field distribution E that randomly generates a complex amplitude 超构表面 , the electric field distribution E of the metasurface input in each subsequent iteration 超构表面 are all the metasurface electric field distribution E calculated last time. 超构表面 .

2. The method for actively controlling holography of a free-form metasurface according to claim 1, wherein: The holographic calculation method includes an algorithm for calculating a holographic image based on electric field distribution, including fast Fourier transform, diffraction integral or angular spectrum diffraction.

3. The method for actively controlling holography of a free-form metasurface according to claim 1, wherein: The holographic optimization algorithm includes an annealing algorithm, a genetic algorithm or a gradient descent algorithm.

4. A holographic element, characterized in that: It includes: A flexible substrate having a micro-nanostructure array provided thereon, wherein the phase distribution of the micro-nanostructure array is obtained according to the active control holographic method of the free-form metasurface according to claim 1.

5. The holographic element according to claim 4, wherein: The array arrangement of the micro-nano structure array utilizes the geometric phase or transmission phase principle and the metasurface phase distribution Φ 超构表面 get.

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