Meta-structure lens design method

Abstract

The invention relates to the technical field of super-structure lens design methods, and provides a super-structure lens design method, which comprises the following steps of: performing reverse design on a lens phase according to a focusing requirement, evaluating whether the phase has a proper infinitesimal structure for matching, and continuously optimizing to obtain a super-structure. Finally, the matching phase of each metamaterial lens unit better meets the focusing requirement and better fits the phase capable of being regulated and controlled by an actual infinitesimal structure, and therefore the designed metamaterial lens can have the achromatic performance of a larger caliber and a wider working wave band within the limitation range of materials and the technology.

Description

Technical Field

[0001] The present invention relates to the technical field of meta-lens design methods, and in particular to a meta-lens design method. Background Art

[0002] Traditional optical lenses have chromatic aberration problems under broadband incident light due to the dispersion effect of device materials. The chromatic aberration caused by dispersion will also have an adverse effect on the optical imaging system, seriously reducing the focusing efficiency and imaging quality. At the same time, the traditional achromatic design method is to cascade multiple optical lenses with different surfaces. This method will increase the volume, weight, complexity and cost of the optical system, and is not very applicable in imaging fields such as nuclear industry and medicine that require high temperature resistance, radiation resistance and lightweight integration.

[0003] In order to provide clearer images and reduce the color edges of images, researchers at home and abroad have proposed various broadband achromatic meta-lens design schemes. With the in-depth research on metasurfaces in light field control, meta-lenses have received widespread attention. Meta-lenses designed based on the principle of meta-surfaces are famous for their flatness, lightness, and ability to efficiently control light wave amplitude, phase, polarization, and frequency through subwavelength-sized micro-element structures. It is composed of subwavelength micro-element arrays, naturally has no spherical aberration, has a high degree of control freedom and ultra-thin thickness, and is convenient for the integration and miniaturization of optical devices, while also having broadband achromatic focusing performance. And because of its light and thin structure, high diffraction efficiency, and wide applicable spectral range, and can be made of materials such as silicon and germanium, meta-lenses can be used in extreme environments such as high temperature and high radiation, laying a solid foundation for the research of miniaturized, high-performance imaging detection equipment suitable for nuclear facility environments.

[0004] However, most of the existing metalens design methods start from the ideal lens phase formula to calculate the metalens phase and design the metalens structure. This method is limited by the limited electromagnetic control capability of the microstructure. As the lens aperture increases, the microstructure cannot simultaneously meet the phase control requirements of multiple wavelengths. Therefore, it is difficult to obtain a large-aperture, broadband, high-diffraction-efficiency achromatic metalens. Summary of the invention

[0005] The present invention proposes a meta-lens design method. According to the focusing requirements, the lens phase is reversely designed, and whether the phase is matched with a suitable micro-element structure is evaluated. Through continuous optimization, the matching phase of each meta-lens unit is finally made to better meet the focusing requirements and to be more in line with the actual phase that can be controlled by the micro-element structure. As a result, the designed meta-lens has a larger aperture and a wider working band achromatic performance within the limitations of materials and processes.

[0006] The technical solution of the present invention is as follows:

[0007] A meta-lens design method comprises the following steps:

[0008] S100: Determine suitable materials as the substrate and micro-element structure of the wide-band achromatic meta-lens, and determine the lens size, focal length, and working band;

[0009] S200: Reverse design of the meta-lens phase arrangement using the inverse optimization algorithm;

[0010] S300: importing the optimized phase into the micro-element structure database for matching to obtain the actual matching phase, evaluating the focusing performance of the actual matching phase to determine whether it meets the design requirements. If it does not meet the design requirements, return to S200 to re-optimize the phase. If it meets the design requirements, proceed to S400;

[0011] S400: After arranging the matched micro-elements according to the corresponding phases, simulation verification is performed;

[0012] S500: The design is completed through simulation verification.

[0013] Furthermore, the working band determination method in step S100 is:

[0014] The scanning range of the metalens working band is determined, and based on computer performance, several discrete wavelengths are selected from the continuous working band as simulation calculation wavelengths.

[0015] Furthermore, the method for determining the base of the lens element in step S100 is:

[0016] The base length and width of the lens element are taken as the period of the element.

[0017] Furthermore, the lens size determination method in step S100 is:

[0018] The size of the designed meta-lens is determined according to the number of micro-elements.

[0019] Furthermore, the method for determining the microelement structure and material in step S100 is:

[0020] S110: Both the substrate and the nanorods are made of materials commonly used in optical lenses;

[0021] S120: There are five types of microelement: square cylinder, circular cylinder, annular cylinder, a single base supporting four rectangular cylinders, and a single base supporting four circular cylinders. The geometric parameters of the rectangular cylinder and circular cylinder are the side length L and the radius R, respectively. The geometric parameters of the annular cylinder are the inner diameter R1 and the outer diameter R2, and the latter two are consistent with the geometric parameters of the individual rectangular cylinders and circular cylinders.

[0022] Furthermore, the reverse optimization algorithm in step S200 includes:

[0023] S210: Optimizing the lens phase surface;

[0024] S220: Filling the optimized phase surface with the micro-element database;

[0025] S230: After the optimized phase surface is filled into the micro-element structure, the formed meta-lens performs wavefront modulation on the incident light field;

[0026] S240: incident light of different wavelengths is modulated by the meta-lens to obtain a corresponding focused light field on a focusing plane;

[0027] S250: Calculate the loss between the actual focusing plane light field and the ideal focusing plane light field using a loss function;

[0028] S260: Return to step S210 through reverse iteration.

[0029] Furthermore, the modulation method of step S230 includes:

[0030] The incident light field U of the i-th wavelength in_i After (x,y) passes through the meta-lens, the outgoing light field U at the rear surface of the meta-lens can be obtained out_i (x,y), then the phase The modulation process formula is:

[0031] Among them, U out_i (x,y) and U in_i (x, y) corresponds to the complex amplitudes of the output and input light fields at the i-th wavelength, respectively, and j is an imaginary unit;

[0032] Represents the phase regulation of the input light field by the lens. After calculating the loss between the actual output light field and the ideal output light field, the gradient descent algorithm is used to reversely update the phase required for regulation according to the loss.

[0033] Furthermore, the loss function calculation formula in step S250 is:

[0034] loss = loss1 + loss2;

[0035]

[0036] Among them, loss1 represents the calculation of the light field distribution of the outgoing light corresponding to the i-th wavelength after metasurface modulation on the target diffraction plane and the set target light field corresponding to the i-th wavelength The square of the difference between them is then summed up to get loss1 at different wavelengths. represents the ideal complex amplitude distribution of the i-th wavelength in the focal plane, which is defined as the ideal distribution of the incident light in the focal plane after passing through the metalens. The characteristic of this distribution is that all the energy is concentrated in the specified area;

[0037] loss2 is used to evaluate the matching degree between the actual phase controlled by the microelement and the designed phase plane, and return the corresponding loss value. and They represent the optimized phase at the i-th wavelength and the actual phase of the microelement at the corresponding spatial position (x, y). It indicates the transmittance of the actual element at the i-th wavelength at the corresponding spatial position (x, y).

[0038] Furthermore, the verification method in step S400 includes:

[0039] S410: Selecting an achromatic meta-lens with a working wavelength, focal length, micro-element period, height, lens size and corresponding numerical aperture, and obtaining the light intensity distribution in the xz plane, the light intensity distribution at the focal plane and a two-dimensional normalized intensity distribution curve of incident light of different wavelengths after passing through the designed device;

[0040] S420: setting the evaluation size of the focusing efficiency again, obtaining the focusing efficiency distribution diagram of the meta-lens at different wavelengths and the focal length offset distribution diagram of the meta-lens at each wavelength, and performing analysis;

[0041] S430: On the basis of the above-mentioned small-sized metalens, an attempt is made to further expand the size of the metalens, and an attempt is made to reduce the numerical aperture of the metalens to reduce the demand for micro-element control capability, and the light intensity distribution on the xz plane, the light intensity distribution at the focal plane, and a two-dimensional normalized intensity distribution curve are obtained;

[0042] S440: After setting the evaluation size of the focusing efficiency, a focusing efficiency distribution diagram of the meta-lens at different wavelengths and a focal length offset distribution diagram of the meta-lens at each wavelength are obtained for analysis;

[0043] S450: Put this parameter into the electromagnetic field vector analysis software, build a complete meta-lens and use vector diffraction for simulation verification, and observe the distribution of the output light field.

[0044] The working principle and beneficial effects of the present invention are:

[0045] The present invention discloses an end-to-end achromatic meta-lens reverse design method. Through the analysis of scalar diffraction theory, meta-lens theory and gradient descent algorithm, a polarization-independent achromatic meta-lens with wide band, high focusing efficiency and simple micro-element structure is optimized. This method makes full use of the end-to-end advantage of the reverse design algorithm that does not require the use of phase formula forward design and manual intervention adjustment in the intermediate process. The achromatic effect of the lens is improved by defining the metric index of the achromatic performance of the meta-lens, and calculating the optimized lens phase and maximizing the index. Not only is the method simple and intuitive, but the focusing effect is also better than that achieved by the traditional design method based on the phase formula due to the algorithm's precise control of the phase of each micro-element of the meta-lens and the adjustment of the micro-element arrangement. The meta-lens designed on this basis not only has good achromatic performance, but also has a light and thin structure, low cost, convenient design steps, and can be used in extreme environments such as high temperature and high radiation. It can be used as an imaging device in nuclear facility environments.

[0046] In order to overcome the limitations of aperture and achromatic performance brought about by forward designing a meta-lens based on the ideal lens phase formula, the present invention provides an end-to-end achromatic meta-lens design method based on inverse design. Using the inverse design concept, the phase of the lens is reversely iterated and optimized by defining the loss function and performance index, and the matching degree of the micro-element structure is evaluated at the same time, and the achromatic effect of the meta-lens is improved by minimizing the loss function. Optimization is performed directly according to the design requirements without the need for manual participation in the intermediate steps. The design process is extremely simplified, and the phase of each micro-element position can be directly optimized according to the design goal. At the same time, the phase is further optimized according to the matching degree of the micro-element structure library, and finally the optimal meta-lens micro-element arrangement is obtained, which effectively improves the focusing efficiency of the broadband achromatic meta-lens. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0048] Figure 1 Design a flow chart for the optimization of the diffractive neural network algorithm for the design of a meta-lens;

[0049] Figure 2 This is a diagram showing the actual optimization process of the achromatic meta-lens;

[0050] Figure 3 A top view of a lens with a size of 400 μm (the number of microelements is 64×64);

[0051] Figure 4 The light intensity distribution on the xz plane, the light intensity distribution at the focal plane, and the two-dimensional normalized intensity distribution curves of the incident light of different wavelengths after passing through the achromatic meta-lens with an aperture of 400μm;

[0052] Figure 5 This is the focusing efficiency distribution diagram of the achromatic meta-lens with an aperture of 400μm at different wavelengths;

[0053] Figure 6 The distribution diagram of focal length offset (percentage) of the achromatic metalens with an aperture of 400 μm at various wavelengths;

[0054] Figure 7 This is a simulation analysis result diagram of a broadband achromatic meta-lens with an aperture of 1600μm (the number of micro-elements is 256×256);

[0055] Figure 8 The light intensity distribution on the xz plane, the light intensity distribution at the focal plane, and the two-dimensional normalized intensity distribution curves of the incident light of different wavelengths after passing through the achromatic meta-lens with an aperture of 1600μm;

[0056] Fig. 9 The focal length offset (percentage) distribution diagram of the achromatic metalens with an aperture of 1600μm at various wavelengths;

[0057] Fig.10 A top view of a lens with a size of 1600μm (the number of elements is 256×256) (only a portion is captured because there are too many elements). DETAILED DESCRIPTION

[0058] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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 work are within the scope of protection of the present invention.

[0059] like Figure 1-9 As shown, a meta-lens design method is composed of multiple micro-element structures arranged in an array, wherein the micro-element structure includes a substrate and micro-elements arranged on the substrate, and micro-elements of different shapes and sizes can adjust the phase of the incident light in different ways. The optimization design method can design the phase and structure of the meta-lens end-to-end according to the performance requirements, so that the incident light in the target band is focused on the same position, achieving the effect of broadband achromatism, and the focusing performance is insensitive to the polarization characteristics of the incident light, which can be applied to thermal imaging, medical diagnosis and other fields.

[0060] A preferred embodiment of the present invention is a long-infrared wide-band polarization-insensitive achromatic metalens design. In the long-infrared band, due to its longer working band, the element size of the metalens can be designed at the micron level, which can reduce the difficulty of manufacturing the metalens.

[0061] The specific steps include:

[0062] S100: Determine suitable materials as the substrate and micro-element structure of the wide-band achromatic meta-lens, and determine the lens size, focal length, and working band;

[0063] The above working band determination method is:

[0064] The scanning range of the metalens working band is determined to be λ=9-12 μm. Based on the limitation of computer performance, 7 discrete wavelengths are selected from the continuous working band as simulation calculation wavelengths.

[0065] The method for determining the base of the above-mentioned lens element is:

[0066] The length and width of the base of the lens element are taken as the period of the element, fixed as P x ×P y =6.2μm×6.2μm, the microelement height is fixed at h=8μm.

[0067] Method for determining lens size in step S100:

[0068] The size of the designed meta-lens is determined according to the number of micro-elements, such as 64×64, 128×128, or 256×256.

[0069] Since the ability of micro-elements to control phase is limited, a lens that is too large will result in reduced focusing efficiency and achromatic performance. Therefore, it is necessary to design a lens of appropriate size to ensure good achromatic performance. This example designs 64×64 (aperture is about 400μm) and 256×256 (aperture is about 1600μm) as representatives.

[0070] The above-mentioned microelement structure and material determination method are as follows:

[0071] S110: The substrate and nanorods are made of commonly used materials for optical lenses, such as silicon, titanium dioxide, quartz, etc.

[0072] The refractive index of silicon in the long infrared band is about 3.4. It is low-cost and easy to process. It also has high transmittance and phase modulation capabilities, making it an ideal dielectric material.

[0073] S120: There are five types of microelement: square cylinder, circular cylinder, annular cylinder, a single base supporting four rectangular cylinders, and a single base supporting four circular cylinders. The geometric parameters of the rectangular cylinder and circular cylinder are the side length L and the radius R, respectively. The geometric parameters of the annular cylinder are the inner diameter R1 and the outer diameter R2, and the latter two are consistent with the geometric parameters of the individual rectangular cylinders and circular cylinders.

[0074] The geometric parameters of the micro-element structure are all adjustable variables to control the phase. And they all have high rotational symmetry, which makes the superlens polarization-independent.

[0075] S200: The inverse optimization algorithm is used to reversely design the phase arrangement of the meta-lens. Each microelement corresponds to a phase unit to be optimized. The focusing process is regarded as an optimizable object. The free-space diffraction of the incident light through the meta-lens is the process of diffraction. After obtaining the output light field at each wavelength, the system loss value can be calculated based on the loss value.

[0076] In this embodiment, the phase control of the meta-lens is taken as an optimizable object and optimized according to the calculated loss. The above-mentioned inverse optimization algorithm specifically includes:

[0077] S210: Optimizing the lens phase surface;

[0078] S220: Filling the optimized phase surface with the micro-element database;

[0079] S230: After the optimized phase surface is filled into the micro-element structure, the formed meta-lens performs wavefront modulation on the incident light field;

[0080] In order to make full use of the micro-element structures with limited types and control capabilities, and to further improve the focusing and imaging performance of the meta-lens by optimizing the metric indicators, the present invention attempts to use the incident light plane and the focusing plane as the input and output of the system respectively, and the meta-lens phase as the intermediate variable, and reversely optimize the intermediate variable, that is, the lens micro-element arrangement, according to the difference between the ideal output and the actual output, to obtain a meta-lens with better focusing effect. Here we use the gradient descent algorithm for optimization, and use the form of complex amplitude light field to represent the input and output light signals. The above-mentioned meta-lens phase modulation method for the light field can be expressed as:

[0081] The incident light field U of the i-th wavelength in_i After (x,y) passes through the meta-lens, the outgoing light field U at the rear surface of the meta-lens can be obtained out_i (x,y), then the phase The modulation process formula is:

[0082] Among them, U out_i (x,y) and U in_i (x, y) correspond to the complex amplitudes of the output and input light fields at the i-th wavelength, and j is an imaginary unit;

[0083] Represents the phase regulation of the input light field by the lens. After calculating the loss between the actual output light field and the ideal output light field, the gradient descent algorithm is used to reversely update the phase required for regulation according to the loss.

[0084] It represents the ideal complex amplitude distribution of the i-th wavelength in the focal plane, which is defined as the ideal distribution of the incident light in the focal plane after passing through the metalens. The characteristic of this distribution is that all the energy is concentrated in a specified area (the specified area is generally set to a microelement size).

[0085] The image formed by the incident light passing through the meta-lens and focusing it in the specified area of ​​the focal plane is taken as the target image of the end-to-end system. If it is all focused in the specified area, it is considered that the lens achieves the target focusing effect. On this basis, a loss function is established, which mainly includes the difference between the actual image and the target image obtained after the incident light passes through the meta-lens and the matching difference between the designed micro-element structure and the optimized phase surface. After the loss is calculated, the micro-element phase of the meta-lens is continuously adjusted using the gradient descent algorithm, so that the actual output light field is constantly close to the target output light field, and the light in the working band is focused on the same position as much as possible. Finally, the most suitable micro-element structure is filled in the trained phase surface to realize the achromatic function of the single-layer meta-lens. Compared with the traditional method, the inverse phase optimization algorithm can not only realize end-to-end optimization and simplify the device design process as much as possible, but also give the best micro-element arrangement as much as possible under the limited modulation ability of the micro-element, further improve the focusing effect of the lens, and provide an effective way to develop a wide-band achromatic meta-lens.

[0086] S240: incident light of different wavelengths is modulated by the meta-lens to obtain a corresponding focused light field on a focusing plane;

[0087] S250: Calculate the loss between the actual focusing plane light field and the ideal focusing plane light field using a loss function;

[0088] The loss function calculation formula in step S250 is:

[0089] loss = loss1 + loss2;

[0090]

[0091] The first part of the loss function, loss1, is determined by the difference between the actual output light field and the ideal output light field formed by focusing all the input light in the specified area, and returns the corresponding loss value; where loss1 represents the calculation of the light field distribution of the outgoing light corresponding to the i-th wavelength after metasurface modulation on the target diffraction plane. and the set target light field corresponding to the i-th wavelength The square of the difference between them is then summed up to get loss1 at different wavelengths. represents the ideal complex amplitude distribution of the i-th wavelength in the focal plane, which is defined as the ideal distribution of the incident light in the focal plane after passing through the metalens. The characteristic of this distribution is that all the energy is concentrated in the specified area. When loss1 decreases, the light field distribution of the corresponding optimized phase plane in the focal plane is close to the target light field distribution.

[0092]

[0093] loss2 is used to evaluate the matching degree between the actual phase controlled by the microelement and the designed phase plane, and return the corresponding loss value. and They represent the optimized phase at the i-th wavelength and the actual phase of the microelement at the corresponding spatial position (x, y). It represents the transmittance of the actual microelement at the i-th wavelength at the corresponding spatial position (x, y). The main purpose of this equation is to make the optimized phase surface as close as possible to the phase that can be actually controlled by the microelement in the database. When loss2 decreases until it stabilizes, the optimized phase surface is close to the actual phase surface obtained by the corresponding metasurface microelement combination.

[0094] By reasonably adjusting the weights of loss1 and loss2 and adding them together, the total loss is calculated, and the gradient descent reverse iteration is used for optimization calculation After repeated iterations and adjustments to the phase unit, the sum of the loss values ​​will continue to decrease until convergence, and the lens focusing efficiency will be improved again; set the metrics, which correspond to the performance indicators such as focusing efficiency and energy size of different wavelengths obtained at the focal plane after the meta-lens obtained after screening is passed through by incident light of various wavelengths. By reasonably setting loss1 and loss2, when the loss value decreases and these performance parameters increase, the results corresponding to the different wavelength output phase planes are saved until no better results appear.

[0095] S260: Return to step S210 through reverse iteration.

[0096] S300: Import the optimized phase into the micro-element structure database for matching to obtain the actual matching phase, evaluate the focusing performance of the actual matching phase, and determine whether it meets the design requirements. If it does not meet the design requirements, return to S200 to re-optimize the phase. If it meets the design requirements, enter S400;

[0097] S400: After arranging the matched micro-elements according to the corresponding phases, simulation verification is performed to observe the actual focusing and achromatic effect within the working band. In this embodiment, the most suitable micro-elements are selected from the micro-elements to fill each phase unit, so as to obtain a complete meta-lens.

[0098] Corresponding microelements can be selected to fill in the meta-lens to simulate the actual situation, conduct simulation verification, and observe its actual focusing and achromatic effect within the working band.

[0099] A meta-lens device is made according to the obtained device parameters through micro-nano manufacturing technology, and then a test optical system is built to conduct experimental tests and research on the function and performance of the meta-lens device.

[0100] The above verification method is to design two meta-lenses with different aperture sizes, including:

[0101] S410: Select 9μm, 9.5μm, 10μm, 10.5μm, 11μm, 11.5μm, 12μm as the working wavelength, the focal length is f=800μm, the microelement period is P x ×P y =6.2μm×6.2μm, height is 8μm; lens size is 64×64 (aperture is about 400μm), corresponding to the achromatic meta-lens with numerical aperture NA of 0.33. After the incident light of different wavelengths passes through the designed device, the light intensity distribution on the xz plane, the light intensity distribution at the focal plane, and the two-dimensional normalized intensity distribution curve are as follows Figure 4 shown.

[0102] The focusing efficiency distribution of the meta-lens at different wavelengths is shown in the figure below. Figure 5 As shown, the focal length offset (percentage) distribution of the metalens at each wavelength is as follows Figure 6 Based on the comprehensive analysis of the pictures and tabular data in the paper, the small-sized meta-lens with an aperture of 400 μm designed in this chapter basically realizes the achromatic focusing function in the wavelength range of 9 to 12 μm, and has high focusing efficiency, achromatic ability and a half-maximum full width close to the diffraction limit.

[0103] S420: After setting the evaluation size of the focusing efficiency to 7×7, a focusing efficiency distribution diagram of the meta-lens at different wavelengths and a focal length offset distribution diagram of the meta-lens at each wavelength are obtained for analysis;

[0104] S430: Based on the above-mentioned small-sized superlens, try to further expand the size of the superlens, and try to reduce the numerical aperture of the superlens to reduce the demand for micro-element control capabilities. The obtained light intensity distribution in the xz plane, the light intensity distribution at the focal plane, and the two-dimensional normalized intensity distribution curve are as follows: Figure 4 As shown;

[0105] Specifically, the working wavelength λ is 9-12μm, and 9μm, 9.5μm, 10μm, 10.5μm, 11μm, 11.5μm, and 12μm are selected as the working wavelengths; the focal length f=6400μm, the microelement period and height remain unchanged, the lens size is increased to 256×256 (aperture is about 1600μm), and the corresponding numerical aperture NA is 0.16 for the achromatic meta-lens.

[0106] S440: After setting the evaluation size of the focusing efficiency to 15 (95 μm×95 μm), the focusing efficiency distribution of the meta-lens at different wavelengths is obtained as follows: Figure 5 The focal length offset (percentage) distribution of the metalens at each wavelength is shown as Figure 6 , for analysis.

[0107] Combined with the comprehensive analysis of the data in the above charts, the meta-lens with an aperture of 1600 μm designed in this embodiment basically realizes the achromatic focusing function in the wavelength range of 9 to 12 μm and has high focusing efficiency, achromatic ability and a half-maximum full width close to the diffraction limit.

[0108] S450: Put this parameter into the electromagnetic field vector analysis software, build a complete meta-lens and use vector diffraction for simulation verification, and observe the distribution of the output light field.

[0109] The finite time-domain difference method was used to verify the obtained meta-lens, and the obtained focusing effect was basically consistent with the diffraction simulation, which not only shows that the optimization design method and procedure are reliable, but also has better performance than the traditional phase formula design method, and can achieve a better achromatic effect. The simulation verification results were sent to process the physical device of the meta-lens, and the obtained meta-lens was used to build an optical system for experiments. The experimental results show that the actual focusing efficiency of the meta-lens is consistent with the simulation, and it has a good wide-band achromatic effect.

[0110] S500: The design is completed through simulation verification.

[0111] Compared with the existing traditional meta-lens design technology, the present invention does not use the method based on the traditional lens formula to calculate the phase, but through the reverse design of the phase optimization algorithm, by setting the loss function and index to determine the performance of the meta-lens, and using the gradient descent reverse iteration to maximize the index and minimize the loss function, so that the phase and micro-element arrangement of the lens are optimized. This method uses an end-to-end design concept, directly optimizes the incident light field to obtain the outgoing light field, without artificially designed feature extraction or other intermediate steps in the middle, simplifies the design process of the meta-lens, reduces the cost of manual intervention, and because the reverse design algorithm can reversely optimize each micro-element phase according to the difference between the actual phase plane and the phase plane of the ideal focusing effect, and optimizes the micro-element arrangement according to the difference between the actual micro-element structure and the optimized phase plane, compared with the traditional design method, this algorithm can further improve the lens focusing effect and achromatic performance. The wide-band achromatic polarization-insensitive meta-lens designed on this basis is not only simple in design, but also has a good effect, a relatively simple micro-element structure, easy processing and mass production, and greatly reduces the manufacturing cost of the optical system. At the same time, because it is made of materials such as silicon and germanium, it can adapt to high temperature, high radiation and other environments, so it is also suitable for imaging in nuclear facility environments and has strong practicality.

[0112] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A meta-lens design method, characterized in that: The steps include: S100: Determine suitable materials as the substrate and micro-element structure of the wide-band achromatic meta-lens, and determine the lens size, focal length, and working band; S200: Reverse design of the meta-lens phase arrangement using the inverse optimization algorithm; S300: importing the optimized phase into the micro-element structure database for matching to obtain the actual matching phase, evaluating the focusing performance of the actual matching phase to determine whether it meets the design requirements. If it does not meet the design requirements, return to S200 to re-optimize the phase. If it meets the design requirements, proceed to S400; S400: After arranging the matched micro-elements according to the corresponding phases, simulation verification is performed; S500: The design is completed through simulation verification.

2. A meta-lens design method as claimed in claim 1, characterized in that: The method for determining the working band in step S100 is: The scanning range of the metalens working band is determined, and based on computer performance, several discrete wavelengths are selected from the continuous working band as simulation calculation wavelengths.

3. A meta-lens design method according to claim 2, characterized in that: The method for determining the base of the lens element in step S100 is: The base length and width of the lens element are taken as the period of the element.

4. A meta-lens design method according to claim 3, characterized in that: Method for determining lens size in step S100: The size of the designed meta-lens is determined according to the number of micro-elements.

5. A meta-lens design method according to claim 4, characterized in that: The method for determining the microelement structure and material in step S100 is: S110: Both the substrate and the nanorods are made of materials commonly used in optical lenses; S120: There are five types of microelement: square cylinder, circular cylinder, annular cylinder, a single base supporting four rectangular cylinders, and a single base supporting four circular cylinders. The geometric parameters of the rectangular cylinder and circular cylinder are the side length L and the radius R, respectively. The geometric parameters of the annular cylinder are the inner diameter R1 and the outer diameter R2, and the latter two are consistent with the geometric parameters of the individual rectangular cylinders and circular cylinders.

6. A method for designing a meta-lens according to claim 1 or 2 or 3 or 4 or 5, characterized in that: The reverse optimization algorithm in step S200 includes: S210: Optimizing the lens phase surface; S220: Filling the optimized phase surface with the micro-element database; S230: After the optimized phase surface is filled into the micro-element structure, the formed meta-lens performs wavefront modulation on the incident light field; S240: incident light of different wavelengths is modulated by the meta-lens to obtain a corresponding focused light field on a focusing plane; S250: Calculate the loss between the actual focusing plane light field and the ideal focusing plane light field using a loss function; S260: Return to step S210 through reverse iteration.

7. A meta-lens design method according to claim 6, characterized in that: The modulation method of step S230 includes: The incident light field U of the i-th wavelength in_i After (x,y) passes through the meta-lens, the outgoing light field U at the rear surface of the meta-lens can be obtained out_i (x,y), then the phase The modulation process formula is: Among them, U out_i (x,y) and U in_i (x, y) corresponds to the complex amplitudes of the output and input light fields at the i-th wavelength, respectively, and j is an imaginary unit; Represents the phase regulation of the input light field by the lens. After calculating the loss between the actual output light field and the ideal output light field, the gradient descent algorithm is used to reversely update the phase required for regulation according to the loss.

8. A meta-lens design method according to claim 7, characterized in that: The loss function calculation formula in step S250 is: loss = loss1 + loss2; Among them, loss1 represents the calculation of the light field distribution of the outgoing light corresponding to the i-th wavelength after metasurface modulation on the target diffraction plane and the set target light field corresponding to the i-th wavelength The square of the difference between them is then summed up to get loss1 at different wavelengths. represents the ideal complex amplitude distribution of the i-th wavelength in the focal plane, which is defined as the ideal distribution of the incident light in the focal plane after passing through the metalens. The characteristic of this distribution is that all the energy is concentrated in the specified area; loss2 is used to evaluate the matching degree between the actual phase controlled by the microelement and the designed phase plane, and return the corresponding loss value. and They represent the optimized phase at the i-th wavelength and the actual phase of the microelement at the corresponding spatial position (x, y). It indicates the transmittance of the actual element at the i-th wavelength at the corresponding spatial position (x, y).

9. A method for designing a meta-lens according to claim 1 or 2 or 3 or 4 or 5, characterized in that: The verification method in step S400 includes: S410: Selecting an achromatic meta-lens with a working wavelength, focal length, micro-element period, height, lens size and corresponding numerical aperture, and obtaining the light intensity distribution in the xz plane, the light intensity distribution at the focal plane and a two-dimensional normalized intensity distribution curve of incident light of different wavelengths after passing through the designed device; S420: setting the evaluation size of the focusing efficiency again, obtaining the focusing efficiency distribution diagram of the meta-lens at different wavelengths and the focal length offset distribution diagram of the meta-lens at each wavelength, and performing analysis; S430: On the basis of the above-mentioned small-sized metalens, an attempt is made to further expand the size of the metalens, and an attempt is made to reduce the numerical aperture of the metalens to reduce the demand for micro-element control capability, and the light intensity distribution on the xz plane, the light intensity distribution at the focal plane, and a two-dimensional normalized intensity distribution curve are obtained; S440: After setting the evaluation size of the focusing efficiency, a focusing efficiency distribution diagram of the meta-lens at different wavelengths and a focal length offset distribution diagram of the meta-lens at each wavelength are obtained for analysis; S450: Put this parameter into the electromagnetic field vector analysis software, build a complete meta-lens and use vector diffraction for simulation verification, and observe the distribution of the output light field.

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