Design method of multi-layer super-structure lens group

Abstract

The invention relates to the technical field of super-structure lens design methods, provides a design method of a multi-layer super-structure lens group, can realize a broadband achromatic function, and solves the problems that a single-layer achromatic super-structure lens is insufficient in phase regulation and control capability, the caliber cannot be increased and the like. Comprising the following steps: S100, determining an appropriate material as a substrate and an infinitesimal structure of the multilayer metamaterial lens, and determining initial parameters; s200, performing design optimization on phase regulation and control of the multi-layer super-structure lens according to focusing requirements and the infinitesimal database by utilizing a diffraction neural network to obtain optimal phase arrangement; s300, after the multi-layer lens phase arrangement is obtained, infinitesimal elements with appropriate geometric parameters are selected from the infinitesimal element database to fill each layer of super-structure lens so as to accurately match the phase arrangement required by the super-structure lens, and a multi-layer super-structure lens group is obtained; s400, performing analog simulation verification on the actually designed functions of the multilayer super-structure lens group in a computer; and S500, if the result obtained by simulation verification is consistent with the expectation, manufacturing the super-structure lens according to the device parameters obtained by optimization, and completing the design.

Description

Technical Field

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

[0002] Optical systems are widely used in our lives. For example, mobile phones and cameras all rely on lenses to provide clear images. Traditional refractive optical lenses mainly rely on their curvature and thickness to refract light, and manipulate the phase of light by accumulating the optical path. Such lenses all have certain chromatic aberrations, which will have an adverse effect on the optical system, seriously reducing the focusing efficiency and imaging quality. Traditional achromatic methods usually require multiple optical lenses with different refractive indices to be cascaded, which not only makes the optical system bulky, heavy and costly, but also makes it difficult to achieve wide-band achromatic effects.

[0003] In this context, the emergence of meta-lenses provides a solution to the above problems. However, existing achromatic meta-lenses are mainly based on single-layer metasurfaces, which have problems such as complex micro-element structure, relatively small numerical aperture, low convergence efficiency and small aperture.

[0004] Chinese patent CN110376731A discloses a method for constructing a broadband achromatic meta-lens group based on a multi-layer meta-surface. On the basis of constructing focusing meta-lens and diverging meta-lens samples, the Abel constant of each sample is calculated, and then the combination of focusing meta-lens and diverging meta-lens with the smallest dispersion is solved and optimized. Then, the dispersion characteristics of the broadband achromatic meta-lens group are obtained by full-wave simulation and compared with the single-layer achromatic meta-lens. The achromatic meta-lens with a large working bandwidth has a diffraction-limited focusing capability in the wavelength range of 1000nm to 1700nm. It includes two stacked meta-surfaces, through which the required focusing phase and dispersion compensation can be independently controlled. In addition to the large working bandwidth, the average focusing efficiency of the lens is higher than 64% in the near-infrared region.

[0005] Chinese patent CN116893457A discloses a mid-infrared refractive-diffractive hybrid system for achromatic aberration and its preparation method. The system consists of a refractive lens and a meta-lens, which has the effect of effectively reducing off-axis aberrations and balancing chromatic aberrations. In the same year, Chinese patent CN217639613U disclosed a metalens group and an optical system containing it, including four meta-lenses. The nanostructure of each meta-lens satisfies the corresponding phase distribution, and the corresponding phase distribution enables the metalens group to correct chromatic aberration and aberration on the basis of meeting the imaging requirements. This design can reduce the TTL (Total Track Length, total system length) of imaging devices such as lenses using the meta-lens group, which is suitable for imaging devices with strict TTL requirements.

[0006] From the above research, it can be seen that in order to improve the achromatic performance of the optical system and reduce the overall length of the system, each team has proposed its own solution. However, most of the existing design methods are based on the ideal lens phase formula to calculate the phase of each layer of the lens to achieve the focusing effect. Not only is the calculation process complicated, but also for the forward-designed meta-lens group, we rely heavily on experience to judge its actual achromatic performance when designing it, and there is no way to further improve the focusing effect of the designed lens group. At the same time, limited by the limited electromagnetic control ability, in order to obtain a better focusing effect, on the one hand, it is necessary to design a complex micro-element structure, which leads to processing difficulties; on the other hand, it is necessary to increase optical devices, resulting in a large system volume and difficulty in miniaturization. On the contrary, if the above adjustments are not made, the focusing efficiency of the lens group is low, and it has no advantage over other similar works. Therefore, when the lens aperture increases and the target band becomes wider, it is difficult for traditional optical design methods to design a meta-lens group with good focusing and imaging effects when the micro-element structure is relatively simple and the system is small.

[0007] Therefore, it is necessary to design a large-aperture broadband achromatic meta-lens group with small TTL and high focusing efficiency. Unlike the forward design, the idea of ​​reverse designing the lens phase according to the target image can continuously optimize the phase that needs to be adjusted on each sub-wavelength unit according to the results. How to use the reverse design idea to make the constructed meta-lens group have a larger aperture, a wider working band and better achromatic effect within the limitations of materials and processes is a difficult point and needs further exploration. Summary of the invention

[0008] The present invention proposes a design method for a multi-layer meta-lens group, which can achieve a wide-band achromatic function, solve the problems of insufficient phase control ability of a single-layer achromatic meta-lens and inability to increase the aperture, and make the design of the meta-lens group simpler and more direct; and enable multiple meta-lenses in the lens group to have better achromatic performance while having a large enough aperture, thereby achieving a broadband, polarization-insensitive achromatic effect.

[0009] The technical solution of the present invention is as follows:

[0010] A method for designing a multi-layer meta-lens group comprises the following steps:

[0011] S100: Determine suitable materials as the substrate and microstructure of the multilayer meta-lens, and determine initial parameters;

[0012] S200: Using the diffractive neural network, according to the focusing requirements and the micro-element database, the multi-layer meta-lens phase control is designed and optimized to obtain the optimal phase arrangement;

[0013] S300: After obtaining the phase arrangement of the multi-layer lens, select micro-elements with suitable geometric parameters from the micro-element database and fill them into each layer of the meta-lens to accurately match the phase arrangement required by the meta-lens, thereby obtaining a multi-layer meta-lens group;

[0014] S400: verifying the actual designed functions of the multi-layer meta-lens group by simulation on a computer;

[0015] S500: If the simulation verification result is consistent with the expectation, a meta-lens is manufactured according to the optimized device parameters to complete the design.

[0016] Furthermore, the design method in step S200 takes the phase control of the meta-lens group as an optimizable object and optimizes it according to the calculated loss, as follows:

[0017] S210: Use parallel light to sequentially impinge on the phase plane of each meta-lens. If it is in the initial state, randomly set the phase arrangement of each meta-lens to obtain the actual light field of the target plane; the input and output optical signals are represented in the form of complex amplitude distribution of the light field;

[0018] The phase modulation of the light field by the meta-lens group can be expressed as:

[0019]

[0020] in to Corresponding to the complex amplitude distribution of the incident light field on the front surface of each meta-lens;

[0021] to represents the phase control of the input light field by each meta-lens, to is the complex amplitude distribution of the light field emitted from the rear surface of each meta-lens;

[0022] S220: Compare the difference between the actual light field complex amplitude at the focal plane and the ideal light field complex amplitude, and the difference between the phase control required for each layer of the meta-lens and the actual phase control that can be achieved by the micro-element in the database, and calculate the system loss using the loss functions designed with the above two sets of differences;

[0023] S230: Based on the calculated loss value, use the stochastic gradient descent algorithm to reversely update the phase required to be adjusted for each layer of the meta-lens to

[0024] S240: After obtaining the updated phase arrangement of each layer of the meta-lens, the lens performance is evaluated; the most suitable micro-element structure is filled into each layer and each phase unit to construct a meta-lens group, and parallel light is incident on the meta-lens group to obtain the actual light field distribution on the focusing plane, and the focusing performance of the meta-lens group is judged according to the light field distribution;

[0025] S250: If the focusing performance reaches the expected effect, the phase arrangement of each layer of the output lens is carried out for subsequent experimental work; if the focusing performance does not reach the expected effect, return to S210 to re-acquire the actual light field of the focusing plane, and after repeated multiple times, the final phase arrangement of the meta-lens group is obtained.

[0026] Furthermore, the method for acquiring the complex amplitude of the actual light field of the target plane in step S210 is:

[0027] S211: The incident light is phase-modulated by the first layer of meta-lens, and the light is freely diffracted in space after passing through;

[0028] S212: The phase of the second meta-lens is modulated again, and this process is repeated until all meta-lenses are passed;

[0029] S213: After passing through the last layer of meta-lens phase, the light is freely diffracted and the actual complex amplitude distribution is obtained at the designed focusing plane.

[0030] Furthermore, the loss function calculation method in step S220 is:

[0031] S214: The first part of the loss function is determined by the difference between the complex amplitude distribution of the actual output light field on the focusing plane and the complex amplitude distribution of the ideal output light field, and returns the corresponding loss value loss a :

[0032]

[0033] in, is the actual complex amplitude distribution of the outgoing light of the i-th wavelength on the focal plane, is the complex amplitude distribution of the ideal output light field, and refers to the ideal distribution of the incident light on the focal plane after passing through the meta-lens; when loss a When it decreases, the complex amplitude distribution of the incident light modulated by the optimized phase plane on the focusing plane is close to the complex amplitude distribution of the target light field;

[0034] S215: Evaluate the matching degree between the actual micro-element control phase and the designed phase surface, and return the corresponding loss value loss b :

[0035]

[0036] lossb It is used to evaluate the matching degree between the actual controlled phase of the microelement and the phase required by the lens, where the variable to They represent the optimized phase of each meta-lens at the i-th wavelength at the micro-element position (x, y) corresponding to the lens; the variable to They represent the micro-element control phases matched in the micro-element database at the micro-element position (x, y). to They represent the transmittance of the microelement at the i-th wavelength in the microelement database at the microelement position (x, y) respectively;

[0037] S216: By adjusting the loss a 、loss b The weights of the two are added together to calculate the total loss.

[0038] Furthermore, step S300 includes:

[0039] The meta-lens group is optimized using a diffractive neural network, and the input and output optical signals are represented in the form of complex amplitude distribution of the light field.

[0040] The phase modulation of the light field by the meta-lens group can be expressed as:

[0041]

[0042] in to Corresponding to the complex amplitude distribution of the incident light field on the front surface of each meta-lens;

[0043] to represents the phase control of the input light field by each meta-lens, to is the complex amplitude distribution of the light field emitted from the rear surface of each meta-lens;

[0044] After calculating the loss between the actual light field on the focusing plane and the complex amplitude distribution of the ideal light field, the diffraction neural network optimization algorithm is used to reversely update the phase required for each layer according to the loss. to

[0045] Furthermore, in order to ensure that the metalens group works effectively within the working range, combined with the computer performance limitations, seven discrete wavelengths were selected from the continuous working band as simulation calculation wavelengths, and the size of the designed metalens was determined according to the number of microelements.

[0046] Furthermore, both the substrate and the nanocolumns are made of silicon, and the types of microelements are divided into five types: square columns, circular columns, circular ring columns, a single substrate carrying four rectangular columns, and a single substrate carrying four circular columns.

[0047] The working principle and beneficial effects of the present invention are:

[0048] The present invention discloses a design method for a multilayer meta-lens group, which can realize a wide-band achromatic function and belongs to the field of optical elements. The meta-lens group is composed of a plurality of meta-lenses with the same aperture and based on a meta-surface; the meta-surface is composed of a plurality of sub-wavelength micro-element structures arranged in an array; the micro-element structure includes a substrate and micro-elements arranged on the substrate. Micro-elements with different geometric parameters and shapes can regulate the phase of the incident light differently. The meta-lens group solves the problems of insufficient phase regulation ability of a single-layer achromatic meta-lens and inability to increase the aperture, and also makes the design of the meta-lens group simpler and more direct. It can make the multiple meta-lenses in the lens group have better achromatic performance while having a large enough aperture, so as to achieve a broadband, polarization-insensitive achromatic effect. The meta-lens group can be applied to medical diagnosis, VR / AR, remote sensing and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0050] Figure 1 To construct a meta-lens micro-element diagram;

[0051] Figure 2 for Figure 1 Top view;

[0052] Figure 3 Flowchart for optimizing the design of the meta-lens using a diffractive neural network algorithm;

[0053] Figure 4 This is a diagram showing the actual optimization process of the double-layer achromatic meta-lens group;

[0054] Figure 5 This is a top view of the lens, and a complete GDS layout of the lens with a size of 128×128;

[0055] Figure 6 The light intensity distribution on the xz plane, the light intensity distribution on 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 512×512 (aperture is about 3200μm);

[0056] Figure 7 is the proportion of energy focused in the specified area on the target plane of the above lens;

[0057] Figure 8The 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 1200×1200 (aperture is about 7440μm);

[0058] Fig. 9 is the proportion of energy focused in the specified area on the target plane of the above lens;

[0059] Fig.10 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 2420×2420 (aperture is about 1.5 cm);

[0060] Fig.11 is the proportion of energy focused in the specified area on the target plane of the above lens;

[0061] Fig.12 The light intensity distribution on the xz plane, the light intensity distribution at the focal plane, and the two-dimensional normalized intensity distribution curves are obtained after the incident light of different wavelengths passes through the achromatic meta-lens with an aperture of 128×128 (aperture is about 800μm);

[0062] Fig.13 is the proportion of energy focused in the specified area on the target plane of the above lens;

[0063] Fig.14 The results obtained by using software to simulate the vector diffraction of an achromatic meta-lens with an aperture of 128×128 (aperture of about 800μm). DETAILED DESCRIPTION

[0064] 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.

[0065] Embodiment 1

[0066] like Figure 1-9As shown in the figure, a design method for a multi-layer meta-lens group includes a plurality of meta-lenses composed of a substrate and micro-element structures arranged on the substrate. In order to make full use of the micro-element structure database with limited control capability, this method regards the incident light plane and the focusing plane as the input and output of the system respectively, and takes the phase control of each layer of meta-lens as an intermediate variable. By comparing the difference between the ideal output and the actual output, the intermediate variable is reversely optimized, and the micro-element arrangement with better evaluation indicators is selected, so as to obtain a meta-lens group with better focusing effect.

[0067] This embodiment uses the inverse design concept and the diffraction neural network algorithm to reversely optimize the phase of the multi-layer meta-lens by defining the loss between the complex amplitude distribution of the target light field in the focal plane and the complex amplitude distribution of the actual light field and the loss between the phase that can be controlled by the micro-element structure in the database and the actual light field phase, and adjust its micro-element arrangement. When the loss is reduced until it tends to be stable, the phase arrangement of the meta-lens group with the best achromatic effect can be obtained, and then micro-elements are selected in the micro-element structure database according to the phase arrangement to fill in and obtain a multi-layer meta-lens group.

[0068] This design method can not only accurately control the phase of all metasurfaces in the lens group, but also effectively solve the problems of existing single-layer achromatic metalens, such as narrow bandwidth, poor focusing effect, and inaccurate matching between the database's micro-element phase control capability and the designed phase surface; and to a certain extent, it can freely set the distance between lenses, alleviating the problems of existing achromatic metalens groups such as long TTL and inability to miniaturize.

[0069] The specific steps include:

[0070] S100: Determine suitable materials as the substrate and microstructure of the multilayer meta-lens, and determine initial parameters, including but not limited to lens size, distance between multiple lenses, focal length (the distance from the last meta-lens to the focusing point), and operating band;

[0071] In order to ensure that the metalens group works effectively within the working range, combined with the computer performance limitations, this embodiment selects seven discrete wavelengths from the continuous working band as simulation calculation wavelengths, and determines the size of the designed metalens according to the number of microelements.

[0072] Both the substrate and the nanocolumns are made of silicon, which has a refractive index of about 3.4 in the long infrared band, is low in cost and easy to process, and has high transmittance and phase modulation capabilities, making it an ideal dielectric material.

[0073] There are five types of micro-element: square column, circular column, circular column, single substrate supporting four rectangular columns, and single substrate supporting four circular columns. The geometric parameters of the micro-element structure are all adjustable variables. And they all have high rotational symmetry, which makes the superlens polarization-independent.

[0074] S200: Using the diffractive neural network algorithm to optimize the design of the phase control of the multi-layer meta-lens, each microelement corresponds to a phase unit to be optimized. to Considered as an optimizable object, after phase control of each meta-lens and free-space diffraction, the output light field of the incident light in the working band on the focusing plane can be obtained, and the system loss value can be calculated based on the loss function.

[0075] Specific:

[0076] S210: Use parallel light to sequentially impinge on the phase plane of each meta-lens. If it is in the initial state, randomly set the phase arrangement of each meta-lens to obtain the actual light field of the target plane; the input and output optical signals are represented in the form of complex amplitude distribution of the light field;

[0077] The phase modulation of the light field by the meta-lens group can be expressed as:

[0078]

[0079] in to Corresponding to the complex amplitude distribution of the incident light field on the front surface of each meta-lens;

[0080] to represents the phase control of the input light field by each meta-lens, to is the complex amplitude distribution of the light field emitted from the rear surface of each meta-lens;

[0081] S220: Compare the difference between the actual light field complex amplitude at the focal plane and the ideal light field complex amplitude, and the difference between the phase control required for each layer of the meta-lens and the actual phase control that can be achieved by the micro-element in the database, and calculate the system loss using the loss functions designed with the above two sets of differences;

[0082] The loss function mainly includes the following two parts: one is the difference between the actual complex amplitude distribution obtained after the incident light passes through the multi-layer metalens and the target complex amplitude distribution, where the target complex amplitude distribution represents the light field distribution obtained when all the light is converged within the specified area of ​​the focusing plane after the incident light passes through the metalens; the other is the matching difference between the phase that can be actually controlled by the micro-element structure and the phase required after the lens is optimized.

[0083] S230: Based on the calculated loss value, use the stochastic gradient descent algorithm to reversely update the phase required to be adjusted for each layer of the meta-lens to

[0084] After calculating the loss value, this embodiment uses the gradient descent algorithm to reversely optimize the phase arrangement of each lens. to Not only does it gradually approach the phase that can be actually controlled in the micro-element database, but it also makes the actual output light field continuously close to the target output light field, and the light in the working band is focused on the same position as much as possible.

[0085] Unlike single-layer designs, in multi-layer designs, the phase modulation of each layer needs to be optimized separately to ensure that the interaction between multiple phase planes can jointly achieve the ideal achromatic effect. After continuous training to improve the focusing effect to a stable state, the obtained micro-element arrangement is filled into the lens to achieve the achromatic function of the multi-layer meta-lens. Through this multi-layer design method, the achromatic performance of a single-layer lens in a wide band can be effectively improved, further improving the imaging quality of the optical system.

[0086] S240: After obtaining the updated phase arrangement of each layer of the meta-lens, the lens performance is evaluated; the most suitable micro-element structure is filled into each layer and each phase unit to construct a meta-lens group, and parallel light is incident on the meta-lens group to obtain the actual light field distribution on the focusing plane, and the focusing performance of the meta-lens group is judged according to the light field distribution;

[0087] S250: If the focusing performance reaches the expected effect, the phase arrangement of each layer of the output lens is carried out for subsequent experimental work; if the focusing performance does not reach the expected effect, return to S210 to re-acquire the actual light field of the focusing plane, and after repeated multiple times, the final phase arrangement of the meta-lens group is obtained.

[0088] S300: After obtaining the arrangement of microelements, select the corresponding microelements to fill into the meta-lens to obtain a multi-layer meta-lens group. At the same time, observe its actual focusing and achromatic effects within the working band. Use micro-nano manufacturing technology to make a meta-lens according to the optimized device parameters. Subsequently, build a test optical system and conduct experimental tests on the prepared meta-lens device to evaluate its function and performance. The effectiveness and reliability of the meta-lens in practical applications are verified through experiments, providing a basis for further optimization and application;

[0089] S400: verifying the actual designed functions of the multi-layer meta-lens group by simulation on a computer;

[0090] S500: If the simulation verification result is consistent with the expectation, a meta-lens is manufactured according to the optimized device parameters to complete the design.

[0091] The design method in step S200 takes the phase control of the meta-lens group as an optimizable object and optimizes it according to the calculated loss, as follows:

[0092] The method for obtaining the complex amplitude of the actual light field of the target plane in step S210 is:

[0093] S211: The incident light is phase-modulated by the first layer of meta-lens, and the light is freely diffracted in space after passing through;

[0094] S212: The phase of the second meta-lens is modulated again, and this process is repeated until all meta-lenses are passed;

[0095] S213: After passing through the last layer of meta-lens phase, the light is freely diffracted and the actual complex amplitude distribution is obtained at the designed focusing plane.

[0096] The loss function calculation method in step S220 is:

[0097] S214: The first part of the loss function is determined by the difference between the complex amplitude distribution of the actual output light field on the focusing plane and the complex amplitude distribution of the ideal output light field, and returns the corresponding loss value loss a :

[0098]

[0099] in, is the actual complex amplitude distribution of the outgoing light of the i-th wavelength on the focal plane, is the complex amplitude distribution of the ideal output light field, and refers to the ideal distribution of the incident light on the focal plane after passing through the meta-lens; when loss a When it decreases, the complex amplitude distribution of the incident light modulated by the optimized phase plane on the focusing plane is close to the complex amplitude distribution of the target light field;

[0100] S215: Evaluate the matching degree between the actual micro-element control phase and the designed phase surface, and return the corresponding loss value loss b :

[0101]

[0102] loss b It is used to evaluate the matching degree between the actual controlled phase of the microelement and the phase required by the lens, where the variable to They represent the optimized phase of each meta-lens at the i-th wavelength at the micro-element position (x, y) corresponding to the lens; the variable to They represent the micro-element control phases matched in the micro-element database at the micro-element position (x, y). to They represent the transmittance of the microelement at the i-th wavelength in the microelement database at the microelement position (x, y) respectively;

[0103] S216: By adjusting the loss a 、loss b The weights of the two are added together to calculate the total loss.

[0104] The main purpose of this equation is to make the optimized phase plane not only achieve the achromatic effect, but also make the phase it regulates as close as possible to the phase that can be actually regulated by the micro-element in the micro-element database, so as to obtain the optimal micro-element arrangement. b When it decreases until it stabilizes, the actual phase control capability of the microelement in the database can better meet the control requirements of the optimized phase surface.

[0105] By reasonably adjusting the loss a 、loss b The weights of the two are added together to calculate the total loss, and the phase arrangement is updated using gradient descent reverse iteration to optimize to 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. When the loss value decreases and these performance parameters increase, the micro-element arrangement corresponding to the resulting phase surface is saved until no better results appear.

[0106] Embodiment 2

[0107] This embodiment exemplifies the design of a double-layer achromatic meta-lens group in the infrared band. Since the working band is relatively long, the micro-element size of the meta-lens can be designed at the micron level, reducing the difficulty of aligning and preparing the meta-lens group.

[0108] The specific design and production process is as follows:

[0109] In order to ensure that the meta-lens group works effectively within the working range of λ: 9-12μm, due to computer performance limitations, we selected seven discrete wavelengths from the continuous working band as the simulation calculation wavelengths. The base length and width of the lens element is the period of the element, which is fixed at P x ×P y =6.2 μm×6.2 μm, and the height of the micro-element is fixed to h=8 μm. Next, the size of the designed meta-lens is determined according to the number of micro-elements, such as 64×64 or 128×128.

[0110] Microelement structure and material selection. In this embodiment, the substrate and nanocolumns are both made of silicon (Si), a common material for optical lenses. It has a refractive index of about 3.4 in the long infrared band, is low in cost and easy to process, and has high transmittance and phase modulation capabilities. It is an ideal dielectric material. There are five types of microelements: square column, circular column, circular column, single substrate carrying four rectangular columns, and single substrate carrying four circular columns. Figure 1 , Figure 2 As shown. The geometric parameters of the rectangular column and the circular column are the side length L and the radius R, respectively, and the geometric parameters of the circular column are the inner diameter R1 and the outer diameter R2, and the latter two are consistent with the geometric parameters of the individual rectangular column and circular column. The geometric parameters of the micro-element structure are all adjustable variables. And they all have high rotational symmetry, which makes the superlens have the characteristics of polarization independence.

[0111] Phase optimization algorithm design, the design process is as follows Figure 3 In this implementation case, we take the phase control of the meta-lens group as an optimizable object and optimize it according to the calculated loss. Figure 4 As shown, the incident light field of the i-th wavelength After passing through the meta-lens, the outgoing light field at the focus can be obtained The phase The modulation process is shown in the phase modulation formula of the light field by the meta-lens group. is the ideal complex amplitude distribution of the outgoing light of the ith wavelength on the focusing plane, which is defined as the light field distribution formed when all the incident light is focused into the specified area (the area is generally set to a microelement size). The loss can be calculated according to the following loss function:

[0112] loss=loss1+loss b ;

[0113] in, They represent the optimized phase surfaces of the two meta-lenses at the i-th wavelength and the phase distribution in the corresponding micro-element database at the corresponding spatial position (x, y). Represents the transmittance distribution in the microelement database at the corresponding wavelength. Then, based on the loss value, the phase of the meta-lens is inversely optimized using the gradient descent algorithm. The overall focusing effect of the lens on this band is continuously improved, and the phase adjustment is continuously close to the phase that can be adjusted by the microelement in the database. After the loss drops to a stable state, the microelement that best matches the phase of the meta-lens is selected from the microelement database and filled in, and finally a better achromatic lens is obtained.

[0114] After obtaining the optimized microelement arrangement, the lens performance is verified using vector diffraction simulation software. By selecting the most suitable microelement from the microelement and filling each phase unit, a complete meta-lens can be obtained. Here we selectively establish three sizes of meta-lens groups, namely 512×512 (3200μm×3200μm), 1200×1200 (7.5mm×7.5mm), and 2420×2420 (1.5cm×1.5cm), and put the 128×128 size meta-lens into the vector diffraction simulation software to simulate the actual lens, proving that the simulation effect is effective.

[0115] 9μm, 9.5μm, 10μm, 10.5μm, 11μm, 11.5μm, and 12μm are selected as the working wavelengths. The distance between the two lenses is f1=500μm, the focal length (the distance from the second lens to the focusing position) is f2=3000μm, and the microelement period is P x ×P y =6.2μm×6.2μm, height is 8μm. The lens size is 512×512 (aperture is about 3200μm), corresponding to the achromatic meta-lens with numerical aperture NA of 0.45. The light intensity distribution of 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 the device is designed are as follows Figure 6 After setting the evaluation size of the focusing efficiency to 6×6 (37μm×37μm), the focusing efficiency distribution of the meta-lens at different wavelengths is shown in Figure 7 As shown in the figure, the double-layer meta-lens group with an aperture of 3200μm designed in this chapter basically realizes the achromatic focusing function in the wavelength range of 9 to 12μm, and has high focusing efficiency, achromatic ability and a half-maximum full width close to the diffraction limit.

[0116] Based on the above-mentioned size superlens, we try to further expand the size of the superlens. The working wavelength is still λ: 9~12μm, and 9μm, 9.5μm, 10μm, 10.5μm, 11μm, 11.5μm, and 12μm are selected as the working wavelengths. The distance between the two lenses is f_1=1000μm, the focal length (the distance from the second lens to the focusing position) f_2=7000μm, the microelement period and height remain unchanged, the lens size is increased to 1200×1200 (aperture is about 7500μm), and the corresponding numerical aperture NA is 0.47 for the achromatic metalens. After the incident light of different wavelengths passes through the designed device, the 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 8 After setting the evaluation size of the focusing efficiency to 6×6 (37μm×37μm), the focusing efficiency distribution of the meta-lens at different wavelengths is shown in Fig. 9As shown in the figure, the double-layer meta-lens group with an aperture of 7500μm designed in this chapter basically realizes the achromatic focusing function in the wavelength range of 9 to 12μm and has high focusing efficiency, achromatic ability and a half-maximum full width close to the diffraction limit.

[0117] Based on the above lenses, we explored the limit of lens aperture within the computer performance range and obtained a meta-lens group with an aperture of 1.5 cm. We set the distance between the two lenses to 1 cm, the focal length of the lens to 3 cm, and the corresponding numerical aperture NA to 0.24, and finally obtained a meta-lens group with a size of 2420×2420 (1.5 cm×1.5 cm). The intensity distribution of incident light of different wavelengths after the device is designed is shown in the following figure: Fig.10 After setting the evaluation size of the focusing efficiency to 6 (37μm×37μm), the focusing efficiency distribution of the meta-lens at different wavelengths is shown in Fig.11 The double-layer meta-lens group with an aperture of 1.5 cm designed in this chapter basically achieves the achromatic focusing function in the wavelength range of 9 to 12 μm.

[0118] Due to the limitation of computer performance and the large size of the above lenses, a meta-lens group of 128×128 in size was established using the above method (the distance between the two lenses is 200um and the focal length is 750um). The obtained light intensity distribution in the xz plane, the light intensity distribution at the focal plane, the two-dimensional normalized intensity distribution curve, and the focusing efficiency distribution at different wavelengths are shown in Figure 2. Fig.12 , Fig.13 The obtained parameters are put into the software, a complete meta-lens is built, and then vector diffraction is used for simulation verification to observe the distribution of the outgoing light field. Fig.14 As shown, the xz diagram and energy distribution of the corresponding wavelength can be obtained, and it can be concluded that the finite time-domain difference method is used to verify the obtained meta-lens, and the obtained focusing effect is basically consistent with the diffraction simulation. This study not only proves the reliability of the optimization design method and procedure, but also shows that its performance is better than the traditional phase formula design method, and it performs well in the achromatic effect. The simulation verification results show that this design method can be used to process and manufacture meta-lens physical devices. Experiments were carried out using the optical system built with the obtained meta-lens. The experimental results show that the actual focusing efficiency of the meta-lens is consistent with the simulation results, showing an excellent wide-band achromatic effect.

[0119] Each layer of the multi-layer meta-lens group has independent modulation capability, which solves the problem of insufficient modulation capability of a single-layer achromatic meta-lens. It can not only expand the aperture range with achromatic effect, but also achieve better achromatic focusing effect in a wider band. At the same time, this embodiment does not use the method of calculating imaging based on the traditional lens formula to calculate its phase, but optimizes the phase of each layer through the diffraction neural network algorithm, abandons the cumbersome calculation process during forward design, and obtains the optimal phase arrangement of the multi-layer meta-surface by minimizing the loss function and maximizing the index. This method avoids the feature extraction or other intermediate steps of manual design, simplifies the design process of the meta-lens, and reduces the cost of manual intervention. By using the gradient descent algorithm, the phase of each microelement is reversely optimized according to the loss between the actual phase plane and the ideal focusing effect phase plane, and at the same time, according to the loss between the actual microelement structure and the optimized phase plane, the phase plane is made to fit the phase that can be adjusted by the database as much as possible. When the loss drops to a stable state, the best phase arrangement is obtained, and then the most suitable microelement can be selected from the microelement database to fill it in to obtain the meta-lens group. Compared with traditional design methods, this algorithm can further improve the focusing effect and achromatic performance of the lens.

[0120] In summary, this meta-lens group can not only improve the problems of insufficient phase modulation capability of single-layer achromatic meta-lens, such as inability to expand aperture and poor focusing efficiency, but also effectively reduce the weight, volume and processing cost of the optical system, facilitate batch processing and production, and has strong practicality.

[0121] 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 design method for a multi-layer meta-lens assembly, characterized in that: The steps include: S100: Determine suitable materials as the substrate and microstructure of the multilayer meta-lens, and determine initial parameters; S200: Using the diffractive neural network, according to the focusing requirements and the micro-element database, the multi-layer meta-lens phase control is designed and optimized to obtain the optimal phase arrangement; S300: After obtaining the phase arrangement of the multi-layer lens, select micro-elements with suitable geometric parameters from the micro-element database and fill them into each layer of the meta-lens to accurately match the phase arrangement required by the meta-lens, thereby obtaining a multi-layer meta-lens group; S400: verifying the actual designed functions of the multi-layer meta-lens group by simulation on a computer; S500: If the simulation verification result is consistent with the expectation, a meta-lens is manufactured according to the optimized device parameters to complete the design.

2. The method for designing a multilayer meta-lens assembly according to claim 1, wherein: The design method in step S200 takes the phase control of the meta-lens group as an optimizable object and optimizes it according to the calculated loss, as follows: S210: Use parallel light to sequentially impinge on the phase plane of each meta-lens. If it is in the initial state, randomly set the phase arrangement of each meta-lens to obtain the actual light field of the target plane; the input and output optical signals are represented in the form of complex amplitude distribution of the light field; The phase modulation of the light field by the meta-lens group can be expressed as: in to Corresponding to the complex amplitude distribution of the incident light field on the front surface of each meta-lens; to represents the phase control of the input light field by each meta-lens, to is the complex amplitude distribution of the light field emitted from the rear surface of each meta-lens; S220: Compare the difference between the actual light field complex amplitude at the focal plane and the ideal light field complex amplitude, and the difference between the phase control required for each layer of the meta-lens and the actual phase control that can be achieved by the micro-element in the database, and calculate the system loss using the loss functions designed with the above two sets of differences; S230: Based on the calculated loss value, use the stochastic gradient descent algorithm to reversely update the phase required to be adjusted for each layer of the meta-lens to S240: After obtaining the updated phase arrangement of each layer of the meta-lens, the lens performance is evaluated; the most suitable micro-element structure is filled into each layer and each phase unit to construct a meta-lens group, and parallel light is incident on the meta-lens group to obtain the actual light field distribution on the focusing plane, and the focusing performance of the meta-lens group is judged according to the light field distribution; S250: If the focusing performance reaches the expected effect, the phase arrangement of each layer of the output lens is carried out for subsequent experimental work; if the focusing performance does not reach the expected effect, return to S210 to re-acquire the actual light field of the focusing plane, and after repeated multiple times, the final phase arrangement of the meta-lens group is obtained.

3. The design method of a multilayer meta-lens assembly according to claim 4, characterized in that: The method for obtaining the complex amplitude of the actual light field of the target plane in step S210 is: S211: The incident light is phase-modulated by the first layer of meta-lens, and the light is freely diffracted in space after passing through; S212: The phase of the second meta-lens is modulated again, and this process is repeated until all meta-lenses are passed; S213: After passing through the last layer of meta-lens phase, the light is freely diffracted and the actual complex amplitude distribution is obtained at the designed focusing plane.

4. The design method of a multilayer meta-lens assembly according to claim 3, characterized in that: The loss function calculation method in step S220 is: S214: The first part of the loss function is determined by the difference between the complex amplitude distribution of the actual output light field on the focusing plane and the complex amplitude distribution of the ideal output light field, and returns the corresponding loss value loss a : in, is the actual complex amplitude distribution of the outgoing light of the i-th wavelength on the focal plane, is the complex amplitude distribution of the ideal output light field, and refers to the ideal distribution of the incident light on the focal plane after passing through the meta-lens; when loss a When it decreases, the complex amplitude distribution of the incident light modulated by the optimized phase plane on the focusing plane is close to the complex amplitude distribution of the target light field; S215: Evaluate the matching degree between the actual micro-element control phase and the designed phase surface, and return the corresponding loss value loss b : loss b It is used to evaluate the matching degree between the actual controlled phase of the microelement and the phase required by the lens, where the variable to They represent the optimized phase of each meta-lens at the i-th wavelength at the micro-element position (x, y) corresponding to the lens; the variable to They represent the micro-element control phases matched in the micro-element database at the micro-element position (x, y). to They represent the transmittance of the microelement at the i-th wavelength in the microelement database at the microelement position (x, y) respectively; S216: By adjusting the loss a 、loss b The weights of the two are added together to calculate the total loss.

5. The method for designing a multilayer meta-lens assembly according to claim 1, 2, 3 or 4, characterized in that: In order to ensure that the metalens group works effectively within the working range, combined with the computer performance limitations, seven discrete wavelengths were selected from the continuous working band as simulation calculation wavelengths, and the size of the designed metalens was determined according to the number of microelements.

6. The method for designing a multilayer meta-lens assembly according to claim 1, 2, 3 or 4, characterized in that: Both the substrate and nanocolumns are made of silicon, and there are five types of microelements: square columns, circular columns, ring columns, a single substrate carrying four rectangular columns, and a single substrate carrying four circular columns.

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