Large-view-field multi-wavelength achromatic double-piece cascade super-structure lens device and design method and application thereof

Abstract

The invention belongs to the technical field of micro-nano optics, and particularly relates to a large-view-field multi-wavelength achromatic double-piece cascade super-structure lens device and a design method and application thereof. The device comprises two cascaded super-structure lenses which are sequentially arranged from an object plane to an image plane, each cascaded super-structure lens is composed of achromatic super-structure atoms which are periodically arranged, incident light can be cooperatively regulated and controlled, and aberration correction is achieved while focusing is conducted. By optimizing the phase distribution of the two cascaded super-structure lenses and the distance between the two cascaded super-structure lenses and selecting adaptive achromatic super-structure atoms, the device can be adaptive to multiple wavelengths or specific single wavelengths. The design method of the device comprises the following steps: determining device parameters according to requirements, optimizing the phase distribution of the two cascaded super-structure lenses and the distance between the two cascaded super-structure lenses, and finally selecting adaptive achromatic super-structure atoms so as to complete the design. The device is suitable for multi-wavelength or specific single-wavelength, has the effects of large view field and high image quality, and can be applied to the fields of imaging modules, near-to-eye display, laser beam shaping, laser radar and the like.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano optics and optical imaging technology, specifically relating to a large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device, its design method, and its application. Background Technology

[0002] Optical lens modules are widely used in fields such as imaging, display, laser shaping, and precision measurement, serving as core components for beam control. As optical systems develop towards miniaturization and integration, the demand for small-sized, wide-field-of-view, and high-image-quality lens modules is becoming increasingly urgent.

[0003] Existing optical lens modules typically include various components such as spherical lenses, aspherical lenses, mirrors, and freeform surfaces. However, as traditional optical devices, they are limited by their physical mechanisms, resulting in large size and weight, limited light field manipulation capabilities, and aberrations. They cannot simultaneously provide good image quality and high lightweight design. Therefore, traditional optical lens modules struggle to meet the demands for small size, large field of view, and high image quality, necessitating the development of novel optical elements to address these issues.

[0004] Metalenses are a novel type of planar optical element that has emerged in recent years, composed of subwavelength structural units. Unlike traditional refractive lenses, which accumulate phase gradually as light propagates within a medium, metalenses rely on the interaction between light waves and subwavelength structural units to customize and manipulate multidimensional physical quantities of electromagnetic waves (including amplitude, phase, and polarization state), thereby achieving rich and flexible optical field control functions. Metalenses are significantly thinner than traditional refractive lenses, offering advantages such as lightweight design, design flexibility, strong controllability, and ease of integration.

[0005] However, current metalenses are limited by their controllability, resulting in severe chromatic aberration and a small imaging field of view. These problems also restrict their application in imaging, display, and beam shaping. Therefore, overcoming the limitations of metalenses in chromatic aberration and imaging field of view is a key issue that urgently needs to be addressed to promote their widespread application. Summary of the Invention

[0006] The purpose of this invention is to provide a dual-layer cascaded metalens device with a large field of view and multi-wavelength achromatic properties, as well as its design method and application. By coordinating the incident light through two metalenses, it is possible to achieve multi-wavelength color imaging with a large field of view and high image quality.

[0007] To achieve the above objectives, the first aspect of the present invention provides a large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device, comprising a first metalens and a second metalens arranged sequentially along the object plane to the image plane. The two metalenses cooperate with each other to achieve aberration correction while focusing.

[0008] A second aspect of the present invention provides a design method for a large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device, characterized by comprising the following steps: S1. Determine the operating wavelength, field of view, and diagonal length of the image plane of the metalens device according to the target requirements; calculate the effective focal length of the metalens based on the field of view and diagonal length of the image plane. S2. Using the field of view, working wavelength, effective focal length, image plane size, total system length, and diameter of the metalens as constraints, and image quality as the evaluation index, the phase distribution of the two metalenses and the distance between the two metalenses are used as optimization variables to progressively optimize the phase distribution of the two metalenses at the corresponding working wavelength, thereby obtaining the target phase distribution; the total system length is the distance from the first metalens to the image plane; S3. Select the material and shape of meta-atoms that meet the achromatic requirements, construct a meta-atom library according to the correspondence between meta-atom structure parameters and phase values, and then determine the meta-atom structure parameters of each meta-lens according to the target phase distribution and the transmittance of meta-atoms. S4. The achromatic performance and energy utilization performance of the dual-layer cascaded metalens system are quantitatively evaluated by numerical analysis of focal offset and efficiency in order to optimize the meta-atomic structure parameters.

[0009] Furthermore, in step S2, the phase distribution is optimized according to the following phase distribution formula:

[0010] in, The total number of terms in the polynomial. For order, For the first Phase coefficient; The distance from a point on the surface of the metalens to the center; The normalized radius.

[0011] Furthermore, in step S3, the matching between the metaatomic structural parameters and the target phase, as well as the transmittance of the metaatoms, are quantitatively evaluated using the evaluation function shown below:

[0012]

[0013] in, For the first meta-lens Evaluation function for each superatom. The total number of operating wavelengths, For the first The metalens at the working wavelength is the first The target phase value of each superatomic atom. For the first The metalens at the working wavelength is the first The actual phase value of each superatom. For the first The metalens at the working wavelength is the first Transmittance of each superatom For the first Weights for each operating wavelength This represents the total number of metaatoms on the metalens. The mean of the evaluation function for all metaatoms on the metalens; the weights of different working wavelengths are changed according to design requirements to achieve more targeted selection of metaatomic structure parameters; Evaluation function The smaller the value, the more accurately the phase corresponding to the selected metaatomic structure parameters matches the target phase, and the higher the transmittance of the metaatoms, the better it meets the design requirements. During the design process, structures are selected from the metaatomic structure library that... The structural parameters of the group of superatoms with the smallest numerical values.

[0014] In particular, the present invention is not limited to this type of evaluation function, and other types of evaluation functions can be selected according to actual needs.

[0015] Furthermore, the achromatic performance and energy utilization performance of the dual-layer cascaded metalens device are evaluated by focusing offset and efficiency, respectively. If the focusing offset or efficiency does not meet the design requirements, one or more combinations of the following three optimization operations are performed, iteratively, until both the focusing offset and efficiency meet the design requirements: (1) Re-optimize the target phase distribution: Adjust the phase coefficient in the phase distribution formula of the dual-layer cascaded metalens to optimize the phase distribution that better meets the requirements of achromatic performance and energy utilization performance; (2) Expanding the meta-atomic structure library: Expanding or reconstructing the structural parameter space of meta atoms, including but not limited to adjusting the shape, material and size of meta atoms, in order to expand the range of phase values ​​and transmittance that meta atoms can achieve; (3) Reselecting metaatoms: Based on the updated phase distribution or the expanded metaatom structure library, adjust the weights of each working wavelength in the evaluation function and reselect the structural parameters of the metaatoms.

[0016] The formula for calculating the focus offset is as follows:

[0017]

[0018] in, For the first The first operating wavelength The focal offset of each field of view For the first The first operating wavelength The focal length of each field of view The focal length of the reference field of view at the reference operating wavelength. Mean value of focus shift across the entire field of view at all operating wavelengths The total number of operating wavelengths, This represents the total number of samples taken from the field of view angle. The efficiency is calculated using the following formula:

[0019] in, For the first The first operating wavelength The efficiency of a single field of view can be calculated by dividing the energy within the effective area of ​​the focused spot by the total energy incident on the cascaded dual-lens superlens. This represents the average efficiency across the entire operating wavelength and field of view. The total number of operating wavelengths, This represents the total number of samples taken from the field of view angle.

[0020] Furthermore, in step S2, the phase distribution is the phase distribution calculated from the Binary 2 surface type; The imaging quality evaluation metrics include the root mean square (RMS) radius of the dot plot, point spread function (PSF), modulation transfer function (MTF), field curvature, and distortion.

[0021] Furthermore, in step S2, the diameter of the first meta-lens is 0.5~8 mm, the diameter of the second meta-lens is 1~10 mm, and the diameter of the second meta-lens is larger than that of the first meta-lens; the total length of the system is less than or equal to 20 mm.

[0022] Furthermore, both the first metalens and the second metalens include a substrate and meta atoms distributed on the substrate; The superatomic structural parameters include the material, shape, and size of the superatomic atom. The superatomic atom is an isotropic or anisotropic superatomic atom with C4 symmetry. The structure of the isotropic superatomic atom includes one or more combinations of cylinders, square cylinders, hollow annular cylinders, hollow square prisms, cross-shaped cylinders, and Boolean operations on these shapes.

[0023] Furthermore, in step S3, isotropic meta-atoms with C4 symmetry can be used to construct meta-lens devices, giving them polarization-independent operating characteristics. Alternatively, anisotropic meta-atoms can be used to construct meta-lens devices, giving them polarization multiplexing or polarization selection operating characteristics.

[0024] Furthermore, in step S1, the working wavelength is either a polychromatic light wavelength or a monochromatic light wavelength; The field of view of the image plane is 10~60°, and the diagonal length of the image plane is 1~10 mm.

[0025] The present invention also provides a large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device, which is designed using any of the above-described design methods.

[0026] The present invention also provides an application of the above-described large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device for imaging, display, beam collimation or focusing.

[0027] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages: 1. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device provided by this invention increases the design freedom by adding a metalens to a single metalens and introducing the spacing between the two metalenses as an additional parameter. The two metalenses cooperate with each other to achieve aberration correction while focusing, thus enabling effective correction of various aberrations such as coma, astigmatism, and distortion under a large field of view, achieving imaging with a large field of view and high image quality. By designing and arranging metalenses with metaatoms of different materials, shapes, and sizes, multi-wavelength achromatic effects are achieved without being constrained by device size. Therefore, this invention can achieve multi-wavelength achromatic effects in large-size devices.

[0028] 2. Based on the requirement of small size and large field of view, this invention determines the range of field of view angle, working wavelength, effective focal length, image plane size, total system length and metalens diameter, and uses these as constraints for metalens design. The phase distribution of the metalens is simulated and optimized by using the Binary 2 surface type, resulting in a more accurate target phase distribution for each wavelength, which meets the requirements of practical applications.

[0029] 3. This invention uses numerical quantitative evaluation of the matching between the phase corresponding to the meta-atomic structure parameters and the target phase, as well as the transmittance of the meta-atoms, through the evaluation function, thereby continuously optimizing the meta-atomic structure parameters to improve design accuracy.

[0030] 4. This invention quantitatively evaluates the achromatic performance and energy utilization performance of a dual-layer cascaded metalens system by numerically assessing the focal offset and efficiency, thereby evaluating the overall performance of the system to ensure that the design meets the requirements. Attached Figure Description

[0031] Figure 1 This is a schematic diagram illustrating the effect of a large field-of-view, multi-wavelength, achromatic, cascaded dual-layer superlens.

[0032] Figure 2 Flowchart for the design of a large field-of-view, multi-wavelength, achromatic, cascaded dual-layer metalens.

[0033] Figure 3 The diagram shows the structure and field of view of a large field-of-view multi-wavelength achromatic double-layer cascaded superlens; a) shows the specific structure and dimensions of the large field-of-view multi-wavelength achromatic double-layer cascaded superlens; b) shows the field of view of the large field-of-view multi-wavelength achromatic double-layer cascaded superlens and four typical fields of view selected from it.

[0034] Figure 4 The phase distribution of a large field-of-view multi-wavelength achromatic double-layered metalens with RGB three colors (wavelengths of 630 nm, 526 nm, and 455 nm) is shown in a and b, respectively.

[0035] Figure 5 Five typical metaatomic structures that can be used in a large field-of-view multi-wavelength achromatic double-layer cascaded metalens for RGB three-color ... two-layer cascaded metalens (a) and the arrangement of metaatomic atoms in the double-layer cascaded metalens for RGB three-color three-color three-color three-color three-color three-color two-layer cascaded metalens (b).

[0036] Figure 6 The imaging performance of a large field-of-view multi-wavelength achromatic dual-layer cascaded superlens for RGB three colors at the red (wavelength 630 nm) working wavelength is shown in the following figures: a) dot plots at 0°, 5°, 10° and 15° fields of view; b) PSF at the above four typical fields of view; c) MTF at the above four typical fields of view; d) field curvature curves at 0~15° fields of view; e) distortion curves at 0~15° fields of view; and f) grid distortion across the entire image plane.

[0037] Figure 7 The imaging performance of a large field-of-view multi-wavelength achromatic double-layer cascaded metalens with RGB three colors at the green (wavelength 526 nm) working wavelength is shown in Figure 1. a) is a dot plot at 0°, 5°, 10°, and 15° fields of view; b) is the point spread function at the four typical fields of view; c) is the modulation transfer function at the four typical fields of view; d) is the field curvature curve at 0–15°; e) is the distortion curve at 0–15°; and f) is the grid distortion across the entire image plane.

[0038] Figure 8 The imaging performance of a large field-of-view multi-wavelength achromatic double-layer cascaded metalens with RGB three colors at the blue (wavelength 455 nm) working wavelength is shown in Figure 1. a) is a dot plot at 0°, 5°, 10°, and 15° fields of view; b) is the point spread function (PSF) at the four typical fields of view; c) is the modulation transfer function (MTF) at the four typical fields of view; d) is the field curvature curve at 0–15°; e) is the distortion curve at 0–15°; and f) is the grid distortion across the entire image plane.

[0039] Figure 9 The phase distribution of a large field-of-view dual-layer cascaded metalens for a single green wavelength (526 nm) is shown; a and c are planar diagrams of the phase distribution of the two metalenses, and the phase distribution of the metalenses is a centrally symmetrical annular structure; b and d are cross-sectional diagrams of the phase distribution passing through the center of the two metalenses.

[0040] Figure 10 Two metaatomic structures (a and b) that can be used for a large field-of-view dual-layer cascaded metalens for a single green wavelength (wavelength 526 nm) and the metaatomic arrangement in a dual-layer cascaded metalens for a single green wavelength (c, taking a prismatic metaatomic structure as an example).

[0041] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1-First metaatom; 2-First substrate; 3-Second metaatom; 4-Second substrate; 5-Image plane. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0043] Please see Figure 1 and 2 This invention provides a design method for a large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device. The metalens device includes a first metalens and a second metalens arranged sequentially along the object-to-image plane direction. The design method includes the following steps: S1. Determine the operating wavelength, field of view, and diagonal length of the image plane of the metalens device according to the target requirements; calculate the effective focal length of the metalens based on the field of view and diagonal length of the image plane. S2. Using the field of view, effective focal length, working wavelength, image plane size, total system length, and diameter of the metalens as constraint indicators, and image quality as the evaluation indicator, the phase distribution of the two metalenses and the distance between the two metalenses are used as optimization variables to progressively optimize the phase distribution of the two metalenses at the corresponding working wavelength to obtain the target phase distribution; the total system length is the distance from the first metalens to the image plane; S3. Select the material and shape of meta-atoms that meet the achromatic requirements, and then determine the meta-atomic structure parameters of each meta-lens based on the target phase distribution and the transmittance of the meta-atoms. S4. The achromatic performance and energy utilization performance of the dual-layer cascaded metalens system are quantitatively evaluated numerically through focal offset and efficiency, thereby assessing the overall performance of the system and optimizing the meta-atomic structure parameters to ensure the design meets requirements. Both the first and second metalenses are composed of periodically arranged achromatic meta-atoms. The meta-atoms are artificial subwavelength structures made of materials that are transparent or have low absorptivity in the operating wavelength range. The achromatic meta-atoms can provide designed phase delays for multiple different incident wavelengths. By synergistically controlling the incident light through the two metalenses, large field of view and high image quality color imaging can be achieved. In this invention, a customized dual-layer cascaded metalens design can be realized according to the intended field of view size, image plane size, and exit pupil size.

[0044] Specifically, Figure 2 This document presents a design flowchart for a large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens. The design process is primarily divided into two parts: overall metalens design and meta-atom design. First, the overall cascaded metalens design is performed through steps such as target requirement analysis and index quantification, material selection and initial structural design, software modeling, and ray tracing, obtaining the target phase distribution of the metalens at multiple operating wavelengths. Then, based on the design requirements, suitable materials and shapes for the achromatic meta-atoms are selected, and a database of the correspondence between meta-atom structural parameters and optical response is established. Meta-atoms with corresponding structural parameters are matched according to the target phase distribution, considering the influence of meta-atom transmittance. An evaluation function is used to quantitatively assess the matching between the phase corresponding to the meta-atom structural parameters and the target phase, as well as the transmittance of the meta-atoms. Next, the achromatic performance and energy utilization performance of the dual-layer cascaded metalens system are quantitatively evaluated using focal offset and efficiency values ​​to ensure the design meets the requirements. Finally, the fabrication feasibility of the meta-atoms is analyzed to ensure that the designed meta-atoms meet the requirements of the dual-layer cascaded metalens and are compatible with current fabrication processes, demonstrating fabrication feasibility. Finally, a design solution that meets the requirements is output, thus completing this design process.

[0045] Specifically, in step S1, the working wavelength is a polychromatic light wavelength or a monochromatic light wavelength; by selecting appropriate metaatomic materials, shapes and sizes, and simultaneously changing the phase distribution of the corresponding cascaded metalenses, the dual-layer cascaded metalenses can operate at multiple wavelengths or a specific single wavelength.

[0046] The field of view of the image plane is 10~60°, and the diagonal length of the image plane is 1~10 mm.

[0047] In step S2, the phase distribution is optimized according to the following formula:

[0048] in, The total number of terms in the polynomial. For order, For the first Phase coefficient; The distance from a point on the surface of the metalens to the center; The normalized radius.

[0049] In step S2, the phase distribution is the phase distribution calculated from the Binary 2 surface type; The imaging quality evaluation indicators include the root mean square radius of the dot plot, dot spread function, modulation transfer function, field curvature, and distortion.

[0050] The diameter of the first meta-lens is 0.5~8 mm, the diameter of the second meta-lens is 1~10 mm, and the diameter of the second meta-lens is larger than that of the first meta-lens; the total length of the system is less than or equal to 20 mm.

[0051] In step S3, the matching between the metaatomic structural parameters and the target phase, as well as the transmittance of the metaatoms, are quantitatively evaluated using the evaluation function shown below:

[0052]

[0053] in, For the first meta-lens Evaluation function for each superatom. The total number of operating wavelengths, For the first The metalens at the working wavelength is the first The target phase value of each superatomic atom. For the first The metalens at the working wavelength is the first The actual phase value of each superatom. For the first The metalens at the working wavelength is the first Transmittance of each superatom For the first Weights for each operating wavelength This represents the total number of metaatoms on the metalens. The mean of the evaluation function for all metaatoms on the metalens; the weights of different working wavelengths are changed according to design requirements to achieve more targeted selection of metaatomic structure parameters; Evaluation function The smaller the value, the more accurately the phase corresponding to the selected metaatomic structure parameters matches the target phase, and the higher the transmittance of the metaatoms, the better it meets the design requirements. During the design process, structures are selected from the metaatomic structure library that... The structural parameters of the group of superatoms with the smallest numerical values.

[0054] In step S4, the overall achromatic performance of the dual-layer cascaded metalens system is evaluated by the focal offset, and the energy utilization performance of the dual-layer cascaded metalens system is evaluated by the efficiency. If the focal offset or efficiency does not meet the design requirements, one or more combinations of the following three optimization operations are performed, which can be iterated until both the focal offset and efficiency meet the design requirements: (1) Re-optimize the target phase distribution: Adjust the phase coefficient in the phase distribution formula of the dual-layer cascaded metalens to optimize the phase distribution that better meets the requirements of achromatic performance and energy utilization performance; (2) Expanding the meta-atomic structure library: Expanding or reconstructing the structural parameter space of meta atoms, including but not limited to adjusting the shape, material and size of meta atoms, in order to expand the range of phase values ​​and transmittance that meta atoms can achieve; (3) Reselecting metaatoms: Based on the updated phase distribution or the expanded metaatom structure library, adjust the weights of each working wavelength in the evaluation function and reselect the structural parameters of the metaatoms.

[0055] Specifically, the average focus shift across the entire field of view at the full operating wavelength is calculated using the following formula:

[0056]

[0057] in, For the first The first operating wavelength The focal offset of each field of view For the first The first operating wavelength The focal length of each field of view The focal length of the reference field of view (usually the intermediate field of view) at the reference operating wavelength (usually the middle wavelength). Mean value of focus shift across the entire field of view at all operating wavelengths The total number of operating wavelengths, This represents the total number of samples taken from the field of view angle.

[0058] The magnitude of the average focal shift across the entire field of view at all operating wavelengths reflects the achromatic performance of the dual-layer cascaded metalens system at a large field of view. When the average focal shift across the entire field of view at all operating wavelengths is less than a set threshold, and the focal length fluctuation at each operating wavelength and each field of view is within the allowable range, it indicates that the focal lengths at each operating wavelength and each field of view are relatively close, and the achromatic performance of the dual-layer cascaded metalens system meets the requirements.

[0059] Furthermore, when calculating focus offset, different operating wavelengths and fields of view can be assigned corresponding weights according to design requirements. The weighting coefficients for key operating wavelengths and fields of view can be increased, allowing the average focus offset to more accurately reflect the performance of these key operating wavelengths and fields of view, thus achieving a more targeted achromatic performance evaluation that better meets design requirements.

[0060] The average efficiency across the entire field of view at all operating wavelengths is calculated using the following formula:

[0061] in, For the first The first operating wavelength The efficiency of a single field of view can be calculated by dividing the energy within the effective area of ​​the focused spot by the total energy incident on the cascaded dual-lens superlens. This represents the average efficiency across the entire operating wavelength and field of view. The total number of operating wavelengths, This represents the total number of samples taken from the field of view angle.

[0062] The average efficiency across the entire operating wavelength and field of view reflects the energy utilization capability of a dual-layer cascaded metalens system. When the average efficiency across the entire operating wavelength and field of view is greater than a set threshold, and the efficiency fluctuations at each operating wavelength and field of view are within the allowable range, it indicates that the system's energy utilization is stable and efficient across multiple wavelengths and a large field of view, and the efficiency performance of the dual-layer cascaded metalens system meets the requirements.

[0063] Furthermore, when calculating efficiency, different operating wavelengths and fields of view can be assigned appropriate weights according to design requirements. The weighting coefficients of key operating wavelengths and fields of view can be increased, so that the average efficiency can more accurately reflect the performance of key operating wavelengths and fields of view, thereby achieving a more targeted energy utilization performance assessment that better meets design requirements.

[0064] Both the first and second metalenses include a substrate and metaatoms distributed on the substrate. The metaatomic structural parameters include the material, shape, and size of the metaatoms. The metaatoms are isotropic or anisotropic metaatoms with C4 symmetry. The isotropic metaatoms have structures including cylinders, square prisms, hollow annular prisms, hollow square prisms, cross-shaped prisms, and one or more combinations of Boolean operations on these shapes. This invention can use isotropic metaatoms with C4 symmetry to construct metalens devices, giving them polarization-independent operating characteristics. Alternatively, anisotropic metaatoms can be used to construct metalens devices, giving them polarization multiplexing or polarization selection operating characteristics.

[0065] In summary, this invention first obtains the phase distribution of two cascaded metalenses at multiple operating wavelengths through overall system optimization. Then, it constructs the multi-wavelength phase distribution through achromatic metaatomic structure design. The achromatic performance and energy utilization performance of the dual-layer cascaded metalens system are evaluated by calculating the focus offset and efficiency. Finally, a fabrication feasibility analysis is conducted to ensure that the metaatomic structure is compatible with current fabrication processes and has fabrication feasibility, thereby ensuring that the designed metaatomic structure can meet the requirements of dual-layer cascaded metalenses.

[0066] The present invention also provides a large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device, which is designed using any of the above-described design methods.

[0067] The large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device designed in this invention can be used for imaging, display, beam collimation, or focusing. In the cascaded metalens imaging system, the light beam passes sequentially through the first metalens and the second metalens, and is finally focused onto the image plane 5.

[0068] The first metalens consists of a first substrate 2 and a first metaatom 1 thereon, and the second metalens consists of a second substrate 4 and a second metaatom 3 thereon. In this system, the two metalenses cooperate to achieve aberration correction while focusing. In this invention, the metaatoms are all located on the object-side of the substrate. However, depending on design and manufacturing requirements, the metaatoms can be adjusted to the image-side of the substrate, or one metalens can have its metaatoms located on the object-side of the substrate, while the other metalens has its metaatoms located on the image-side of the substrate. All of these configurations achieve the designed functionality of the device.

[0069] Example 1 Taking a collimating lens module in waveguide AR display as an example, a typical application of a large field-of-view multi-wavelength achromatic dual-layer cascaded metalens, a specific design is demonstrated. Figure 3This diagram shows the structure and field of view of the collimating lens module. The actual propagation path of light in this module is as follows: light originates from the image plane, passes sequentially through the second and first metalenses, is collimated, and exits through the aperture stop. To facilitate ray tracing and image quality evaluation, a reverse ray tracing method, as shown in diagram a, is used in the system design. After passing through the aperture stop, the light beam passes sequentially through the first and second metalenses, and is finally focused onto the image plane. The specific design process includes: first, determining the working wavelength, aperture, and field of view based on design requirements. ), like the length of the face diagonal ( Design parameters such as field of view and image plane diagonal length are used to calculate the effective focal length of the metalens. The calculation formula is as follows:

[0070] The aperture is constrained by an aperture stop, the size of which is chosen to be 2 mm to match the size of the waveguide coupling grating used. The field of view is chosen to be 30° to satisfy large field of view imaging. The image face diagonal length is chosen to be 3.33 mm, corresponding to a commonly used 0.13-inch microdisplay. Calculations show that the effective focal length of the metalens should be 6.2 mm. The specific design specifications are shown in the table below: Table 3-1 Design Specifications for Meta-Lens

[0071] After determining the design specifications of the metalens, system optimization was performed using optical simulation software, and its imaging quality was evaluated using assessment metrics. The phase distribution of the metalens was simulated using a binary 2-plane model in the optical simulation software, and can be calculated using the following formula:

[0072] in, The total number of terms in the polynomial. The order is (the lens is radially symmetrical). For the first The coefficient of the first phase; The distance from a point on the surface of the metalens to the center; The normalized radius.

[0073] By changing the coefficients of the metalens phase distribution formula and the distance between the two metalenses L The imaging quality of the dual-layer cascaded metalens was optimized, and the phase coefficients corresponding to different working wavelengths were improved. The optimization results differ. Order The choice of order depends on the actual design requirements. A certain order can be selected initially for optimization. If the design requirements cannot be met, the order can be increased, and optimization can continue until the requirements are satisfied. In this embodiment, we take... This allows for an accurate description of the phase distribution of the metalens.

[0074] In simulating this device, ray tracing was employed. Parallel rays entered from the exit pupil and were focused onto the image plane after passing through the metalens. The constraints for optimizing this structure included: effective focal length, total system length, lens diameter, modulation transfer function, distortion, and root mean square radius of the dot plot. The final optimized metalens structure is shown below. Figure 3 As shown in Figure a, the distance between the aperture stop and the first metalens is 1.79 mm, the distance between the first and second metalenses is 5 mm, the distance between the second metalens and the image plane is 2.38 mm, the thickness of the metalens substrate is 0.5 mm, and the diameters of the first and second metalenses are 2.96 mm and 4.03 mm, respectively. The total length of this cascaded metalens system is only 10.17 mm, and its volume is only 0.13 cm². 3 Furthermore, it uses only two-piece structures, achieving both lightweight design and low complexity.

[0075] Figure 3 Figure b shows the field of view of this large field of view multi-wavelength achromatic double-layer cascaded superlens. Since the field of view is centrally symmetrically distributed, the system is also a centrally symmetrical system. Therefore, it is only necessary to select four typical fields of view of 0°, 5°, 10° and 15° in one quadrant to represent the entire field of view.

[0076] Figure 4 The phase distribution of a large field-of-view multi-wavelength achromatic double-layer cascaded metalens with RGB three colors (wavelengths of 630 nm, 526 nm, and 455 nm, respectively). Figure 4 In the diagram, 'a' and 'b' represent the phase distribution along the diameters of the first and second metalenses, respectively. Different metalens phase distributions were optimized for RGB wavelengths of 630 nm, 526 nm, and 455 nm. These phase distributions were derived using the phase distribution formula. It can be seen that the phase distribution of the same metalens is only related to the distance from a certain point on the surface of the metalens to the center. Therefore, the phase values ​​of all points on the surface of the metalens that are equidistant from the center are the same.

[0077] Figure 5 Five typical metaatomic structures (a) and the arrangement of metaatomic atoms (b) of a large field-of-view, multi-wavelength, achromatic, double-layered metalens for RGB three-color applications are shown. Figure 5As shown in Figure a, by selecting appropriate metaatomic materials, shapes, and sizes, five different metaatomic structures were designed to meet the dispersion requirements of a three-color metalens. Typical multi-wavelength achromatic metaatomic structures include cylinders, square cylinders, hollow toroidal cylinders, hollow square prisms, cross-shaped cylinders, and one or more combinations of these shapes using Boolean operations. The columnar nanostructures of the metaatoms are made of materials that are transparent or have low absorption in the target wavelength band; preferred materials include titanium dioxide (TiO2), tantalum pentoxide (Ta2O5), and silicon nitride (SiN). X The substrate is made of a transparent material, preferably fused silica glass (SiO2). P is the meta-atomic period, H is the height of the columnar structure, D is the diameter of the cylindrical structure, W is the width of the square columnar structure, W1 is the outer width of the square hole column, W2 is the inner width of the square hole column, D1 is the outer diameter of the circular hole column, D2 is the inner diameter of the circular hole column, W3 is the width of the long side of the cross column, and W4 is the width of the short side of the cross column. This invention can use isotropic meta-atoms with a C4 symmetric structure to construct metalens devices, giving them polarization-independent operating characteristics. Alternatively, anisotropic meta-atoms can be used to construct metalens devices, giving them polarization multiplexing or polarization-selective operating characteristics. Figure 5 Figure b shows the arrangement of meta atoms on an RGB color achromatic cascaded metalens. The arrangement of meta atoms is obtained by matching different structures in the structure library based on the target phase distribution and considering the transmittance. Nanopillars of different types and sizes are neatly arranged according to the period P, and the whole presents a centrally symmetrical ring distribution.

[0078] Figure 6 The imaging performance of a large field-of-view, multi-wavelength achromatic double-layer cascaded metalens with RGB three-color technology at the red wavelength (630 nm). Figure 6 In the diagram, 'a' represents a point array on the image plane of the cascaded superlens. Figure 6 In the middle, b represents the PSF of the cascaded metalens; Figure 6 In the middle, c represents the MTF of the cascaded metalens; Figure 6 In the middle, d represents the field curvature curve of the field of view from 0 to 15°; Figure 6 In the middle, e represents the distortion curve of the field of view from 0 to 15°; Figure 6 In figure f, grid distortion is represented. In figure a, the maximum RMS radius of the point plot for each field of view is 5.955 μm. The black circle in the figure represents the Airy disk, with a radius of 2.392 μm. The RMS radii of the point plots for each field of view are all within three times the radius of the Airy disk, proving that the cascaded metalens system achieves good focusing performance. Figure 6In section b, the full width at half maximum (FWHM) of the PSF for each field of view is smaller than the Airy disk radius of the system, proving that the cascaded metalens system has reached the diffraction limit. In section c, the MTF for each field of view is greater than 0.28 at a spatial frequency of 200 lp / mm, meeting the human eye's requirement for clear imaging with an MTF greater than 0.2, indicating that the system has high spatial resolution. In section d, the maximum field curvature in the 0~15° field of view is controlled at 0.0619 mm, corresponding to an edge defocus of approximately 0.998% of the effective focal length of 6.2 mm. This defocus has virtually no impact on image quality, proving that the cascaded metalens system has good imaging performance. In section e, the maximum distortion in the 0~15° field of view is controlled within 0.034%, a level of distortion that is imperceptible to the human eye. Figure 6 The grid distortion diagram in the middle of the image intuitively reflects that the cascaded hyperlens system produces virtually no distortion of the image within the designed field of view, proving that the distortion of the system has been effectively controlled.

[0079] Figure 7 The imaging performance of a large field-of-view, multi-wavelength achromatic double-layer cascaded metalens with RGB three-color technology at the green (wavelength 526 nm) working wavelength is shown in Figure a. a) is the dot plot on the image plane of the cascaded metalens; b) is the PSF (Power Scattering Factor) of the cascaded metalens; c) is the MTF (Mean Transformation Factor) of the cascaded metalens; d) is the field curvature curve of the 0–15° field of view; e) is the distortion curve of the 0–15° field of view; and f) is the grid distortion. In Figure a, the maximum RMS radius of the dot plot for each field of view is 4.638 μm. The black circles in the figure represent Airy disks, with a radius of 1.993 μm. The RMS radii of the dot plots for each field of view are all within three times the Airy disk radius, proving that the cascaded metalens system achieves good focusing performance; b) the full width at half maximum (FWHM) and full width at half maximum (FWHM) of the corresponding PSF for each field of view are all smaller than the Airy disk radius of the system, proving that the cascaded metalens system has reached the diffraction limit; c) the MTF for each field of view is greater than 0.25 at a spatial frequency of 200 lp / mm, meeting the human eye's requirement for clear imaging with an MTF greater than 0.2, indicating that the system has high spatial resolution; d) the maximum field curvature is controlled at 0.0608 mm within the 0~15° field of view range, corresponding to an edge defocus of approximately 6.2 times the effective focal length. The defocusing amount is 0.981% of mm, which has virtually no impact on image quality, proving that the cascaded metalens system has good imaging performance; in e, the maximum distortion value is controlled within 0.049% in the 0~15° field of view, which is imperceptible to the human eye; in f, the grid distortion diagram intuitively reflects that the cascaded metalens system produces virtually no distortion to the image within the designed field of view, proving that the distortion of the system is effectively controlled.

[0080] Figure 8The imaging performance of a large field-of-view, multi-wavelength achromatic double-layer cascaded metalens with RGB three-color technology at the blue (wavelength 455 nm) working wavelength is shown in Figure a. a) is the dot plot on the image plane of the cascaded metalens; b) is the PSF (Power Scattering Factor) of the cascaded metalens; c) is the MTF (Mean Transformation Factor) of the cascaded metalens; d) is the field curvature curve of the 0–15° field of view; e) is the distortion curve of the 0–15° field of view; and f) is the grid distortion. In Figure a, the maximum RMS radius of the dot plot for each field of view is 5.796 μm. The black circles in the figure represent Airy disks, with a radius of 1.715 μm. The RMS radii of the dot plots for each field of view are all within four times the Airy disk radius, proving that the cascaded metalens system achieves good focusing performance. In b, the full width at half maximum (FWHM) of the PSF for each field of view is smaller than the Airy disk radius of the system, proving that the cascaded metalens system has reached the diffraction limit. In c, the MTF for each field of view is greater than 0.22 at a spatial frequency of 200 lp / mm, meeting the human eye's requirement for clear imaging with an MTF greater than 0.2, indicating that the system has high spatial resolution. In d, the maximum field curvature in the 0~15° field of view range is controlled at 0.0599 mm, corresponding to an edge defocus of approximately 6.2 times the effective focal length. The defocusing amount is 0.966% of mm, which has virtually no impact on image quality, proving that the cascaded metalens system has good imaging performance; in e, the maximum distortion value is controlled within 0.07% in the 0~15° field of view, which is imperceptible to the human eye; in f, the grid distortion diagram intuitively reflects that the cascaded metalens system produces virtually no distortion to the image within the designed field of view, proving that the distortion of the system is effectively controlled.

[0081] Example 2 In this invention, the large field-of-view multi-wavelength achromatic double-layer cascaded metalens can operate at multiple wavelengths simultaneously. In addition, by selecting appropriate metamaterials, shapes and sizes, the phase distribution of the metalens can be changed, enabling the large field-of-view multi-wavelength achromatic double-layer cascaded metalens to operate at a specific single wavelength.

[0082] Figure 9 The image shows the phase distribution of a large field-of-view, single-wavelength, cascaded dual-layer metalens (taking a single green working wavelength of 526 nm as an example). a and c are planar views of the phase distribution of the first metalens 1 and the second metalens 2, respectively. b and d are cross-sectional views of the phase distribution of the first metalens 1 and the second metalens 2 through the center of the circle, respectively. The phase distribution of the metalens is a centrally symmetric annular distribution, and the phase values ​​of all points on the surface of the metalens at the same distance from the center are the same.

[0083] Figure 10This paper presents two metaatomic structures (a and b) that can be used for large-field-of-view single-wavelength dual-layer cascaded metalenses (taking a single green working wavelength of 526 nm as an example), as well as the metaatomic arrangement in a single-wavelength cascaded metalens (c, taking a prismatic metaatomic structure as an example). The columnar nanostructure of the metaatoms is made of materials with high refractive index and low absorption in the working wavelength range. Preferred materials include titanium dioxide (TiO2), tantalum pentoxide (Ta2O5), and silicon nitride (SiN). X Gallium nitride (GaN) and hafnium oxide (HfO2) are used as substrates. Substrate 2 is made of a transparent material, preferably fused silica glass (SiO2). Considering the polarization-independent design requirements, isotropic metaatoms with C4 symmetry are used. Typical structures include square prisms and cylinders, as shown in a and b, respectively. Here, P is the period of the metaatoms, H is the height of the nanopillars, W is the width of the nanopillars, and D is the diameter of the nanopillars. By selecting a suitable period P and nanopillar height H, arbitrary control of the light wavefront can be achieved by changing the structural dimensions W or D of the nanopillars within a certain range, while ensuring high transmittance of the metaatoms. c shows the arrangement of metaatoms on a single-wavelength cascaded metalens. The arrangement of metaatoms is obtained by matching different structures from the structure library based on the target phase distribution and considering transmittance. Nanopillars of different sizes are neatly arranged according to the period P, presenting a centrally symmetrical ring distribution.

[0084] In summary, this invention combines the imaging principles of geometric optics systems and the principles of micro-nano optics light field manipulation. It utilizes the imaging principles of geometric optics systems to control the macroscopic imaging performance at the system level, establishing an overall geometric optics model to meet the imaging requirements of large field-of-view, multi-wavelength achromatic imaging. Considering the entire field of view, aberration optimization is used to determine the target phase distribution of each metalens in the dual-layer cascaded structure at multiple wavelengths. Based on the aforementioned multi-wavelength target phase distribution, and through the principles of micro-nano optics light field manipulation, suitable achromatic metaatomic materials, shapes, and sizes are selected, enabling the same metaatom to simultaneously provide the required target phase at multiple wavelengths, thus realizing the construction of achromatic metaatomic micro-nano structures.

[0085] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A large field-of-view, multi-wavelength achromatic dual-layer cascaded metalens device, characterized in that, It includes a first metalens and a second metalens arranged sequentially from the object plane to the image plane. The two metalenses work together to achieve aberration correction while focusing.

2. A design method for a large field-of-view, multi-wavelength achromatic, dual-layer cascaded metalens device as described in claim 1, characterized in that, Includes the following steps: S1. Determine the operating wavelength, field of view, and diagonal length of the image plane of the metalens device according to the target requirements; calculate the effective focal length of the metalens based on the field of view and diagonal length of the image plane. S2. Using the field of view, working wavelength, effective focal length, image plane size, total system length, and diameter of the metalens as constraints, and image quality as the evaluation index, the phase distribution of the two metalenses and the distance between the two metalenses are used as optimization variables to progressively optimize the phase distribution of the two metalenses at the corresponding working wavelength to obtain the target phase distribution; the total system length is the distance from the first metalens to the image plane; S3. Select the material and shape of meta-atoms that meet the achromatic requirements, construct a meta-atom library according to the correspondence between meta-atom structure parameters and phase values, and then determine the meta-atom structure parameters of each meta-lens according to the target phase distribution and the transmittance of meta-atoms. S4. The achromatic performance and energy utilization performance of the dual-layer cascaded metalens system are quantitatively evaluated by numerical analysis of focal offset and efficiency in order to optimize the meta-atomic structure parameters.

3. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device according to claim 2, characterized in that, In step S2, the phase distribution is optimized according to the following phase distribution formula: in, The total number of terms in the polynomial. For order, For the first Phase coefficient; The distance from a point on the surface of the metalens to the center; The normalized radius.

4. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device according to claim 3, characterized in that, In step S3, the matching between the phase corresponding to the meta-atomic structural parameters and the target phase, as well as the transmittance of the meta-atoms, are quantitatively evaluated using the evaluation function shown below: in, For the first meta-lens Evaluation function for each superatom. The total number of operating wavelengths, For the first The metalens at the working wavelength is the first The target phase value of each superatomic atom. For the first The metalens at the working wavelength is the first The actual phase value of each superatomic atom For the first The metalens at the working wavelength is the first Transmittance of each superatom For the first Weights for each operating wavelength This represents the total number of metaatoms on the metalens. The mean of the evaluation function for all metaatoms on the metalens; the weights of different working wavelengths are changed according to design requirements to achieve more targeted selection of metaatomic structure parameters; Evaluation function The smaller the value, the more accurately the phase corresponding to the selected metaatomic structure parameters matches the target phase, and the higher the transmittance of the metaatoms, the better it meets the design requirements. During the design process, structures are selected from the metaatomic structure library that... The structural parameters of the group of superatoms with the smallest numerical values.

5. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device according to claim 4, characterized in that, In step S4, the achromatic performance and energy utilization performance of the dual-layer cascaded metalens device are evaluated by focusing offset and efficiency, respectively. If the focusing offset or efficiency does not meet the design requirements, one or more combinations of the following three optimization operations are performed iteratively until both the focusing offset and efficiency meet the design requirements: (1) Re-optimize the target phase distribution: Adjust the phase coefficient in the phase distribution formula of the dual-layer cascaded metalens to optimize the phase distribution that better meets the requirements of achromatic performance and energy utilization performance; (2) Expanding the meta-atomic structure library: Expanding or reconstructing the structural parameter space of meta atoms, including but not limited to adjusting the shape, material and size of meta atoms, in order to expand the range of phase values ​​and transmittance that meta atoms can achieve; (3) Reselecting metaatoms: Based on the updated phase distribution or the expanded metaatom structure library, adjust the weights of each working wavelength in the evaluation function and reselect the structural parameters of the metaatoms; The formula for calculating the focus offset is as follows: in, For the first The first operating wavelength The focal offset of each field of view For the first The first operating wavelength The focal length of each field of view The focal length of the reference field of view at the reference operating wavelength. Mean value of focus shift across the entire field of view at all operating wavelengths The total number of operating wavelengths, This represents the total number of samples taken from the field of view. The efficiency is calculated using the following formula: in, For the first The first operating wavelength The efficiency of a single field of view can be calculated by dividing the energy within the effective area of ​​the focused spot by the total energy incident on the cascaded dual-lens superlens. This represents the average efficiency across the entire operating wavelength and field of view. The total number of operating wavelengths, This represents the total number of samples taken from the field of view angle.

6. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device according to claim 2, characterized in that, In step S2, the phase distribution is the phase distribution calculated from the Binary 2 surface type; The imaging quality evaluation indicators include the root mean square radius of the dot plot, dot spread function, modulation transfer function, field curvature, and distortion.

7. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device according to claim 2, characterized in that, Both the first metalens and the second metalens include a substrate and meta atoms distributed on the substrate; The metaatomic structural parameters include the material, shape, and size of the metaatoms.

8. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device according to claim 7, characterized in that, The superatoms are isotropic or anisotropic superatoms with C4 symmetry; wherein the structures of the isotropic superatoms include cylinders, square cylinders, hollow annular cylinders, hollow square prisms, cross-shaped cylinders, and one or more combinations of Boolean operations on these shapes. Among them, when isotropic meta-atoms with C4 symmetry are used to construct meta-lens devices, they have polarization-independent operating characteristics; when anisotropic meta-atoms are used to construct meta-lens devices, they have polarization multiplexing or polarization selection operating characteristics.

9. The design method of the large field-of-view multi-wavelength achromatic dual-layer cascaded metalens device according to claim 2, characterized in that, In step S1, the working wavelength is either a polychromatic light wavelength or a monochromatic light wavelength.

10. An application of the large field-of-view, multi-wavelength achromatic, dual-layer cascaded metalens device as described in claim 1, characterized in that, Used for imaging, display, beam collimation, or focusing.

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