A focusing lens that achieves the super Rayleigh limit and its design method

Abstract

This application provides a focusing lens and its design method for achieving the Rayleigh limit, belonging to the field of optical component technology. The function of this focusing lens can be implemented by several devices. The principle of this focusing lens is to convert linearly polarized light into a focused vector beam with a transverse wave vector distribution and range that meet the requirements by vector beam modulation, ring beam modulation, and focusing. By using light with the required transverse wave vector components for focusing, a focused field that meets the requirements is formed, thereby achieving the Rayleigh diffraction limit. This focusing lens can be widely used in the fields of photolithography, optical super-resolution imaging, and precision measurement of nanostructures.

Description

Technical Field

[0001] This application relates to the field of optical element technology, and in particular to a focusing lens that achieves the super Rayleigh limit and its design method. Background Technology

[0002] In the fields of optical imaging and lithography, optical super-resolution imaging, and precision measurement of nanostructures, lenses, as core components, are key indicators that determine system performance. The resolution of traditional optical lenses is fundamentally limited by the diffraction phenomenon caused by the wave nature of light; this limitation is commonly referred to as the "diffraction limit." The diffraction limit does not originate from manufacturing or assembly errors of the lens, but rather is an inherent theoretical boundary determined by the laws of physics.

[0003] In related technologies, the Rayleigh diffraction limit provides a criterion for determining whether details of two point light sources or objects are resolvable. According to the Rayleigh criterion, the resolvable critical state is defined as when the principal maxima centers of two point light sources of equal intensity coincide with the first dark ring of another source. The formula for the theoretical resolvable angle is... ,in For theoretical resolution angle; For wavelength, The aperture diameter can also be expressed as in numerical aperture systems. ;in The Rayleigh limit, from the perspective of point source imaging, solidifies the limitation of diffraction on resolution: if the spatial distance between any two point sources is too close, resulting in severe overlap of diffraction patterns, the system will be unable to distinguish them as two independent objects.

[0004] In response, with the ever-increasing demand for higher resolution imaging in fields such as semiconductor manufacturing, bioimaging, and astronomy, existing lens technologies, limited by the aforementioned diffraction limit, are struggling to meet the needs of observing nanoscale structures or resolving point sources extremely close to the target. For example, in photolithography, the diffraction limit restricts the smallest feature size of manufactured integrated circuits; in optical microscopy, it hinders the direct observation of delicate biological processes such as subcellular structures. Therefore, there is an urgent need to develop novel lens structures, materials, or imaging methods that can overcome or circumvent the Rayleigh diffraction limit to significantly improve the resolution of optical systems. Summary of the Invention

[0005] The main objective of this application is to propose a focusing lens and its design method for achieving the Rayleigh diffraction limit. This focusing lens converts the light emitted from the light source into a focused vector beam with a corresponding transverse wave vector range that meets the requirements by performing vector beam modulation, ring beam modulation and focusing. This achieves focusing beyond the Rayleigh diffraction limit.

[0006] To achieve the above objectives, one aspect of this application proposes a focusing lens that achieves the super Rayleigh limit, wherein the function of the focusing lens is implemented by a plurality of devices; wherein, When the function of the focusing lens is realized by a single device, the device that realizes the function of the focusing lens includes a designed lens composed of a number of nanocells arranged in an annular region; In the designed lens Each nanocell is formed by combining a first nanounit and a second nanounit with orthogonal rotation angles; the rotation angle of each nanounit satisfies a preset numerical relationship with the spatial azimuth angle, so that linearly polarized light forms a vector beam after passing through the designed lens; the vector beam is a beam with non-uniformly distributed polarization state on the cross-section; A plurality of nanocells are arranged radially along the annular region; the spacing between the plurality of nanocells satisfies a preset condition to ensure that the vector beams passing through the annular region converge at the same position to form a focused vector beam; the transverse wave vector distribution of the focused vector beam corresponding to the focusing plane optical field is annular; the range of the transverse wave vector of the corresponding focusing plane optical field satisfies a preset range.

[0007] In some embodiments, in the designed lens, the ratio between the rotation angle and the spatial azimuth angle of each nanounit is one-half.

[0008] In some embodiments, in the design lens, parallel light passing through the design lens converges at the design focal point; the spacing between each nanocell is calculated based on the operating wavelength of the incident light, the background refractive index, and the angle between the line connecting the nanocell position and the design intersection point and the normal direction.

[0009] In some embodiments, when the function of the focusing lens is implemented by three discrete devices, the devices implementing the function of the focusing lens further include a liquid crystal device or a preset polarization control device for generating a vector beam, an annular aperture for generating an annular beam, and a lens for focusing the beam.

[0010] In some embodiments, when the function of the focusing lens is implemented by two discrete devices, the devices implementing the function of the focusing lens further include a liquid crystal device or a preset polarization control device for generating a vector beam, and a preset planar diffraction lens; the preset planar diffraction lens is used to achieve single-ring or multi-ring focusing.

[0011] To achieve the above objectives, another aspect of this application proposes a lens design method applied to the designed lens, the design method comprising the following steps: Obtain the working wavelength of the incident light; Obtain the initial degree of freedom values ​​of the first and second nanounits in each nanounit cell to obtain the initial nanounit combination parameters corresponding to each nanounit cell; Based on the set of degrees of freedom of the preset target nanounit and the working wavelength of the incident light, the initial nanounit combination parameters corresponding to each nanounit cell are adjusted until the preset requirements are met, and the nanounit combination parameters corresponding to each nanounit cell are determined according to the adjustment results. The degree of freedom values ​​of the first and second nanounits in each nanounit cell are determined based on the nanounit combination parameters corresponding to each nanounit cell.

[0012] In some embodiments, the nanounit combination parameters corresponding to each nanocell are determined in the following manner: Based on the preset set of degrees of freedom of the target nanounit and the working wavelength of the incident light, numerical simulations are performed on the degrees of freedom values ​​of the first and second nanounits in the nanocell. The nanounit combination parameters corresponding to the nanocell are adjusted according to the results of the numerical simulation until both the first and second nanounits in the nanocell can achieve the polarization conversion capability of a half-wave plate at the working wavelength of the incident light. The nanounit combination parameters corresponding to the nanocell are determined according to the adjustment results.

[0013] In some embodiments, after determining the degree-of-freedom values ​​of the first and second nanounits in the nanocell, the method further includes: Numerical simulation is performed on the grating formed by the first and second nanounits in the nanocell. The positional relationship between the first and second nanounits is adjusted according to the results of the numerical simulation until both the first and second nanounits in the nanocell can achieve the polarization conversion capability of a half-wave plate at the working wavelength of the incident light and the far-field diffraction intensity of the grating meets the preset conditions. The positional relationship between the first and second nanounits is determined according to the adjustment results.

[0014] In some embodiments, a focused spot is formed by converging parallel light through the designed lens; the method further includes: Numerical simulations were performed on an experimental lens composed of several nanocells. The angular period of each nanocell was adjusted according to the results of the numerical simulation until the shape of the focused spot formed by the convergence of parallel light through the experimental lens met the preset conditions. The angular period of each nanocell was determined according to the adjustment results.

[0015] In some embodiments, a focused spot is formed by converging parallel light through the designed lens; the method further includes: Numerical simulations were performed using an experimental lens composed of several nanocells. The ratio of the inner and outer diameters of the annular region was adjusted based on the simulation results until the shape of the focused spot formed by the convergence of parallel light through the experimental lens met the preset conditions. The ratio of the inner and outer diameters of the annular region was then determined based on the adjustment results.

[0016] The embodiments of this application include at least the following beneficial effects: This application provides a focusing lens that achieves the super Rayleigh limit and its design method. The function of the focusing lens can be implemented by several devices. When the function of the focusing lens is implemented by a single device, the device implementing the function of the focusing lens may include a designed lens composed of several nanocells arranged in an annular region. On one hand, each nanocell in the designed lens contains two nanounits. By setting the arrangement of the nanounits, vector beam modulation is achieved, so that linearly polarized light forms a vector beam after passing through the designed lens, thereby reducing the influence caused by the asymmetry of the defocusing field when focusing linearly polarized light and preparing for subsequent modulation. On the other hand, in lens focusing, the light rays at the edge of the lens are deflected at a larger angle than the light rays near the center. The larger the deflection angle, the larger the transverse wave vector component of the light rays. The focusing field formed by the focused light with a larger transverse wave vector component is... The smaller the size, the better. In lens design, by combining the annular region arrangement of nanocells and setting the spacing between the nanocells, annular beam modulation and focusing are achieved. Only the vector beams passing through the annular region converge at the same position, that is, the light from the lens edge is focused, thereby obtaining a focused vector beam with the required transverse wave vector range and distribution. By using light with the required transverse wave vector components for focusing, the Rayleigh diffraction limit is exceeded. In this regard, the focusing lens principle provided in the embodiments of this application is to convert linearly polarized light into a focused vector beam with the required transverse wave vector distribution and range by performing vector beam modulation, annular beam modulation, and focusing. By using light with the required transverse wave vector components for focusing, a focused field that meets the requirements is formed, thereby breaking through the diffraction limit and significantly improving the resolution of the optical system. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a focusing lens that achieves the super Rayleigh limit, provided in an embodiment of this application. Figure 2 This is a schematic diagram illustrating the focusing of linearly polarized light under different modulation conditions provided in the embodiments of this application; Figure 3 This is a schematic diagram of the structure of a lens provided in an embodiment of this application; Figure 4 This is a schematic diagram of the nanocells and their components provided in the embodiments of this application; Figure 5This is an optional structural diagram of a focusing lens that achieves the super Rayleigh limit, provided in an embodiment of this application; Figure 6 This is a schematic diagram comparing the focusing effects of two different devices capable of achieving super Rayleigh limit focusing, as provided in the embodiments of this application. Figure 7 This is an optional flowchart of a lens design method provided in an embodiment of this application; Figure 8 This is a schematic diagram of the path for focusing light using different lenses, provided in an embodiment of this application. Figure 9 This is a schematic diagram showing the relationship between the angular radiant flux and the deflection angle obtained by different lenses after light incident, according to embodiments of this application. Figure 10 This is a schematic diagram showing the relationship between the minimum deflection angle of different lenses provided in the embodiments of this application and the ratio of the inner and outer diameters of the annular aperture and the radiant flux. Figure 11 This is another schematic diagram showing the relationship between the minimum deflection angle of different lenses provided in the embodiments of this application and the ratio of the inner and outer diameters of the annular aperture and the radiant flux. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0020] Before providing a detailed description of the embodiments of this application, some of the nouns and terms involved in the embodiments of this application will be explained first. The nouns and terms involved in the embodiments of this application are subject to the following interpretations.

[0021] 1) Diffraction limit: refers to the theoretical minimum spatial resolution determined by the wave properties of light. It is an obstacle that traditional optical microscopes cannot overcome, limiting the system's ability to resolve adjacent microstructures and making it difficult to clearly present the details of even smaller nanostructures. The value of the diffraction limit is related to the wavelength of light and the numerical aperture of the objective lens. The minimum resolution that can be achieved using a traditional objective lens in the visible light range is about 200 nm.

[0022] 2) Spatial resolution: This is the minimum distance between two adjacent points in a sample that a microscope can distinguish. It is an important indicator of the clarity of microscope images. Higher spatial resolution allows us to see the detailed features of nanostructures more clearly, such as the shape, size, and arrangement of nanoparticles.

[0023] 3) Sub-100 nanometers: This indicates a spatial resolution in the range of 10-100 nanometers. It is superior to the resolution of traditional optical microscopes. At this scale, nanostructures can be imaged and measured with greater precision, and many nanoscale features and details that are difficult to detect with traditional microscopes can be observed. It is widely used in the field of nanoscience research.

[0024] 4) Transverse wave vector: The component of the wave vector on the interface (or the plane perpendicular to the propagation direction), which corresponds to the spatial frequency of the light field in Fourier optics (i.e., the transverse coordinate of the angular spectrum) and is used to describe the propagation direction and transverse structure of the plane wave component.

[0025] In the fields of optical imaging and lithography, optical super-resolution imaging, and precision measurement of nanostructures, lenses, as core components, are key indicators that determine system performance. The resolution of traditional optical lenses is fundamentally limited by the diffraction phenomenon caused by the wave nature of light; this limitation is commonly referred to as the "diffraction limit." The diffraction limit does not originate from manufacturing or assembly errors of the lens, but rather is an inherent theoretical boundary determined by the laws of physics.

[0026] In related technologies, the Rayleigh diffraction limit provides a criterion for determining whether details of two point light sources or objects are resolvable. According to the Rayleigh criterion, the resolvable critical state is defined as when the principal maxima centers of two point light sources of equal intensity coincide with the first dark ring of another source. The formula for the theoretical resolvable angle is... ,in For the theoretical resolution angle, For wavelength, The aperture diameter can also be expressed as in numerical aperture systems. ;in The Rayleigh limit, from the perspective of point source imaging, solidifies the limitation of diffraction on resolution: if the spatial distance between any two point sources is too close, resulting in severe overlap of diffraction patterns, the system will be unable to distinguish them as two independent objects.

[0027] In response, with the ever-increasing demand for higher resolution imaging in fields such as semiconductor manufacturing, bioimaging, and astronomy, existing lens technologies, limited by the aforementioned diffraction limit, are struggling to meet the needs of observing nanoscale structures or resolving point sources extremely close to the target. For example, in photolithography, the diffraction limit restricts the smallest feature size of manufactured integrated circuits; in optical microscopy, it hinders the direct observation of delicate biological processes such as subcellular structures. Therefore, there is an urgent need to develop novel lens structures, materials, or imaging methods that can overcome or circumvent the Rayleigh diffraction limit to significantly improve the resolution of optical systems.

[0028] This application provides a focusing lens and its design method for achieving the Rayleigh limit. The focusing lens first performs vector beam modulation on the incident linearly polarized light to reduce the impact of asymmetry in the focusing field during focusing and to prepare for subsequent modulation. In lens focusing, the light rays at the lens edge are deflected at a larger angle than those near the center. Light rays with larger deflection angles correspond to larger transverse wave vector components, resulting in smaller focusing fields. The focusing lens provided in this application, by performing annular beam modulation and focusing on the modulated vector beam, can focus only the edge rays, forming a vector focused beam. The transverse wave vector distribution of the light field corresponding to this vector focused beam is annular, and its range satisfies a preset range. By using light corresponding to the transverse wave vector that meets the requirements for focusing, the focusing lens provided in this application can obtain a focused vector beam that exceeds the Rayleigh diffraction limit.

[0029] like Figure 1 As shown, Figure 1 This is a schematic diagram of a focusing lens that achieves super Rayleigh diffraction limit according to an embodiment of this application; wherein, (1) Vector beam modulation: In conventional optical imaging, the optical field of linearly polarized light is usually approximated as a scalar field, without considering its vector characteristics (polarization characteristics). However, in fields such as photolithography, super-resolution optical imaging, or precision measurement of nanostructures, we need to generate extremely small-scale optical fields through focusing with high numerical apertures. In this case, the vector characteristics of the optical field will have a significant impact on the focused field, leading to asymmetry and a large scale of the focused field in the polarization direction, which is not conducive to precision measurement. Therefore, it is necessary to use a vector beam (a beam with a non-uniformly distributed polarization state across its cross-section) for focusing, forming the desired vector optical field at the focal point. This allows for subsequent ring beam modulation and focusing to achieve super-Rayleigh diffraction-limited focusing.

[0030] (2) Ring beam modulation: In lens focusing, light rays incident on different positions of the lens exit at different angles, converging at the focal point. Rays closer to the center are deflected at smaller angles, while those at the lens edges are deflected at larger angles. Although the overall wave vector of light rays is fixed in the same medium, the transverse wave vector component (i.e., the wave vector magnitude multiplied by the sine of the deflection angle) of the outgoing light rays is different; the larger the deflection angle, the larger the transverse wave vector component. During focusing, the focused light with a larger transverse wave vector component forms a smaller focused field. Therefore, the design concept of the focusing lens provided in this application is to use only the light corresponding to the largest transverse wave vector for focusing, which forms a narrow ring in the wave vector space of the outgoing light field (hereinafter referred to as the "wave vector ring"). To address this, the focusing lens provided in this application uses ring beam modulation to block or absorb light rays passing through the center of the lens, retaining only light rays passing through the lens edges—that is, only edge rays with large transverse wave vector components.

[0031] (3) Focus: The ring beam is focused to form a focused vector beam; the transverse wave vector distribution of the corresponding focusing plane light field of the focused vector beam is ring-shaped; the range of the transverse wave vector of the corresponding focusing plane light field meets the preset range.

[0032] By focusing the modulated ring beam, a focused vector beam is formed. Furthermore, the transverse wave vector distribution of the optical field of the focusing plane corresponding to the focused vector beam is ring-shaped, i.e., "wave vector ring". From the perspective of Fourier optics, performing a Fourier transform on the optical field of the focusing plane yields the transverse wave vector distribution of the optical field. The "wave vector ring" is a narrow ring generated in the wave vector space of the Fourier transform, where only the transverse wave vector component exists.

[0033] Specifically, due to the transverse wave vector The maximum cannot exceed the total wave vector of light. ,in, To correspond to the deflection angle, The refractive index of the medium, The wavelength of light in a vacuum; the maximum transverse wave vector corresponds to The focused ray is deflected at an angle. In this regard, the transverse wave vector range of the wave vector ring corresponding to the focused vector beam obtained by the focusing lens provided in this application is within... arrive Between, that is, the deflection angle is arrive The wave vector corresponding to the deflected light is the narrow range of the wave vector corresponding to the "wave vector ring" (corresponding to...). , The larger the transverse wave vector, the narrower the range of the formed "wave vector ring", and the smaller the focusing effect can be achieved.

[0034] like Figure 2 The diagram shows the focusing of linearly polarized light under different modulation conditions; the blue arrows represent the wave vector direction of the focused light field, and the red arrows represent the polarization direction. Figure 2 In the diagrams (a) to (d), each figure, from top to bottom, shows the light field distribution on the focal plane, the path of the focused ray, and the incident vector beam; among them, Figure 2 (a) in the figure represents the focusing of linearly polarized light without vector beam modulation and ring beam modulation (or wave vector ring modulation). The size of the focused spot is slightly larger than the diffraction limit due to the influence of vector characteristics. Figure 2 (b) shows the focusing of linearly polarized light modulated by a ring beam. Due to the influence of the light field vector characteristics, the focusing field is asymmetrical and the scale of the focusing field in the polarization direction is large, resulting in poor focusing effect.

[0035] Furthermore, the vector beam is a beam with a non-uniformly distributed polarization state on its cross-section, including radially polarized light (RP) and angularly polarized light (AP). Figure 2 In the diagram, (c) represents the focused light field formed by the addition of a ring beam modulation to radially polarized light (RP). It is a solid focused light field with a sub-diffraction scale. The focused field is symmetrical, and since the transverse electric field components cancel each other out, the center of the focused field is a pure longitudinal component. Figure 2 In the diagram, (d) represents the focused light field formed by modulating angularly polarized light (AP) with a ring beam. Since the transverse electric field components cancel each other out and there is no longitudinal component, it is a hollow focused light field. The hollow part has a sub-diffraction scale and the focused field is symmetrical. To address this, we can convert the linearly polarized light in the two directions into RP and AP light respectively, generate wave vector ring focusing, and then use the vector subtraction between the obtained solid focused light field and the hollow focused light field to obtain a smaller imaging resolution.

[0036] The function of the aforementioned focusing lens can be achieved by several devices; the modulation and focusing functions can be achieved by multiple discrete devices, or by a single device.

[0037] In some embodiments, when the function of the focusing lens is realized by a single device; the device capable of realizing the function of the focusing lens includes a designed lens composed of a plurality of nanocells arranged in an annular region; Figure 3 This is an optional structural diagram of the lens design provided in the embodiments of this application, wherein, Each nanounit is formed by combining a first nanounit and a second nanounit with orthogonal rotation angles; the rotation angle of each nanounit satisfies a preset numerical relationship with the spatial azimuth angle so that linearly polarized light forms a vector beam after passing through a designed lens; the vector beam is a beam with non-uniformly distributed polarization state on the cross-section.

[0038] In some embodiments, a beam of light with non-uniformly distributed polarization states on its cross-section includes radially polarized light and angularly polarized light; the lens provided in this embodiment can convert linearly polarized light with a preset polarization direction into radially polarized light or angularly polarized light, that is, realize polarization conversion.

[0039] Specifically, when the preset polarization direction of polarized light is the x-direction, it forms radially polarized light when passing through the designed lens; when the preset polarization direction of polarized light is the y-direction, it forms angularly polarized light when passing through the designed lens.

[0040] like Figure 4 The diagram shown is a schematic diagram of the nanocells and their components provided in this application. Figure 4 (1) reveals the structure of nanounits. Figure 4 (2) reveals that the first and second nanounits in the nanocell have orthogonal rotation angles. Figure 4 (3) reveals the rotation angle of each nanocell and one of the nanounits. and spatial azimuth The design lens provided in this application achieves vector beam modulation by setting the arrangement of nano-units, so that linearly polarized light forms a vector beam after passing through the design lens, thereby reducing the influence caused by the asymmetry of the defocusing field when focusing linearly polarized light and preparing for subsequent modulation.

[0041] Several nanocells are arranged radially along the annular region; the spacing between the nanocells meets a preset condition to ensure that only vector beams passing through the annular region converge at the same position to form a focused vector beam; the transverse wave vector distribution of the focused vector beam corresponding to the focusing plane optical field is annular; the range of the transverse wave vector corresponding to the focusing plane optical field meets a preset range.

[0042] like Figure 3As shown, the lens provided in this embodiment is composed of several nanocells, each nanocell arranged radially along the annular region; and, in the lens provided in this embodiment, there is actually no structure in the middle of the annular region, and the spacing between the several nanocells meets the preset conditions; by combining the annular region arrangement of the nanocells and setting the spacing between the nanocells, annular beam modulation and focusing (or aperture focusing) is achieved, so that only the vector beam passing through the annular region converges at the same position, that is, the light from the edge of the lens is focused, thereby obtaining a focused vector beam whose corresponding transverse wave vector range and transverse wave vector distribution meet the requirements. By using light whose transverse wave vector components meet the requirements for focusing, the Rayleigh diffraction limit is exceeded; In summary, the design lens provided in this application is essentially a sub-diffraction focusing meta-lens. By setting the arrangement of several nano-units and the numerical relationship between the nano-units in the nano-units, polarization conversion and aperture focusing can be achieved, thereby converting incident ray-polarized light into a super Rayleigh-limited focused vector beam. In addition, the structure of this design lens only includes several nano-units composed of nano-units, which belongs to the submicron scale, and can achieve integration and cost reduction while realizing the super Rayleigh focusing function.

[0043] In some embodiments, in the lens design described above, the ratio between the rotation angle and the spatial azimuth angle of each nanounit is one-half; specifically as shown in equation (1): ; in, The rotation angle of the nanounit. The spatial orientation of the nanounit.

[0044] Rotation angle of nanounits With spatial azimuth Change, and satisfy It enables linearly polarized light to form a vector beam after passing through a designed lens; in addition, it enables a group of polarized lights with different preset polarization directions to form radially polarized light and angularly polarized light respectively after passing through the designed lens provided in this application.

[0045] In some embodiments, in the above-described design lens, parallel light passing through the design lens converges at the design focal point; the spacing between each nanocell is calculated based on the operating wavelength of the incident light, the background refractive index, and the angle between the line connecting the nanocell position and the design intersection point and the normal direction. The spacing between the nanocells is determined by equation (2): ; in The spacing between nanocells. The operating wavelength of the incident light. For the background refractive index, The angle between the line connecting the nanocell location and the design focus and the normal direction.

[0046] The spacing between the nanocells is determined by the first-order diffraction equation of the grating, so that the parallel light passing through the designed lens is focused by the first-order diffraction of the grating at the designed focal point (corresponding to the pixel to be measured). The radially polarized light formed by the designed lens can form a solid focused spot at the sub-diffraction scale, and the angularly polarized light formed by the designed lens can form a hollow focused spot.

[0047] In some embodiments, the nanounits and substrates in the above-described lens structure are made of any one or more optical media materials, such as optical crystals, optical glass, optical thin films, optical plastics, optical metals such as gold, silver, and aluminum, and optical non-metallic materials such as III-V compound semiconductors. The optical crystals include, but are not limited to, optical single crystals, optical polycrystalline materials, and optical amorphous materials.

[0048] In some embodiments, the shape of the nanounit used in the above-designed lens structure is an elliptical cylinder, but the same scheme includes, but is not limited to: rectangular cylinders with biaxial orientation, cross cylinders; various non-biaxial cylinders and asymmetric cylinders with birefringence phase effect.

[0049] In some embodiments, the lens unit described above is provided with patterned micro-nano structures. The array can be obtained by methods such as electron beam lithography, ultraviolet lithography, and laser direct writing, and the etching method can be dry etching or wet etching.

[0050] Regarding the focusing lens function mentioned above, in addition to using the designed lens described above to integrate the functions of wave vector ring focusing and vector light field, it can also be generated using discrete components: In some embodiments, the focusing lens function described above can be implemented by three discrete devices, such as a liquid crystal device or a preset polarization control device for generating a vector beam, an annular aperture (or a conical lens or other device with the same function) for generating an annular beam, and a lens for focusing the beam; wherein, the lens for focusing the beam can be an objective lens, a plane diffraction lens, or other optical devices that can be used for focusing; such as Figure 5 As shown, the function of the focusing lens is achieved by the liquid crystal device 1, the annular aperture 2, and the objective lens 3.

[0051] In some embodiments, the above-mentioned focusing lens function can also be generated by discrete devices in pairs, such as liquid crystal devices or preset polarization control devices for generating vector beams, and preset planar diffraction lenses for achieving single-ring or multi-ring focusing.

[0052] In this regard, the aforementioned lens design has significant advantages over combined devices, including but not limited to: (1) It can achieve smaller resolutions; like Figure 6 As shown, Figure 6 The comparison of focusing spot effects between a designed lens capable of achieving super Rayleigh limit focusing and a discrete component combination of "objective lens + polarization converter + annular stop" under the same incident light wavelength and numerical aperture. Figure 6 (a) in this embodiment shows the focusing effect achieved using the lens design provided in this embodiment; Figure 6 (b) shows the focusing effect achieved by combining a discrete component "objective lens + polarization converter + annular aperture"; it can be seen that the size of the light spot formed by focusing with the designed lens is smaller than that achieved by combining discrete components. Therefore, the designed lens provided in the embodiment can achieve a smaller resolution.

[0053] (2) It can be miniaturized and integrated, making it easy to form a meta-lens array and simultaneously form multiple sub-diffraction focal points.

[0054] (3) It can integrate multiple functions without aligning multiple discrete components; integrating multiple discrete components requires precise alignment on the optical axis, which increases the design difficulty of the focusing lens.

[0055] (4) It can generate sub-100 nanometer scale sub-diffraction focusing spots on a thickness of micrometers. Compared with the method of generating sub-diffraction focusing spots using traditional vortex wave plates and high numerical aperture objectives, it has the advantages of low cost, small size and easy integration.

[0056] Figure 7 This is an optional flowchart of a lens design method provided in an embodiment of this application. This design method is applied to the lens design described above. The design method includes, but is not limited to, steps S100 to S400, wherein... Step S100: Obtain the working wavelength of the incident light.

[0057] Obtain the operating wavelength of the incident light as the data basis for lens design.

[0058] Step S200: Obtain the initial degree of freedom values ​​of the first and second nanounits in each nanounit cell, and obtain the initial nanounit combination parameters corresponding to each nanounit cell.

[0059] Obtain the initial degrees of freedom values ​​of the two nanounits in each nanounit cell, determine the nanounit combination parameters of each nanounit cell, and determine the initial values ​​of the variation parameters used for adjustment.

[0060] Step S300: Based on the preset set of degrees of freedom of the target nanounit and the working wavelength of the incident light, adjust the initial nanounit combination parameters corresponding to each nanounit cell until the preset requirements are met, and determine the nanounit combination parameters corresponding to each nanounit cell based on the adjustment results.

[0061] The parameters are adjusted according to the set of degrees of freedom of the target nanounit and the working wavelength of the incident light until the preset conditions are met, so as to realize the functions related to the nanounits in the above-mentioned lens design, thereby determining the nanounit combination parameters corresponding to each nanocell.

[0062] The set of degrees of freedom of the aforementioned target nanounit includes the shape of the nanounit, the size of the nanounit, and the material of the nanounit; wherein, the target nanounit is a nanounit with an independently variable biaxial structure, such as the major axis and minor axis of an elliptical cylinder that can change independently, or the length and width of a cuboid that can change independently.

[0063] Step S400: Determine the degree of freedom values ​​of the first and second nanounits in each nanounit cell based on the nanounit combination parameters corresponding to each nanounit cell.

[0064] Finally, based on the combination parameters of the nanounits corresponding to each nanounit cell, the degree of freedom values ​​of the two nanounits in the nanounit cell are determined, thus completing the design of the lens.

[0065] In some embodiments, in step S300, the nanounit combination parameters corresponding to each nanocell are determined in the following manner: Based on the preset set of degrees of freedom of the target nanounit and the working wavelength of the incident light, numerical simulations are performed on the degrees of freedom values ​​of the first and second nanounits in the nanounit cell. The combination parameters of the nanounits corresponding to the nanounit cell are adjusted according to the results of the numerical simulation until the first and second nanounits in the nanounit cell can achieve the polarization conversion capability of a half-wave plate at the working wavelength of the incident light. The combination parameters of the nanounits corresponding to the nanounit cell are determined according to the adjustment results.

[0066] The set of degrees of freedom for the pre-defined target nanometer includes the shape, size, and material of the nanounit.

[0067] Based on the initial nanounit combination parameters corresponding to the nanounit cell, the operating wavelength of the incident light, and the degree set of the target nanounit, the target nanounit is determined by combining numerical simulation. That is, the nanounit needs to achieve the polarization conversion capability of a half-wave plate at the operating wavelength of the incident light. Finally, the nanounit combination parameters corresponding to each nanounit cell are determined.

[0068] In some embodiments, after determining the degree-of-freedom values ​​of the first and second nanounits in the nanounit cell, the method further includes: Numerical simulations were performed on the grating formed by the first and second nanounits in the nanounit cell. The positional relationship between the first and second nanounits was adjusted based on the results of the numerical simulation until both the first and second nanounits in the nanounit cell could achieve the polarization conversion capability of the half-wave plate and the far-field diffraction intensity of the grating met the preset requirements at the working wavelength of the incident light. The positional relationship between the first and second nanounits was determined based on the adjustment results.

[0069] After completing the design of the degrees of freedom of the first and second nanounits in the nanounit cell, it is necessary to optimize the positional parameters between the nanounit combinations, i.e., the distance between the center points of the two nanounits. The optimization method is to perform numerical simulation after combining them, simulating the far-field diffraction intensity after they form a grating. The optimization objective is to make the 0th order diffraction the weakest, the +1st and -1st order diffraction the strongest, and the +1st and -1st order diffraction intensities varying at different rotation angles. The values ​​below are roughly equal.

[0070] In some embodiments, parallel light rays can be converged to form a focused spot by designing the lens; the method further includes: Numerical simulations were performed using an experimental lens composed of several nanocells. The angular period of each nanocell was adjusted based on the simulation results until the shape of the focused spot formed by the convergence of parallel light through the experimental lens met the preset conditions. The angular period of each nanocell was then determined based on the adjustment results.

[0071] After arranging the nanocells into a ring lens, the angular period of each nanocell needs to be optimized. When optimizing the angular period of each cell (i.e. how many cells make up a ring structure), the angular period is adjusted by simulating the final focused spot shape. The optimization goal is to make the focusing intensity higher and the focal spot half-width smaller.

[0072] In some embodiments, parallel light rays can be converged to form a focused spot by designing the lens; the method further includes: Numerical simulations were performed using an experimental lens composed of several nanocells. The ratio of the inner and outer diameters of the annular region was adjusted based on the simulation results until the shape of the focused spot formed by the convergence of parallel light through the experimental lens met the preset requirements. The ratio of the inner and outer diameters of the annular region was then determined based on the adjustment results.

[0073] The ratio of the inner and outer diameters of the annular region of the lens designed in this application also needs to be optimized. Theoretically, a larger ratio of inner and outer diameters results in a smaller full width at half maximum (FWHM) of the focal spot, but at the same time, the transmitted light intensity is lower, leading to lower focusing efficiency. Therefore, optimization is needed to balance focusing efficiency and FWHM. Compared to the traditional structure of "objective lens + polarization converter + annular stop", a significant advantage of the lens design provided in this application is that we can achieve a very small FWHM with a small ratio of inner and outer diameters.

[0074] like Figure 8 As shown, Figure 8 This is a schematic diagram of the path for focusing light using different lenses, provided in an embodiment of this application. Figure 8 (a) in the diagram is a schematic diagram of the path of incident light with uniform intensity distribution being focused by the objective lens; Figure 8 (b) is a schematic diagram of the path of incident light with uniform intensity distribution focusing through the lens provided in this application; the size of the focused spot of a conventional lens depends on the numerical aperture of the focusing lens. ,in This refers to the maximum angle at which the lens focuses the light. The method of this invention achieves sub-diffraction focusing using radially polarized (RP) light. The core principle is to block light rays focused at small angles, allowing only light rays focused at large angles to pass through. Based on the characteristics of RP, large-angle light rays, after focusing, can form a symmetrical sub-diffraction focal spot. Therefore, in the design of the objective lens, for wide-field imaging, the path of light focusing generally satisfies the Abbe sine condition, which can be equivalent to […] under normal incidence. Figure 8 As shown in (a), when the lens is designed using an aberration-correcting design (the lens provided in this application), it satisfies... Figure 8 The tangent condition model is shown in (b) of the diagram. It can be seen that when the intensity of the incident light is uniformly distributed, the proportion of large-angle rays in the focused lens provided in this application will be greater than that of the objective lens, and this difference will become more pronounced as the NA increases.

[0075] like Figure 9 As shown, Figure 9 (a) is a schematic diagram showing the relationship between the angular radiative flux and the deflection angle obtained after the incident light is uniformly incident on the objective lens; Figure 9 (b) represents the angular radiant flux and deflection angle obtained after the incident light is uniformly incident on the lens provided in this application. A diagram illustrating the relationship between them; for this, let's assume... Let be the radial coordinates in a polar coordinate system with the lens center as the origin. The distribution of the amplitude of the incident light field across the lens aperture is the pupil function. ,but The corresponding radiation flux density at is Since all light rays are focused at the focal point, the angle of deflection is... It is also the polar angular coordinate of a spherical coordinate system with the focus as the origin. The radiant flux per unit angle is defined as the angular radiant flux density. Then, by the law of conservation of energy, we can obtain equations (3) and (4): (3) (4) in, and Here, represents the refractive index at the incident end and the refractive index at the exit end, respectively. The focal length of the lens. The projection function of light rays has different forms for the objective lens and the lens design provided in this application. Objective lens: = = Lens design: .

[0076] Assuming the incident light is uniformly incident, then The angular radiative flux densities of the objective lens and the superlens can be obtained as follows: and Ignoring the preceding factors, we can simply consider... and As shown in the figure, within the deflection angle (80°) range of the meta-lens we designed so far, we can already see a very significant difference in angular radiation flux.

[0077] like Figure 10 As shown, Figure 10 This is a schematic diagram showing the relationship between the minimum deflection angle of different lenses provided in the embodiments of this application and the ratio of the inner and outer diameters of the annular aperture and the radiant flux. Figure 10 (a) in the figure is a comparison of the ratio of the inner and outer diameters of the annular aperture required to achieve the corresponding minimum deflection angle for the objective lens and the lens designed in this invention, with the maximum deflection angle fixed at 79°. Figure 10Figure (b) shows a schematic diagram illustrating the ratio of radiant flux between the designed lens and the objective lens provided by this invention at different minimum deflection angles, with deflection angles ranging from 0 to 79°. As can be seen from the figure, to achieve the extremely narrow angle range (e.g., 78°-79°) required for RP sub-diffraction focusing, the ratio of the inner and outer diameters (annular factor) of the annular aperture required by the designed lens provided by this invention is much smaller than that of the objective lens. For example, to achieve an extremely narrow angle range of 78°-79°, the designed meta-lens only needs an annular factor of 0.915, while the objective lens needs an annular factor of 0.996. At the same aperture, the ratio of their radiant flux (i.e., the area of ​​the annular region) is 23.13, representing a difference of more than twenty times in energy. Furthermore, due to diffraction effects, the objective lens cannot actually achieve such a high annular factor.

[0078] like Figure 11 As shown, Figure 11 This is another schematic diagram illustrating the relationship between the minimum deflection angle of different lenses provided in the embodiments of this application and the ratio of the inner and outer diameters of the annular aperture and the radiant flux; Figure 11 In (a), the ratio of the inner and outer diameters of the annular aperture required to achieve the corresponding minimum deflection angle when the maximum deflection is 89° is given by the objective lens and the lens designed in this invention. Figure 11 Figure (b) shows the ratio of the radiation flux of the lens and objective lens provided by this invention under different minimum deflection angles, with the deflection angle ranging from 0 to 89°. As can be seen from the figure, in extreme cases, if the maximum deflection angle is set to 89°, which is close to the ultimate NA, the ratio of their radiation fluxes increases sharply as the angle range decreases. Since the maximum deflection angle corresponds to an infinitely large design lens area, the ratio of radiation fluxes should eventually approach infinity at the ultimate NA.

[0079] This application provides a lens design method, relating to the field of optical devices. The lens design method provided in this application can be applied to a terminal, a server, or software running on a terminal or server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or in-vehicle terminal, but is not limited to these. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the lens design method, but is not limited to the above forms.

[0080] The method described in this application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0081] The lens design method provided in this embodiment further optimizes the designed lens by combining numerical simulation methods: (1) Make the angular period (i.e. the number of nanocells) of the lens meet the preset requirements, so that the lens has higher focusing intensity, smaller focal spot half width, and higher focusing efficiency.

[0082] (2) The arrangement of several nanocells that make up the lens is in a ring shape, so that the ratio of the inner and outer rings of the ring region meets the preset requirements, thereby achieving a smaller focal spot half-width at half-maximum when the ratio of the inner and outer diameters is small, and achieving higher performance while further reducing the size of the structure.

[0083] (3) Optimize the positional relationship between nanounits in each nanocell within the lens so that the far-field diffraction intensity of the grating composed of nanounits in each nanocell meets the preset requirements, thereby improving the imaging performance of the lens.

[0084] In summary, the lens design method provided in this application can automate the simulation optimization of lenses by combining numerical simulation methods.

[0085] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of this application, and do not constitute a limitation on the technical solutions provided in this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in this application are also applicable to similar technical problems.

[0086] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0087] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0088] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0089] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0090] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0091] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0092] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0093] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0094] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0095] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A focusing lens that achieves the super Rayleigh limit, characterized in that, The function of the focusing lens is achieved by several devices; among them... When the function of the focusing lens is realized by a single device, the device that realizes the function of the focusing lens includes a designed lens composed of a number of nanocells arranged in an annular region; In the designed lens Each nanocell is formed by combining a first nanounit and a second nanounit with orthogonal rotation angles; the rotation angle of each nanounit satisfies a preset numerical relationship with the spatial azimuth angle, so that linearly polarized light forms a vector beam after passing through the designed lens; the vector beam is a beam with non-uniformly distributed polarization state on the cross-section; A plurality of nanocells are arranged radially along the annular region; the spacing between the plurality of nanocells satisfies a preset condition to ensure that the vector beams passing through the annular region converge at the same position to form a focused vector beam; the transverse wave vector distribution of the focused vector beam corresponding to the focusing plane optical field is annular; the range of the transverse wave vector of the corresponding focusing plane optical field satisfies a preset range.

2. The focusing lens according to claim 1, characterized in that, In the designed lens, the ratio between the rotation angle and the spatial azimuth angle of each nanounit is one-half.

3. The focusing lens according to claim 1, characterized in that, In the design lens, parallel light passing through the design lens converges at the design focal point; the spacing between each nanocell is calculated based on the operating wavelength of the incident light, the background refractive index, and the angle between the line connecting the nanocell position and the design intersection point and the normal direction.

4. The focusing lens according to claim 1, characterized in that, When the function of the focusing lens is implemented by three discrete devices, the devices that implement the function of the focusing lens also include a liquid crystal device or a preset polarization control device for generating a vector beam, an annular aperture for generating an annular beam, and a lens for focusing the beam.

5. The focusing lens according to claim 1, characterized in that, When the function of the focusing lens is implemented by two discrete devices; the devices that implement the function of the focusing lens also include a liquid crystal device or a preset polarization control device for generating a vector beam, and a preset planar diffraction lens; the preset planar diffraction lens is used to achieve single-ring or multi-ring focusing.

6. A lens design method, applied to a focusing lens as described in any one of claims 1 to 3, characterized in that, The design method is applied to the designed lens; the design method includes the following steps: Obtain the working wavelength of the incident light; Obtain the initial degree of freedom values ​​of the first and second nanounits in each nanounit cell to obtain the initial nanounit combination parameters corresponding to each nanounit cell; Based on the set of degrees of freedom of the preset target nanounit and the working wavelength of the incident light, the initial nanounit combination parameters corresponding to each nanounit cell are adjusted until the preset requirements are met, and the nanounit combination parameters corresponding to each nanounit cell are determined according to the adjustment results. The degree of freedom values ​​of the first and second nanounits in each nanounit cell are determined based on the nanounit combination parameters corresponding to each nanounit cell.

7. The method according to claim 6, characterized in that, The nanounit combination parameters corresponding to each nanocell are determined in the following manner: Based on the preset set of degrees of freedom of the target nanounit and the working wavelength of the incident light, numerical simulations are performed on the degrees of freedom values ​​of the first and second nanounits in the nanocell. The nanounit combination parameters corresponding to the nanocell are adjusted according to the results of the numerical simulation until both the first and second nanounits in the nanocell can achieve the polarization conversion capability of a half-wave plate at the working wavelength of the incident light. The nanounit combination parameters corresponding to the nanocell are determined according to the adjustment results.

8. The method according to claim 7, characterized in that, After determining the degrees of freedom values ​​of the first and second nanounits in the nanocell, the method further includes: Numerical simulation is performed on the grating formed by the first and second nanounits in the nanocell. The positional relationship between the first and second nanounits is adjusted according to the results of the numerical simulation until both the first and second nanounits in the nanocell can achieve the polarization conversion capability of a half-wave plate at the working wavelength of the incident light and the far-field diffraction intensity of the grating meets the preset conditions. The positional relationship between the first and second nanounits is determined according to the adjustment results.

9. The method according to claim 6, characterized in that, A focused spot is formed by converging parallel light through the designed lens; the method further includes: Numerical simulations were performed on an experimental lens composed of several nanocells. The angular period of each nanocell was adjusted according to the results of the numerical simulation until the shape of the focused spot formed by the convergence of parallel light through the experimental lens met the preset conditions. The angular period of each nanocell was determined according to the adjustment results.

10. The method according to claim 6, characterized in that, A focused spot is formed by converging parallel light through the designed lens; the method further includes: Numerical simulations were performed using an experimental lens composed of several nanocells. The ratio of the inner and outer diameters of the annular region was adjusted based on the simulation results until the shape of the focused spot formed by the convergence of parallel light through the experimental lens met the preset conditions. The ratio of the inner and outer diameters of the annular region was then determined based on the adjustment results.

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