Optical lens

Abstract

This optical lens is used for light in a prescribed object wavelength region. The optical lens comprises a substrate and a plurality of microstructures provided on a surface of the substrate. The plurality of microstructures are arranged at an interval shorter than the shortest wavelength in the object wavelength region. The interval differs depending on the position on the surface, in accordance with the size of a change in a phase profile of the optical lens.

Description

Optical Lenses

[0001] The present disclosure relates to optical lenses.

[0002] In recent years, research and development of metalenses, which have fine surface structures known as metasurfaces, has progressed. Metasurfaces are surfaces with metamaterial structures that realize optical functions not found in nature. Metalenses can achieve optical functions equivalent to those achieved by combining multiple conventional optical lenses with a single thin, flat structure. Therefore, metalenses can contribute to the miniaturization and weight reduction of lens-equipped devices, such as cameras, LiDAR sensors, projectors, and augmented reality (AR) displays. Examples of metalenses and devices using metalenses are disclosed in, for example, Patent Documents 1 and 2.

[0003] Patent Literature 1 discloses a metalens including a substrate and a plurality of nanostructures arranged on the substrate. In this metalens, each of the plurality of nanostructures produces an optical phase shift that varies depending on its position, and the optical phase shift due to each nanostructure defines the phase profile of the metalens. The optical phase shift of each nanostructure depends on the position of the nanostructure and the size or orientation of the nanostructure. Examples of nanostructures given include nanofins and nanopillars. Patent Literature 1 describes that a desired phase shift can be achieved by adjusting the angle at which each nanofin is arranged or the size of each nanopillar.

[0004] Patent Literature 2 discloses a miniaturized lens assembly including a metalens, and an electronic device including the same. The metalens disclosed in Patent Literature 2 includes a nanostructure array and is configured to form the same phase delay profile for at least two different wavelengths of light included in incident light. In this metalens, to achieve a desired phase delay profile, the width of each of the multiple internal pillars included in the nanostructure array is appropriately determined according to the required amount of phase delay.

[0005] JP 2019-516128 A JP 2021-71727 A

[0006] When designing a metalens, it is necessary to reproduce the ideal phase profile as accurately as possible. However, with conventional metalenses, it has been difficult to accurately reproduce the ideal phase profile, especially in areas where the phase profile changes sharply.

[0007] The present disclosure provides an optical lens that makes it easy to reproduce a desired phase profile.

[0008] An optical lens according to one aspect of the present disclosure is used for light in a predetermined target wavelength range, and includes a substrate and a plurality of microstructures provided on a surface of the substrate. The microstructures are arranged at intervals shorter than the shortest wavelength in the target wavelength range. The intervals vary depending on the position on the surface depending on the magnitude of change in the phase profile of the optical lens.

[0009] A general or specific aspect of the present disclosure may be realized as a system, an apparatus, a method, an integrated circuit, a computer program, or a recording medium such as a computer-readable recording disk, or as any combination of a system, an apparatus, a method, an integrated circuit, a computer program, and a recording medium. The computer-readable recording medium may include a non-volatile recording medium such as a CD-ROM (Compact Disc-Read Only Memory). An apparatus may be composed of one or more devices. When an apparatus is composed of two or more devices, the two or more devices may be located in a single device or may be located separately in two or more separate devices. In this specification and claims, the term "apparatus" may refer not only to a single device but also to a system consisting of multiple devices.

[0010] According to one aspect of the present disclosure, an optical lens that can easily reproduce a desired phase profile can be realized.

[0011] FIG. 1 is a perspective view schematically illustrating an example of a metalens. FIG. 2 is a perspective view schematically illustrating an example of the structure of a single unit cell. FIG. 3 is a diagram schematically illustrating the function of a metalens. FIG. 4A is a graph illustrating an example of an ideal phase profile. FIG. 4B is a diagram illustrating an example of a phase profile achieved by a conventional periodic arrangement. FIG. 4C is a diagram illustrating an example of a phase profile achieved by an embodiment of the present disclosure. FIG. 5 is a diagram illustrating unit cell spacing conditions for fabricating a metalens that achieves a desired phase profile. FIG. 6A is a diagram illustrating an example of an ideal phase profile. FIG. 6B is a diagram illustrating a phase profile wrapped in a phase range from -π to π. FIG. 6C is a diagram illustrating an example of sampling for achieving an ideal phase profile. FIG. 7 is a diagram illustrating an example of the relationship between the sampling number N and diffraction efficiency. FIG. 8 is a diagram schematically illustrating an example of a metalens. FIG. 9A is a diagram illustrating an ideal phase profile in an example. FIG. 9B is a diagram illustrating the distribution of derivatives of the phase profile shown in FIG. 9A. FIG. 9C is a diagram illustrating the distribution of upper limits of the spacing between microstructures. Figure 10 is a schematic cross-sectional view illustrating an example metalens with a light modulating layer. Figure 11 is a diagram illustrating an example metalens in which the light modulating layer includes a plurality of other microstructures.

[0012] Exemplary embodiments of the present disclosure will be described below. The embodiments described below are all comprehensive or specific examples. The numerical values, shapes, components, component placement and connection configurations, steps, and step order shown in the following embodiments are merely examples and are not intended to limit the present disclosure. Furthermore, among the components in the following embodiments, components that are not recited in the independent claims that represent the highest concepts will be described as optional components. Furthermore, each figure is a schematic diagram and is not necessarily an exact illustration. Furthermore, in each figure, the same or similar components are assigned the same reference numerals. Duplicate descriptions may be omitted or simplified.

[0013] In this disclosure, the term "light" is not limited to visible light (wavelength of about 400 nm to about 700 nm) but also refers to invisible light. Invisible light refers to electromagnetic waves within the wavelength range of ultraviolet light (wavelength of about 10 nm to about 400 nm), infrared light (wavelength of about 700 nm to about 1 mm), or radio waves (wavelength of about 1 mm to about 1 m). The optical lenses in this disclosure can be used not only for visible light but also for invisible light such as ultraviolet light, infrared light, or radio waves.

[0014] (Findings that Form the Basis of the Present Disclosure) First, an example of the basic configuration of an optical lens in the present disclosure and the findings of the present inventors will be described.

[0015] In the following description, optical lenses are also referred to as "metalens." A metalens is an optical element that has a plurality of microscopic structures on its surface that are smaller than the wavelength of incident light, and that achieves lens function by the phase shift caused by these microscopic structures. By appropriately designing the shape, size, orientation, and arrangement of each microscopic structure, it is possible to adjust the optical properties of incident light, such as the phase, amplitude, or polarization.

[0016] Figure 1 is a perspective view schematically illustrating an example of a metalens. The metalens 100 shown in Figure 1 includes a substrate 110 and a plurality of microstructures 120 provided on the surface of the substrate 110. In this example, each of the microstructures 120 is a columnar body (also called a "pillar") having a shape similar to a cylinder. A unit element in the metalens 100 that includes one microstructure 120 is called a "unit cell." The metalens 100 is an assembly of a plurality of unit cells.

[0017] 2 is a perspective view schematically illustrating an example of the structure of one unit cell. One unit cell includes a portion of a substrate 110 and one microstructure 120 protruding from the portion of the substrate 110. Each unit cell generates a phase shift in incident light according to the structure of the microstructure 120.

[0018] FIG. 3 is a diagram schematically illustrating the function of metalens 100. In FIG. 3, arrows indicate exemplary light rays. Metalens 100 in this example has the function of focusing incident light, similar to a conventional convex lens. In the example of FIG. 3, incident light entering from the substrate side of metalens 100 is focused by undergoing different phase changes depending on the position through the array of microstructures 120. The shape, width, height, orientation, and the like of each microstructure 120 are appropriately determined to achieve desired focusing characteristics. The structure of each microstructure 120 can be appropriately determined, for example, based on data indicating the phase profile to be achieved and the results of electromagnetic field simulations.

[0019] Each of the microstructures 120 has a subwavelength size (e.g., width and height) that is shorter than the wavelength of light incident on metalens 100, and may be arranged at subwavelength intervals or periods. The "spacing" of the microstructures 120 is the distance between the centers of two adjacent microstructures 120 when viewed in a direction perpendicular to the surface of substrate 110.

[0020] Metalens 100 may be designed to achieve desired optical properties for light in a predetermined target wavelength range. The target wavelength range may be, for example, a wavelength range defined by a specification. If the lower limit of the target wavelength range is, for example, 1 μm, the size and spacing of microstructures 120 may be set to a value less than 1 μm. Such microstructures with nanoscale sizes smaller than 1 μm are sometimes referred to as "submicron structures" or "nanostructures." If the target wavelength range is in the infrared region, the size and spacing of microstructures 120 may be greater than 1 μm.

[0021] The number of microstructures 120 provided on the surface of metalens 100 is determined to an appropriate number depending on the lens characteristics that are to be achieved. The number of microstructures 120 is, for example, in the range of 100 to 10,000, and in some cases may be less than 100 or more than 10,000.

[0022] Here, we will briefly explain an example of a conventional metalens design method. One conventional metalens design method is disclosed in, for example, Patent Document 2. In the method disclosed in Patent Document 2, a plurality of columnar microstructures are arranged at a constant period from the center of the lens toward the periphery. The width of the microstructures at each position is determined to an optimal value so as to achieve a desired phase delay amount. This achieves a phase profile in which the phase decreases from the center of the metalens toward the periphery.

[0023] However, according to the study by the present inventors, it was found that the above-mentioned method of changing the width of each microstructure while fixing the period may not be able to reproduce an ideal phase profile. In particular, it was found that it is difficult to achieve an ideal phase shift at a point where the phase changes sharply in the ideal phase profile, and that improvement is necessary.

[0024] This issue is thought to arise from the fact that, when all the microstructures are arranged at a fixed period, the number of microstructures near the edge of the lens is insufficient, making it impossible to obtain a sufficient phase shift. Given that the period (i.e., spacing) of the unit cells in the metalens is Δx, the wavelength of the incident light in free space is λ, and the numerical aperture is NA, the period Δx is determined from the sampling theorem to satisfy the following inequality (1):

[0025] When microstructures are arranged at a constant period Δx that satisfies this condition, the number of microstructures (i.e., the number of samples) tends to be excessive near the center of the lens, while the number of samples tends to be minimal near the edges. If only the minimum number of samples is used near the edges where the phase change is steep, the phase reproducibility near the edges becomes low, making it difficult to achieve the desired focusing characteristics. Furthermore, if the period of the microstructures is made sufficiently small to improve the phase reproducibility near the edges of the lens, the number of samples near the center becomes excessive. If the period of the microstructures is small and the number of samples becomes excessive, for example, the following problems may occur.

[0026] - Decreased processing accuracy - Reduced durability of the microstructure (for example, collapse of pillars) - Increased process variation due to increased microloading effect The above problems can become particularly pronounced when producing large-area lenses or rotationally asymmetric lenses.

[0027] The present inventors have identified the above-mentioned problems and have investigated optical lens configurations to solve the problems. As a result, they have discovered that the above-mentioned problems can be solved by changing the spacing between microstructures depending on the position in accordance with the ideal phase profile to be realized. The configurations of optical lenses according to embodiments of the present disclosure will be described below.

[0028] An optical lens according to an exemplary embodiment of the present disclosure is used for light in a predetermined target wavelength range. The optical lens includes a substrate and a plurality of microstructures provided on a surface of the substrate. The microstructures are arranged at intervals shorter than the shortest wavelength in the target wavelength range. The intervals are determined to vary depending on the position on the surface according to the phase profile that the optical lens is to achieve.

[0029] Here, the "target wavelength range" refers to the wavelength range of light in which the optical lens is intended to be used, and can be determined based on the specifications of the optical lens or the specifications of the device in which the optical lens is installed. The target wavelength range may include, for example, at least a portion of the visible light wavelength range (approximately 400 nm to approximately 700 nm). Alternatively, the target wavelength range may include at least a portion of the ultraviolet wavelength range (wavelengths of approximately 10 nm to approximately 400 nm). Alternatively, the target wavelength range may include at least a portion of the infrared wavelength range (approximately 700 nm to approximately 1 mm). Alternatively, the target wavelength range may include at least a portion of the radio wave wavelength range (wavelengths of approximately 1 mm to approximately 1 m). In one example, the target wavelength range may include at least a portion of the infrared wavelength range from 2.5 μm to 25 μm. The 2.5 μm to 25 μm wavelength range may be suitable for use in sensing devices that utilize infrared light, such as LiDAR sensors or infrared cameras. In this disclosure, the term "wavelength" refers to the wavelength in free space unless otherwise specified.

[0030] The substrate and each microstructure 120 may be made of a material that is translucent to light in the target wavelength range. Here, "translucent" means having the property of transmitting incident light with a transmittance of more than 50%. In some embodiments, the substrate 110 and each microstructure 120 may be made of a material that transmits light in the target wavelength range with a transmittance of 80% or more.

[0031] The "spacing" of the microstructures means the distance between the centers of two adjacent microstructures when viewed from a direction perpendicular to the surface of the substrate (hereinafter also referred to as the "lens surface"). If the shortest wavelength in the target wavelength range is, for example, 2.5 μm, the distance between the centers of any two adjacent microstructures among the multiple microstructures is shorter than 2.5 μm. Note that since the width of the microstructures is smaller than the spacing between the microstructures, the width of the microstructures is also shorter than the shortest wavelength in the target wavelength range.

[0032] The spacing between the microstructures is determined according to the phase profile that the optical lens is to achieve. The phase profile represents the distribution within the lens surface of the amount of phase shift of the outgoing light relative to the phase of the incoming light of the optical lens (hereinafter, sometimes simply referred to as "phase"). The phase profile can be expressed, for example, by a function of the phase with respect to the position within the lens surface or the distance from the optical axis. The phase indicated by the phase profile differs depending on the position within the lens surface. In this embodiment, the spacing between the microstructures is determined so as to differ depending on the position on the lens surface (e.g., the distance from the optical axis) according to the phase profile that is to be achieved.

[0033] The spacing between the microstructures varies depending on the derivative value with respect to the position of the phase indicated by the phase profile. For example, if the absolute value of the derivative value with respect to the position of the phase indicated by the phase profile at a first position on the surface of the substrate is greater than the absolute value of the derivative value with respect to the position of the phase at a second position on the surface, the spacing between the microstructures at the first position can be determined to be smaller than the spacing between the microstructures at the second position. In this way, the multiple microstructures can be arranged so that the spacing between the microstructures becomes smaller as the absolute value of the derivative value with respect to the position of the phase indicated by the phase profile becomes larger.

[0034] According to the above configuration, in areas where the phase change in the phase profile to be realized is steep, microstructures are arranged more densely than in areas where the phase change is gradual. This configuration makes it possible to more accurately reproduce an ideal phase profile in areas where the phase change is steep. It also makes it possible to prevent excessive arrangement of microstructures in areas where the phase change is gradual (e.g., the center). As a result, problems such as a decrease in the processing accuracy of the microstructures, a decrease in the durability of the microstructures, and an increase in process variation during manufacturing can be avoided.

[0035] The above effects will now be described in more detail with reference to FIGS. 4A to 4C.

[0036] 4A is a graph showing an example of an ideal phase profile. This phase profile represents the relative phase Φ as a function of the distance r from the optical axis (e.g., the central axis of the optical lens) at the lens surface. In this phase profile, the phase Φ decreases monotonically with increasing distance r.

[0037] 4B is a diagram showing an example of a phase profile realized by a conventional periodic arrangement. In this example, a plurality of microstructures 120 are periodically arranged. As shown in FIG. 4B, this configuration fails to reproduce an ideal phase change near the edge of the lens where the phase change is steep.

[0038] 4C is a diagram showing an example of a phase profile realized by an embodiment of the present disclosure. In the example shown in FIG. 4C, the microstructures 120 are arranged so that the spacing between the microstructures 120 is smaller in a region where the distance r from the optical axis is large. This improves the reproducibility of the phase profile, especially near the end where the distance r is large.

[0039] As described above, with the optical lens of this embodiment, the spacing between the microstructures 120 is appropriately determined according to the rate of change of the phase relative to the position indicated by the ideal phase profile. In particular, the microstructures 120 are arranged so that the spacing between the microstructures is small in areas where the phase change is steep. This makes it possible to more accurately reproduce the ideal phase profile, thereby improving the performance of the lens.

[0040] Next, a more specific example of a method for determining the interval between the microstructures 120 in accordance with the phase profile will be described.

[0041] Figure 5 is a diagram illustrating the conditions related to the spacing of unit cells for producing a metalens that achieves a desired phase profile. The upper diagram (a) in Figure 5 schematically shows how light incident on metalens 100 changes its path at the lens surface. The lower diagram (b) in Figure 5 is a schematic enlarged view of the area surrounded by the dashed circle in the upper diagram (a).

[0042] The ideal phase profile of metalens 100 that realizes the lens function is expressed, for example, by the following function Φ(r): where r is the distance from the optical axis, and a ｉ is a predetermined coefficient.

[0043] In the example of FIG. ｓ is incident on the metalens 100 from a medium (e.g., air) with a refractive index n at an incident angle θ ｉ and wave number k ｉ Metalens 100 may be used in conjunction with an image sensor, for example, in an imaging device. Metalens 100 may also be used in telescopes, microscopes, or scanning optical devices. ｉ is the wave number corresponding to the shortest wavelength λ in the target wavelength range, and the incident angle θ ｉis the maximum half angle of view of metalens 100 (i.e., the maximum angle of incidence of light that can be used in a device including metalens 100). The maximum angle of incidence of light here may be, for example, the maximum angle of view of a device such as an imaging device, telescope, or microscope that includes metalens 100, or the maximum scanning angle of a scanning optical device that includes metalens 100. Note that metalens 100 is not limited to these applications. The plurality of microstructures 120 may have a maximum K ０ The optical element is formed so as to give the incident light a wave number component (i.e., a spatial frequency component) of .gtoreq.1.

[0044] Maximum spatial frequency component K in the unit cell ０ The minimum sampling interval P required to provide is determined based on the sampling theorem. The sampling theorem states that the original signal can be restored by sampling at a frequency that is more than twice the maximum frequency contained in a continuous signal. According to the sampling theorem, the interval P can be determined so as to satisfy the following inequality (4).

[0045] Therefore, the spacing P(r) of the microstructures 120 at a position at a distance r from the optical axis can be determined to satisfy the following inequality:

[0046] By determining the position of each microstructure 120 so as to satisfy this inequality, it is possible to appropriately arrange each microstructure 120 according to the steepness of the phase. This improves the characteristics in regions where the phase change is steep, and improves the light collection efficiency. Furthermore, in areas where the rate of phase change is small, the spacing between the microstructures 120 can be made relatively large. This also provides the effects of improving processing accuracy during manufacturing, reducing processing time, and improving durability.

[0047] A more preferred arrangement of the microstructure 120 will now be described with reference to FIGS. 6A to 6C.

[0048] FIG. 6A shows an example of an ideal phase profile. FIG. 6B shows a phase profile wrapped in a phase range from −π to π. FIG. 6C shows an example of sampling for achieving an ideal phase profile. The black dots in FIG. 6C indicate examples of the positions of the microstructures 120 (i.e., sampling points). As shown in these figures, an appropriate number of microstructures 120 are arranged for each of the multiple sections wrapped between −π and π. According to the sampling theorem, two or more microstructures 120 are arranged for each continuous section from −π to π. In this example, the phase steepness (i.e., differential value) differs between the center and the edges of the lens. The rate of change of the phase Φ with respect to a change in position r is greater near the edges than near the center. Therefore, the spacing P2 between the microstructures 120 near the edges is smaller than the spacing P1 between the microstructures 120 near the center. By arranging the microstructures 120 in this manner, the ideal phase profile can be reproduced more accurately.

[0049] The more the number of microstructures 120 included in one continuous section from -π to π, i.e., the number of samples, is increased, the more the reproducibility of the phase profile improves. For example, by arranging three or more or four or more microstructures 120 in each section, the reproducibility of the phase profile can be further improved.

[0050] If the difference between the left and right sides of the above inequality (4) is small, the wrapping phase is reproduced at two points, which may result in low reproducibility. Therefore, we expand equation (4) to the following equation (6), where N is an integer equal to or greater than 2.

[0051] In this case, the interval P(r) between the microscopic structures 120 at a position at a distance r from the optical axis is determined so as to satisfy the following equation (7).

[0052] 7 is a diagram showing an example of the relationship between the sampling number N and the diffraction efficiency η. ２The relational expression (1 / N) is known. A practical diffraction efficiency is, for example, 80% or more. From FIG. 7, if N≧4, the diffraction efficiency is 80% or more. Therefore, N may be set to an integer of, for example, 4 or more. As an example, when N=4, the spacing P(r) of the microstructures 120 satisfies the following equation (8).

[0053] By arranging the microstructures 120 so as to satisfy the formula (8), it is possible to further suppress the deterioration of the light-collecting performance near the end where the phase change is steep.

[0054] Note that if the sampling number N is too large, as described above, undesirable problems such as a decrease in processing accuracy, a decrease in durability, or an increase in process variation during manufacturing may occur. For this reason, a lower limit may be set for the spacing P(r) of the microstructures 120. For example, the value on the right side of equation (7) when N = 8 or N = 10 may be set as the lower limit of P(r). As an example, when the value when N = 8 is set as the lower limit, the spacing P(r) of the microstructures 120 satisfies the following equation (9).

[0055] By arranging the microstructures 120 so as to satisfy the formula (9), problems such as a decrease in processing accuracy, a decrease in durability, or an increase in process variations during manufacturing can be effectively suppressed.

[0056] The spacing P(r) of the microstructures 120 may be determined so as to satisfy both Equation (8) and Equation (9). Such a configuration can achieve both an ideal phase profile near the edge of the lens and advantages in manufacturing.

[0057] (Examples) Next, examples of the metalens 100 will be described.

[0058] FIG. 8 is a schematic diagram illustrating an example of a metalens 100. In this example, the substrate 110 and the plurality of microstructures 120 are made of the same material. The substrate 110 and each microstructure 120 are made of a material primarily composed of silicon with a (100) crystal plane orientation. The silicon may also have a (110) or (111) crystal plane orientation. Alternatively, a material other than silicon may be used.

[0059] The thickness of the substrate 110 of the metalens 100 is 500 μm. The shape of the substrate 110 is square, as shown in FIG. 1 , and its size is 8 mm × 8 mm. A plurality of microstructures 120 are arranged within a circular region with a diameter of 8 mm on the surface of the substrate 110. FIG. 8 schematically shows a cross section of a certain portion of the metalens 100.

[0060] Each of the microstructures 120 shown in FIG. 8 is a cylindrical pillar. The target wavelength is 10.6 μm. The width D of each microstructure 120 is determined within a range of 1 μm to 3 μm according to the target value of the phase at that position. The height of each microstructure 120 is 7 μm. The maximum angle of view of the metalens 100 is ±30° (i.e., the maximum half angle of view is 30°). The microstructures 120 are arranged two-dimensionally as shown in FIG. 1. The microstructures 120 are periodically arranged from the center to the edge at intervals that satisfy the above formula (5). Note that these numerical values ​​are merely examples and may be adjusted as appropriate depending on the application or purpose of the metalens 100.

[0061] The metalens 100 can be fabricated using common semiconductor manufacturing techniques such as lithography. For example, the metalens 100 can be fabricated by the following method. First, a silicon substrate having a main crystal plane oriented in the (100) plane is prepared as the substrate 110. Next, a positive resist is applied to the main surface of the silicon substrate by a method such as spin coating. Next, light or an electron beam is irradiated at desired locations, and then a development process is performed. This removes the resist from the locations irradiated with light or an electron beam. This silicon substrate is then irradiated with SF ６The etching is performed using a reactive ion etching technique or the like using an etching gas such as a gas. This etches the main surface of the silicon substrate where the resist has been removed. Then, a wet process using a resist remover or the like is performed. ２ Resist remaining on the main surface of the silicon substrate is removed by a dry process such as ashing. Through these steps, metalens 100 having substrate 110 and each of microstructures 120 can be produced.

[0062] FIG. 9A shows an ideal phase profile in this example. FIG. 9B shows the distribution of differential values ​​of the phase profile shown in FIG. 9A. FIG. 9C shows the distribution of the upper limit of the spacing between the microstructures 120. In each of these figures, the upper diagram shows the two-dimensional distribution of each value within the lens surface, and the lower diagram shows its dependence on the coordinate r, which indicates the distance from the optical axis within the lens surface. FIG. 9B shows the distribution of values ​​obtained by inverting the sign of the absolute value of the value obtained by differentiating the ideal phase profile Φ(r) with respect to the coordinate r. As shown in FIG. 9B, the phase change becomes steeper as one approaches the edge of the lens. For this reason, as shown in FIG. 9C, the spacing between the microstructures 120 is set to a smaller value as one approaches the edge of the lens. In the example shown in FIG. 9C, the spacing between the microstructures 120 is determined to be smaller than 11 μm near the center of the lens and smaller than 4 μm near the edge of the lens. In this way, the microstructures 120 are arranged more densely in areas where the phase change is steeper. This structure makes it possible to achieve characteristics close to an ideal phase profile.

[0063] (Modifications) Next, modifications of the metalens 100 will be described.

[0064] In the above embodiment, each microstructure 120 is a convex body having a cylindrical shape, but each microstructure 120 may have a shape other than a cylindrical shape. For example, each microstructure 120 may be a columnar body having an elliptical cylinder or polygonal prism shape other than a cylindrical shape. Alternatively, each microstructure 120 may be a pyramidal body having an elliptical cone (including a circular cone) or a polygonal pyramid shape. Furthermore, each microstructure 120 is not limited to a convex body, but may also be a concave body. The convex or concave body constituting the microstructure 120 may have any structure, such as a columnar body having an elliptical cylinder or polygonal prism shape, or a pyramidal body having an elliptical cone or polygonal pyramid shape.

[0065] In the above example, the substrate 110 and each of the plurality of microstructures 120 are made of the same material, but they may also be made of different materials. To suppress unwanted reflection or refraction between the substrate 110 and the array of the plurality of microstructures 120, the difference between the refractive index of the substrate 110 and the refractive index of each of the plurality of microstructures 120 may be, for example, 10% or less, 5% or less, or 3% or less of the smallest refractive index of the refractive index of the substrate 110 and the refractive index of each of the plurality of microstructures.

[0066] The substrate 110 and each of the microstructures 120 may be made of a material primarily composed of at least one selected from the group consisting of silicon, germanium, chalcogenide, chalcohalide, zinc sulfide, zinc selenide, fluoride compounds, thallium halide, sodium chloride, potassium chloride, potassium bromide, cesium iodide, and plastic (e.g., polyethylene). Here, the term "primary component" refers to the component that is contained in the material in the highest proportion, expressed in mole percent. When the substrate 110 and each of the microstructures 120 are made of such materials, the transmittance of infrared light in the range of 2.5 μm to 25 μm can be increased.

[0067] In order to improve transmittance, an AR (Anti-Reflection) functional film may be additionally formed. In addition to the AR functional film, various light modulation layers having a light modulation function may be provided on metalens 100.

[0068] FIG. 10 is a schematic cross-sectional view showing an example of a metalens 100 including a light modulation layer 130. In this example, the metalens 100 includes a light modulation layer 130 having a light modulation function on the surface of the substrate 110 opposite the surface on which the microstructures 120 are provided. The light modulation layer 130 may have an anti-reflection function for incident light, or may have other functions. For example, the light modulation layer 130 may function as a high-pass filter, low-pass filter, or band-pass filter that transmits only light in a target wavelength range. Alternatively, the light modulation layer 130 may be a polarization filter that transmits only specific polarizations of incident light. The light modulation layer 130 may also be a filter that attenuates or amplifies the transmission intensity of incident light in a specific wavelength range. The light modulation layer 130 may be an ND (Neutral Density) filter. The light modulation layer 130 may have a function of refracting incident light at a specific angle. The light modulation layer 130 may be composed of a single layer or multiple layers depending on the desired light modulation function. The light modulation layer 130 can be formed using a film formation method such as vacuum deposition or sputtering.

[0069] FIG. 11 shows an example of a metalens 100 in which the light modulation layer 130 includes a plurality of other microstructures 140 that are different from the microstructures 120. In this example, an array of microstructures 120 is provided on one surface of the substrate 110, and an array of other microstructures 140 is provided on the opposite surface of the substrate 110. Each of the other microstructures 140 may be a convex or concave body. The convex or concave body may be, for example, a cone having the shape of an elliptical cone or a polygonal pyramid, or a column having the shape of an elliptical cylinder or a polygonal cylinder. The shape, size, and arrangement of the other microstructures 140 may be different from the shape, size, and arrangement of the microstructures 120. The other microstructures 140 can be fabricated using a method similar to the fabrication process for each microstructure 120 described in the above example. By providing an array of microstructures (i.e., a metasurface) on both sides of the substrate 110, as in this example, it becomes easier to achieve a lens function that would be difficult to achieve using only one side.

[0070] The optical lenses of the present disclosure are widely applicable to devices that utilize lenses, such as cameras, LiDAR sensors, projectors, AR displays, telescopes, microscopes, or scanning optical devices.

[0071] 100 Metalens 110 Substrate 120 Microstructure 130 Light modulation layer 140 Microstructure

Claims

1. An optical lens for use with light in a predetermined target wavelength range, A substrate; A plurality of microstructures provided on a surface of the substrate; Equipped with the plurality of microstructures are arranged at intervals shorter than the shortest wavelength in the target wavelength range, the spacing varies with position on the surface depending on the magnitude of the change in the phase profile of the optical lens; Optical lens.

2. The optical lens according to claim 1 , wherein the interval varies depending on a differential value with respect to a position of the phase indicated by the phase profile.

3. 3. The optical lens of claim 2, wherein when an absolute value of the differential value of the phase indicated by the phase profile at a first position on the surface is greater than an absolute value of the differential value at a second position on the surface, the spacing of the microstructures at the first position is smaller than the spacing of the microstructures at the second position.

4. The distance from the optical axis on the surface is r, the function of the phase shown by the phase profile with respect to the distance r is Φ(r), the shortest wavelength in the target wavelength range is λ, the refractive index of the medium surrounding the optical lens is n, and the maximum angle of view of the optical lens is ±θ ｉ Then, the interval P(r) of the microstructure at a position of distance r is expressed as follows: [0010] The optical lens according to claim 1 , which satisfies the following:

5. The interval P(r) is [0025] The optical lens according to claim 4 , which satisfies the following:

6. The interval P(r) is [0030] The optical lens according to claim 4 , which satisfies the following:

7. 7. The optical lens according to claim 1, wherein each of the plurality of microstructures is a convex body or a concave body, and the convex body or the concave body is a pyramid body having an elliptical cone or a polygonal pyramid shape, or a columnar body having an elliptical cylinder or a polygonal cylinder shape.

8. The optical lens according to claim 1 , wherein the substrate and each of the plurality of microstructures are translucent to light in the target wavelength range.

9. 7. The optical lens according to claim 1, wherein the difference between the refractive index of the substrate and the refractive index of each of the plurality of microstructures is 10% or less of the smallest refractive index among the refractive index of the substrate and the refractive index of each of the plurality of microstructures.

10. The optical lens according to claim 1 , wherein the substrate and each of the plurality of microstructures are made of the same material.

11. 7. The optical lens of claim 1, wherein the wavelength range of interest includes at least a portion of the infrared wavelength range from 2.5 μm to 25 μm.

12. 7. The optical lens according to claim 1, wherein the substrate and each of the plurality of microstructures are made of a material containing at least one selected from the group consisting of silicon, germanium, chalcogenide, chalcohalide, zinc sulfide, zinc selenide, a fluoride compound, thallium halide, sodium chloride, potassium chloride, potassium bromide, cesium iodide, and plastic as a main component.

13. The optical lens according to claim 1 , wherein the optical lens is made of a material containing silicon as a main component, and the crystal plane orientation of the silicon is (100), (110), or (111).

14. The optical lens according to claim 1 , further comprising a light modulating layer having a light modulating function on a surface of the substrate opposite to the surface.

15. the light modulating layer includes a plurality of other microstructures; The optical lens according to claim 14, wherein each of the other plurality of microstructures is a convex body or a concave body, and the convex body or the concave body is a pyramid having an elliptical cone or a polygonal pyramid shape, or a columnar body having an elliptical cylinder or a polygonal cylinder shape.

16. The optical lens according to claim 14 , wherein the light modulation layer has an anti-reflection function for incident light.

17. The optical lens according to claim 14 , wherein the light modulation layer functions as any one of a high-pass filter, a low-pass filter, and a band-pass filter that transmits only light in the target wavelength range.

18. The optical lens according to claim 14 , wherein the light modulation layer has a function of transmitting only a specific polarized light of incident light.

19. The optical lens according to claim 14 , wherein the light modulation layer has a function of attenuating or amplifying the transmission intensity of incident light in a specific wavelength range.

20. The optical lens according to claim 14 , wherein the light modulation layer has a function of refracting incident light at a specific angle.

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