Meta-lens, method for manufacturing same, and lighting device

Abstract

Provided is a meta-lens capable of converting a beam profile from a Gaussian distribution to a top hat distribution by a nanostructure in only one main surface of a substrate. A meta-lens (1) is configured such that a plurality of nano-sized pillars (3) are provided on one main surface of a light-transmitting substrate (2). The pillars (3) positioned further on an inner side than a distance r from the optical center are typically arranged such that a change in a cross-section thereof is represented by a function that satisfies three specific conditions.

Description

Metalens, manufacturing method thereof, and lighting device

[0001] The present invention relates to a metalens, a method for manufacturing the same, and a lighting device.

[0002] Illumination for pathological diagnosis and the like generally requires a wide illumination range and a high and uniform intensity distribution. Furthermore, a laser or a light-emitting diode is used as the light source for such illumination. Light emitted from such light sources is typically a Gaussian beam having a radiant intensity distribution with a Gaussian distribution. Therefore, in the above illumination, it is required to convert the beam profile of the light emitted from the light source from a Gaussian distribution to a top-hat profile having a substantially uniform radiant intensity distribution.

[0003] The conversion of the beam profile from a Gaussian to a top-hat profile can be achieved by an optical system including an aspheric lens, but illumination devices in compact devices such as endoscopes require more compact optical systems to convert the beam profile.

[0004] A known technique for converting a beam profile using such a compact optical system is to place a double-sided metalens, which has pillars on both the incident and output principal surfaces, in the optical path of light emitted from a light source. In this technique, the nanostructure on the input side collimates the light emitted from the light source, and the nanostructure on the output side controls the radiation angle of the emitted light (see, for example, Patent Document 1).

[0005] US Patent Application Publication No. 2023 / 0258316

[0006] However, in the conventional technology described above, it is necessary to form nanostructures with different functions on both main surfaces of the substrate in order to control the emitted light, and there is still room for further study from the perspective of controlling the beam profile by forming nanostructures on only one main surface of the substrate.

[0007] One aspect of the present invention aims to provide a metalens that can convert a beam profile from a Gaussian distribution to a top-hat distribution using nanostructures on only one main surface of a substrate.

[0008] In order to solve the above problems, a metalens according to one aspect of the present invention is a metalens comprising an optically transparent substrate and a plurality of optically transparent nano-sized pillars arranged on one main surface of the substrate, wherein, when the optical center of the metalens is taken as the origin, the area S of each of the pillars located at a distance r from the optical center is expressed by a function S(r) that satisfies the following three conditions: (1) it is continuous in the range -r0≦r≦r0 (r0>0); (2) it has a minimum value at r=0; and (3) it has a maximum value at r=±r1 (0<r1<r0).

[0009] Alternatively, in order to solve the above-mentioned problems, a metalens according to one aspect of the present invention is a metalens comprising an optically transparent substrate and a plurality of optically transparent nano-sized pillars arranged on one main surface of the substrate, wherein, when the optical center of the metalens is taken as the origin, the area occupancy Σ of the pillars at a point a distance r from the optical center is expressed by a function Σ(r) that satisfies the following three conditions: (1) it is continuous in the range -r0≦r≦+r0 (r0>0); (2) it has a minimum value at r=0; and (3) it has a maximum value at r=±r1 (0<r1<r0).

[0010] In order to solve the above-described problems, an illumination device according to one aspect of the present invention includes a light source that emits a Gaussian beam, and the above-described metalens that is disposed in the optical path of the light emitted from the light source.

[0011] In order to solve the above-mentioned problems, a method for manufacturing a metalens according to one aspect of the present invention comprises arranging optically transparent pillars on one main surface of an optically transparent substrate so that the phase distribution of light transmitted through the metalens is the sum of a first phase distribution of a lens that converts a specific Gaussian beam into collimated light and a second phase distribution of a metasurface that converts the beam profile of the collimated light of the specific Gaussian beam into a top-hat shape.

[0012] According to one aspect of the present invention, it is possible to provide a metalens that can convert a beam profile from a Gaussian distribution to a top-hat distribution using nanostructures on only one main surface of a substrate.

[0013] FIG. 1 is a schematic diagram illustrating the configuration of a metalens according to one embodiment of the present invention; FIG. 2 is a diagram illustrating the arrangement of pillars in a metalens according to one embodiment of the present invention; FIG. 3 is a diagram illustrating an example of the distribution of pillar widths in a metalens according to one embodiment of the present invention; FIG. 4 is a diagram illustrating an example of the distribution of pillar cross-sectional areas in a metalens according to one embodiment of the present invention; FIG. 5 is a diagram illustrating an example of the distribution of pillar area occupancy in a metalens according to one embodiment of the present invention; FIG. 6 is a diagram illustrating an example of the radiant intensity distribution of laser light irradiating a metalens according to one embodiment of the present invention; FIG. 7 is a diagram illustrating the beam shape related to a metalens according to one embodiment of the present invention; and FIG. 8 is a diagram illustrating an example of a continuous phase distribution (unwrap phase distribution) and a phase distribution folded into the range of 0 to 2π (wrap phase distribution) obtained by (1) a spherical lens for collimated light (SL), (2) a Gaussian-top-hat transformation metasurface (GTBS), and (3) a sum of them (GTBS+SL) when the numerical aperture of the light source is NA=0.22 and the top-hat beam divergence angle θ=5°. 8 is a diagram showing an example of the relationship between the distance from the optical center of the metalens and the width of the pillar when square pillars of the same height are arranged according to the wrap phase distributions of (1) SL, (2) GTBS, and (3) GTBS+SL in FIG. 8. Also shown is an example of the relationship between the distance from the optical center of the metalens and the cross-sectional area of ​​the pillar when square pillars of the same height are arranged according to the wrap phase distributions of (1) to (3) in FIG. 8. Also shown is an example of the relationship between the distance from the optical center of the metalens and the area occupancy of the pillar when square pillars of the same height are arranged according to the wrap phase distributions of (1) to (3) in FIG. 8. Also shown is an example of the relationship between the distance from the optical center of the metalens and the radius of the pillar when cylindrical pillars of the same height are arranged according to the wrap phase distributions of (1) to (3) in FIG. FIG. 9 is a diagram showing an example of the relationship between the distance from the optical center of a metalens and the cross-sectional area of ​​the pillars when cylindrical pillars of the same height are arranged according to the wrap phase distributions (1) to (3) of FIG. 8. FIG. 10 is a diagram showing an example of the relationship between the distance from the optical center of a metalens and the area occupancy of the pillars when cylindrical pillars of the same height are arranged according to the wrap phase distributions (1) to (3) of FIG.15A and 15B are diagrams showing an example of the unwrap phase distribution and wrap phase distribution of GTBS+SL when NA=0.1, 0.2, or 0.3 and θ=5°. 15B are diagrams showing an example of the relationship between the distance from the optical center and the width of the pillar when square pillars of the same height are arranged according to the wrap phase distribution of FIG. 15A. 15C are diagrams showing an example of the relationship between the distance from the optical center and the area occupancy of the pillar when square pillars of the same height are arranged according to the wrap phase distribution of FIG. 15A. 15C are diagrams showing an example of the wrap phase distribution of SL, GTBS, and GTBS+SL when NA=0.1 and θ=15°. 15C are diagrams showing an example of the wrap phase distribution of GTBS+SL when NA=0.1, 0.2, 0.3, or 0.4 and θ=15°. 15C are diagrams showing a schematic configuration of a lighting device according to one embodiment of the present invention. 15D are diagrams showing the results of measuring the beam intensity of the metalens (GTBS+SL) of Example 1. FIG. 1 shows the results of measuring the beam intensity of the GTBS metasurface of Comparative Example 1. FIG. 2 shows the relationship between the distance from the optical center and the area occupancy of the pillars in the metalens of Example 2. FIG. 3 shows the distribution of beam intensity in the x-z plane of the metalens of Example 2. FIG. 4 shows the distribution of beam intensity at a specific transmission distance in the metalens of Example 2. FIG. 5 shows the relationship between the distance from the optical center and the area occupancy of the pillars in the GTBS metasurface of Comparative Example 2. FIG. 6 shows the distribution of beam intensity in the x-z plane of the metalens of Comparative Example 2. FIG. 7 shows the distribution of beam intensity at a specific transmission distance in the metalens of Comparative Example 2. FIG. 8 shows the relationship between the distance from the optical center and the area occupancy of the pillars in the metalens of Example 3. FIG. 9 shows the distribution of beam intensity in the x-z plane of the metalens of Example 3. FIG. 10 shows the distribution of beam intensity at a specific transmission distance in the metalens of Example 3. FIG. 11 shows the relationship between the distance from the optical center and the area occupancy of the pillars in the GTBS metasurface of Comparative Example 3. FIG. 12 shows the distribution of beam intensity in the x-z plane of the metalens of Comparative Example 3. FIG. 13 shows the distribution of beam intensity at a specific transmission distance in the metalens of Comparative Example 3.

[0014] [Metalens] An embodiment of the present invention will now be described. Fig. 1 is a diagram schematically illustrating the configuration of a metalens according to an embodiment of the present invention. Fig. 2 is a diagram illustrating the arrangement of pillars in a metalens according to an embodiment of the present invention. As shown in Fig. 1, metalens 1 is composed of an optically transparent substrate 2 and a plurality of optically transparent nano-sized pillars 3. Substrate 2 is, for example, a circular flat plate when viewed from above.

[0015] The pillars 3 are disposed over the entirety of one principal surface of the substrate 2. In this embodiment, the one principal surface of the substrate 2 is microscopically divided into lattice-like unit sections, with one pillar 3 disposed in each unit section. The pillars 3 are disposed in each unit section in an appropriate form depending on the position of the unit section on the principal surface and the optical properties required of the metalens 1.

[0016] Furthermore, apart from the above-mentioned unit sections, one main surface of the substrate 2 is macroscopically divided into a circular central portion 10 and an annular peripheral portion 20 surrounding it, as shown in FIG. 2. In this embodiment, the peripheral portion 20 is divided from the inside into a first peripheral portion 21, a second peripheral portion 22, ..., and an nth peripheral portion 2n, all of which are annular. n represents the order of the annular peripheral portions when counting from the central portion 10, and is a positive integer equal to or greater than 1. As the diameter of the metalens increases, n also generally increases. For example, when the diameter of the metalens is 50 μm, n can be 3. In this case, as shown in FIG. 2, the peripheral portion is represented by a triple annular region.

[0017] In this embodiment, when the optical center of the metalens (e.g., the center of the central portion 10) is taken as the origin, the area S of each pillar 3 located at a point that is a distance r from the optical center can be expressed by a function S(r) that satisfies the following three conditions. Alternatively, in this embodiment, the area occupancy Σ of the pillar 3 at a point that is a distance r from the optical center can be expressed by a function Σ(r) that satisfies the following three conditions. Alternatively, in this embodiment, the width W of the pillar 3 at a point that is a distance r from the optical center can be expressed by a function W(r) that satisfies the following three conditions: (1) It is continuous in the range −r0≦r≦r0 (r0>0). (2) It has a minimum value at r=0. (3) It has a maximum value at r=±r1 (0<r1<r0).

[0018] The "area of ​​the pillar" may be any representative value of the size of the area that the pillar occupies on the main surface of the substrate. For example, the area of ​​the pillar may be the area when the pillar is projected onto the main surface along the optical axis. In this case, if the pillar has a cylindrical shape, the area of ​​the pillar may be the base area or cross-sectional area of ​​the pillar. In the following description, an embodiment of the present invention will be described using an example in which the pillar has a square prism or a cylinder shape, and the area of ​​the pillar will be described as the cross-sectional area of ​​the pillar.

[0019] Fig. 3 is a diagram showing an example of the distribution of pillar widths in a metalens according to this embodiment, Fig. 4 is a diagram showing an example of the distribution of pillar cross-sectional areas in a metalens according to this embodiment, and Fig. 5 is a diagram showing an example of the distribution of pillar area occupancy rates in a metalens according to this embodiment. Figs. 3 to 5 show an example of a metalens in which n in Fig. 2 is 3. Note that in the metalens 1 of this embodiment, the center-to-center distance between adjacent pillars 3 is constant, and the height of the pillars 3 is also constant. Furthermore, in this specification, "pillar area occupancy rate" refers to the ratio Sp / Su of the pillar cross-sectional area Sp to the area Su of a unit section of the substrate.

[0020] FIG. 3 shows a phase distribution (also referred to as a "wrap phase distribution") folded (or wrapped) in the range of 0 to 2π. In the folded phase distribution, a discontinuous step of 2π occurs. The first peripheral portion 21 to the third peripheral portion 23 correspond to the phase folding. As shown in FIG. 3, the pillar width in the central portion 10 continuously changes from a minimum value at the optical center to a maximum value outside of that. From the central portion 10 to the first peripheral portion 21, from the first peripheral portion 21 to the second peripheral portion 22, and from the second peripheral portion 22 to the third peripheral portion 23, the pillar width discontinuously increases. In each of the first peripheral portion 21, the second peripheral portion 22, and the third peripheral portion 23, the pillar width continuously decreases from the inside to the outside.

[0021] As shown in Figure 4, the distribution of pillar cross-sectional areas in the metalens varies in a similar manner to the distribution of pillar widths described above with respect to Figure 3. Also, as shown in Figure 5, the distribution of pillar area fractions in the metalens varies in a similar manner to the distribution of pillar widths described above with respect to Figure 3.

[0022] The metalens of this embodiment has the above-described pillar arrangement (distribution) characteristics, and is therefore able to output incident Gaussian beam light as a light beam having a substantially top-hat beam profile. This will be explained in more detail in the Examples below. A method for manufacturing the metalens of this embodiment will be described below.

[0023] [Method of Manufacturing a Metalens] The metalens of the present embodiments can be manufactured by arranging optically transparent pillars on one major surface of an optically transparent substrate so that the phase distribution of light transmitted through the metalens is a phase distribution that is the sum of a specific first phase distribution and a specific second phase distribution.

[0024] Here, the incident light that is set when designing a metalens will be described. Figure 6 is a diagram showing an example of the radiant intensity distribution of a laser beam that irradiates a metalens according to this embodiment. As shown in Figure 6, the laser beam is a Gaussian beam, and has a radiant intensity distribution with a Gaussian distribution.

[0025] FIG. 7 is a diagram illustrating the beam shape related to the metalens according to this embodiment. Laser light emitted from a laser, which is a light source, has a divergence angle α, as shown in FIG. 7 . α is expressed as "n × sin α," where NA is the numerical aperture of the light source (a laser, or an optical element such as a lens or optical fiber associated with the light-emitting device), and n is the refractive index of the medium of the optical element associated with the light-emitting device. Furthermore, a Gaussian beam that passes through an optical element that converts the laser light into a top-hat beam profile, and that is arranged on the optical path of the laser light, may have a top-hat beam divergence angle θ that is different from the aforementioned α.

[0026] The first phase distribution is a phase distribution of a lens that converts a specific Gaussian beam into collimated light, and is expressed, for example, by the following formula (1): In formula (1), x represents the distance from the optical axis of the lens on the x-axis perpendicular to the optical axis, y represents the distance from the optical axis on the y-axis perpendicular to both the optical axis and the x-axis, and f represents the focal length of the lens.

[0027]

[0028] Although Equation (1) represents the phase distribution when the lens is a spherical lens, the first phase distribution is not limited to the phase distribution of a spherical lens. The first phase distribution can be determined depending on the conditions of the incident light, and may be any phase distribution of a lens that converts the incident light into collimated light. For this reason, the first phase distribution may be the phase distribution of an aspherical lens.

[0029] The second phase distribution is a phase distribution of a metasurface that converts the beam profile of collimated light of a specific Gaussian beam into a top-hat shape, and is expressed by the following equation (2), which is described, for example, in Xin Tan et al., "Diffractive phase elements for beam shaping: a new design method," APPLIED OPTICS, Vol. 34, No. 8, 10 March 1995, p. 1317. In equation (2), r is the distance from the optical axis of the metasurface, λ is the wavelength of the specific Gaussian beam, D is the diameter of the metasurface, w1 is the beam waist diameter of the specific Gaussian beam, w2 is the beam diameter of a beam having a substantially uniform intensity distribution, l is the propagation distance, and ξ is the radial distance from the origin of the metasurface.

[0030]

[0031] For convenience, among optical elements having pillars, the one in this embodiment will be referred to as a "metalens," and the others will be referred to as "metasurfaces."

[0032] Adding the first and second phase distributions together yields a phase distribution that satisfies the aforementioned conditions 1 to 3. Figure 8 shows examples of (1) the phase distribution of a spherical lens (SL) for collimated light, (2) the phase distribution of a Gaussian-to-top-hat transformation metasurface (GTBS), and (3) the phase distribution of their sum (GTBS + SL) when the numerical aperture NA of the light source is 0.22 and the divergence angle θ (on the top-hat beam side) is 5°.

[0033] The top three figures in Fig. 8 all show continuous phase distributions (unwrap phase distributions), and the bottom three figures all show phase distributions folded into the range of 0 to 2π (wrap phase distributions). The two figures on the left side of Fig. 8 show the unwrap and wrap phase distributions of SL, the two figures in the middle show the unwrap and wrap phase distributions of GTBS, and the two figures on the right side show the unwrap and wrap phase distributions of GTBS+SL (i.e., for this embodiment). In the phase distribution of GTBS+SL, a curve that satisfies the three conditions described above is present in the center.

[0034] In addition, the phase distribution diagrams in this embodiment are diagrams in which the phase delay is shown as positive unless otherwise specified.

[0035] In the manufacture of the metalens of this embodiment, a plurality of optically transparent pillars are then disposed on one major surface of the substrate. The positions of the pillars are the unit sections of the substrate described above. The size of the pillars to be disposed in the unit sections can be determined based on the phase distribution of GTBS+SL. For example, if the pillars are shaped like regular square prisms and have a constant height, pillars having a cross-sectional area corresponding to the phase shift amount at that position are disposed in the unit sections. In this manner, in the above case, the cross-sectional area of ​​the pillars to be disposed in the unit sections is determined based on the correlation between the cross-sectional area of ​​the pillars and the phase shift amount.

[0036] For example, in the case of pillar cross-sectional area, the correlation is calculated by using pillars of a single shape (such as a square pillar) and scanning the pillar height and pillar cross-sectional area for transmittance, and scanning the pillar height and pillar cross-sectional area for phase shift. Based on these results, the correlation between the phase shift and pillar cross-sectional area when the height is constant can be calculated. Similar to the cross-sectional area of ​​the pillar, this correlation can also be calculated for information about pillar size other than the cross-sectional area, such as pillar height, pillar width, or pillar area occupancy.

[0037] 9 shows an example of the relationship between the distance from the optical center of the metalens and the "width" of the pillars when square pillars of the same height are arranged according to the (1) SL wrap phase distribution, (2) GTBS wrap phase distribution, and (3) GTBS+SL wrap phase distribution in FIG. 8 . In FIG. 9 , the upper diagram shows the distance from the center of the substrate and the width of the square pillars located there, with the higher the distance, the larger the pillar width. The lower diagram shows the pillar width and its distribution when the metalens is viewed in plan, with the darker the area, the smaller the pillar width at that position, and the lighter the area, the larger the pillar width at that position.

[0038] The pillar width distribution at the center of an SL metasurface, in which pillars are arranged based on the SL phase distribution, is convex upward, just like the phase distribution, while the pillar width distribution at the center of a GTBS metasurface based on the GTBS phase distribution is convex downward, just like the phase distribution. In contrast, the pillar width distribution at the center of the metalens of this embodiment, based on the GTBS+SL phase distribution, forms a curve that, like the phase distribution, satisfies the three conditions described above. In this way, the pillar width distribution in the GTBS+SL metasurface is distinctive from that of the SL metasurface and the GTBS metasurface.

[0039] Figure 10 shows an example of the relationship between the distance from the optical center of the metalens and the "cross-sectional area" of the pillars when square pillars of the same height are arranged according to the wrap phase distributions (1) to (3) in Figure 8. The uppermost diagram indicates that the higher the pillar, the larger the cross-sectional area. The lower diagram indicates the cross-sectional area and its distribution of the pillars when the metalens is viewed in plan, with the darker the area, the smaller the cross-sectional area of ​​the pillar at that position, and the lighter the area, the larger the cross-sectional area of ​​the pillar at that position.

[0040] 11 is a diagram showing an example of the relationship between the distance from the optical center of the metalens and the "area occupancy rate" of the pillars when square pillars of the same height are arranged according to the wrap phase distributions (1) to (3) in FIG. 8. The diagram at the top indicates that the higher the area occupancy rate of the pillars, the greater the area occupancy rate. The diagram at the bottom shows the area occupancy rate of the pillars and its distribution when the metalens is viewed in plan, with the darker the area, the smaller the area occupancy rate of the pillar at that position, and the lighter the area, the greater the area occupancy rate of the pillar at that position.

[0041] 10 and 11, i.e., the cross-sectional area of ​​the pillars and the area occupancy rate of the pillars, respectively, show the same tendency as in FIG. 9, i.e., the width of the pillars.

[0042] Similarly, the cases of cylindrical pillars are shown in FIGS. 12 to 14 . FIG. 12 shows an example of the relationship between the distance from the optical center of the metalens and the radius of the pillars when cylindrical pillars of the same height are arranged according to the wrap phase distributions (1) to (3) of FIG. 8 . FIG. 13 shows an example of the relationship between the distance from the optical center of the metalens and the cross-sectional area of ​​the pillars when cylindrical pillars of the same height are arranged according to the wrap phase distributions (1) to (3) of FIG. 8 . FIG. 14 shows an example of the relationship between the distance from the optical center of the metalens and the area occupancy of the pillars when cylindrical pillars of the same height are arranged according to the wrap phase distributions (1) to (3) of FIG. 8 . As shown in FIGS. 12 to 14 , the same trends as those for the square pillars shown in FIGS. 9 to 11 are also observed with cylindrical pillars.

[0043] Here, we consider the beam shape before it enters the metalens. FIG. 15 shows an example of the unwrap and wrap phase distributions of GTBS+SL when NA = 0.1, 0.2, or 0.3 and θ = 5°. The top three figures in FIG. 15 show the unwrap phase distribution, and the bottom three figures show the wrap phase distribution. Furthermore, the two figures on the left side of FIG. 15 show the phase distribution when NA is 0.1 (α is 5.7°), the two figures in the middle show the phase distribution when NA is 0.2 (α is 11.5°), and the two figures on the right side show the phase distribution when NA is 0.3 (α is 17.5°).

[0044] 15, it is clear that as the NA increases, the phase value increases and the difference between the maximum and minimum values ​​in the central portion decreases. Furthermore, according to Fig. 15, when the divergence angle α of the incident light is greater than the top-hat beam divergence angle θ, the curvature of the inflection points in the phase distribution decreases, and the shape of the phase distribution approaches that of SL even more.

[0045] Fig. 16 shows an example of the relationship between the distance from the optical center and the pillar width when square pillars of the same height are arranged in accordance with the wrap phase distribution of Fig. 15. Fig. 17 shows an example of the relationship between the distance from the optical center and the pillar area occupancy when square pillars of the same height are arranged in accordance with the wrap phase distribution of Fig. 15. Both Fig. 16 and Fig. 17 show, from left to right, the pillar widths or pillar area occupancy rates and their distributions when NAs are 0.1, 0.2, and 0.3.

[0046] 16 and 17, the curve showing the change in information about pillar size with respect to the distance from the optical center satisfies the three conditions described above. Furthermore, as NA(α) increases with respect to θ, the maximum value of the curve decreases, and the length of the curve in the direction along the principal surface of the substrate tends to decrease (shrink toward the optical center). Furthermore, as NA(α) decreases with respect to θ, the maximum value of the curve increases, and the length of the curve in the direction along the principal surface of the substrate tends to increase, with the position of the maximum value in the direction along the principal surface of the substrate tending to be farther from the optical center.

[0047] As shown in Figures 15 to 17, the metalens of this embodiment can be constructed by arranging pillars based on the phase distribution shown in Figure 15. In this way, the metalens of this embodiment can be constructed by arranging pillars as described above, even when taking into account the beam shape of incident light.

[0048] We will also consider the shape of the beam emitted from the metalens. FIG. 18 shows an example of the wrap phase distributions of SL, GTBS, and GTBS+SL when NA = 0.1 and θ = 15°. From left to right, FIG. 18 shows the wrap phase distributions of SL, GTBS, and GTBS+SL. According to FIG. 18, when the top-hat beam divergence angle θ becomes larger compared to the divergence angle α of the incident light, the inflection point of the phase distribution becomes farther from the optical center and the change in the phase value becomes larger, and the shape of the phase distribution is thought to become closer to that of GTBS.

[0049] Figure 19 shows an example of the wrap phase distribution of GTBS+SL when NA = 0.1, 0.2, 0.3, or 0.4 and θ = 15°. In Figure 19, the upper left shows the wrap phase distribution of GTBS+SL when NA = 0.1, the upper left shows the wrap phase distribution of GTBS+SL when NA = 0.2, the upper right shows the wrap phase distribution of GTBS+SL when NA = 0.3, and the lower right shows the wrap phase distribution of GTBS+SL when NA = 0.4. According to Figure 19, as the top-hat beam divergence angle θ increases and the NA (α) also increases, the phase distribution approaches more closely from that of GTBS to that of GTBS+SL, and the aforementioned inflection point specific to the phase distribution of GTBS+SL tends to move toward the center.

[0050] 15 to 19 , in this embodiment, in which desired optical properties are achieved by pillars that vary only in cross-sectional area at fixed positions on a substrate, it is considered preferable that the ratio of α to θ (α / θ) be 0 to 0.6 when θ is 5 to 30° and the NA is 0.1 to 0.4, from the perspective of realizing the above-described function (curve) that satisfies the above-described three conditions in the center of the metalens. Depending on the application of the metalens, the beam shapes of the incident and exiting light may be limited. In such cases, the metalens of this embodiment suitable for the application can be manufactured by performing the manufacturing steps described above within a range that corresponds to the beam shape conditions.

[0051] According to the manufacturing method of this embodiment, it is possible to manufacture a metalens that does not satisfy at least one of the three conditions related to the pillars of the metalens according to this embodiment described above, but it is possible to easily design and manufacture a metalens that can substantially convert the beam profile of a Gaussian beam into a top hat shape. In this way, it can be said that a metalens that can substantially convert the beam profile of a Gaussian beam into a top hat shape is a metalens manufactured by the manufacturing method of this embodiment described above.

[0052] Although the metalens manufactured by the manufacturing method of this embodiment can essentially convert the beam profile of a Gaussian beam into a top-hat shape through the above-described simple design, circumstances exist that make it impossible or impractical to directly identify the metalens by its structure or characteristics. A distinctive feature of this metalens, resulting from such a simple design, is expressed by a distinctive change in the shape of the pillars in the center. Considering that lenses are generally designed according to the incident beam, it is clear that this function can also be achieved by structures other than the above-described distinctive features. However, it is impossible to specifically specify in words what state of the structure other than the above-described distinctive features must provide the above-described conversion function. Identifying the structure that provides this function beyond the above-described distinctive features may be possible by comparing and examining the pillar arrangement and the target beam conditions under numerous and diverse conditions. However, such an investigation requires a significant amount of time and cost, and is virtually impractical given the nature of patent applications, which require speed, etc.

[0053] [Lighting Device] A lighting device according to one embodiment of the present invention includes a light source that emits a Gaussian beam and a metalens according to the present embodiment that is disposed in the optical path of the light emitted from the light source. One aspect of the lighting device is shown in FIG.

[0054] As shown in FIG. 20 , the lighting device 100 includes a laser 31, an optical fiber 32, and a metalens 1. The laser 31 generates laser light with a wavelength of, for example, 805 nm. The optical fiber 32 is optically connected to the laser 31, transmits the laser light generated by the laser, and emits it from its tip. The laser light, which is a Gaussian beam, is emitted from the tip of the optical fiber 32. The laser 31 and the optical fiber 32 constitute the light source 30 of the lighting device 100.

[0055] The metalens 1 is the metalens of the present embodiment described above. The metalens 1 is disposed at a position away from the tip of the optical fiber 32, on the optical path of the light emitted from the optical fiber 32, with the main surface having the pillars facing forward. Furthermore, the tip of the optical fiber 32 and the metalens 1 may be held by a probe. This configuration is suitable from the perspective of configuring an illumination device to be used in an endoscope.

[0056] The lighting device of the present embodiment includes a Gaussian beam light source and the metalens of the present embodiment described above, and is therefore capable of emitting light rays with a substantially top-hat beam profile.

[0057] Lighting devices according to embodiments of the present invention may be configured so that the metalens directly receives laser light from a laser without using an optical fiber. Optically, a configuration consisting of only a laser, an optical fiber, and a metalens, as shown in Figure 20, or a simpler configuration consisting of only a laser and a metalens, is preferable from the perspective of miniaturizing lighting devices.

[0058] Alternatively, the illumination device according to the embodiment of the present invention may further include an additional optical configuration, such as an optical element disposed in the optical system of the light source for adjusting the laser beam divergence angle α. Such a configuration including an additional optical configuration is preferable from the viewpoint of improving the performance of the illumination device.

[0059] The light source preferably includes a laser from the viewpoint of high output power and the resulting wide range of applications, but may include a device other than a laser as long as it generates a Gaussian beam. For example, the light source may include a light-emitting diode as a beam generating source.

[0060] [Summary] A first aspect of the present invention is a metalens (1) comprising an optically transparent substrate (2) and a plurality of optically transparent nano-sized pillars (3) disposed on one main surface of the substrate, wherein, when the optical center of the metalens is the origin, the area S of each pillar located at a distance r from the optical center is expressed by a function S(r) that satisfies the following three conditions: (1) it is continuous in the range -r0≦r≦r0 (r0>0), (2) it has a minimum value at r=0, and (3) it has a maximum value at r=±r1 (0<r1<r0).

[0061] A second aspect of the present invention is a metalens comprising an optically transparent substrate and a plurality of optically transparent nano-sized pillars arranged on one main surface of the substrate, wherein, when the optical center of the metalens is taken as the origin, the area occupancy Σ of the pillars at a point a distance r from the optical center is expressed by a function Σ(r) that satisfies the following three conditions: (1) it is continuous in the range -r0≦r≦+r0 (r0>0), (2) it has a minimum value at r=0, and (3) it has a maximum value at r=±r1 (0<r1<r0).

[0062] According to the first or second aspect of the present invention, a metalens having pillars on one main surface of a substrate can substantially convert a Gaussian beam into a top-hat beam. Thus, the first or second aspect provides a metalens that can convert a beam profile from a Gaussian distribution to a top-hat distribution using nanostructures on only one main surface of the substrate.

[0063] A third aspect of the present invention is the first or second aspect, in which pillars are disposed in each of the unit sections regularly set on the main surface, and the pillars have the same shape and height, but have different cross-sectional areas depending on the position of the unit section from the optical center. According to the third aspect, by adjusting any one of the shape, height, and cross-sectional area of ​​the pillars, it is possible to easily determine the pillars that produce the desired phase. Therefore, the third aspect is even more effective in terms of ease of designing the metalens.

[0064] A fourth aspect of the present invention is a lighting device comprising a light source that emits a Gaussian beam and the above-described metalens disposed in the optical path of the light emitted from the light source. In the fourth aspect, the above-described metalens is disposed in the optical path of the Gaussian beam from the light source. Thus, according to the fourth aspect, it is possible to realize a compact lighting device in which the beam profile is substantially converted from a Gaussian distribution to a top-hat distribution using a metalens having a simple configuration on only one main surface of a substrate.

[0065] A fifth aspect of the present invention is the fourth aspect, wherein the light source includes a laser. The fifth aspect is even more effective from the viewpoint of high energy intensity of the irradiated light and improved versatility of the lighting device.

[0066] A sixth aspect of the present invention is a method for manufacturing a metalens, in which optically transparent pillars are arranged on one main surface of an optically transparent substrate so that the phase distribution of light transmitted through the metalens is the sum of a first phase distribution of a lens that converts a specific Gaussian beam into collimated light and a second phase distribution of a metasurface that converts a specific Gaussian beam into a top-hat profile. According to the sixth aspect, it is possible to design and manufacture a metalens having pillars on one main surface of the substrate, which metalens can substantially convert the beam profile of a Gaussian beam into a top-hat profile, by the simple operation of adding together the first phase distribution and the second phase distribution, both of which can be calculated. Thus, according to the sixth aspect, it is possible to provide a metalens that can convert a beam profile from a Gaussian distribution to a top-hat distribution using nanostructures on only one main surface of the substrate.

[0067] A seventh aspect of the present invention relates to the sixth aspect, wherein the first phase distribution is expressed by the following formula (1): In formula (1), x represents the distance from the optical axis of the spherical lens on an x-axis orthogonal to the optical axis, y represents the distance from the optical axis on a y-axis orthogonal to both the optical axis and the x-axis, and f represents the focal length of the spherical lens. The seventh aspect is even more effective from the viewpoint of easily determining the arrangement of pillars of a metalens that can substantially convert the beam profile of a Gaussian beam into a top-hat shape.

[0068]

[0069] An eighth aspect of the present invention is the sixth or seventh aspect, wherein the second phase distribution is expressed by the following formula (2): In formula (2), r is the distance from the optical axis of the metasurface, λ is the wavelength of light having a radiant intensity distribution that is a Gaussian distribution of a specific Gaussian beam, D is the diameter of the metasurface, w1 is the beam waist diameter of the specific Gaussian beam of light having a radiant intensity distribution that is a Gaussian distribution, w2 is the beam diameter when the radiant intensity distribution of the light having a radiant intensity distribution that is a Gaussian distribution of a beam with a substantially uniform intensity distribution becomes uniform, l is the propagation distance, and ξ is the radial distance from the origin of the metasurface. The eighth aspect is even more effective from the viewpoint of easily determining the arrangement of pillars of a metalens that can substantially convert the beam profile of a Gaussian beam into a top-hat shape.

[0070]

[0071] A ninth aspect of the present invention is directed to any of the sixth to eighth aspects, wherein information regarding pillar size is determined based on a correlation between information regarding pillar size and the amount of phase shift when the pillar shape and the pillar arrangement on the principal surface are specified, and pillars having the determined size are arranged on the principal surface. The ninth aspect is even more effective from the viewpoint of easily determining the arrangement of pillars of a metalens that can substantially convert the beam profile of a Gaussian beam into a top-hat shape.

[0072] According to the present invention, it is possible to easily design and realize a metalens that essentially converts a Gaussian beam into a top-hat beam. The present invention, which has such effects, is expected to contribute to the promotion of industries that use metalenses and the expansion of technological innovation, and is expected to contribute to the achievement of, for example, Goal 9 of the Sustainable Development Goals (SDGs) proposed by the United Nations, "Build resilient infrastructure, promote inclusive and sustainable industrialization, and foster innovation."

[0073] The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention. Specific examples of embodiments of the present invention will be described below.

[0074] Example 1 A metalens 1 according to this embodiment was manufactured using the method described in this embodiment, and an illumination device such as the one shown in FIG. 20 was constructed. The beam intensity distribution was then measured using a beam profiler 110. An 805 nm fiber-coupled laser was used as the light source 30. The optical path length of the light incident on the metalens (the distance from the tip of the optical fiber 32 to the other main surface of the substrate of the metalens 1) was 2 cm, and the transmission distance D2 was 20 cm. The diameter of the metalens 1 was 5 mm, the light incident on the metalens 1 was a Gaussian beam, and the numerical aperture NA of the optical fiber 32 was 0.1. The metalens 1 was positioned along the X-Y plane perpendicular to the optical axis, with the direction along the optical axis at the tip of the optical fiber 32 being the Z direction. The intensity distribution of light emitted from the metalens 1 over a propagation distance of 20 cm, measured by the beam profiler 110, is shown in FIG. 21.

[0075] As shown in Figure 21, metalens 1 exhibits an intensity distribution that includes areas of high radiation intensity not only at the optical center but also on both sides of the optical center. In this way, metalens 1 exhibits a top-hat beam profile with a relatively uniform intensity distribution.

[0076] Comparative Example 1: The beam intensity distribution was measured in the same manner as in Example 1, except that a GTBS metasurface was used instead of metalens 1. The GTBS metasurface was constructed by arranging pillars with different cross-sectional areas in the same manner as in this embodiment, based on the phase distribution calculated from the above-mentioned equation (2). Figure 22 shows the intensity distribution of light emitted from the GTBS metasurface over a propagation distance of 20 cm.

[0077] As shown in Figure 22, the radiation intensity distribution of the GTBS metasurface is strong at the optical center and weakens with increasing distance from the optical center. Thus, a Gaussian beam profile was confirmed for the GTBS metasurface, where the radiation intensity decreases with increasing distance from the optical center.

[0078] Example 2 In accordance with the method described in the embodiment of the present invention, the phase distribution of GTBS+SL was determined under the following conditions, and a metalens was designed in which square pillars with different cross-sectional areas were arranged on one main surface of a substrate according to the phase distribution. The designed beam diameter of the uniformly irradiated area at a propagation distance of 100 μm was 39.4 μmΦ. NA=0.22, α=12.7°, θ=5°

[0079] FIG. 23 shows the relationship between the area occupancy of the pillars in the metalens of this example and the distance from the optical center of the pillars.

[0080] Furthermore, the calculation results of the beam intensity distribution in the xz plane of the metalens when a Gaussian beam of the above α is incident on the metalens of this example along the Z direction, which is the optical axis direction, are shown in Figure 24. Furthermore, the calculation results of the beam profile of the output light from the metalens over a propagation distance of 100 μm are shown in Figure 25.

[0081] As shown in Figure 25, a substantially top-hat shaped beam profile is observed in the metalens model of this example. Furthermore, the metalens model of this example results in a substantially uniform beam intensity over a range equivalent to the designed beam diameter (39.4 µm Φ) of the uniformly irradiated area.

[0082] [Comparative Example 2] The phase distribution of the GTBS was calculated under the same conditions as in Example 2 according to the method for calculating the phase distribution of the GTBS from the above-mentioned equation (2), and a GTBS metasurface was designed in accordance with the phase distribution, in which square pillars with different cross-sectional areas were arranged on one main surface of a substrate, as in Example 2. The relationship between the area occupancy of the pillars in the GTBS metasurface of this comparative example and the distance from the optical center of the pillars is shown in Figure 26.

[0083] The beam profile of the GTBS metasurface model of this comparative example was calculated in the same manner as in Example 2. The calculated results of the beam intensity distribution in the xz plane of the GTBS metasurface are shown in Figure 27. The calculated results of the beam profile of the emitted light from the GTBS metasurface at a propagation distance of 100 μm are shown in Figure 28.

[0084] As shown in Figure 28, the GTBS metasurface model of this comparative example has poor illuminance distribution within the illumination area, resulting in a bright spot in the center. Furthermore, as is clear from a comparison of Figures 25 and 28, although the designed beam diameter of the uniformly illuminated area is 39.4 μmΦ, the same as in Example 2, the illumination area is wider than the designed value, and the illuminance is lower even with the same laser output as in Example 2.

[0085] Example 3 As in Example 2, the phase distribution of GTBS+SL was determined under the following conditions according to the method described in the embodiment of the present invention, and a metalens was designed in which square pillars with different cross-sectional areas were arranged on one main surface of a substrate in accordance with the phase distribution. The designed beam diameter of the uniformly irradiated area at a propagation distance of 100 μm was 57.2 μmΦ. NA=0.4, α=23.6°, θ=10°

[0086] FIG. 29 shows the relationship between the area occupancy of the pillars in the metalens of this example and the distance from the optical center of the pillars.

[0087] Furthermore, the calculation results of the beam intensity distribution in the xz plane of the metalens when a Gaussian beam of the above α is incident on the metalens of this example along the Z direction, which is the optical axis direction, are shown in Figure 30. Furthermore, the calculation results of the beam profile of the output light from the metalens over a propagation distance of 100 μm are shown in Figure 31.

[0088] As shown in Figure 31, a substantially top-hat beam profile is observed in the metalens model of this example, similar to Example 2. Furthermore, similar to Example 2, the metalens model of this example also results in a substantially uniform beam intensity over a range equivalent to the beam diameter (57.2 µm Φ) of the designed uniformly irradiated area.

[0089] Comparative Example 3 The phase distribution of the GTBS was calculated under the same conditions as in Example 3 according to the method for calculating the phase distribution of the GTBS from the above-mentioned equation (2), and a GTBS metasurface was designed in accordance with the phase distribution, in which square pillars with different cross-sectional areas were arranged on one main surface of a substrate, as in Example 3. The relationship between the area occupancy of the pillars in the GTBS metasurface of this comparative example and the distance from the optical center of the pillars is shown in Figure 32.

[0090] In addition, the beam profile of the GTBS metasurface model of this comparative example was calculated in the same manner as in Example 3. The calculation results of the beam intensity distribution in the xz plane of the GTBS metasurface are shown in Figure 33. The calculation results of the beam profile of the emitted light from the GTBS metasurface at a propagation distance of 100 μm are shown in Figure 34.

[0091] As shown in Figure 34, the GTBS metasurface model of this comparative example has low uniformity in the illuminance distribution within the illumination area. Furthermore, as is clear from a comparison between Figure 31 and Figure 34, although the designed beam diameter of the uniformly illuminated area is 57.2 μmΦ, the same as that of Example 3, the illumination area is wider than the designed value, and the illuminance is lower even with the same laser output as Example 3.

[0092] REFERENCE SIGNS LIST 1 Metalens 2 Substrate 3 Pillar 10 Central portion 20 Peripheral portion 21 First peripheral portion 22 Second peripheral portion 23 Third peripheral portion 2n Nth peripheral portion 30 Light source 31 Laser 32 Optical fiber 100 Illumination device 110 Beam profiler

Claims

1. A metalens comprising an optically transparent substrate and a number of optically transparent nano-sized pillars disposed on one main surface of the substrate, wherein, when the optical center of the metalens is the origin, the area S of each of the pillars located at a point a distance r from the optical center is expressed by a function S(r) that satisfies the following three conditions: (1) it is continuous in the range -r0≦r≦r0 (r0>0); (2) it has a minimum value at r=0; and (3) it has a maximum value at r=±r1 (0<r1<r0).

2. A metalens comprising an optically transparent substrate and a plurality of optically transparent nano-sized pillars disposed on one main surface of the substrate, wherein, when the optical center of the metalens is the origin, the area occupancy Σ of the pillars at a point a distance r from the optical center is expressed by a function Σ(r) that satisfies the following three conditions: (1) it is continuous in the range -r0≦r≦+r0 (r0>0); (2) it has a minimum value at r=0; and (3) it has a maximum value at r=±r1 (0<r1<r0).

3. The metalens described in claim 1 or 2, wherein each of the pillars is disposed in each of unit sections regularly set on the principal surface, and the pillars have the same shape and height, and have different cross-sectional areas depending on the position of the unit section from the optical center.

4. A lighting device comprising: a light source that emits a Gaussian beam; and the metalens according to claim 1 or 2 that is arranged in the optical path of light emitted from the light source.

5. The illumination device of claim 4, wherein said light source comprises a laser.

6. A method for manufacturing a metalens, comprising arranging optically transparent pillars on one main surface of an optically transparent substrate so that the phase distribution of light transmitted through the metalens is the sum of a first phase distribution of a lens that converts a specific Gaussian beam into collimated light, and a second phase distribution of a metasurface that converts the specific Gaussian beam into a top-hat shape.

7. The method for producing a metalens according to claim 6, wherein the first phase distribution is represented by the following formula (1): In formula (1), x represents the distance from the optical axis of the lens along an x-axis perpendicular to the optical axis, y represents the distance from the optical axis along a y-axis perpendicular to both the optical axis and the x-axis, and f represents the focal length of the lens.

8. The method for producing a metalens according to claim 6, wherein the second phase distribution is represented by the following formula (2): In equation (2), r is the distance from the optical axis of the metasurface, λ is the wavelength of the particular Gaussian beam, D is the diameter of the metasurface, w1 is the beam waist diameter of the particular Gaussian beam, w2 is the diameter of a beam having a substantially uniform intensity distribution, l is the propagation distance, and ξ is the radial distance from the origin of the metasurface.

9. The method for manufacturing a metalens as described in claim 6, comprising determining information regarding the size of the pillars based on a correlation between information regarding the size of the pillars and an amount of phase shift when the shape of the pillars and the arrangement of the pillars on the primary surface are specified, and arranging the pillars having the determined size on the primary surface.

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