A metasurface structure

Abstract

This invention provides a metasurface structure comprising: a substrate, a plurality of nanostructures, and a filler surrounding the nanostructures, wherein the plurality of nanostructures are periodically arranged on at least one side of the substrate; the refractive index of the target element at different locations is different, and the refractive index distribution of the target element is a gradient distribution; the target element includes at least a portion of the nanostructures and / or the target element includes at least a portion of the filler; the material of the substrate is different from the material of the nanostructures. The metasurface structure provided by this invention can expand the equivalent refractive index range of the nanounits, thereby better correcting chromatic aberration in the metasurface structure; it can also improve the numerical aperture and resolution of the metasurface structure, which is more conducive to high-resolution imaging and has important applications in large numerical aperture superlenses, chromatic aberration correction superlenses, and many other fields.

Description

Technical Field

[0001] This invention relates to the field of metasurface technology, and more specifically, to a metasurface structure. Background Technology

[0002] Metasurfaces are subwavelength artificial nanostructure films that can modulate the phase, amplitude, polarization, and other properties of incident radiation through their nanostructures.

[0003] For existing metasurfaces, the design variables are nanostructure parameters, such as the length, width, height, and shape of the nanostructure. This makes it difficult to fabricate such metalenses with large numerical apertures and results in weak chromatic aberration correction capabilities, thus limiting the design possibilities for chromatic aberration corrective metalenses. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to provide a metasurface structure.

[0005] This invention provides a metasurface structure, comprising: a substrate, a plurality of nanostructures, and a filler surrounding the nanostructures, wherein the plurality of nanostructures are periodically arranged on at least one side of the substrate;

[0006] The target element has different refractive indices at different locations, and the refractive index distribution of the target element is a gradual distribution; the target element includes at least a portion of the nanostructure and / or the target element includes at least a portion of the filler;

[0007] The material of the substrate is different from the material of the nanostructure.

[0008] In one possible implementation, along the surface direction of the metasurface structure, the refractive index distribution includes at least one convex distribution with a high refractive index in the middle and low refractive indices on both sides.

[0009] In one possible implementation, the convex distribution includes a first parabolic distribution with a convex shape.

[0010] In one possible implementation, the first parabolic distribution satisfies:

[0011]

[0012] Where, n 1,max denoted as the maximum refractive index in the first parabolic distribution, r1 represents the distance between the target element and the position corresponding to the maximum refractive index in the first parabolic distribution, n1(r1) represents the refractive index of the target element at a distance of r1 from the position corresponding to the maximum refractive index in the first parabolic distribution, and β1 represents the refractive index variation coefficient.

[0013] In one possible implementation, the convex distribution includes a convex Gaussian distribution.

[0014] In one possible implementation, the convex Gaussian distribution satisfies:

[0015]

[0016] Where, n 2,max denoted as the maximum refractive index in the Gaussian distribution, r2 represents the distance between the target element and the position corresponding to the maximum refractive index in the convex Gaussian distribution, n2(r2) represents the refractive index of the target element at a distance of r2 from the position corresponding to the maximum refractive index in the convex Gaussian distribution, β2 represents the refractive index variation coefficient, σ2 represents the standard deviation of the convex Gaussian distribution, and a is an adjustment coefficient, where a>0.

[0017] In one possible implementation, where the refractive index comprises an odd number of convex distributions, the location corresponding to the maximum refractive index in one of the convex distributions is the center of the metasurface structure.

[0018] In one possible implementation, along the surface direction of the metasurface structure, the refractive index distribution includes at least one concave distribution with a low refractive index in the middle and a high refractive index on both sides.

[0019] In one possible implementation, the concave distribution includes a concave second parabolic distribution.

[0020] In one possible implementation, the second parabolic distribution satisfies:

[0021]

[0022] Where, n 3,min denoted as the minimum refractive index in the second parabolic distribution, r3 represents the distance between the target element and the position corresponding to the minimum refractive index in the second parabolic distribution, n3(r3) represents the refractive index of the target element at a distance of r3 from the position corresponding to the minimum refractive index in the second parabolic distribution, and β3 represents the refractive index variation coefficient.

[0023] In one possible implementation, the concave distribution includes a concave Gaussian distribution.

[0024] In one possible implementation, the concave Gaussian distribution satisfies:

[0025]

[0026] Where, n 4,maxLet r4 represent the preset maximum refractive index, r4 represent the distance between the target element and the position corresponding to the minimum refractive index in the concave Gaussian distribution, n4(r4) represent the refractive index of the target element at a distance of r4 from the position corresponding to the minimum refractive index in the concave Gaussian distribution, σ4 represent the standard deviation of the concave Gaussian distribution, and b represent the preset adjustment coefficient, where 0 < r4 < σ4. <b<1。

[0027] In one possible implementation, where the refractive index comprises an odd number of concave distributions, the position corresponding to the minimum refractive index in one of the concave distributions is the center of the metasurface structure.

[0028] In one possible implementation, the target element is made of a graded refractive index material;

[0029] Alternatively, the target element may be made of a material with different doping concentrations.

[0030] In the solution provided by this invention, the refractive index of the nanostructure and / or filler is gradually distributed. Nanostructures and fillers with different refractive indices can expand the equivalent refractive index range of the nanounits, thereby better correcting chromatic aberration in the metasurface structure. Furthermore, it can improve the numerical aperture and resolution of the metasurface structure, which is more conducive to high-resolution imaging and has important applications in large numerical aperture superlenses, chromatic aberration correction superlenses, and other fields. The substrate material is different from the nanostructure material, allowing the substrate to act as a stop layer, avoiding height differences at the etching bottom due to loading effects, and ensuring the height consistency of the nanostructure. In addition, the metasurface structure has high transmittance.

[0031] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 A schematic diagram of a metasurface structure provided in an embodiment of the present invention is shown;

[0034] Figure 2 A side view of the metasurface structure provided in an embodiment of the present invention is shown;

[0035] Figure 3A schematic diagram of the nanounit structure in the metasurface structure provided in the embodiment of the present invention is shown;

[0036] Figure 4 The relationship between phase and transmittance and incident light wavelength is shown in the direct calculation method provided in the embodiments of the present invention.

[0037] Figure 5 An electron microscope image of a conventional metasurface is shown;

[0038] Figure 6 This diagram illustrates a convex refractive index distribution provided in an embodiment of the present invention.

[0039] Figure 7 This diagram illustrates a concave refractive index distribution provided in an embodiment of the present invention.

[0040] Figure 8 Another schematic diagram of the convex refractive index distribution provided in an embodiment of the present invention is shown;

[0041] Figure 9 Another schematic diagram of the refractive index concave distribution provided in an embodiment of the present invention is shown;

[0042] Figure 10 The equivalent refractive index range corresponding to intrinsic silicon nanostructures is shown;

[0043] Figure 11 The equivalent refractive index range corresponding to the doped silicon nanostructure provided in the embodiments of the present invention is shown.

[0044] icon:

[0045] 10-substrate, 20-nanostructure, 30-filler. Detailed Implementation

[0046] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0047] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0048] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0049] An embodiment of the present invention provides a metasurface structure, see [link to embodiment]. Figure 1 As shown, it includes: a substrate 10, a plurality of nanostructures 20 and a filler 30 surrounding the nanostructures 20, the plurality of nanostructures 20 being periodically arranged on at least one side of the substrate 10; Figure 1 Only six nanostructures 20 are shown in the figure. The filler 30 fills the space around the multiple nanostructures 20. The filler 30 can be a gaseous filler (e.g., air, nitrogen, etc.), a solid filler (e.g., silicon nitride, etc.), or a liquid filler if conditions permit. This embodiment does not limit the specific filler.

[0050] Furthermore, the refractive index of the target element varies at different locations, and the refractive index distribution of the target element is a gradual distribution; the target element includes at least a portion of the nanostructure 20 and / or the target element includes at least a portion of the filler 30. The materials of the substrate 10, the nanostructure 20, and the filler 30 are different from each other.

[0051] In this embodiment of the invention, the refractive index of the target element in the metasurface structure is gradually changing. The target element can be at least part (partial or all) of the nanostructure 20, or at least part of the filler 30; that is, in this embodiment of the invention, the refractive index of at least part of the nanostructure 20 is gradually changing, and / or, the refractive index of at least part of the filler 30 is gradually changing. For example, the refractive indices of multiple nanostructures 20 are gradually changing, and the refractive index of the filler 30 is the same; or, the refractive indices of multiple nanostructures 20 are the same, and the refractive index of the filler 30 is gradually changing; or, the refractive indices of multiple nanostructures 20 are gradually changing, and the refractive index of the filler 30 is also gradually changing. Wherein, at least part of the nanostructure 20 refers to multiple nanostructures 20 within the same connected region, and at least part of the filler 30 refers to the filler 30 located within the same connected region. The connected region corresponding to the nanostructure 20 and the connected region corresponding to the filler 30 can be the same connected region or two different connected regions; this embodiment does not limit this.

[0052] Because multiple nanostructures 20 are periodically arranged on one side of the substrate 10, the refractive index distribution of at least some of the nanostructures 20 or at least some of the filler 30 is a gradually changing distribution, for example, the refractive index gradually increases or gradually decreases. Taking the nanostructure 20 as an example of a gradually changing refractive index, see [reference needed]. Figure 2 As shown, the target element includes nanostructures 21, 22, 23, 24, 24, 26, and 27. The filler 30 between the nanostructures is air, meaning the refractive index of the filler 30 is uniform. Centered on nanostructure 21, the refractive index of other nanostructures increases (or decreases) with distance from nanostructure 21. For example, the refractive indices of nanostructures 21, 23, 25, and 27 gradually increase, and the refractive indices of nanostructures 21, 22, 24, and 26 also gradually increase, thus forming a nanostructure with a gradually increasing refractive index distribution.

[0053] It should be noted that the "gradual distribution" in the embodiments of the present invention can be a continuous gradual distribution, that is, the refractive index gradually changes with a unit of one nanostructure; for example, Figure 2 The refractive indices of nanostructures 21, 23, 25, and 27 are all different and gradually increase. Alternatively, this "gradual distribution" can also be a discrete gradual distribution, where the refractive index gradually changes per unit region composed of multiple nanostructures. For example, Figure 2 The refractive indices of nanostructures 21, 23, 25, and 27 are partially the same and gradually increase, resulting in a ring-shaped, gradually changing refractive index distribution. For example, n 21 =n 23 <n 25 =n 27 , where n i denoted by i, representing the refractive index of nanostructure i.

[0054] In this embodiment of the invention, the nanostructures 20 are periodically arranged on one side of the substrate 10, and can be divided into multiple nanounits by artificial means. Each nanounit includes at least one nanostructure 20 and surrounding filler 30; wherein, for example... Figure 1 As shown, the dashed lines indicate the division of the nanounits, which is divided into 6 nanounits. Each nanostructure 20 is located at the centroid of the nanounit. The structure of one nanounit can be found in [reference needed]. Figure 3 As shown; or, the nanostructure 20 can also be located at the vertex position of the nanounit. This embodiment does not limit the way the nanounits are divided.

[0055] For each nanounit, the equivalent refractive index can be determined based on either the duty cycle method or a direct calculation method. The equivalent refractive indices obtained by the two methods are essentially the same. Specifically:

[0056] The duty cycle method calculates the equivalent refractive index and equivalent extinction coefficient of the nanounit composed of nanostructure 20 and filler 30 based on the refractive index and extinction coefficient of nanostructure 20, the refractive index and extinction coefficient of filler 30, and the proportion of nanostructure 20 and filler 30 in the nanounit. The calculation formulas are shown in formulas (1), (2), and (3):

[0057] n1(λ)=ρ′n u (λ)+ρ″n f (λ), (1)

[0058] k1(λ)=ρ′k u (λ)+ρ″k f (λ), (2)

[0059] ρ′+ρ″=1, (3)

[0060] Where λ is the wavelength of light, n1(λ) is the calculated equivalent refractive index of the nanounit, and k1(λ) is the calculated equivalent extinction coefficient of the nanounit; u (λ) is the refractive index of nanostructure 20, n f (λ) is the refractive index of filler 30; k u (λ) is the extinction coefficient of nanostructure 20, k f (λ) is the extinction coefficient of filler 30; ρ′ is the ratio of the area of ​​nanostructure 20 to the area of ​​nanounit, and ρ″ is the ratio of the area of ​​filler 30 to the area of ​​nanounit.

[0061] The implementation method for calculating the equivalent refractive index and equivalent extinction coefficient of nanounits by direct calculation is as follows:

[0062] The phase of nanounits at different wavelengths was directly calculated using the finite element method. The phase at different wavelengths obtained from the transmittance T(λ) The curve of transmittance T(λ) is as follows Figure 4 As shown, Figure 4 The horizontal axis represents wavelength, the left vertical axis represents transmittance, and the right vertical axis represents phase. The equivalent refractive index n1(λ) for any wavelength is obtained using the tangent method, and the equivalent extinction coefficient k1(λ) for any wavelength is directly obtained from the definition of the extinction coefficient. The equivalent refractive index and the equivalent extinction coefficient satisfy the following formulas (4) and (5):

[0063]

[0064]

[0065] Where h is the height of nanostructure 20, and T0 is the intensity of the incident light. Let T(λ) be the phase of the nanounit at wavelength λ, and T(λ) be the transmittance of the nanounit at wavelength λ.

[0066] As shown in the above, as indicated by formula (1), the equivalent refractive index of the nanounit is similar to the refractive index n of the nanostructure 20. u (λ), the refractive index n of filler 30 f (λ) Related. Traditional superlenses have nanostructures with the same refractive index, or the filling material also has the same refractive index. This means the effective refractive index of a traditional superlens is mainly related to the proportion ρ′, resulting in a limited effective refractive index range for the metasurface. This limits the design capabilities for large numerical aperture superlenses and chromatic aberration correction superlenses. In the embodiments of this invention, at least one of the nanostructure 20 or the filling material 30 has a gradually changing refractive index; that is, the refractive index of the nanostructure 20 at different locations is different, or the refractive index of the filling material 30 at different locations is different. In other words, the refractive index of the nanostructure 20 or the filling material 30 is within a range. When the refractive index of at least one of them is within a range, the corresponding effective refractive index range increases, thereby expanding the effective refractive index range.

[0067] The equivalent refractive index range and the maximum aperture of the metasurface (e.g., a superlens) satisfy the following relationship:

[0068]

[0069] Where, Δn eff For the equivalent refractive index range, r maxd is the maximum aperture of the metasurface, d is the height of the nanostructure 20, and f is the focal length of the metasurface.

[0070] When the equivalent refractive index range expands to k times its original value (k > 1), that is, the equivalent refractive index range changes from Δn... eff Expanded to kΔn eff Therefore, the maximum aperture of the metasurface structure provided in this embodiment of the invention is increased to r′. max :

[0071]

[0072] Therefore, this metasurface structure can better correct chromatic aberration; and, with the chromatic aberration correction range remaining unchanged, when the aperture of the metasurface structure increases, its numerical aperture and resolution correspondingly improve, which is more conducive to high-resolution imaging.

[0073] Furthermore, the material of the metasurface structure substrate 10 is different from the material of the nanostructure 20. Specifically, the etching rates of the substrate 10 and the nanostructure 20 are different, and the etching rate of the substrate 10 is much lower than that of the nanostructure 20; for example, the etching rates differ by at least 10 times. The substrate 10 acts as a stop layer for the nanostructure 20 during etching, thereby reducing the loading effect.

[0074] For existing superlenses, if the etching rates of the nanostructure and the substrate are similar (specifically, if the nanostructure and the substrate are made of the same material, their etching rates are also identical), the different duty cycles in different periods during the etching process will lead to differences in etching rates (e.g., the flow rate of the etching gas), resulting in a loading effect during etching and causing a stepped bottom. Electron micrographs of existing superlenses exhibiting this loading effect can be found in [reference needed]. Figure 5 As shown, Figure 5 In this context, Δh represents the stepped height difference caused by the load effect. Figure 5 It is known that this height difference Δh accounts for nearly 1 / 5 of the total height of the nanostructure, greatly affecting the nanostructure's ability to modulate light. Furthermore, when the nanostructure used is one with a gradually changing refractive index, an additional difference in etching depth is introduced, making the loading effect even more pronounced.

[0075] In this embodiment of the invention, the material of the substrate 10 is different from that of the nanostructure 20, resulting in completely different etching rates. Furthermore, the etching rate of the substrate 10 is much lower than that of the nanostructure 20. During the etching of the nanostructure 20, because the etching rate of the substrate 10 is low (or even negligible, i.e., the substrate 10 cannot be etched), the substrate 10 acts as a stop layer. By appropriately extending the etching time, the height of all nanostructures 20 can be ensured to be consistent, thereby avoiding height differences caused by the loading effect.

[0076] Furthermore, the material of the metasurface structure substrate 10 is different from the material of the nanostructure 20, resulting in a sufficient difference between the equivalent refractive index of the nanounit and the refractive index of the substrate 10, thereby improving the transmittance of the metasurface structure. Optionally, the materials of the metasurface structure substrate 10, the nanostructure 20, and the filler 30 are all different.

[0077] This invention provides a metasurface structure in which the refractive index of the nanostructure 20 and / or filler 30 is gradually distributed. The different refractive indices of the nanostructure 20 and filler 30 can expand the equivalent refractive index range of the nanounits, thereby better correcting chromatic aberration in the metasurface structure. Furthermore, it can improve the numerical aperture and resolution of the metasurface structure, which is more conducive to high-resolution imaging and has important applications in large numerical aperture superlenses, chromatic aberration correction superlenses, and other fields. The material of the substrate 10 is different from that of the nanostructure 20, allowing the substrate 10 to act as a stop layer, avoiding height differences at the etched bottom due to the loading effect, and ensuring the height consistency of the nanostructure 20. Moreover, the metasurface structure has high transmittance.

[0078] Optionally, to achieve a gradient refractive index, in this embodiment of the invention, the target element is made of a gradient refractive index material; that is, the material of the nanostructure 20 is a gradient refractive index material, and / or, the material of the filler 30 is a gradient refractive index material. This gradient refractive index material can be, for example, a GRIN (Gradient-Index) material.

[0079] Alternatively, the target element may be made of materials with different doping concentrations; that is, the nanostructure 20 as a whole may be made of the same material, but the doping concentration of the nanostructure 20 at different locations may be different, and / or, the filler 30 may be made of the same material as a whole, but the doping concentration of the filler 30 at different locations may be different. For example, the nanostructure 20 may be made of silicon and doped with impurities, resulting in different doping concentrations of the nanostructure 20 at different locations, thus causing the refractive index of the nanostructure 20 to be different and to exhibit a gradual distribution.

[0080] Optionally, to facilitate the implementation of a gradual refractive index change in the manufacturing process, the refractive index distribution of the target element may exhibit a simple convex or concave distribution. For example, along the surface direction of the metasurface structure, the refractive index distribution may include at least one convex distribution with a high refractive index in the middle and low refractive indices on both sides. Alternatively, along the surface direction of the metasurface structure, the refractive index distribution may include at least one concave distribution with a low refractive index in the middle and high refractive indices on both sides.

[0081] In this embodiment of the invention, the metasurface structure is essentially a planar structure, and the surface direction of the metasurface structure refers to a direction on the surface of the planar structure. For example... Figure 2 As shown, Figure 2 This is a side view of a metasurface structure. Figure 2 The left-right direction in the diagram represents one surface direction of the metasurface structure. The location of the target element corresponding to the point of extreme refractive index (maximum or minimum) is taken as a reference point, and the surface direction of the metasurface structure is the direction passing through this reference point on the surface of the metasurface structure. For example, if the center of the metasurface structure has the maximum or minimum refractive index, the surface direction of the metasurface structure is the direction passing through this center, such as the radial direction of the metasurface structure.

[0082] For example, see Figure 6 As shown, the refractive index distribution of the target element is convex; or, see [reference needed]. Figure 7 As shown, the refractive index distribution of the target element is concave.

[0083] Optionally, the convex distribution may include a convex first parabolic distribution. Alternatively, the convex distribution may include a convex Gaussian distribution. Figure 6 An example is shown using a convex Gaussian distribution; and, Figure 6 Taking the target element as a nanostructure as an example, the refractive index distribution of the nanostructure conforms to a convex Gaussian distribution. Figure 6 The grayscale value of medium and nanostructures represents the magnitude of the refractive index.

[0084] Alternatively, the convex Gaussian distribution satisfies:

[0085]

[0086] Where, n 2,max denoted by r2, r2 represents the distance between the target element and the position corresponding to the maximum refractive index in the convex Gaussian distribution, n2(r2) represents the refractive index of the target element at a distance r2 from the position corresponding to the maximum refractive index in the Gaussian distribution, β2 represents the refractive index variation coefficient, σ2 represents the standard deviation of the convex Gaussian distribution, and a is an adjustment coefficient, where a>0; generally, a≥1.

[0087] In this embodiment of the invention, for a convex distribution, the refractive index distribution of the target element is related to the distance between the target element and the position corresponding to the maximum refractive index. In a convex Gaussian distribution, this distance is represented by r2, which is also the radius of the target element (with the center of the circle corresponding to the position of maximum refractive index). See also Figure 6 As shown, the position corresponding to the maximum refractive index in this Gaussian distribution is the center of the metasurface structure. Therefore, using the center of this metasurface structure as a reference, the refractive indices of other nanostructures 20 can be determined. If the metasurface structure is circular, then the aforementioned distance r2 represents the radius corresponding to the location of the nanostructure 20. For example... Figure 6As shown, since the refractive index of nanostructure 20 is gradually changing, the refractive index range of Δn can be introduced due to the gradually changing refractive index of the nanostructure, thereby expanding the equivalent refractive index range.

[0088] Optionally, the first parabolic distribution satisfies:

[0089]

[0090] Where, n 1,max denoted as the maximum refractive index in the first parabolic distribution, r1 represents the distance between the target element and the position corresponding to the maximum refractive index in the first parabolic distribution, n1(r1) represents the refractive index of the target element at a distance of r1 from the position corresponding to the maximum refractive index in the first parabolic distribution, and β1 represents the refractive index variation coefficient.

[0091] Similar to the convex Gaussian distribution described above, this first parabolic distribution is a convex parabolic distribution, and the refractive index of the target element is related to its distance from the position corresponding to the maximum refractive index (here, r1 represents this distance). For example, the position corresponding to the maximum refractive index in this first parabolic distribution can also be the center of the metasurface structure.

[0092] Those skilled in the art will understand that the convex distribution (and the concave distribution described below) in this embodiment refers to the distribution along the surface direction of the metasurface structure, which is a two-dimensional distribution; however, since the nanostructures 20 of the metasurface structure are laid flat on the substrate 10, the refractive index distribution of all nanostructures 20 can be described by a three-dimensional distribution, such as a three-dimensional Gaussian distribution, which is essentially the same as the description method in this embodiment.

[0093] Optionally, similar to the convex distribution described above, the concave distribution may include a concave second parabolic distribution. Alternatively, the concave distribution may include a concave Gaussian distribution. Figure 7 An example is shown using a concave Gaussian distribution; and, Figure 7 Taking the target element as a nanostructure as an example, the refractive index distribution of the nanostructure conforms to a concave Gaussian distribution. Figure 7 The grayscale value of medium and nanostructures represents the magnitude of the refractive index.

[0094] For example, a concave Gaussian distribution satisfies:

[0095]

[0096] Where, n 4,maxσ represents the preset maximum refractive index, r4 represents the distance between the target element and the position corresponding to the minimum refractive index in the concave Gaussian distribution, n4(r4) represents the refractive index of the target element at a distance of r4 from the position corresponding to the minimum refractive index in the concave Gaussian distribution, σ4 represents the standard deviation of the concave Gaussian distribution, and b represents the preset adjustment coefficient, where 0 < σ. <b<1。

[0097] In this embodiment of the invention, n 4,max This represents the preset maximum refractive index. This maximum refractive index is only used to determine the refractive index distribution and is not used to indicate that the refractive index of a specific target element is n. 4,max For example, the location of the minimum refractive index in a concave Gaussian distribution can be the center of the metasurface structure.

[0098] Alternatively, the second parabolic distribution satisfies:

[0099]

[0100] Where, n 3,min denoted by r3, r3 represents the distance between the target element and the position corresponding to the minimum refractive index in the second parabolic distribution, n3(r3) represents the refractive index of the target element at a distance of r3 from the position corresponding to the minimum refractive index in the second parabolic distribution, and β3 represents the refractive index variation coefficient.

[0101] Alternatively, the refractive index distribution may include multiple convex or multiple concave distributions. See also Figure 8 As shown, the refractive index distribution includes two convex distributions; or, see [link to relevant documentation]. Figure 9 As shown, the refractive index distribution includes two concave distributions.

[0102] Optionally, if the refractive index distribution includes an even number of convex distributions, the refractive index distribution can be centrosymmetric, with the center of the metasurface structure being a minimum value of the refractive index. See [link to relevant documentation] for details. Figure 8 As shown. Alternatively, if the refractive index distribution includes an odd number of convex distributions, where the position corresponding to the maximum refractive index in one of the convex distributions is the center of the metasurface structure.

[0103] Correspondingly, if the refractive index distribution includes an even number of concave distributions, the refractive index distribution can be centrosymmetric, and the center of the metasurface structure is a maximum value of the refractive index. For details, please refer to [link to relevant documentation]. Figure 9 As shown. Alternatively, if the refractive index distribution includes an odd number of concave distributions, where the position corresponding to the minimum refractive index in one of the concave distributions is the center of the metasurface structure.

[0104] The metasurface structure is described in detail below through an embodiment.

[0105] In this embodiment of the invention, the nanostructure 20 is made of silicon-doped material, the substrate 10 is chalcogenide glass, the operating wavelength is 8-12 μm, and the filler 30 is air. The nanostructure 20 is arranged in a periodic hexagonal pattern and includes nanopillars, nanopores, hollow nanopillars, and ring-shaped nanopore structures. The height of the nanostructure 20 is 11.8 μm, the period is 3.04 μm, and the minimum linewidth is 700 nm. When intrinsic silicon is used as the nanostructure material, see [reference needed]. Figure 10 As shown, its equivalent refractive index range Δn eff The value is 1.2. Compared to metasurfaces with intrinsic silicon nanostructures, the equivalent refractive index range Δn of metasurfaces with silicon nanostructures of different doping concentrations in the embodiments of this invention is 1.2. eff It is 1.7 (corresponding to a doping concentration from 10). 19 cm -2 (Up to 0), see details. Figure 11 As shown in equation (6), when using a gradient refractive index (doped) nanostructure, with a focal length of 1 mm, the chromatic aperture increases from 337.76 μm to 402.60 μm, the numerical aperture increases from 0.167 to 0.197, and the resolution increases from 30 μm to 25.4 μm.

[0106] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A metasurface structure, characterized in that, include: The substrate (10), a plurality of nanostructures (20), and a filler (30) surrounding the nanostructures (20), wherein the plurality of nanostructures (20) are periodically arranged on at least one side of the substrate (10); the material of the substrate (10) is different from the material of the nanostructures (20); The target element includes at least a portion of the nanostructure (20) and / or the target element includes at least a portion of the filler (30). The refractive index of the target element is different at different locations, and the refractive index distribution of the target element along the surface direction of the metasurface structure is a gradual distribution, which expands the equivalent refractive index range to increase the numerical aperture of the metasurface structure.

2. The metasurface structure according to claim 1, characterized in that, Along the surface direction of the metasurface structure, the refractive index distribution includes at least one convex distribution with a high refractive index in the middle and low refractive indices on both sides.

3. The metasurface structure according to claim 2, characterized in that, The convex distribution includes a first parabolic distribution with a convex shape.

4. The metasurface structure according to claim 3, characterized in that, The first parabolic distribution satisfies: ； in, This represents the maximum refractive index in the first parabolic distribution. The distance between the target element and the position corresponding to the maximum refractive index in the first parabolic distribution is represented by n1(r1), the refractive index of the target element at a distance of r1 from the position corresponding to the maximum refractive index in the first parabolic distribution is represented by β1, and the refractive index variation coefficient is represented by β1.

5. The metasurface structure according to claim 2, characterized in that, The convex distribution includes a convex Gaussian distribution.

6. The metasurface structure according to claim 5, characterized in that, The convex Gaussian distribution satisfies: ； Where, n 2,max denoted as the maximum refractive index in the Gaussian distribution, r2 represents the distance between the target element and the position corresponding to the maximum refractive index in the convex Gaussian distribution, n2(r2) represents the refractive index of the target element at a distance of r2 from the position corresponding to the maximum refractive index in the convex Gaussian distribution, β2 represents the refractive index variation coefficient, σ2 represents the standard deviation of the convex Gaussian distribution, and a is an adjustment coefficient, where a>0.

7. The metasurface structure according to claim 2, characterized in that, When the refractive index includes an odd number of convex distributions, the position corresponding to the maximum refractive index in one of the convex distributions is the center of the metasurface structure.

8. The metasurface structure according to claim 1, characterized in that, Along the surface direction of the metasurface structure, the refractive index distribution includes at least one concave distribution with a small refractive index in the middle and a large refractive index on both sides.

9. The metasurface structure according to claim 8, characterized in that, The concave distribution includes a concave second parabolic distribution.

10. The metasurface structure according to claim 9, characterized in that, The second parabolic distribution satisfies: ； Where, n 3,min denoted as the minimum refractive index in the second parabolic distribution, r3 represents the distance between the target element and the position corresponding to the minimum refractive index in the second parabolic distribution, n3(r3) represents the refractive index of the target element at a distance of r3 from the position corresponding to the minimum refractive index in the second parabolic distribution, and β3 represents the refractive index variation coefficient.

11. The metasurface structure according to claim 8, characterized in that, The concave distribution includes a concave Gaussian distribution.

12. The metasurface structure according to claim 11, characterized in that, The concave Gaussian distribution satisfies: ； Where, n 4,max Let r4 represent the preset maximum refractive index, r4 represent the distance between the target element and the position corresponding to the minimum refractive index in the concave Gaussian distribution, n4(r4) represent the refractive index of the target element at a distance of r4 from the position corresponding to the minimum refractive index in the concave Gaussian distribution, σ4 represent the standard deviation of the concave Gaussian distribution, and b represent the preset adjustment coefficient, where 0 < r4 < σ4. <b<1。 13. The metasurface structure according to claim 8, characterized in that, When the refractive index includes an odd number of concave distributions, the position corresponding to the minimum refractive index in one of the concave distributions is the center of the metasurface structure.

14. The metasurface structure according to any one of claims 1-13, characterized in that, The target element is made of a graded refractive index material; Alternatively, the target element may be made of a material with different doping concentrations.

Images