CN114660683A - Super surface structure - Google Patents
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- CN114660683A CN114660683A CN202210461490.XA CN202210461490A CN114660683A CN 114660683 A CN114660683 A CN 114660683A CN 202210461490 A CN202210461490 A CN 202210461490A CN 114660683 A CN114660683 A CN 114660683A
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Abstract
The invention provides a super-surface structure, comprising: the nano-structure comprises a substrate, a plurality of nano-structures and a filler positioned around the nano-structures, wherein the nano-structures are periodically arranged on at least one side of the substrate; the refractive indexes of the target elements at different positions are different, and the refractive index distribution of the target elements is a gradient distribution; the target element comprises at least part of the nanostructures and/or the target element comprises at least part of the filler; the substrate is of a different material than the nanostructure. The super-surface structure provided by the embodiment of the invention can expand the equivalent refractive index interval of the nano unit, thereby better correcting the chromatic aberration of the super-surface structure; the numerical aperture of the super-surface structure can be improved, the resolution ratio is correspondingly improved, high-resolution imaging is facilitated, and the method has important application in aspects such as a large-numerical-aperture super-lens and a chromatic aberration correction super-lens.
Description
Technical Field
The invention relates to the technical field of super surfaces, in particular to a super surface structure.
Background
The super-surface is a layer of sub-wavelength artificial nanostructure film, and the phase, amplitude, polarization and other characteristics of incident radiation can be modulated through the nanostructure in the film.
For existing meta-surfaces, the design variables are nanostructure parameters, such as the length, width, height, shape, etc. of the nanostructure. The super lens is difficult to manufacture with large numerical aperture, has weak chromatic aberration correction capability, and limits the capability of chromatic aberration correction in the aspect of design.
Disclosure of Invention
In order to solve the above problems, embodiments of the present invention provide a super-surface structure.
The embodiment of the invention provides a super-surface structure, which comprises: the nano-structure comprises a substrate, a plurality of nano-structures and a filler positioned around the nano-structures, wherein the nano-structures are periodically arranged on at least one side of the substrate;
the refractive indexes of the target elements at different positions are different, and the refractive index distribution of the target elements is a gradient distribution; the target element comprises at least part of the nanostructures and/or the target element comprises at least part of the filler;
the substrate is of a different material than the nanostructure.
In a possible implementation manner, the refractive index distribution comprises at least one convex distribution with a large middle refractive index and small side refractive indexes along the surface direction of the super-surface structure.
In a possible implementation, the convex profile comprises a first parabolic profile of a convex profile.
In one possible implementation, the first parabolic profile satisfies:
wherein n is1,maxRepresents the maximum refractive index, r, in the first parabolic profile1Representing the distance between the target element and the position corresponding to the maximum refractive index in the first parabolic profile，n1(r1) Represents a distance r between positions corresponding to the maximum refractive index in the first parabolic profile1Refractive index of the target element of (1), beta1Representing the index of change coefficient of the refractive index.
In one possible implementation, the convex profile comprises a convex gaussian profile.
In one possible implementation, the gaussian distribution of the convex profile satisfies:
wherein n is2,maxRepresents the maximum refractive index in the Gaussian distribution, r2Represents the distance between the target element and the position corresponding to the maximum refractive index in the Gaussian distribution of the convex type, n2(r2) The distance between the positions corresponding to the maximum refractive index in the convex Gaussian distribution is represented by r2Refractive index of target element of (1), beta2Denotes the coefficient of variation of refractive index, σ2A is a standard deviation of the convex Gaussian distribution, a is an adjustment coefficient, and a>0。
In a possible implementation, in a case where the refractive index includes an odd number of convex profiles, a maximum refractive index corresponding position in one of the convex profiles is a center of the super surface structure.
In one possible implementation, the refractive index profile includes at least one concave profile with a small middle refractive index and a large two-side refractive index along the surface direction of the super-surface structure.
In one possible implementation, the concave distribution includes a second parabolic distribution of the concave shape.
In one possible implementation, the second parabolic profile satisfies:
wherein the content of the first and second substances,n3,minrepresenting the minimum refractive index, r, in said second parabolic profile3Representing the distance, n, between the target element and the location corresponding to the smallest refractive index in said second parabolic profile3(r3) Represents a distance r from a position corresponding to the minimum refractive index in the second parabolic profile3Refractive index of the target element of (1), beta3Representing the index of change coefficient of the refractive index.
In one possible implementation, the concave distribution comprises a concave gaussian distribution.
In one possible implementation, the gaussian distribution of the concave shape satisfies:
wherein n is4,maxDenotes a predetermined maximum refractive index, r4Representing the distance between the target element and the position corresponding to the minimum refractive index in the Gaussian distribution of the concave form, n4(r4) Represents a distance r between positions corresponding to the minimum refractive index in the concave Gaussian distribution4Of the target element, σ4A standard deviation of the concave Gaussian distribution, b is a preset adjustment coefficient, and 0<b<1。
In a possible implementation, in a case where the refractive index includes an odd number of concave distributions, a minimum refractive index corresponding position in one of the concave distributions is a center of the super-surface structure.
In one possible implementation, the target element is a graded index material;
alternatively, the target elements are made of materials with different doping concentrations.
In the scheme provided by the embodiment of the invention, the refractive indexes of the nano structures and/or the fillers are gradually distributed, and the nano structures and the fillers with different refractive indexes can expand the equivalent refractive index interval of the nano units, so that the chromatic aberration of the super-surface structure can be better corrected; the numerical aperture of the super-surface structure can be improved, the resolution ratio is correspondingly improved, high-resolution imaging is facilitated, and the method has important application in aspects such as a large-numerical-aperture super-lens and a chromatic aberration correction super-lens. The material of the substrate is different from that of the nano structure, so that the substrate can play a role of a stop layer, the problem of height difference of the etched bottom caused by a load effect is avoided, and the height consistency of the nano structure can be ensured; moreover, the super-surface structure has higher transmittance.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic structural diagram of a super-surface structure provided by an embodiment of the invention;
FIG. 2 illustrates a side view of a super-surface structure provided by an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a nano-unit in a super-surface structure provided by an embodiment of the invention;
FIG. 4 shows the phase and transmittance as a function of the wavelength of the incident light for the direct calculation provided by an embodiment of the present invention;
FIG. 5 illustrates an electron micrograph of a conventional super-surface;
FIG. 6 shows a schematic diagram of a convex profile of refractive index provided by an embodiment of the present invention;
FIG. 7 is a schematic diagram illustrating a concave profile of refractive index provided by an embodiment of the present invention;
FIG. 8 shows another schematic diagram of a refractive index profile provided by an embodiment of the present invention;
FIG. 9 shows another schematic of a concave profile of refractive index provided by an embodiment of the present invention;
FIG. 10 shows the corresponding equivalent refractive index interval for intrinsic silicon nanostructures;
fig. 11 shows the equivalent refractive index interval corresponding to the doped silicon nanostructure provided by the embodiment of the present invention.
Icon:
10-substrate, 20-nanostructure, 30-filler.
Detailed Description
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are used merely for convenience of description and simplification of the description, but do not indicate or imply that the device or element referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating 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 the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood according to specific situations by those of ordinary skill in the art.
Referring to fig. 1, a super-surface structure provided in an embodiment of the present invention includes: a substrate 10, a plurality of nanostructures 20, and a filler 30 positioned around the nanostructures 20, the plurality of nanostructures 20 being periodically arranged on at least one side of the substrate 10; only 6 nanostructures 20 are shown in fig. 1. The filler 30 is filled around the plurality of nanostructures 20, and the filler 30 may be specifically a gas filler (for example, air, nitrogen, or the like), may be a solid filler (for example, silicon nitride, or the like), and may be a liquid filler when conditions allow, which is not limited in this embodiment.
The refractive indexes of the target elements at different positions are different, and the refractive index distribution of the target elements is in a gradient distribution; the target element comprises at least part of the nanostructures 20 and/or the target element comprises at least part of the filler 30. The material of the substrate 10, the material of the nanostructure 20, and the material of the filler 30 are different from each other.
In the embodiment of the present invention, the refractive index of the target element in the super-surface structure is graded, and the target element may be at least a part (part or all) of the nano-structure 20, or may be at least a part of the filler 30; that is, in embodiments of the present invention, the refractive index of at least a portion of the nanostructures 20 is graded, and/or the refractive index of at least a portion of the filler 30 is graded. For example, the refractive index of the plurality of nanostructures 20 is graded, and the refractive index of the filler 30 is the same; alternatively, the refractive index of the plurality of nanostructures 20 is the same, and the refractive index of the filler 30 is gradually changed; alternatively, the refractive index of the plurality of nanostructures 20 is graded, and the refractive index of the filler 30 is also graded. Wherein at least some of the nanostructures 20 refer to a plurality of nanostructures 20 in the same communication region, and at least some of the fillers 30 refer to the fillers 30 located in the same communication region. The communication region corresponding to the nanostructure 20 and the communication region corresponding to the filler 30 may be the same communication region, or may be two different communication regions, which is not limited in this embodiment.
Since the plurality of nanostructures 20 are periodically arranged on one side of the substrate 10, the refractive index profile of at least a portion of the nanostructures 20 or at least a portion of the filler 30 as a whole is a graded profile, for example, the refractive index is gradually increased, or the refractive index is gradually decreased, etc. Taking the nano-structure 20 as an example of graded index, referring to fig. 2, the target element includes nano- structures 21, 22, 23, 24, 26, and 27, and the filler 30 between the nano-structures is air, i.e. the refractive index of the filler 30 is uniform. With the nanostructure 21 as the center, the farther away from the nanostructure 21, the larger (or smaller) the refractive index of the other nanostructures. For example, the refractive index of the nanostructures 21, 23, 25, 27 gradually increases, and the refractive index of the nanostructures 21, 22, 24, 26 gradually increases, thereby forming nanostructures whose refractive index is graded.
It should be noted that the "graded distribution" in the embodiment of the present invention may be a continuous graded distribution, that is, the refractive index gradually changes with one nanostructure as a unit; for example, the refractive indices of the nanostructures 21, 23, 25, 27 in fig. 2 are different from each other and gradually increase. Alternatively, the "graded distribution" may be a discrete graded distribution in which the refractive index gradually changes per unit area of the nanostructure. For example, the refractive index of the nanostructures 21, 23, 25, 27 in fig. 2 is partially the same and gradually increases, so that the refractive index profile of the nanostructures is in a ring-shaped gradient profile; e.g. n21＝n23<n25＝n27Wherein n isiRepresenting the refractive index of the nanostructure i.
In the embodiment of the present invention, the nanostructures 20 are periodically arranged on one side of the substrate 10, and can be divided into a plurality of nanometer units by artificial division, wherein each nanometer unit comprises at least one nanostructure 20 and the filler 30 around the nanostructure 20; wherein, as shown in fig. 1, the dotted line represents the division manner of the nano unit, which totally divides 6 nano units, each nano structure 20 is located at the position of the center of gravity of the nano unit, and the structure of one nano unit can be seen in fig. 3; alternatively, the nanostructure 20 may be located at the vertex of the nano unit, and the division manner of the nano unit is not limited in this embodiment.
Wherein, for each nanometer unit, the equivalent refractive index of the nanometer unit can be determined based on a duty ratio method or a direct calculation method, and the equivalent refractive indexes calculated by the two methods are basically the same. Specifically, the method comprises the following steps:
the duty ratio method is to calculate the equivalent refractive index and the equivalent extinction coefficient of the nano unit composed of the nano structure 20 and the filler 30 according to the refractive index and the extinction coefficient of the nano structure 20, the refractive index and the extinction coefficient of the filler 30 and the ratio of the nano structure 20 and the filler 30 in the nano unit, and the calculation formulas are shown as formula (1), formula (2) and formula (3):
n1(λ)＝ρ′nu(λ)+ρ″nf(λ)， (1)
k1(λ)＝ρ′ku(λ)+ρ″kf(λ)， (2)
ρ′+ρ″＝1， (3)
wherein, the incident is the wavelength of light, n1(lambda) is the calculated equivalent refractive index of the nano-elements, k1(lambda) calculating to obtain the equivalent extinction coefficient of the nano unit; n isu(λ) is the refractive index of the nanostructure 20, nf(λ) is the refractive index of the filler 30; k is a radical ofu(λ) is the extinction coefficient, k, of the nanostructure 20f(λ) is the extinction coefficient of the filler 30; ρ' is the ratio of the area of the nanostructure 20 to the area of the nano-unit, and ρ ″ is the ratio of the area of the filler 30 to the area of the nano-unit.
The embodiment of calculating the equivalent refractive index and the equivalent extinction coefficient of the nano-unit by the direct calculation method is as follows:
directly calculating the phases of the nanometer units under different wavelengths by adopting a finite element analysis method
And transmittance T (λ), obtained phases at different wavelengths
And transmittance T (λ) are shown in FIG. 4, which is a graph of the cross-section of the fiber in FIG. 4The index indicates the Wavelength (Wavelength), the left ordinate indicates the transmittance (Transmission), and the right ordinate indicates the Phase (Phase). Obtaining the equivalent refractive index n corresponding to any wavelength by using a tangent method1(lambda), the equivalent extinction coefficient k corresponding to any wavelength is directly obtained by the definition of the extinction coefficient1(lambda). The equivalent refractive index and the equivalent extinction coefficient satisfy the following formula (4) and formula (5):
where h is the height of the nanostructures 20, T0 is the intensity of the incident light,
is the phase of the nano-unit at the wavelength λ, and T (λ) is the transmittance of the nano-unit at the wavelength λ.
From the above, as shown in the formula (1), the equivalent refractive index of the nano-unit and the refractive index n of the nano-structure 20u(lambda), refractive index n of filler 30f(λ) correlation. The nano-structure of the traditional super-lens has the same refractive index, or the filled material has the same refractive index, so that the equivalent refractive index of the traditional super-lens is mainly related to the ratio rho', and the equivalent refractive index interval of the super-surface is limited, thereby limiting the capability of the design of the super-lens with large numerical aperture and the chromatic aberration correction super-lens. In the embodiment of the present invention, at least one of the nanostructures 20 or the fillers 30 is graded in refractive index, that is, the refractive index of the nanostructures 20 at different positions is different, or the refractive index of the fillers 30 at different positions is different, that is, the refractive index of the nanostructures 20 or the fillers 30 is a range, and when the refractive index of at least one of the nanostructures 20 or the fillers 30 is a range, the corresponding equivalent refractive index interval is increased, so as to extend the equivalent refractive index interval.
And the equivalent refractive index interval and the maximum caliber of the super surface (such as a super lens) satisfy the following relation:
wherein, Δ neffIs an equivalent refractive index interval, rmaxIs the maximum caliber of the super surface, d is the height of the nanostructure 20, and f is the focal length of the super surface.
When the equivalent refractive index interval is expanded to k times of the original value (k is more than 1), namely the equivalent refractive index interval is increased from delta neffSpread to k Δ neffThe maximum caliber of the super-surface structure provided by the embodiment of the invention is increased to r'max：
Therefore, the super-surface structure can better correct chromatic aberration; and under the condition that the chromatic aberration correction range is not changed, when the caliber of the super-surface structure is increased, the numerical aperture and the resolution ratio are correspondingly improved, and high-resolution imaging is facilitated.
In addition, the material of the super-surface structure substrate 10 is different from the material of the nano-structure 20, specifically, the etching speed of the material of the substrate 10 is different from that of the nano-structure 20, and the etching speed of the material of the substrate 10 is much lower than that of the material of the nano-structure 20; for example, the etching rates of the two are not different by a factor of 10. The substrate 10 acts as a stop layer for the nanostructures 20 during etching, so that the loading effect can be reduced.
For the existing superlens, if the etching speeds of the nano structure and the substrate are similar (especially, the materials of the nano structure and the substrate are the same, and the etching speeds of the nano structure and the substrate are also completely the same), in the etching process, due to different duty ratios of different periods, the etching speeds (such as the flow rate of etching gas and the like) are different, so that a load effect is generated during etching, and the etching bottom is stepped; when the existing superlens has a load effect, an electron microscope image of the superlens can be seen in fig. 5, and Δ h in fig. 5 represents a step-like height difference caused by the load effect, and as can be seen from fig. 5, the height difference Δ h almost occupies 1/5 of the height of the whole nanostructure, and the modulation effect of the nanostructure on light is greatly influenced. When the adopted nano structure is a nano structure with gradually changed refractive index, the difference of etching depth is additionally introduced, and the loading effect is more obvious.
In the embodiment of the present invention, the material of the substrate 10 is different from the material of the nanostructure 20, so that the etching rates of the substrate 10 and the nanostructure 20 are completely different, and the etching rate of the material of the substrate 10 is much lower than that of the material of the nanostructure 20. When the nano-structure 20 is etched, since the etching speed of the substrate 10 is low (even negligible, that is, the substrate 10 cannot be etched), the substrate 10 functions as a stop layer, and the height uniformity of all the nano-structures 20 can be ensured by properly prolonging the etching time, so that the height difference caused by the load effect can be avoided.
And, the material of the super surface structure substrate 10 is different from that of the nano structure 20, so that there is enough difference between the equivalent refractive index of the nano unit and the refractive index of the substrate 10, which can improve the transmittance of the super surface structure. Optionally, the material of the super surface structure substrate 10, the material of the nano structure 20 and the material of the filler 30 are different from each other.
According to the super-surface structure provided by the embodiment of the invention, the refractive indexes of the nano-structure 20 and/or the filler 30 are gradually distributed, and the nano-structure 20 and the filler 30 with different refractive indexes can expand the equivalent refractive index interval of nano units, so that the chromatic aberration of the super-surface structure can be better corrected; the numerical aperture of the super-surface structure can be improved, the resolution ratio is correspondingly improved, high-resolution imaging is facilitated, and the method has important application in aspects such as a large-numerical-aperture super-lens and a chromatic aberration correction super-lens. The material of the substrate 10 is different from that of the nano structure 20, so that the substrate 10 can play a role of a stop layer, the problem of height difference of the etching bottom caused by a load effect is avoided, and the height consistency of the nano structure 20 can be ensured; moreover, the super-surface structure has higher transmittance.
Optionally, in order to implement the gradual refractive index change, in the embodiment of the present invention, the target element is made of a gradual refractive index material; i.e., the material of the nanostructures 20 is a graded index material, and/or the material of the filler 30 is a graded index material. The graded Index material may be, for example, a GRIN (Gradient-Index) material or the like.
Alternatively, the target element is made of materials with different doping concentrations; i.e. the nanostructures 20 as a whole are of the same material, but the doping concentration of the nanostructures 20 is different at different locations, and/or the filler 30 as a whole is of the same material, but the doping concentration of the filler 30 is different at different locations. For example, the nano-structure 20 is made of silicon, and doped with impurities, and the doping concentration of the nano-structure 20 at different positions is different, so that the refractive index of the nano-structure 20 is different and is distributed in a gradual manner.
Optionally, in order to facilitate the realization of the refractive index gradual change in the process, the refractive index distribution of the target element is in a simple convex distribution or a concave distribution. For example, the refractive index profile includes at least one convex profile having a large middle refractive index and a small side refractive index along the surface direction of the super-surface structure. Or the refractive index distribution comprises at least one concave distribution with a small middle refractive index and large two sides refractive index along the surface direction of the super-surface structure.
In an embodiment of the present invention, the super-surface structure is a substantially planar structure, and the surface direction of the super-surface structure refers to a direction on the surface of the planar structure. As shown in fig. 2, fig. 2 is a side view of the super-surface structure, and the left-right direction in fig. 2 is a surface direction of the super-surface structure. The position of the target element corresponding to the point with the refractive index of the extreme value (maximum value or minimum value) is used as a reference point, and the surface direction of the super-surface structure is the direction passing through the reference point in the surface of the super-surface structure. For example, the center of the super-surface structure has the maximum refractive index or the minimum refractive index, and the surface direction of the super-surface structure is a direction passing through the center, for example, a radial direction of the super-surface structure.
For example, referring to fig. 6, the refractive index distribution of the target element has a convex distribution; alternatively, referring to fig. 7, the refractive index distribution of the target element is in a concave distribution.
Alternatively, the convex profile may comprise a convex first parabolic profile. Alternatively, the convex profile may comprise a convex gaussian profile. FIG. 6 illustrates a convex Gaussian distribution; in fig. 6, the target device is a nanostructure as an example, that is, the refractive index distribution of the nanostructure is in accordance with a convex gaussian distribution, and the gradation of the nanostructure in fig. 6 indicates the magnitude of the refractive index.
Optionally, the gaussian distribution of the convex profile satisfies:
wherein n is2,maxDenotes the maximum refractive index, r, in a convex Gaussian distribution2Denotes the distance between the target element and the position corresponding to the maximum refractive index in the Gaussian distribution of the convex type, n2(r2) Denotes the distance r between the positions corresponding to the maximum refractive index in the Gaussian distribution2Refractive index of the target element of (1), beta2Denotes the coefficient of variation of the refractive index, σ2A standard deviation of a Gaussian distribution representing a convex type, a is an adjustment coefficient, and a>0; in general, a.gtoreq.1.
In the embodiment of the present invention, in the convex distribution, the refractive index distribution of the target element is related to the distance from the target element to the maximum refractive index corresponding position, and in the convex gaussian distribution, r is used2Represents the distance, the distance r2And also the radius of the target element (the center of the circle is the position corresponding to the maximum refractive index). Referring to fig. 6, the position corresponding to the maximum refractive index in the gaussian distribution is the center of the super-surface structure, and the refractive indexes of the nanostructures 20 at other positions can be determined by taking the center of the super-surface structure as a reference; if the super-surface structure is circular, the distance r is set as described above2Indicating the radius to which the nanostructure 20 is positioned. As shown in FIG. 6, since the refractive index of the nanostructures 20 is graded, the graded refractive index nanostructures can introduce a refractive index range of Δ nFurther, the equivalent refractive index range can be expanded.
Optionally, the first parabolic profile satisfies:
wherein n is1,maxDenotes the maximum refractive index in the first parabolic profile, r1Representing the distance between the target element and the position corresponding to the maximum refractive index in the first parabolic profile, n1(r1) Denotes a distance r between positions corresponding to the maximum refractive index in the first parabolic profile1Refractive index of the target element of (1), beta1Representing the index of change coefficient of the refractive index.
Similar to the convex gaussian distribution described above, the first parabolic distribution is a convex parabolic distribution, and the refractive index of the target element is a distance (here, r) from the position corresponding to the maximum refractive index1Indicating the distance). For example, the maximum refractive index corresponding position in the first parabolic profile may also be the center of the super-surface structure.
It will be understood by those skilled in the art that the convex distribution (and the concave distribution described below) in the present embodiment refers to a distribution along the surface direction of the super-surface structure, which is a two-dimensional distribution; however, since the nanostructures 20 of the super-surface structure are tiled on the substrate 10, the refractive index distribution of all the nanostructures 20 can be described by a three-dimensional distribution, such as a three-dimensional gaussian distribution, which is substantially the same as that described in the present embodiment.
Alternatively, the concave distribution may comprise a concave second parabolic distribution, similar to the convex distribution described above. Alternatively, the concave distribution may comprise a concave gaussian distribution. FIG. 7 illustrates a concave Gaussian distribution; in fig. 7, the target element is taken as an example of the nanostructure, that is, the refractive index distribution of the nanostructure is in accordance with a concave gaussian distribution, and the grayscale of the nanostructure in fig. 7 indicates the magnitude of the refractive index.
For example, the gaussian distribution of the concave type satisfies:
wherein n is4,maxDenotes a predetermined maximum refractive index, r4Denotes the distance between the target element and the position corresponding to the minimum refractive index in the Gaussian distribution of the concave form, n4(r4) Denotes the distance r between the positions corresponding to the minimum refractive index in the concave Gaussian distribution4Of the target element, σ4Standard deviation of concave Gaussian distribution, b is preset adjustment coefficient, and 0<b<1。
In the embodiment of the invention, n4,maxIndicating a predetermined maximum refractive index, which is used only for determining the refractive index profile and is not used for indicating that the refractive index of a certain target element is n4,max. For example, the minimum index corresponding position in the concave gaussian distribution may be the center of the super-surface structure.
Alternatively, the second parabolic profile satisfies:
wherein n is3,minDenotes the minimum refractive index, r, in the second parabolic profile3Representing the distance between the target element and the location corresponding to the smallest refractive index in the second parabolic profile, n3(r3) Denotes a distance r between positions corresponding to the minimum refractive index in the second parabolic profile3Refractive index of the target element of (1), beta3Representing the index of change coefficient of the refractive index.
Further alternatively, the refractive index distribution may include a plurality of convex distributions or a plurality of concave distributions. Referring to fig. 8, the refractive index profile includes two convex profiles; alternatively, as shown in fig. 9, the refractive index profile includes two concave profiles.
Alternatively, if the refractive index profile comprises an even number of convex profiles, the refractive index profile may be centrosymmetric, and the center of the super-surface structure is a minimum value of the refractive index, as shown in fig. 8. Or, if the refractive index distribution 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 super-surface structure.
Accordingly, if the refractive index profile comprises an even number of concave profiles, the refractive index profile may be centrosymmetric, with the center of the super-surface structure being a maximum of the refractive index, as shown in fig. 9. Or, if the refractive index distribution 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 super-surface structure.
The super-surface structure is described in detail below by one embodiment.
In the embodiment of the present invention, the nano-structure 20 is made of a silicon-doped material, the substrate 10 is chalcogenide glass, the working wavelength is 8 to 12 μm, and the filler 30 is air. The nano structures 20 are arranged according to a regular hexagon period, the nano structures 20 comprise nano columns, nano holes, hollow nano columns and annular nano hole structures, the height of the nano structures 20 is 11.8 mu m, the period is 3.04 mu m, and the minimum line width is 700 nm. When intrinsic silicon is used as the nanostructure material, the equivalent refractive index interval Δ n is shown in fig. 10effIs 1.2. Compared with the super-surface with the nano-structure of intrinsic silicon, the super-surface with the nano-structure of silicon with different doping concentrations has the equivalent refractive index interval delta neffIs 1.7 (corresponding to a doping concentration of from 10)19cm-2To 0), see in particular fig. 11. From equation (6), when graded index (doped) nanostructures are used, the achromatic 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 when the focal lengths are all 1 mm.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes or substitutions within the technical scope of the present invention, and the present invention shall be covered by the claims. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (14)
1. A super-surface structure, comprising: a substrate (10), a plurality of nanostructures (20), and a filler (30) located around the nanostructures (20), the plurality of nanostructures (20) being periodically arranged on at least one side of the substrate (10);
the refractive indexes of the target elements at different positions are different, and the refractive index distribution of the target elements is a gradient distribution; the target element comprises at least part of the nanostructures (20) and/or the target element comprises at least part of the filler (30);
the material of the substrate (10) is different from the material of the nanostructures (20).
2. A super-surface structure according to claim 1, wherein the refractive index profile comprises at least one convex profile with a large middle refractive index and a small side refractive index along the surface direction of the super-surface structure.
3. A super-surface structure according to claim 2, wherein said convex profile comprises a convex first parabolic profile.
4. A super-surface structure according to claim 3, wherein the first parabolic profile satisfies:
wherein n is1,maxRepresents the maximum refractive index, r, in the first parabolic profile1Representing the distance between the target element and the position corresponding to the maximum refractive index in said first parabolic profile, n1(r1) Represents a distance r between positions corresponding to the maximum refractive index in the first parabolic profile1Refractive index of the target element of (1), beta1Indicating the index of change coefficient of the refractive index.
5. A super-surface structure according to claim 2, wherein said convex profile comprises a convex gaussian profile.
6. A super-surface structure according to claim 5, wherein the convex Gaussian distribution satisfies:
wherein n is2,maxRepresents the maximum refractive index in the Gaussian distribution, r2N represents the distance between the target element and the position corresponding to the maximum refractive index in the convex Gaussian distribution2(r2) The distance between the positions corresponding to the maximum refractive index in the convex Gaussian distribution is represented by r2Refractive index of the target element of (1), beta2Denotes the coefficient of variation of the refractive index, σ2A is a standard deviation of the convex Gaussian distribution, a is an adjustment coefficient, and a>0。
7. A super-surface structure according to claim 2, wherein in case the refractive index comprises an odd number of convex profiles, the corresponding position of maximum refractive index in one of the convex profiles is the center of the super-surface structure.
8. The super-surface structure according to claim 1, wherein the refractive index profile comprises at least one concave profile with a small refractive index in the middle and a large refractive index on both sides along the surface direction of the super-surface structure.
9. The super-surface structure according to claim 8, wherein the concave distribution comprises a concave second parabolic distribution.
10. The super-surface structure according to claim 9, wherein the second parabolic profile satisfies:
wherein n is3,minRepresenting the minimum refractive index, r, in said second parabolic profile3Representing the distance, n, between the target element and the location corresponding to the smallest refractive index in said second parabolic profile3(r3) Represents a distance r between positions corresponding to the minimum refractive index in the second parabolic profile3Refractive index of target element of (1), beta3Representing the index of change coefficient of the refractive index.
11. The super-surface structure according to claim 8, wherein the concave profile comprises a concave gaussian profile.
12. A super-surface structure according to claim 11, wherein the concave gaussian distribution satisfies:
wherein n is4,maxDenotes a predetermined maximum refractive index, r4Representing the distance between the target element and the position corresponding to the minimum refractive index in the Gaussian distribution of the concave form, n4(r4) Represents a distance r between positions corresponding to the minimum refractive index in the concave Gaussian distribution4Of the target element, σ4A standard deviation of the concave Gaussian distribution, b is a preset adjustment coefficient, and 0<b<1。
13. The super-surface structure according to claim 8, wherein in case the refractive index comprises an odd number of concave distributions, the minimum refractive index corresponding position in one of the concave distributions is the center of the super-surface structure.
14. The super surface structure according to any one of claims 1 to 13,
the target element is made of a gradient refractive index material;
alternatively, the target elements are made of materials with different doping concentrations.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115079415A (en) * | 2022-07-12 | 2022-09-20 | 深圳迈塔兰斯科技有限公司 | Hole light near-to-eye display system |
| US11927769B2 (en) | 2022-03-31 | 2024-03-12 | Metalenz, Inc. | Polarization sorting metasurface microlens array device |
| US11978752B2 (en) | 2019-07-26 | 2024-05-07 | Metalenz, Inc. | Aperture-metasurface and hybrid refractive-metasurface imaging systems |
| US11988844B2 (en) | 2017-08-31 | 2024-05-21 | Metalenz, Inc. | Transmissive metasurface lens integration |
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- 2022-04-28 CN CN202210461490.XA patent/CN114660683A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US11988844B2 (en) | 2017-08-31 | 2024-05-21 | Metalenz, Inc. | Transmissive metasurface lens integration |
| US11978752B2 (en) | 2019-07-26 | 2024-05-07 | Metalenz, Inc. | Aperture-metasurface and hybrid refractive-metasurface imaging systems |
| US11927769B2 (en) | 2022-03-31 | 2024-03-12 | Metalenz, Inc. | Polarization sorting metasurface microlens array device |
| CN115079415A (en) * | 2022-07-12 | 2022-09-20 | 深圳迈塔兰斯科技有限公司 | Hole light near-to-eye display system |
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