WO2013060119A1

WO2013060119A1 - Metamaterial and method for designing refractive index distribution thereof

Info

Publication number: WO2013060119A1
Application number: PCT/CN2012/073749
Authority: WO
Inventors: 刘若鹏; 季春霖; 岳玉涛; 杨青
Original assignee: 深圳光启高等理工研究院; 深圳光启创新技术有限公司
Priority date: 2011-10-28
Filing date: 2012-04-10
Publication date: 2013-05-02
Also published as: CN102544742A

Abstract

Provided is a metamaterial, which comprises a functional layer formed by superposing a plurality of functional metamaterial sheet layers having the same thickness and refractive index distribution. Each functional metamaterial sheet layer comprises a base material and a plurality of artificial metal microstructures periodically arranged on the base material. The refractive index of the functional metamaterial sheet layer is concentrically distributed about the center point of the functional metamaterial sheet layer, the refractive index being the largest at the center of circle, and being the same at the same radius. Also provided are a metamaterial and a method for designing refractive index distribution thereof. The refractive index distribution on the functional metamaterial sheet layers is obtained through an initial phase method. Since the refractive index distribution on the metamaterial sheet layers is obtained through the initial phase method, the application range is wide, and the calculation process is easily programmed and coded. A user only needs to master the use method of the code, which facilitates large-scale popularization.

Description

Design method of refractive index distribution of metamaterial and its metamaterial

[Technical Field]

The invention relates to the technical field of artificial electromagnetic materials, in particular to a metamaterial. 【Background technique】

"Supermaterial" refers to artificial composite structures or composite materials that have extraordinary physical properties not found in natural materials. Through the orderly design of the structure on the key physical scale of the material, it is possible to break through the limitations of certain apparent natural laws, thereby obtaining the extraordinary material function beyond the ordinary nature inherent in nature.

The refractive index distribution inside the metamaterial is a key part of the super-material exhibiting extraordinary functions, and different refractive index distributions correspond to different functions. The more precise the refractive index profile, the better the functionality achieved. However, the current design method of the refractive index distribution of the metamaterial is very complicated on the one hand, and the effect obtained on the other hand is not satisfactory.

[Summary of the Invention]

The technical problem to be solved by the present invention is to provide a design method of a refractive index distribution of a metamaterial which is simple in calculation method and convenient for large-scale implementation, and a metamaterial having the refractive index distribution, in view of the above-mentioned deficiencies of the prior art.

The technical solution adopted by the present invention to solve the technical problem is to provide a metamaterial comprising a functional layer formed by stacking a plurality of functional supermaterial sheets having the same thickness and the same refractive index distribution, each functional super material layer The substrate comprises a plurality of artificial metal microstructures periodically arranged on the substrate, and the refractive index of the functional super material sheet is concentrically distributed with a center point thereof as a center, and the refractive index at the center of the circle is the largest and the same radius The refractive index is the same; the refractive index distribution on the functional metamaterial sheet is obtained by the following steps:

S1: plot the area where the metamaterial is located and the boundary of each layer of the functional metamaterial sheet. At this time, the metamaterial region is filled with air, and the feed is fixed in front of the metamaterial region and the center axis of the feed and the central axis of the metamaterial region are made. Coincidence; the source radiates electromagnetic waves and then tests and records the i-th layer superstructure on the metamaterial functional layer The initial phase of the front surface of the web layer, the initial phase of each point of the front surface of the i-th functional super-material sheet is denoted as (wherein the initial phase at the central axis is denoted as (0);

S2: According to the formula Ψ = . (0) - ^Σ '' ^ ^π , to obtain the phase Ψ of the back surface of the entire metamaterial,

A

Wherein M is the total number of layers of functional metamaterial layers constituting the metamaterial functional layer, d is the thickness of each functional supermaterial sheet layer, is the wavelength of the electromagnetic wave radiated by the feed, and n _max is the functional super material sheet layer Maximum refractive index value;

S3: Substituting the initial phase of the test in step SI according to the formula Ψ = ^Ο -^^ * 2 τ

^O and the reference phase 得到 obtained in step S2, which gives the refractive index distribution of the functional metamaterial sheet),

Where y is the distance from any point on the functional metamaterial sheet to the central axis of the functional metamaterial sheet. Further, the metamaterial further includes first to Nth layer impedance matching layers symmetrically disposed on both sides of the functional layer, wherein the two Nth impedance matching layers are in close contact with the functional layer.

Further, the first to Nth layer impedance matching layers are first to Nth matching metamaterial sheets, and each layer of matching metamaterial sheets includes a second substrate and a plurality of periodically arranged on the second substrate The second artificial metal microstructure; the refractive index of each layer of the matching metamaterial sheet is concentrically distributed with the center point as a center, the refractive index at the center of the circle is the largest, and the refractive index at the same radius is the same; the first to the Nth match The refractive indices at the same radius on the metamaterial sheet are not the same.

Further, the relationship between the first to Nth matching metamaterial sheets and the refractive index distribution of the functional metamaterial sheet is:

N(y)j = n _min + ^^ H (y) - n _min ) where j represents the number of the first to Nth matching metamaterial sheets, and n _mm is the functional metamaterial sheet Minimum refractive index value.

Further, the first substrate and the second substrate are made of the same material, and the first substrate and the second substrate are made of a polymer material, a ceramic material, a ferroelectric material, a ferrite material or a ferromagnetic material. Made of materials.

Further, the first artificial microstructure is the same as the second artificial microstructure material and geometry. Further, the first artificial microstructure and the second artificial microstructure are metal microstructures having a "gong"-shaped geometry, the metal microstructures including a vertical first metal branch and located at the first Two metal branches at both ends of the metal branch and perpendicular to the first metal branch.

Further, the metal microstructure further includes a third metal branch located at each end of each second metal branch and perpendicular to the second metal branch.

Further, the first artificial microstructure and the second artificial microstructure are metal microstructures having a planar snowflake-shaped geometry, the metal microstructures including two first metal branches perpendicular to each other and located at the a second metal branch at both ends of the first metal branch and perpendicular to the first metal branch.

The invention also provides a method for designing a refractive index distribution of a metamaterial, comprising the steps of:

S1: drawing a boundary between the region where the metamaterial is located and the layers of the metamaterial sheet constituting the metamaterial, filling the region of the metamaterial with air, fixing the feed in front of the metamaterial region and making the center axis of the feed and the super The center axis of the material region coincides; the initial phase of the front surface of the i-th layer of the super-material layer on the meta-material layer is tested and recorded after the electromagnetic wave is radiated by the feed, and the initial phase of each point on the front surface of the i-th layer of the super-material layer is recorded as ( , where the initial phase at the central axis is denoted as (0);

S2: According to the formula Ψ = . (0)- ^Σ '' ^ ^π , to obtain the phase Ψ of the back surface of the entire metamaterial,

A

Wherein M is the total number of layers of the super material sheet, d is the thickness of each layer of the super material sheet, is the wavelength of the electromagnetic wave radiated by the feed, and n _max is the maximum refractive index value of the layer of the super material;

S3: According to the formula Ψ = Ο -^^ *2 τ, substituting the initial phase φ 测试 obtained in the step S1 and the reference phase 得到 obtained in the step S2, the refractive index distribution of the metamaterial sheet is obtained, wherein y is super The distance from any point on the layer of material to the central axis of the layer of metamaterial.

Further, after step S1, the initial phase ^0 obtained by the step S1 is further adjusted, so that the initial phase (0) at the central axis of the metamaterial is the maximum value of ^0.

Further, different i values are selected to select different functional supermaterial sheet front surface tests, and refractive index distributions of multiple sets of metamaterial functional layers are obtained, and the obtained plurality of refractive index profiles are compared and Choose the best result.

The refractive index distribution on the super-material layer in the invention is obtained by the initial phase method, and the application range is wide, and the calculation process is easy to realize programmatic and coding, and the user only needs to master the use of the code, which is convenient for large-scale promotion.

[Description of the Drawings]

1 is a schematic perspective view of a basic unit constituting a metamaterial;

2 is a schematic diagram of calculation of a refractive index distribution of a metamaterial of the present invention;

3 is a geometric topological pattern of a man-made metal microstructure of a first preferred embodiment capable of responding to electromagnetic waves to change the refractive index of the base element of the metamaterial;

4 is a derivative pattern of the artificial metal microstructure geometry topographic pattern of FIG. 3;

Figure 5 is a geometric topological pattern of a man-made metal microstructure of a second preferred embodiment capable of responding to electromagnetic waves to change the refractive index of the base element of the metamaterial;

Figure 6 is a derivative pattern of the artificial metal microstructure geometry topographical pattern of Figure 5.

【detailed description】

Light, as a kind of electromagnetic wave, when passing through the glass, because the wavelength of the light is much larger than the size of the atom, we can describe the overall parameters of the glass, such as the refractive index, rather than the details of the atoms that make up the glass. The response of the glass to light. Correspondingly, when studying the response of materials to other electromagnetic waves, the response of any structure in the material that is much smaller than the wavelength of the electromagnetic wave to the electromagnetic wave can also be described by the overall parameters of the material, such as the dielectric constant ε and the magnetic permeability μ. By designing the structure of each point of the material, the dielectric constant and magnetic permeability of each point of the material are the same or different, so that the dielectric constant and magnetic permeability of the material are arranged regularly, and the magnetic permeability and the regular arrangement are regularly arranged. The electrical constant allows the material to have a macroscopic response to electromagnetic waves, such as converging electromagnetic waves, diverging electromagnetic waves, and the like. This type of material with regularly arranged magnetic permeability and dielectric constant is called a metamaterial.

As shown in FIG. 1, FIG. 1 is a schematic perspective view of a basic unit constituting a metamaterial. Metamaterial The base unit comprises an artificial microstructure 1 and a substrate 2 to which the artificial microstructure is attached. In the present invention, the artificial microstructure is an artificial metal microstructure, and the artificial metal microstructure has a planar or stereo topology capable of responding to an incident electromagnetic wave electric field and/or a magnetic field, and changes the artificial metal microstructure on each metamaterial basic unit. The pattern and/or size can change the response of each metamaterial base unit to incident electromagnetic waves. The arrangement of a plurality of metamaterial basic units in a regular pattern enables the metamaterial to have a macroscopic response to electromagnetic waves. Since the supermaterial as a whole needs to have a macroscopic electromagnetic response to the incident electromagnetic wave, the response of each metamaterial basic unit to the incident electromagnetic wave needs to form a continuous response, which requires that the size of each metamaterial basic unit is one tenth to five fifths of the incident electromagnetic wave. First, it is preferably one tenth of the incident electromagnetic wave. In the description of this paragraph, we artificially divide the supermaterial into a plurality of basic units of metamaterials, but it should be understood that this method of division is only convenient for description, and should not be regarded as supermaterial being spliced or assembled by multiple metamaterial basic units. In the actual application, the super material is formed by arranging the artificial metal microstructure period on the substrate, and the process is simple and the cost is low. The periodic arrangement means that the man-made metal microstructures on the basic units of each metamaterial divided by us can produce a continuous electromagnetic response to incident electromagnetic waves. In the present invention, the substrate 2 may be selected from a polymer material, a ceramic material, a ferroelectric material, a ferrite material or a ferromagnetic material, and the polymer material is preferably FR-4 or F4B. The artificial metal microstructure may be arranged on the substrate 2 by etching, electroplating, drilling, photolithography, electron engraving or ion etching, wherein the etching is a superior process, and the step is to cover the metal sheet on the substrate 2 Then, a chemical solvent is used to remove the metal other than the preset artificial metal pattern.

In the present invention, the refractive index distribution of the entire super-material is designed by using the above-described metamaterial principle, and then the artificial metal microstructure is periodically arranged on the substrate 2 according to the refractive index distribution to change the electromagnetic response of the incident electromagnetic wave to achieve the required Features.

For refractive index design on metamaterials, the conventional design method is the formula method, which uses the principle of equal optical path approximation to obtain the corresponding refractive index values at each point of the metamaterial. The refractive index distribution of the metamaterial obtained by the formula method can be applied to the simpler system simulation design. However, due to the fact that the electromagnetic wave distribution is not perfectly consistent with the distribution of electromagnetic waves in the software simulation, the complex method is obtained by the formula method. There is a large error in the refractive index distribution of the metamaterial.

The present invention utilizes an initial phase method to design a refractive index distribution of a metamaterial, and the metamaterial of the present invention is to be realized The function is to convert electromagnetic waves into planar electromagnetic waves to improve the directivity of each electronic component. The metamaterial includes a functional layer, and the functional layer is composed of a plurality of functional supermaterial sheets having the same thickness and the same refractive index distribution, and the functional metamaterial sheet includes the first substrate and the plurality of periodically arranged on the first substrate. The first artificial metal microstructure, the refractive index distribution of the functional super material sheet has a concentric circular distribution on its cross section, that is, the points of the same refractive index on the functional super material sheet form a concentric circle, and the refractive index at the center of the circle is the largest. The maximum refractive index value n _max is a certain value. Similarly, the refractive index distribution of the functional metamaterial sheet is vertically symmetrically distributed on the longitudinal section thereof with its central axis as the axis of symmetry, and the refractive index on the central axis is the maximum refractive index. The value is n _max .

The specific steps of designing the refractive index distribution of the above-mentioned metamaterial by the initial phase method are discussed in detail below: S1: The boundary between the region where the metamaterial is located and the layers of the functional supermaterial sheet are drawn, and the metamaterial region is filled with air, and the feed will be fed. It is fixed in front of the metamaterial region and makes the center axis of the feed coincide with the central axis of the metamaterial region, as shown in Fig. 2. After the feed radiates electromagnetic waves, the initial phase of the front surface of the i-th functional super-material layer on the meta-material functional layer is tested and recorded, and the initial phase of each point of the front surface of the i-th functional super-material layer is recorded as (where The initial phase at the axis is denoted as (0).

In the present invention, the front surface refers to a side surface close to the feed, and the rear surface refers to a side surface away from the feed.

S2: According to the formula Ψ = . (0)- ^Σ '' ^ ^π , to get the phase of the back surface of the entire metamaterial.

A

Wherein M is the total number of layers of functional metamaterial layers constituting the metamaterial functional layer, d is the thickness of each functional supermaterial sheet layer, is the wavelength of the electromagnetic wave radiated by the feed, and n _max is the functional super material sheet layer The maximum refractive index value.

In the above formula, since the object of the present invention is to convert the electromagnetic wave radiated by the feed source into a planar electromagnetic wave radiation after passing through the metamaterial, and at the same time, the metamaterial of the present invention is in the form of a flat plate, it is required to form an isophase surface on the rear surface of the metamaterial. In the present invention, the refractive index at the central axis of the metamaterial is constant, and therefore the phase at the central axis of the back surface of the metamaterial is used as a reference value.

S3: According to the formula Ψ = ^() - ^Σ '· ^ ^{) ά} ^ 2π , substituting the initial phase O obtained in the step S1 and the reference phase 得到 obtained in the step S2, the refractive index of the functional metamaterial layer is obtained. Minute Cloth "(y).

Where y is the distance from any point on the functional metamaterial sheet to the central axis of the functional metamaterial sheet. Preferably, after step S1, the initial phase ^ 0 obtained by the step S1 is adjusted so that the initial phase ^(0) at the central axis of the metamaterial is the maximum value of ^0.

The invention can also obtain the refractive index distribution of the plurality of sets of metamaterial functional layers by selecting different i values, that is, selecting different functional supermaterial sheet front surface tests, and comparing the obtained plurality of sets of refractive index distributions “0 and Choose the best result.

The above steps of the present invention are easy to implement programmatic and coded. After programming and coding, the user only needs to define the initial boundary value boundary of the program to automatically obtain the super material refractive index distribution by the computer. Promotion.

At the same time, due to technical limitations, the refractive index minimum n _mm on the metamaterial functional layer is difficult to reach a value close to air. Therefore, the metamaterial functional layer and the air have a sudden change in refractive index, which will radiate electromagnetic waves to the surface of the metamaterial functional layer. Partial reflection, causing the gain of the electronic component to drop. In order to solve the above problem, in the present invention, preferably, two layers of impedance matching layers are symmetrically disposed on both sides of the functional layer, and each layer of the impedance matching layer is composed of a plurality of layers of matched metamaterial sheets. Each layer of matching metamaterial sheets comprises a second substrate and a second man-made metal microstructure periodically arranged on the second substrate, each layer of matching metamaterial sheets having an equal thickness equal to the thickness of the functional metamaterial sheet, each The refractive index of the point corresponding to the same axis on the super-material layer of the matching layer is graded.

The relationship between the refractive index distribution of each impedance matching layer and the refractive index distribution of the functional metamaterial layer) may be

Where j represents the number of the first to Nth matching metamaterial sheets, the Nth matching metamaterial sheet is in close contact with the metamaterial functional layer, and n _mm is the minimum refractive index value of the metamaterial functional layer.

The geometry of the man-made metal microstructure that satisfies the above-described functional metamaterial sheet and the matching supermaterial sheet refractive index distribution is various, but both are geometric shapes that are responsive to incident electromagnetic waves. The most typical is the "work" shaped artificial metal microstructure. Several man-made metal microstructure geometries are described in detail below. The dimensions of the man-made metal microstructure corresponding to the refractive index of each point on the functional metamaterial sheet and the matching metamaterial sheet can be obtained by computer simulation or manually calculated. In the present invention, in order to facilitate large regulations The first base material and the second base material of the functional metamaterial sheet and the matching metamaterial sheet are made of the same material, and the first metal microstructure and the second metal microstructure have the same geometry.

As shown in FIG. 3, FIG. 3 is a geometric topological pattern of a man-made metal microstructure of a first preferred embodiment capable of responding to electromagnetic waves to change the refractive index of the base element of the metamaterial. In Fig. 3, the man-made metal microstructure has a "work" shape, including a vertical first metal branch 1021 and a second metal branch 1022 that is perpendicular to the first metal branch 1021 and located at opposite ends of the first metal branch. 4 is a derivative pattern of the artificial metal microstructure geometry topography pattern of FIG. 3, which includes not only the first metal branch 1021, the second metal branch 1022, but also a third vertical portion at each end of each second metal branch 1022. Metal branch 1023.

Figure 5 is a geometric topographical pattern of a man-made metal microstructure of a second preferred embodiment capable of responding to electromagnetic waves to change the refractive index of the meta-material base unit. In FIG. 5, the artificial metal microstructure is a flat snowflake type, and includes a first metal branch 1021' perpendicular to each other and a second metal branch 1022' disposed at both ends of the two first metal branches 1021'; FIG. 6 is FIG. a derivative pattern of the man-made metal microstructure geometry topographical pattern, comprising not only two first metal branches 1021 ', four second metal branches 1022, four second metal branches 1022, but also a third metal disposed at both ends Branch 1023,. Preferably, the first metal branches 1021' are equal in length and intersect perpendicular to the midpoint, the second metal branches 1022' are of equal length and the midpoint is at the end of the first metal branch 1021, the third metal branch 1023 is of equal length and midpoint Located at the end of the second metal branch 1022'; the metal branch is arranged such that the artificial metal microstructure is isotropic, that is, the artificial metal microstructure is rotated by 90° in any direction in the plane of the artificial metal microstructure. The structure coincides. The use of isotropic man-made metal microstructures simplifies design and reduces interference.

The embodiments of the present invention have been described above with reference to the drawings, but the present invention is not limited to the specific embodiments described above, and the specific embodiments described above are merely illustrative and not restrictive, and those skilled in the art In the light of the present invention, many forms may be made without departing from the spirit and scope of the invention as claimed.

Claims

Rights request

What is claimed is: 1. A metamaterial, characterized in that: the metamaterial comprises a functional layer formed by stacking a plurality of functional metamaterial layers having the same thickness and the same refractive index distribution, each functional supermaterial layer comprising a substrate and a plurality of man-made metal microstructures periodically arranged on the substrate, wherein the refractive index of the functional metamaterial sheet is concentrically distributed with a center point thereof as a center, and the refractive index at the center of the circle is the largest, and the refractive index at the same radius The same; the refractive index distribution on the functional metamaterial sheet is obtained by the following steps:

S1: plot the area where the metamaterial is located and the boundary of each layer of the functional metamaterial sheet. At this time, the metamaterial region is filled with air, and the feed is fixed in front of the metamaterial region and the center axis of the feed and the central axis of the metamaterial region are made. The initial phase of the front surface of the i-th functional super-material layer on the super-material functional layer is tested and recorded after the electromagnetic wave is radiated by the feed, and the initial phase of each point of the front surface of the i-th functional super-material layer is recorded as ( Where the initial phase at the central axis is recorded as (0);

A

S3: According to the formula Ψ = ) _ ^∑ί · ^ ^{) ά} - 2π , substituting the initial phase obtained in step SI

Where y is the distance from any point on the functional metamaterial sheet to the central axis of the functional metamaterial sheet.

2. The metamaterial according to claim 1, wherein: the metamaterial further comprises first to Nth layer impedance matching layers symmetrically disposed on both sides of the functional layer, wherein the two layers of the Nth impedance matching layer are tight Paste the functional layer.

3. The metamaterial according to claim 2, wherein: the first to Nth layer impedance matching layers are first to Nth matching metamaterial sheets, and each layer of matching metamaterial sheets includes a second base And a plurality of second man-made metal microstructures periodically arranged on the second substrate; each layer matching the refractive index of the layer of the super material to The center point is a concentric circular distribution of the center, the refractive index at the center of the circle is the largest, and the refractive index is the same at the same radius; the refractive indices at the same radius on the first to Nth matching metamaterial sheets are different.

4. The metamaterial according to claim 3, wherein: the relationship between the first to Nth matching metamaterial sheets and the refractive index distribution MO of the functional metamaterial sheet is:

Where j represents the number of the first to Nth matching metamaterial sheets, and n _mm is the minimum refractive index value of the functional metamaterial sheet.

The metamaterial according to claim 3, wherein: the first substrate and the second substrate are made of the same material, and the first substrate and the second substrate are made of a polymer material, Made of ceramic material, ferroelectric material, ferrite material or ferromagnetic material.

6. The metamaterial of claim 3, wherein: the first artificial microstructure is the same as the second artificial microstructure material and geometry.

7. The metamaterial of claim 6, wherein: the first artificial microstructure and the second artificial microstructure are metal microstructures having a "gong" geometry, the metal microstructure comprising a first first metal branch and two second metal branches located at both ends of the first metal branch and perpendicular to the first metal branch.

8. The metamaterial of claim 7 wherein: said metal microstructure further comprises a third metal branch located at each end of each second metal branch and perpendicular to said second metal branch.

9. The metamaterial of claim 6, wherein: the first artificial microstructure and the second artificial microstructure are metal microstructures having a planar snowflake geometry, the metal microstructures comprising Two first metal branches perpendicular to each other and a second metal branch located at both ends of the first metal branch and perpendicular to the first metal branch.

10. The metamaterial of claim 9 wherein: said metal microstructure further comprises a third metal branch positioned at each end of each second metal branch and perpendicular to said second metal branch.

11. A method for designing a refractive index distribution of a metamaterial, comprising:

S1: mapping the area where the metamaterial is located and the boundary of each layer of the metamaterial sheet constituting the metamaterial, Filling the area of the metamaterial with air, fixing the feed in front of the metamaterial region and making the center axis of the feed coincide with the central axis of the metamaterial region; the feed radiates electromagnetic waves and then tests and records the i-th supermaterial sheet on the super-material sheet The initial phase of the front surface of the layer, the initial phase of each point of the front surface of the i-th layer of the metamaterial sheet is denoted as (wherein the initial phase at the central axis is denoted as (0);

S2: According to the formula Ψ = . (0) - ^Σ '' ^ ^π , to obtain the phase Ψ of the back surface of the entire metamaterial, where M is the total number of layers of the super material sheet, d is the thickness of each layer of the super material sheet, and is the radiation of the feed The wavelength of the electromagnetic wave, n _max is the maximum refractive index value of the metamaterial sheet;

S3: Substituting the initial phase obtained in the test in step SI according to the formula Ψ = 2π

φ Μ and the reference phase 得到 obtained in step S2, the refractive index distribution of the metamaterial sheet is obtained, where y is the distance of any point on the metamaterial sheet from the central axis of the metamaterial sheet.

12. The design method according to claim 11, wherein: after step S1, the step of adjusting the initial phase ^ measured in step S1 so that the initial phase (0) at the central axis of the metamaterial is a medium maximum value is further included. .

13. The design method according to claim 11, wherein: different i values are selected to select different functional supermaterial sheet front surface tests to obtain refractive index distribution n(y) of the plurality of sets of metamaterial functional layers. , compare the obtained sets of refractive index profiles and select the optimal results from them.