WO2012139379A1 - 一种汇聚电磁波的超材料 - Google Patents

一种汇聚电磁波的超材料 Download PDF

Info

Publication number
WO2012139379A1
WO2012139379A1 PCT/CN2011/082387 CN2011082387W WO2012139379A1 WO 2012139379 A1 WO2012139379 A1 WO 2012139379A1 CN 2011082387 W CN2011082387 W CN 2011082387W WO 2012139379 A1 WO2012139379 A1 WO 2012139379A1
Authority
WO
WIPO (PCT)
Prior art keywords
metamaterial
refractive index
super
electromagnetic waves
units
Prior art date
Application number
PCT/CN2011/082387
Other languages
English (en)
French (fr)
Inventor
刘若鹏
季春霖
王今金
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 (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 深圳光启高等理工研究院, 深圳光启创新技术有限公司 filed Critical 深圳光启高等理工研究院
Priority to EP11855252.0A priority Critical patent/EP2698650B1/en
Priority to US13/522,493 priority patent/US8681429B2/en
Publication of WO2012139379A1 publication Critical patent/WO2012139379A1/zh

Links

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
    • G02B1/002—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/0087—Simple or compound lenses with index gradient
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/0006—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices
    • H01Q15/0086—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices said selective devices having materials with a synthesized negative refractive index, e.g. metamaterials or left-handed materials
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/02—Simple or compound lenses with non-spherical faces
    • G02B3/08—Simple or compound lenses with non-spherical faces with discontinuous faces, e.g. Fresnel lens

Definitions

  • This invention relates to the field of electromagnetic communications and, more particularly, to a metamaterial that utilizes a metamaterial to converge electromagnetic waves.
  • Metamaterials are a new type of material that consists of a substrate made of a non-metallic material and a plurality of artificial microstructures attached to or embedded in the surface of the substrate.
  • the substrate can be virtually divided into a plurality of square substrate units arranged in a rectangular array, and each of the substrate units is attached with an artificial microstructure to form a metamaterial unit, and the entire metamaterial is hundreds of thousands, millions. Even hundreds of millions of such metamaterial units are composed of crystals that are made up of a myriad of lattices in a certain arrangement.
  • the artificial microstructures on each metamaterial unit are the same or not identical.
  • An artificial microstructure is a cylindrical or flat wire that forms a certain geometric figure, such as a wire that forms a circular, "work" shape.
  • each metamaterial unit Due to the existence of artificial microstructures, each metamaterial unit has an equivalent dielectric constant and equivalent permeability different from that of the substrate itself, so all metamaterials composed of metamaterial units exhibit a special response to electric and magnetic fields. Characteristics; At the same time, the specific structure and shape of the artificial microstructure can be changed, and the equivalent dielectric constant and equivalent permeability of the unit can be changed, thereby changing the response characteristics of the entire metamaterial.
  • the technical problem to be solved by the present invention is to provide a supermaterial that converges electromagnetic waves in view of the deficiencies of the prior art.
  • the technical solution adopted by the present invention to solve the technical problem thereof is: a metamaterial that converges electromagnetic waves, comprising a plurality of super material sheets stacked in an integrated manner in the X direction, each of the super material sheets comprising a plurality of metamaterial units, each The metamaterial units have identical substrate units and artificial microstructures attached to the substrate unit, the metamaterial units being aligned in the y direction perpendicular to the X direction, and simultaneously perpendicular to the x, y directions
  • the directions are arranged in a first array, and the refractive indices of the individual metamaterial units in each row are the same, as described in each column
  • the refractive index of the metamaterial unit is ai , a 2 , a 3 , ..., a s , bi, b 2 , b 3 , ..., b m , d, c 2 , c 3 , , c p , respectively
  • the rate satisfies: a
  • the artificial microstructure is a non-90 degree rotationally symmetric structure, and the artificial microstructure is "work"
  • the glyph or snowflake shape, and the extraordinary optical axis of the index ellipsoid is not perpendicular and not parallel to the y direction.
  • the metamaterial unit has a length in the x, y, and z directions of between one-fifth and one-half of the wavelength of the electromagnetic wave.
  • the artificial microstructure on each column in the y direction is sequentially from the intermediate metamaterial unit to the two ends
  • the angle of the artificial microstructure rotating in a clockwise direction is ⁇ 1 0:
  • the material of the artificial microstructure is metal.
  • the present invention also provides a metamaterial that converges electromagnetic waves, including a plurality of metamaterial sheets stacked in an integrated manner in the X direction, each of the super material sheets including a plurality of metamaterial units, each of the metamaterials
  • the unit has exactly the same substrate unit and an artificial microstructure attached to the substrate unit, the metamaterial unit being aligned in the y direction perpendicular to the X direction, and in the z direction perpendicular to the x and y directions Arranged into a first array, each of the metamaterial units of each row has the same refractive index, and the refractive index of each of the supermaterial units in each column is ai, a 2 , a 3 , , a s , bi , b 2 , b 3 , respectively. , b m , Ci, c 2 , c 3 , ,
  • each refractive index satisfies: ai ⁇ a 2 ⁇ a 3 ⁇ a s , Ci > c 2 > c 3 > c p ; b m
  • p is a natural number not less than 2
  • m is a natural number not less than 1
  • the artificial microstructure is a non-90 degree rotational symmetrical structure, and the extraordinary optical axis of the refractive index ellipsoid is not vertical And not parallel to the y direction.
  • the refractive index of each of the supermaterial units in each column also has the following relationship:
  • each artificial microstructure of each column of metamaterial units in the y direction has a corresponding clock axis of the respective refractive index ellipsoids rotated clockwise, and a refractive index of a row of artificial microstructures having a refractive index of b q
  • the extraordinary optical axis of the ellipsoid is parallel to the y direction.
  • the plurality of metamaterial sheets are completely identical and have the same refractive index distribution.
  • the plurality of metamaterial sheets have different refractive index distributions, and each of the super-material units is formed by stacking rows in the X direction and columns in the y direction, and is centered on a central metamaterial unit.
  • a stack of rows and a column of metamaterial units passing through the central metamaterial unit have refractive indices in the order of ai , a 2 , a 3 , ... , a s , bi , b 2 , b 3 , ... , b m , Ci , c 2 , c 3 , ..., c p .
  • the refractive index of the second array is annularly distributed, and the refractive indices of at least a portion of the metamaterial units of the plurality of metamaterial units passing through any one of the centers of the center are sequentially a l a 2 , a 3 ... ... , a s , bi , b 2 , b 3 , ... , b m , ci , c 2 , c 3 , ..., c p .
  • each artificial microstructure is geometrically similar but the size decreases as the refractive index increases or decreases with the refractive index.
  • the artificial microstructure is a "work" shape or a snowflake shape.
  • the material of the artificial microstructure is metal.
  • the artificial microstructure on each column in the y direction is sequentially from the intermediate metamaterial unit to the two ends
  • the angle of the artificial microstructure rotating in a clockwise direction is ⁇ 1 ⁇ 2 , ⁇ 3 , ..., 0 q , and the rotation angles have the following relationship:
  • the metamaterial unit has a length in the x, y, and z directions of between one-fifth and one-half of the wavelength of the electromagnetic wave.
  • the implementation of the super-material of the electromagnetic wave of the present invention has the following advantageous effects:
  • the super-material of the present invention uses a segmented refractive index distribution to increase the relative change rate of the refractive index, thereby achieving electromagnetic wave convergence while still achieving Greatly reduce the thickness of the metamaterial, which is conducive to miniaturization and light weight of the super material product.
  • Figure 1 is a schematic view showing the structure of each metamaterial sheet
  • Figure 2 is a schematic view showing the refractive index distribution of the metamaterial sheet shown in Figure 1;
  • Figure 3 is a schematic view showing the structure of the first embodiment of the artificial microstructure
  • FIG. 4 is a schematic structural view of a second embodiment of an artificial microstructure
  • Figure 5 is a schematic view showing the structure of a third embodiment of an artificial microstructure
  • Figure 6 is a schematic view showing the aggregation of electromagnetic waves by the super-material sheet shown in Figure 2;
  • Figure 7 is a schematic view showing the direction in which electromagnetic waves propagate in an artificial microstructure
  • FIG. 8 is a schematic diagram of electromagnetic wave propagation when the long-axis direction of the electromagnetic wave propagation ellipsoid is parallel to the y direction;
  • FIG. 9 is a schematic diagram of electromagnetic wave propagation when the long-axis direction of the electromagnetic wave propagation ellipsoid is inclined at a certain angle with respect to the y direction;
  • Figure 10 is a schematic view showing electromagnetic wave propagation when the longitudinal direction of the electromagnetic wave propagation ellipsoid of each artificial microstructure in the y direction is gradually rotated;
  • Figure 11 is a schematic view of a supermaterial in which a plurality of metamaterial sheets are stacked to converge electromagnetic waves;
  • Figure 12 is a graph showing the refractive index profile on a plane formed along the X direction and the y direction of an embodiment.
  • the present invention relates to a metamaterial that converges electromagnetic waves, and since it has a special refractive index distribution, it is possible to achieve electromagnetic wave convergence, and its specific structure and characteristics will be further described below with reference to Figs.
  • the super-material for concentrating electromagnetic waves of the present invention comprises a plurality of super-material sheets 1 each having a front surface and a rear parallel surface as shown in FIG.
  • the thickness direction of the metamaterial sheet 1 is defined as the X direction
  • the length direction of the metamaterial sheet 1 is the y direction
  • the width direction is the z direction x, y, and z directions are perpendicular to each other.
  • the metamaterial sheet layer 1 includes a sheet-like base material 3 which is equally thick and a plurality of artificial microstructures 4 attached to the sheet-like base material 3.
  • the sheet-like substrate 3 is virtually divided into a plurality of identical square-shaped meshes, each of which is a substrate unit, and an artificial microstructure 4 is attached to each of the substrate units, and each base is
  • the material unit and the artificial microstructure 4 attached thereto form a metamaterial unit 2, and the entire metamaterial sheet 1 can be regarded as composed of a plurality of metamaterial units 2 in the zth direction and in the y direction.
  • the square-shaped mesh here may have any freely divided size.
  • the lengths in the y and z directions are one tenth of the wavelength of the electromagnetic wave to be concentrated, the length in the X direction, and the sheet substrate.
  • the thickness of the x direction of 3 is equal.
  • the length of the metamaterial unit of the present invention in the x, y, and z directions may be at one-fifth of the electromagnetic wave wavelength d, preferably less than one tenth of the wavelength.
  • the specific structure of the metamaterial unit 2 is shown in Fig. 3, Fig. 4, and Fig. 5.
  • the metamaterial unit 2 shown in Fig. 3 includes a substrate unit and an artificial microstructure 4 attached to the surface of the substrate unit.
  • the artificial microstructure 4 of this embodiment is a planar "work" shaped wire comprising a linear first wire and two second wires respectively connected perpendicularly at the ends of the first wire.
  • the artificial microstructure 4 shown in FIG. 4 is a planar two-dimensional snowflake type, comprising two first wires perpendicularly intersecting each other into a "ten" shape and four second portions respectively perpendicularly connected at both ends of each of the first wires. metallic line.
  • the three-dimensional artificial microstructure 4 is attached to the inside of the substrate 3 by a certain processing technique.
  • the artificial microstructure 4 of the present invention has various implementations, and any structure having a certain geometric pattern and capable of responding to an electromagnetic field, that is, changing the characteristics of an electromagnetic field, can be used as the artificial micro of the present invention.
  • the structure 4 is attached to the surface of the substrate 3 or embedded inside the substrate 3 to form the metamaterial unit 2 of the present invention.
  • the corresponding metamaterial units 2 Due to the different artificial microstructures 4, the corresponding metamaterial units 2 exhibit different dielectric constants and magnetic permeability, thus generating different electromagnetic responses to electromagnetic waves. Among them, an important response is to change the direction of electromagnetic wave propagation.
  • the superconducting material for concentrating electromagnetic waves of the present invention that is, designing the dielectric constant and magnetic permeability of each of the metamaterial units 2, so that the amount of change of the propagation direction of the electromagnetic waves passing through each of the metamaterial units 2 can be set, and all the metamaterials are Unit 2 works together to converge all incident electromagnetic waves in one direction, even to a point.
  • the variation law of the rate ⁇ can infer the variation law of the dielectric constant ⁇ . Therefore, all of the following descriptions concerning the variation law of the refractive index ⁇ can be understood as the variation law of the dielectric constant which can be similarly derived according to the above formula.
  • each refractive index profile of each metamaterial sheet 1 is as shown in FIG. A row of metamaterial units 2 along the y direction having refractive indices in the order of ai , a 2 , a 3 , , a s , bi , b 2 , b 3 , , b m , Ci , c 2 , c 3 , , c p , each refractive index meets:
  • Ci c 2 > c 3 > c p ( 2 )
  • b m ⁇ ci and 8
  • p are natural numbers not less than 2
  • m is a natural number not less than 1.
  • Each row of metamaterial units 2 along the z direction has the same refractive index.
  • the metamaterial portion where the refractive index 1 to a s is defined is the first-stage metamaterial 100, the meta-material portion where the refractive index is from ⁇ to b m is the intermediate-stage metamaterial, and the meta-material portion where the refractive index is from Cl to c p For the fourth section of metamaterial 400.
  • the relations (1) and (2) are different, the equal sign is obtained, that is, when the refractive indices of the first and third metamaterials 100 and 300 are unevenly distributed, the phase propagation direction of the electromagnetic wave is large toward the refractive index.
  • the electromagnetic wave 100 is incident from the first segment metamaterial, the metamaterial unit leaving the metamaterial will exit the deflector 2 is located, and where the Cl may electromagnetic wave passes through the fourth segment 400 exit metamaterial
  • the metamaterial unit 2 is deflected, that is to say, the electromagnetic waves incident from both sides of the metamaterial on the middle section are concentrated toward the direction of the metamaterial in the middle section to achieve convergence.
  • the refractive index b l b 2 , b 3 , ... , b of each column of the metamaterial unit 2 of the intermediate section metamaterial The following relationship exists between m :
  • Ultra refractive index material portion is defined where b q ⁇ to meta-material 200 of the second section, the refractive index of the metamaterial to part b q b m for the third segment is located meta-material 300.
  • the second and third sections of metamaterials 200 and 300 can also achieve refraction.
  • the metamaterial unit with a rate of b q is deflected and merged. a)
  • the refractive index distribution of the supermaterials in each section is non-uniform
  • the equal sign is used to ensure that the incident electromagnetic waves are deflected toward the metamaterial unit where bq is located, but the convergence does not necessarily occur. Converging to a point, only the electromagnetic waves are close to each other. In order to achieve convergence, it is necessary to make an electromagnetic wave incident from a position close to the metamaterial unit 2 where the refractive index is al, and a larger deflection angle with respect to the incident direction when exiting, from a metamaterial unit close to the refractive index b q The electromagnetic wave incident at a position has a small deflection angle at the time of exit.
  • Metamaterial (6) satisfies the relation of the amount of change in refractive index, for a bundle of parallel incident electromagnetic wave, a refractive index of the amount of change in refractive index metamaterial unit 2 b q both sides is gradually increased to both sides, therefore b q
  • the super material unit 2 is bounded, and the electromagnetic wave incident near the ends of both sides is deflected at a large angle, and the electromagnetic wave incident on the metamaterial unit 2 where bq is located is smaller in the exit deflection angle.
  • the corresponding surface curvature characteristics can be designed to achieve the convergence function.
  • the present invention By designing the artificial microstructures 4 of the respective metamaterial units 2, the dielectric constant ⁇ and the magnetic permeability ⁇ of the unit are obtained, and the refractive index ⁇ is further known, and the adjacent metamaterial units 2 are designed.
  • the amount of change in the refractive index ⁇ enables the electromagnetic wave to be deflected to a specific point, so that convergence can be achieved to a point.
  • the deflection angles ⁇ ⁇ , ⁇ 2, ⁇ 3 , ⁇ 4 with respect to the ⁇ direction of each electromagnetic wave can be measured.
  • the refractive index change ⁇ and the deflection angle ⁇ are obtained (for example, ⁇ ⁇ , ⁇ 2 , ⁇ 3 or ⁇ 4 ). ) has the following relationship:
  • d is the length of the metamaterial sheet 1 in the z direction
  • ⁇ is the difference in refractive index of the adjacent two rows of metamaterial units.
  • d and sinp are known, so ⁇ can be solved.
  • the refractive index of adjacent two rows of metamaterial units can be reversed.
  • Calculating the deflection angle of all the positions, the refractive index distribution of the super material sheet 1 in the y direction is finally obtained.
  • the artificial microstructure 4 is designed, and its dielectric constant and magnetic permeability are obtained through calculation and simulation, and then the shape and size of the artificial microstructure 4 are continuously adjusted until the values of dielectric constant and magnetic permeability satisfy the obtained refractive index. It is sufficient to conform to the above refractive index distribution.
  • the third and fourth sections of the metamaterials 300, 400 of the present invention may be completely symmetrical in structure in the second and first sections of the metamaterials 200, 100, respectively, and the refractive index distribution will also be completely Symmetrical, ie:
  • the refractive indices of the second and third supermaterials 200, 300 are:
  • each refractive index also satisfies:
  • the first section of metamaterial 100 and the second section of metamaterial 200 in the y direction of a column The refractive index has the same initial value and final value, that is, the total refractive index conversion amount of the two-stage supermaterial is equal. Since q>s, that is, the number of super-material units per column of the first-stage metamaterial 100 is greater than that of the second-stage super material 200, the refractive index of the first-stage metamaterial 100 is equal if the total variation is equal. The average rate of change is greater than the second section of metamaterial 200. As shown in FIG. 2, the size of the refractive index is represented by the density of the line. The thinner the line, the larger the refractive index, and the faster the degree of change of the denseness, the larger the rate of change of the refractive index.
  • the third and fourth sections of metamaterials 300, 400 are symmetric with the second and first sections of metamaterial 200, 100, the center line of a row of metamaterial units having a refractive index aq is perpendicular to the surface of the metamaterial. Plane, is a symmetry plane. Therefore, for the sake of brevity of description, only the first and second sections of metamaterials 100, 200 will be described and illustrated below, as shown in FIGS. 8-10.
  • the third and fourth sections of supermaterials 300 and 400 are equally available. b) the refractive index distribution of each segment of the supermaterial is anisotropic and anisotropic
  • the first and second sections of the metamaterial 200 are all materials with a refractive index distribution. At this time, there are three cases for electromagnetic waves incident in the direction parallel to the z direction:
  • each piece of metamaterial is a material with a refractive index hook, the incident direction of the electromagnetic wave is not perpendicular to the metamaterial. On the surface of the sheet 1, electromagnetic waves are deflected.
  • the individual metamaterial units 2 within the metamaterial portion must be isotropic, and further, each of the artificial microstructures 4 of the portion is required to be isotropic.
  • the metamaterial unit 2 exhibits an isotropic property to electromagnetic waves.
  • 90 degree rotational symmetry means that it coincides with the original structure after rotating 90 degrees arbitrarily about a plane perpendicular to the plane on the plane; for a three-dimensional structure, if there are two perpendicular and co-intersection points 3
  • the rotating shaft is such that the structure is rotated 90 degrees around any rotating axis and overlaps with the original structure or is symmetric with the original structure.
  • the structure is a 90-degree rotationally symmetric structure. Therefore, to achieve anisotropy, the artificial microstructure 4 of the present invention cannot be a 90 degree rotationally symmetric structure, i.e., can only be a non-90 degree rotationally symmetric structure.
  • the artificial microstructure 4 of the embodiment shown in FIG. 3 is a non-90 degree rotationally symmetric structure, and the corresponding metamaterial unit 2 is anisotropic; the artificial microstructure 4 of the embodiment shown in FIG. 4 is two first metals.
  • the two-dimensional snowflake artificial microstructure 4 is isotropic; the same is true, the wires are equal and perpendicular to each other, and each of the second wires is equal and equally divided by the connected first wires.
  • the three-dimensional snowflake structure is also isotropic, showing that the three first wires are completely equal and vertically halved to each other, and each of the second wires is equal and equally divided by the connected first wires.
  • the artificial microstructures of the present invention are all anisotropic shape structures.
  • An anisotropic material is capable of deflecting electromagnetic waves when incident electromagnetic waves are not perpendicular to their optical axes.
  • the index ellipsoid 5 is used to indicate the refractive index characteristic, and the size of the index ellipsoid 5 is used to indicate the magnitude of the refractive index.
  • the refractive index ellipse can be calculated by the prior art simulation software and calculation method. Electromagnetic parameter retrieval from inhomogeneous metamaterials, DR Smith, DC Vier, T. Koschny, CM Soukoulis, Physical Review E 71, 036617 (2005).
  • the ordinary optical axis n e (abbreviated as n e axis) of the index ellipsoid 5, and the extraordinary optical axis n. (referred to as n. axis) as shown in FIG. It is assumed that the coordinate origin is at the center of the index ellipsoid 5, and is n.
  • the axis is the X axis
  • the n e axis is the y axis.
  • Any point on the index ellipsoid 5 is represented by n x , n y , and when the electromagnetic wave shown in FIG. 7 passes through the metamaterial unit 2, it uses k x ,
  • the wave propagation ellipsoid 6 corresponding to this index ellipsoid 5 represented by k y has the following relationship:
  • ⁇ is the angular frequency of the electromagnetic wave
  • c is the speed of light
  • the wave propagation ellipsoid 6 is co-centered with the index ellipsoid 5
  • k x , k y are the point coordinates on the wave propagation ellipsoid 6.
  • the wave propagation ellipsoid 6 and the index ellipsoid 5 are geometrically similar, and the long axis direction is the short axis direction of the index ellipsoid 5, and the short axis direction is the long axis direction of the index ellipsoid 5. .
  • the direction of deflection of the electromagnetic wave after passing through the metamaterial unit 2 can be drawn by the wave propagation ellipsoid 6.
  • the electromagnetic wave incident in the direction shown in the figure intersects with the point on the surface of the wave propagation ellipsoid 6 to be emitted, and the intersection of the intersection point with respect to the wave propagation ellipsoid 6 is made from the intersection point.
  • the normal direction of the tangent is the direction of energy propagation of the electromagnetic wave, so the electromagnetic wave propagates in this direction inside the element.
  • the above anisotropic material changes the direction of electromagnetic wave energy propagation without changing the phase propagation direction.
  • the material is a material whose refractive index distribution is hooked.
  • the direction of energy propagation and the direction of phase propagation of electromagnetic waves change after passing through such metamaterials.
  • the effects of non-uniform refractive index distribution and anisotropy on electromagnetic wave propagation will be shown by three embodiments.
  • the super-material sheet layers 1 of the three embodiments shown in FIG. 8, FIG. 9, and FIG. 10 have the refractive index distributions satisfying the characteristics described above, that is, the refractive index of each column of the super-material units in the y direction is a. l a 2 , a 3 , ... , a s , bi , b 2 , b 3 , , b m , Ci , c 2 , c 3 , , c p , and satisfy the relationship (1) to ( 11), and the relations (1) to (6) are not equal when they are equal.
  • the non-uniformity has the same influence on the respective embodiments, that is, the deflection angles of the phase propagation directions are the same for the same incident electromagnetic wave, as shown in FIGS. 8 to 10.
  • the electromagnetic wave passing through the first section of the metamaterial at the same incident position in the same direction has an off angle of ⁇ ⁇ ; and another electromagnetic wave passing through the second section of the metamaterial 200, the deflection angles of the three embodiments are all ⁇ 2.
  • Each of the metamaterial elements shown in Fig. 8 is anisotropic, and the corresponding wave propagation ellipsoid 6 is as shown in the figure.
  • the short axis of the wave propagation ellipsoid 6, that is, the direction of the extraordinary optical axis of each of the metamaterial units 2 is parallel to the ⁇ direction, that is, the incident direction of the electromagnetic wave, and thus does not change the energy propagation direction of the incident electromagnetic wave.
  • the distance from the metamaterial to the point at which the electromagnetic wave leaves the metamaterial is fl.
  • the metamaterial sheet 1 shown in Fig. 9 has the same artificial microstructures 4 of the respective metamaterial units 2 as the artificial microstructures 4 of the respective metamaterial units 2 in the embodiment shown in Fig.
  • each of the artificial microstructures 4 in Fig. 9 corresponds to the corresponding artificial microstructure 4 in Fig. 8 rotated clockwise by an angle of less than 90 degrees.
  • ⁇ such that the short axes of the respective wave propagation ellipsoids 6 are parallel to each other, but the minor axes are not parallel to the z direction, and extend to intersect the symmetry plane to form an acute angle with the symmetry plane that is greater than zero and less than 90 degrees.
  • the energy propagation direction of the electromagnetic wave inside the super-material layer 1 is deflected toward the symmetry plane, which is equivalent to shifting the electromagnetic wave to the symmetry plane; the electromagnetic wave after the translation is away from the super-material sheet.
  • layer 1 emerges, it will be deflected due to the change of refractive index, that is, the electromagnetic wave deflection angle of the two electromagnetic waves which are the same as those of FIG. 8 passes through the first-stage supermaterial is ⁇ 1 , and the deflection of the second-stage super-material 200 is ⁇ 2 angle.
  • the electromagnetic wave of the present embodiment is translated toward the plane of symmetry due to the anisotropy, so that the distance at which the two electromagnetic waves converge at the same point as in Fig. 8 is smaller than the convergence distance fl of Fig. 8 .
  • the metamaterial sheet 1 of FIG. 10, the artificial microstructures 4 of the respective metamaterial units 2 are the same as the embodiment shown in FIG. 9, but the artificial microstructures of each column of metamaterial units in the y direction 4,
  • the respective artificial microstructures 4 in the embodiment shown in Fig. 9 are rotated by an angle, respectively.
  • the refractive index shown in Fig. 9 is a l a 2 , a 3 , ... , a s , bi , b 2 , b 3 , ... , b q , and the wave propagation ellipses
  • the short axis of the ball 6 rotates clockwise with respect to the symmetry plane by the s+q personal microstructure of the corner.
  • the corresponding s+q personal microstructure is rotated clockwise on the basis of Fig. 9.
  • the angles are ⁇ 1 ⁇ 2 , ⁇ 3 , ... , ⁇ 8 , ⁇ 8+1 , ... , ⁇ s+q _!
  • an anisotropic metamaterial unit whose wave propagation ellipsoid 6 rotates clockwise by a corner can reduce the distance of the electromagnetic wave convergence point from the metamaterial.
  • the wave propagation ellipsoid 6 continues to rotate clockwise in the y direction in turn due to further sequential rotation of the artificial microstructures 4. Therefore, the electromagnetic wave is inside the metamaterial, and each time it passes through a metamaterial unit, it will be deflected again toward the symmetry plane.
  • the anisotropic metamaterial unit 2 can reduce the distance from the convergence point of the electromagnetic wave to the metamaterial, that is, reduce the focal length.
  • the anisotropic and the extraordinary optical axis of the refractive index ellipsoid 5 is not perpendicular and is not parallel to the symmetry plane of the metamaterial sheet 1 (for example, FIG. In the embodiment shown in Fig. 10, the electromagnetic wave deflection angle will be smaller than the deflection angles ⁇ 1 and ⁇ 2 in the embodiment shown in Fig. 7. According to the relation (7), it can be inferred that at this time, the length d of the metamaterial sheet 1 made by the former is also reduced. In short, to achieve the same convergence effect, the length d of the supermaterial sheet 1 and the z direction shown in Fig. 9 and Fig. 10 is smaller than that of the super material sheet 1 or the isotropic super material sheet 1 shown in Fig. 8. The advantage of this feature is that it can reduce the use of materials, make the metamaterials smaller, and contribute to lightweight and miniaturization.
  • the super-material for concentrating electromagnetic waves of the present invention is stacked and assembled in a plurality of super-material sheets 1 in the X direction, and each of the super-material sheets 1 is separated by air or filled with dielectric.
  • the constant is close to 1.
  • the artificial microstructure 4 which is anisotropic and can change the direction of propagation of electromagnetic energy can reduce the thickness of the super-material of the entire concentrated electromagnetic wave, thereby reducing material consumption and achieving thinness and miniaturization.
  • Each of the metamaterial sheets 1 constituting the metamaterial may be identical.
  • each of the super material sheets 1 can converge a column of electromagnetic waves passing through the layer to a point, it is superposed in the X direction.
  • the plurality of metamaterial sheets 1 can converge electromagnetic waves into a line parallel to the X direction.
  • the refractive index profiles of the individual metamaterial sheets will not be exactly the same.
  • the super-material unit is formed by stacking rows in the X direction and columns in the y direction, and the refractive index is annularly distributed, and at least includes a circular distribution area and a circular distribution area of the common center, and the ring shape
  • the inner diameter of the distribution zone is substantially the same as the outer diameter of the circular distribution zone, and the refractive index of each metamaterial element on the circumference of the same radius is the same, and the metamaterial element from the outer diameter of the circular distribution zone to the metamaterial element where the center of the circle is located
  • the refractive index in the radial direction is b l b 2 , b 3 , ...
  • the refractive index of the unit in the radial direction is 1 , a 2 , a 3 , ... , a s , and the metamaterial unit where the center of the circle is the central metamaterial unit.
  • the intermediate part of the super material unit passing through a stacking row and a column of metamaterial units of the central metamaterial unit and any one of the supermaterial units passing through the center of the center metamaterial unit The refractive indices of the elements are a l a 2 , a 3 , ..., a s , bi , b 2 , b 3 , ..., b m , d , c 2 , c 3 , ... .. , c p , and the refractive index is symmetrically distributed, that is, the formulas (8) to (10) are satisfied.
  • the resulting refractive index distribution in order to more intuitively represent, on the second array, the supermaterial units having the same refractive index are connected into a line, and the density of the lines is used to indicate the size of the refractive index, and the denser the line is. The higher the rate, the refractive index distribution of the metamaterial conforming to all the above relationships is shown in FIG.
  • the metamaterial unit is actually a cube rather than a point, the above circular and circular shapes are only approximate descriptions, and the actual metamaterial units having the same or substantially the same refractive index are on a zigzag circumference.
  • the H-free metamaterial element is a cube with a side length of 1 mm, and the coordinate origin is the center point of the central metamaterial unit.
  • the coordinates (X, y) are considered to be ⁇ at (3.2, 5.7).
  • the refractive index! ⁇ is actually the refractive index of a square metamaterial unit surrounded by four points (3, 5), (3, 6), (4, 5), (4, 6).
  • the specific design is similar to the programming mode (such as OpenGL) when the computer draws a smooth curve such as a circle or an ellipse with a square pixel.
  • the curve is smooth when the pixel is small relative to the curve, and is relatively smooth at the pixel.
  • the curve shows jagged when the curve is large.
  • the metamaterial of the present invention has the following characteristics:
  • the artificial microstructure 4 on each metamaterial sheet 1 is designed to be anisotropic, and its index ellipsoid 5 is not perpendicular and not parallel to the z direction, so that the energy propagation direction of the electromagnetic wave can be realized in the middle of the metamaterial.
  • the deflection is such that the focal length of the electromagnetic wave convergence at the time of exit is reduced, and the propagation range is narrowed; in other words, the same convergence effect is achieved, and the anisotropic artificial microstructure 4 can make the metamaterial thinner.
  • the artificial microstructure 4 in the y direction is rotated in turn, which can further increase the amount of electromagnetic wave translation inside the metamaterial, thereby reducing the focal length, or similarly reducing the thickness d of the supermaterial.
  • the electromagnetic waves passing through each of the metamaterial units 2 on the metamaterial may be first calculated.
  • the refractive index difference ⁇ of the adjacent two metamaterial units is calculated by the formula (7), and the distribution of the refractive index n of each metamaterial unit in the x and y directions can be reversed by differentiation and integration.
  • the refractive index is determined by the combination of the dielectric constant and the magnetic permeability
  • the refractive index can be adjusted by changing the dielectric constant to achieve a different refractive index distribution of the electromagnetic wave in the xy plane.
  • Changing artificial microstructure The shape and size of 4 can change the dielectric constant of the metamaterial unit 2 in which it is placed, thereby changing the refractive index. For example, by changing the length of the first and second wires of the artificial microstructure 4 in FIGS. 3, 4 and 5, the dielectric constant of the metamaterial unit 2 can be changed.
  • the refractive index of the corresponding metamaterial unit 2 increases as the size of the artificial microstructure 4 increases. Since the refractive index is constant in the z direction, it can be designed that the artificial microstructures 4 of each row of metamaterial units in the z direction are identical.
  • the convergence of electromagnetic waves is achieved by gradually increasing the refractive index in the y direction and/or the X direction to a maximum value and then gradually decreasing.
  • the size of the artificial microstructure 4 is limited by the substrate unit, and the size of the substrate unit must be within one-fifth of the wavelength of the incident electromagnetic wave, the response of the metamaterial unit to the electromagnetic wave is regarded as continuous, and thus the artificial microstructure
  • the maximum size can only be one-fifth of the wavelength of the incident electromagnetic wave.
  • the refractive index value is also limited.
  • the innovation of the present invention is that the first to the first of the refractive index values are segmented.
  • Four sections of metamaterials are used to achieve convergence, and the refractive index variation of each section of the metamaterial along the y direction makes the deflection angle of the electromagnetic wave satisfy the convergence function, and the value of the refractive index itself is always maintained within a range, for example, the first segment of the super The refractive index ai , a 2 , a 3 , ...
  • the metamaterial of the present invention uses a four-stage metamaterial, and each of the supermaterials can reach a maximum value and a minimum value, and The refractive index of the conventional metamaterial only reaches the maximum value and the minimum value in two different sections, respectively. Therefore, the average rate of change of the refractive index of the present invention is twice the average rate of change of the conventional metamaterial, and the deflection angle of the electromagnetic wave is large. In the case of traditional metamaterials, the focal length becomes shorter.
  • the thickness of the metamaterial of the present invention will be thinned, which is advantageous for achieving miniaturization and light weight. Therefore, 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. In the light of the present invention, many forms may be made without departing from the spirit and scope of the invention as claimed.

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Aerials With Secondary Devices (AREA)
  • Laminated Bodies (AREA)

Description

一种汇聚电磁波的超材料
【技术领域】
本发明涉及电磁通信领域， 更具体地说， 涉及一种利用超材料制成的汇聚 电磁波的超材料。
【背景技术】
超材料是一种新型材料， 是由非金属材料制成的基材和附着在基材表面上 或嵌入在基材内部的多个人造微结构构成的。 基材可以虚拟地划分为矩形阵列 排布的多个方形基材单元， 每个基材单元上附着有一个人造微结构从而形成一 个超材料单元， 整个超材料即是由数十万、 百万甚至上亿的这样的超材料单元 组成的， 就像晶体是由无数的晶格按照一定的排布构成的。 每个超材料单元上 的人造微结构相同或者不完全相同。 人造微结构是组成一定几何图形的圓柱形 或扁平状金属丝， 例如组成圓环形、 "工" 形的金属丝等。
由于人造微结构的存在， 每个超材料单元具有不同于基材本身的等效介电 常数和等效磁导率， 因此所有的超材料单元构成的超材料对电场和磁场呈现出 特殊的响应特性； 同时， 对人造微结构设计不同的具体结构和形状， 可改变其 单元的等效介电常数和等效磁导率， 进而改变整个超材料的响应特性。
像透镜能汇聚平行光到一点上一样， 人们也在寻找能够将平面电磁波汇拢 甚至汇聚到一点上的超材料， 只是现有技术尚未做到这一点。
【发明内容】
本发明要解决的技术问题在于， 针对现有技术的缺陷， 提供一种汇聚电磁 波的超材料。
本发明解决其技术问题所采用的技术方案是： 一种汇聚电磁波的超材料， 包 括沿 X方向堆叠成一体的多个超材料片层， 每个超材料片层包括多个超材料单 元， 每个超材料单元具有完全相同的基材单元和附着在所述基材单元上人造微 结构， 所述超材料单元以垂直于 X方向的 y方向为列、 以同时垂直于 x、 y方向 的 z 方向为行排成第一阵列， 每行的各个超材料单元的折射率相同， 每列所述 超材料单元的折射率依次为 ai, a2, a3, ……， as, bi, b2, b3, ……， bm, d, c2, c3, , cp, 各个折射率满足： ai < a2 < a3 < as, Ci > c2 > c3 > cp; 其中 bm<ci, 且8、 p均为不小于 2的自然数， m为不小于 1的自然数； 所述 bl b2, b3, ...... , bm之间存在以下关系： ^ ^ ^ ...... <bq, bq>bq+i
> bq+2 >bq+3...... > bm,且 q为小于 m的自然数； 所述人造微结构为非 90度旋转 对称结构， 所述人造微结构为 "工" 字形或雪花形， 且其折射率椭球的非寻常 光光轴不垂直且不平行于 y方向。
其中, 所述超材料单元其 x、 y、 z方向的长度在电磁波波长的五十分之一 至二分之一之间。
其中， y方向上的每一列上的人造微结构自中间超材料单元向两端分别依次
Figure imgf000004_0001
其中， 人造微结构在顺时针旋转的角度依次为 Θ1 0：
些旋转角度之间具有如下关系： e ez es ...... eq。
其中， 所述人造微结构的材料为金属。
为了解决技术问题， 本发明还提供了一种汇聚电磁波的超材料， 包括沿 X 方向堆叠成一体的多个超材料片层， 每个超材料片层包括多个超材料单元， 每 个超材料单元具有完全相同的基材单元和附着在所述基材单元上人造微结构， 所述超材料单元以垂直于 X方向的 y方向为列、 以同时垂直于 x、 y方向的 z方 向为行排成第一阵列， 每行的各个超材料单元的折射率相同， 每列所述超材料 单元的折射率依次为 ai, a2, a3, , as, bi, b2, b3, , bm, Ci, c2, c3, ,
Cp, 各个折射率满足： ai < a2 < a3 < as, Ci > c2 > c3 > cp; 其中
Figure imgf000004_0002
bm
<ci, 且8、 p均为不小于 2的自然数， m为不小于 1的自然数； 所述人造微结 构为非 90度旋转对称结构， 且其折射率椭球的非寻常光光轴不垂直且不平行于 y方向。
其中， 所述 b b2, b3, ...... , bm之间存在以下关系： ^ ^ ^ ...... <bq, bq > bq+1 > bq+2 >bq+3…… > bm, 且 q为小于 m的自然数。
其中， 每列所述超材料单元的折射率还具有如下关系：
(a2-ai) > (a3-a2)…… > (as-as-1) > (b2-bi) > (b3-b2)…… > (bq- bq),
(bq-bq+i) < (bq+i-bq+2) < (bq+2-bq+3)…… < (bm-1-bm) < (ci-c2) < (c2-c3) < (cp-1-cp)。 其中， 上述折射率还具有如下关系：
a尸 b尸 bm=cp, as=bq=Ci , s=p, q > s JL q > p, q=[(m+l)/2]„
其中， 沿 y方向的每列超材料单元的各个人造微结构其对应的各个折射率 椭球的非寻常光光轴依次顺时针方向旋转， 且折射率为 bq的一行人造微结构的 折射率椭球的非寻常光光轴平行于 y方向。
其中， 所述多个超材料片层完全相同且具有相同的折射率分布。
其中， 所述多个超材料片层具有不同的折射率分布， 在每个由超材料单元 以 X方向为堆叠行、 y方向为列构成第二阵列中， 以一中心超材料单元为圓心， 经过所述中心超材料单元的一堆叠行和一列超材料单元其折射率均依次为 ai , a2， a3, …… , as, bi , b2, b3, …… , bm, Ci , c2, c3, ……， cp。
其中， 所述第二阵列的折射率呈环形分布， 经过所述圓心的任意一条直线 上的多个超材料单元至少部分超材料单元的折射率依次为 al a2, a3, ... ... , as, bi , b2, b3, …… , bm, ci , c2, c3, …… , cp。
其中， 各人造微结构形状几何相似但尺寸随折射率的增大或随折射率的减 小而减小。
其中， 所述人造微结构为 "工" 字形或雪花形。
其中， 所述人造微结构的材料为金属。
其中， y方向上的每一列上的人造微结构自中间超材料单元向两端分别依次
其中， 人造微结构在顺时针旋转的角度依次为 Θ1 θ2, θ3 , ... ... , 0q, 且这 些旋转角度之间具有如下关系：
θι 02 Θ3 9q。
其中, 所述超材料单元其 x、 y、 z方向的长度在电磁波波长的五十分之一 至二分之一之间。
实施本发明的汇聚电磁波的超材料， 具有以下有益效果： 本发明的超材釆 用分段式的折射率分布， 增大了折射率的相对变化率， 因此在实现电磁波汇聚 的同时， 还能极大地减小超材料的厚度， 有利于超材料产品的小型化和轻便化。
【附图说明】 下面将结合附图及实施例对本发明作进一步说明， 附图中：
图 1是每个超材料片层的结构示意图；
图 2是图 1所示超材料片层的折射率分布示意图；
图 3是人造微结构的第一实施例的结构示意图
图 4是人造微结构的第二实施例的结构示意图
图 5是人造微结构的第三实施例的结构示意图
图 6是图 2所示超材料片层对电磁波进行汇聚的示意图；
图 7是电磁波在人造微结构中传播的方向示意图；
图 8是电磁波传播椭球的长轴方向平行于 y方向时的电磁波传播示意图； 图 9是电磁波传播椭球的长轴方向均以一定角度相对于 y方向倾斜时的电 磁波传播示意图；
图 10是沿 y方向的各个人造微结构的电磁波传播椭球的长轴方向依次逐渐 旋转时的电磁波传播示意图；
图 11是由多个超材料片层堆叠成汇聚电磁波的超材料的示意图；
图 12是一实施例沿 X方向和 y方向构成的平面上的折射率分布图。
【具体实施方式】
本发明涉及一种汇聚电磁波的超材料， 由于其具备特殊的折射率分布， 能 够实现电磁波的汇聚， 下文将结合附图 1至 12对其具体结构和特性做进一步说 明。
本发明的汇聚电磁波的超材料， 包括多个超材料片层 1 , 每个超材料片层 1 如图 1所示， 具有前、 后平行的两个表面， 因而为等厚片层。 定义超材料片层 1 的厚度方向为 X方向，超材料片层 1的长度方向为 y方向，宽度方向为 z方向 x、 y、 z方向两两垂直。
超材料片层 1 包括均勾等厚的片状基材 3和附着在片状基材 3上的多个人 造微结构 4。将片状基材 3虚拟地划分为多个完全相同的方体形网格，每个网格 为一个基材单元， 并使得每个基材单元上附着有一个人造微结构 4 , 则每个基材 单元及其上附着的人造微结构 4共同构成一个超材料单元 2 , 整个超材料片层 1 可以看作是由多个超材料单元 2以第 z方向为行、 以 y方向为列组成的第一阵 列。 这里的方体形网格， 可以具有任意自由划分的尺寸， 本发明中优选为 y、 z 方向的长度均为将要汇聚的电磁波的波长的十分之一、 X方向的长度与片状基材 3的 x方向的厚度相等。 当然， 本发明的超材料单元其 x、 y、 z方向的长度在电 磁波波长 d、于五分之一均可， 优选小于波长的十分之一。
超材料单元 2的具体结构如图 3、 图 4、 图 5所示。 图 3所示的超材料单元 2, 包括一个基材单元和附着在该基材单元表面上的人造微结构 4。 本实施例的 人造微结构 4 为平面的 "工" 字形金属丝， 包括直线型的第一金属丝和分别垂 直连接在第一金属丝两端的两根第二金属丝。 图 4所示的人造微结构 4为平面 的二维雪花型， 包括两个相互垂直相交成 "十" 字形的第一金属丝和分别垂直 连接在每个第一金属丝两端的四根第二金属丝。 图 5所示的人造微结构 4为立 体的三维雪花型， 包括三个两两垂直且相交到一点的第一金属丝和分别垂直连 接在每个第一金属丝两端的六根第二金属丝。 立体的人造微结构 4是通过一定 的加工工艺附着到基材 3内部的。
当然， 本发明的人造微结构 4还有多种实现方式， 只要由金属丝或金属线 构成的具有一定几何图形且能够对电磁场产生响应即改变电磁场特性的结构， 均可作为本发明的人造微结构 4附着在基材 3表面上或者嵌入基材 3 内部从而 形成本发明的超材料单元 2。
由于不同的人造微结构 4 ,会使得对应的超材料单元 2呈现出不同的介电常 数和磁导率， 因而对电磁波产生不同的电磁响应。 其中， 一个重要的响应效果 就是改变电磁波的传播方向。 本发明的汇聚电磁波的超材料， 即设计各个超材 料单元 2的介电常数和磁导率， 从而可以设定经过每个超材料单元 2的电磁波 其传播方向的改变量， 则所有的超材料单元 2共同作用， 就可实现使所有的入 射电磁波向一个方向汇聚， 甚至汇聚到一点上。
折射率可以表示电磁波传播方向的改变， 已知折射率 n=V^， 其中 μ为磁 导率， ε为介电常数， 由此可知， 在磁导率 μ不改变的条件下， 已知折射率 η 的变化规律， 即可推知介电常数 ε的变化规律。 因此， 下文中的所有涉及折射 率 η 的变化规律的描述， 均可以理解为根据上述公式可同理类推出介电常数的 变化规律。
每个超材料片层 1的折射率分布如图 2所示。沿 y方向的一列超材料单元 2, 其折射率依次为 ai , a2, a3, , as, bi , b2, b3, , bm, Ci , c2, c3, , cp, 各个折射率满足：
ai < a2 < a3 < as ( 1 )
Ci > c2 > c3 > cp ( 2 ) 其中 bm < ci , 且8、 p均为不小于 2的自然数， m为不小于 1的自 然数。 沿 z方向的每一行超材料单元 2 , 其折射率均相同。
定义折射率 1至 as所在的超材料部分为第一段超材料 100 , 折射率从 ^至 bm所在的超材料部分为中间段超材料， 折射率从 Cl至 cp所在的超材料部分为第 四段超材料 400。 当关系式（1 )、 ( 2 ) 均不同时取等号时， 即第一、 第三段超材料 100、 300 的折射率分布不均勾时， 电磁波的相位传播方向会向折射率大的方向偏折， 因 此， 从第一段超材料 100入射的电磁波， 在离开超材料出射时会向 所在的超 材料单元 2偏折， 而经过第四段超材料 400的电磁波出射时会向 Cl所在的超材 料单元 2偏折， 也就是说从中间段超材料两侧入射的电磁波， 在出射时会向中 间段超材料的方向汇拢， 实现汇聚。
进一步地， 为了使经过中间段超材料的电磁波也会产生汇拢的效果， 中间 段超材料的每列超材料单元 2的折射率 bl b2, b3, ... ... , bm之间存在以下关系：
Figure imgf000008_0001
bq > bq+i > bq+2 > bq+3…… > bm ( 4 ) 其中， q为小于 m的自然数。
定义折射率 ^至 bq所在的超材料部分为第二段超材料 200 ,折射率 bq至 bm 所在的超材料部分为第三段超材料 300。
当关系式（3 )、 （4 )也不同时取等号时， 与第一段超材料 100和第四段超 材料类似， 第二段、 第三段超材料 200、 300也可实现向折射率为 bq的超材料单 元行偏折汇拢。 一）各段超材料折射率分布非均匀
关系式（1 )、 （2 )、 （3 )、 （4 ) 均不同时取等号， 可以确保入射的电磁波均 向 bq所处的超材料单元行偏折， 但这种汇聚并不一定会汇聚到一点上， 只是电 磁波相互靠近。 要实现汇聚到一点， 必须使得从靠近折射率为 al所在的超材料 单元 2 的位置入射的电磁波， 出射时相对于入射方向的偏折角较大， 从靠近折 射率为 bq的超材料单元的位置入射的电磁波， 其出射时的偏折角较小。
已知相邻超材料单元 2之间的折射率变化量越大， 则电磁波的偏折角越大。 因此， 为了实现所有电磁波向一点汇聚， 沿 y方向的每列超材料单元的折射率 还有如下关系：
(a2-ai) > (a3-a2)…… > (as-as-1) > (b2-bi) > (b3-b2)…… > (bq- bq) ( 5 )
(bq-bq+i) < (bq+i-bq+2) < (bq+2-bq+3)…… < (bm-1-bm) < (ci-c2) < (c2-c3) < (cp-1-cp)
( 6 ) 满足上述折射率变化量关系的超材料， 对于一束平行入射的电磁波， 折射 率为 bq的超材料单元 2两侧的折射率变化量向两侧逐渐增大， 因此以 bq所在的 超材料单元 2 为界， 越靠近两侧端部入射的电磁波出射时偏折角度大， 越靠近 bq所在的超材料单元 2入射的电磁波其出射偏折角越小。 通过一定的设计和计 算， 使得这些偏折角依次满足一定的规律， 即可实现汇聚到一点。 类似于凸透 镜， 只要知道各个表面点对光的偏折角度和材料的折射率， 即可设计出相应的 表面曲率特征来实现汇聚功能。 本发明也一样， 通过设计各个超材料单元 2 的 人造微结构 4 , 得到该单元的介电常数 ε和磁导率 μ , 进而得知折射率 η, 通过 设计使得各个相邻超材料单元 2的折射率 η的变化量能实现电磁波向特定一点 上偏折， 即可实现汇聚到一点。
例如， 对于图 6所示的四束电磁波， 分别入射到超材料片层 1的第一、 第 二、 第三和第四段超材料上， 四束电磁波均平行于 ζ 方向。 要使它们经过超材 料片层 1后发生偏折并汇聚到一点， 可以测出各个电磁波出射时相对于 ζ方向 的偏折角 β ΐ , β 2, β 3 , β 4。 根据参考资料 Metamaterials： Theory, Design, and Applications , Publisher: Springer, ISBN 1441905723, 75页 -76页， 得出折射率变 化量 Δη与偏折角 β (例如为 β ΐ , β 2 , β 3或 β 4 )之间有如下关系式：
d»An=sinP ( 7 )
其中， d为沿 z方向的超材料片层 1的长度， Δη为相邻两行超材料单元的 折射率的差。 已知 d和 sinp, 因此 Δη是可以解出来的， 设定一个折射率基数， 即可反推相邻两行超材料单元的折射率。 将所有位置的偏折角计算出来， 即可 最终推出 y方向上的超材料片层 1的折射率分布。设计人造微结构 4 , 并通过计 算和仿真得出其介电常数和磁导率， 然后不断调整人造微结构 4的形状和尺寸， 直到其介电常数和磁导率的值满足得到的折射率符合上述折射率分布即可。
进一步地， 为了简化设计和制造， 本发明的第三、 第四段超材料 300、 400 可分别于第二、 第一段超材料 200、 100在结构上完全对称， 则折射率分布也将 完全对称， 也即：
a尸 cp, a2=cp-i , …… , as-尸 c2, as=c s=p ( 8 ) 且在满足关系式（8) 的条件下，
1 ) 当 m为奇数时， 第二、 第三段超材料 200、 300的折射率满足：
q= ( m+1 ) 12, b尸 bm, b2=bm-1, , bq-尸 bq+1 (9)
2) 当 m为偶数时， 第二、 第三段超材料 200、 300的折射率满足：
q=m/2, b尸 bm, b2=bm-1, , bq=bq+i (10) 上述 q与 m的关系式也可用 q=[(m+l)/2]来表示， [(m+l)/2]表示对 m除以 2 的结果取其整数位所得的值。
更进一步地， 为了便于比较大小， 在以上基础上， 各折射率还满足：
a尸 b尸 bm=cp, as=bq=ci , s=p, q> s (11 ) 由此可知， 第一段超材料 100和第二段超材料 200沿 y方向的一列折射率， 其起始值和最终值都相等， 即两段超材料总的折射率变换量相等。 由于 q>s, 即第一段超材料 100的每列超材料单元的个数大于第二段超材料 200,因而在总 的变化量相等的情况下， 第一段超材料 100 的折射率的平均变化率要大于第二 段超材料 200。 如图 2所示， 用线的疏密来表示折射率的大小， 线越疏表示折射 率越大， 疏密的变化程度越快则折射率的变化率越大。
由于优选第三、 第四段超材料 300、 400与第二、 第一段超材料 200、 100 对称， 经过折射率为 aq的一行超材料单元的中心连线、 且垂直于超材料表面的 平面， 为对称面。 因此， 下文为了描述上的简洁， 只对第一、 第二段超材料 100、 200进行描述和图示， 如图 8至图 10所示。 第三、 第四段超材料 300、 400同理 可得。 二）各段超材料折射率分布均勾且各向异性
当上述关系式（1)、（2)、（3)、（4)均分别同时取等号， 则关系式（5)、 (6) 也均同时取等号且等于零， 也就是说， 这时的第一、 第二段超材料 200 均为折 射率分布均勾的材料。 此时， 对于沿平行于 z方向入射的电磁波， 有三种情况：
1 ) 当各段超材料对电磁波呈各向同性时， 则电磁波不发生偏折；
2)若各段超材料对电磁波呈各向异性， 且其光轴是垂直于入射电磁波时， 则电磁波出射时也不发生偏折；
3)若各段材料对电磁波呈各向异性且其光轴不垂直于入射电磁波时， 电磁 波出射时会偏折。
若各段超材料均为折射率均勾的材料但电磁波的入射方向不垂直于超材料 片层 1的表面， 电磁波都会发生偏折。
要使各段超材料呈各向同性， 则该超材料部分内的各个超材料单元 2必须 为各向同性， 进一步地， 要求该部分的各个人造微结构 4 为各向同性。 当人造 微结构 4为 90度旋转对称结构， 则该超材料单元 2对电磁波呈现各向同性的特 性。
对于二维平面结构， 90度旋转对称是指其在该平面上绕一垂直于该平面的 旋转轴任意旋转 90度后与原结构重合； 对于三维结构， 如果具有两两垂直且共 交点的 3条旋转轴， 使得该结构绕任一旋转轴旋转 90度后均与原结构重合或者 与原结构以一分界面对称， 则该结构为 90度旋转对称结构。 因此， 要实现各向 异性， 则本发明的人造微结构 4不能为 90度旋转对称结构， 即只能为非 90度 旋转对称结构。
例如， 图 3所示实施例的人造微结构 4为非 90度旋转对称结构， 其对应的 超材料单元 2呈各向异性； 图 4所示实施例的人造微结构 4若两个第一金属丝 相等且互相垂直平分、 每个第二金属丝均相等且均被所连接的第一金属丝垂直 平分， 则这样的二维雪花形人造微结构 4为各向同性； 同理， 图 5所示三根第 一金属丝完全相等且相互两两垂直平分、 每个第二金属丝均相等且均被所连接 的第一金属丝垂直平分， 则这样的三维雪花形结构也属于各向同性。 本发明的 人造微结构均为各向异性的形状结构。
各向异性的材料能够在入射电磁波不垂直于其光轴的情况下使电磁波偏 折。 折射率椭球 5用来表示折射率特性， 折射率椭球 5的大小用以表示折射率 的大小。
对于任一给定的超材料单元 2,可通过现有技术的模拟仿真软件和计算方法 算出其折射率椭 ί求 5 , 例^口参考文献 Electromagnetic parameter retrieval from inhomogeneous metamaterials , D. R. Smith, D. C. Vier, T. Koschny, C. M. Soukoulis, Physical Review E 71, 036617 (2005) 。
对于图 3所示实施例中的超材料单元 2 , 其折射率椭球 5的寻常光光轴 ne (简称 ne轴）、 非寻常光光轴 n。 (简称 n。轴）如图 7中所示。 假定坐标原点在 折射率椭球 5的中心上， 且以 n。轴为 X轴， ne轴为 y轴， 折射率椭球 5上的任 意一点用 nx, ny表示， 则当如图 7所示的电磁波经过超材料单元 2时， 其用 kx, ky表示的对应于此折射率椭球 5的波传播椭球 6有以下关系：
kv=nxro/c, kx=nvro/c ( 12 ) 其中， ω为电磁波的角频率， c为光速， 波传播椭球 6与折射率椭球 5共中 心点， kx, ky是波传播椭球 6上的点坐标。 由公式可知， 波传播椭球 6与折射率 椭球 5为几何相似图形， 且其长轴方向为折射率椭球 5的短轴方向， 而短轴方 向为折射率椭球 5的长轴方向。
电磁波经过超材料单元 2后的偏折方向可通过波传播椭球 6画出来。如图 7 所示， 对于如图中所示方向入射的电磁波， 与要出射的波传播椭球 6 的面上一 点相交， 做此相交点关于波传播椭球 6 的切线， 自相交点做的切线的法线方向 即为电磁波的能量传播方向， 因此电磁波在元件内部沿此方向传播。 电磁波沿 此方向前进直至离开超材料时， 所述法线延伸至与出射面相交后， 自出射面上 的交点继续沿与入射方向平行的方向出射， 此出射方向为电磁波相位传播方向。 也就是说， 各向异性材料， 能改变电磁波的能量传播方向， 不改变其相位传播 方向， 电磁波出射时发生平移。 三）各段超材料折射率分布非均勾且各向异性
上述各向异性材料改变电磁波能量传播方向、 不改变相位传播方向的前提 是材料为折射率分布均勾的材料。 对于折射率分布不均勾、 且对电磁波呈各向 异性的超材料， 电磁波穿过这样的超材料后其能量传播方向和相位传播方向都 会改变。 下面将通过三个实施例来显示折射率分布非均勾和各向异性对电磁波 传播的影响。
图 8、 图 9、 图 10所示的三个实施例的超材料片层 1 , 其折射率分布均满足 前文所述的特征，即沿 y方向的每列超材料单元其折射率依次为 al a2, a3, ... ... , as, bi , b2, b3, , bm, Ci , c2, c3, , cp, 且满足关系式 ( 1 )至 ( 11 ), 且关系式（1 ) 至 （6 ) 均不同时取等号。 因此， 由于三个实施例的折射率大小 分布相同， 因此非均匀对各个实施例的影响相同， 即对于同一入射电磁波， 其 相位传播方向的偏折角度均相同， 如图 8至图 10所示， 以同一方向同一入射位 置经过第一段超材料的电磁波， 其出射的偏折角均为 β ΐ ; 另一经过第二段超材 料 200的电磁波， 经过三个实施例时出射的偏折角均为 β 2。
图 8所示的各个超材料单元均为各向异性， 对应的波传播椭球 6如图中所 示。 本实施例中， 波传播椭球 6的短轴也即各个超材料单元 2的非寻常光光轴 的方向平行于 ζ 方向， 也即电磁波的入射方向， 因此不改变入射电磁波的能量 传播方向， 电磁波离开超材料后汇聚到的一点离超材料的距离为 fl。 图 9所示的超材料片层 1 , 其各个超材料单元 2的人造微结构 4均与图 8 所示实施例中的各个超材料单元 2的人造微结构 4——相同 ,使得折射率椭球 5 和波传播椭球 6的大小和形状——相同； 但是， 图 9中的每个人造微结构 4都 相当于图 8中对应的人造微结构 4顺时针旋转了一个小于 90度的角 θ , 使得相 应的各个波传播椭球 6的短轴相互平行， 但短轴不平行于 z方向， 其延伸至与 对称面相交而与对称面形成的夹角为大于零小于 90度的锐角。
根据图 7所示的电磁波传播方向可知， 电磁波在此超材料片层 1 内部的能 量传播方向会向对称面偏折， 等效于使电磁波向对称面平移； 平移后的电磁波 在离开超材料片层 1 出射时， 会因为折射率的变化而偏折， 即与图 8相同的两 束电磁波经过第一段超材料的电磁波偏折角为 β 1 , 经过笫二段超材料 200的偏 折 β 2角。 在出射的偏折角相等的情况下， 本实施例的电磁波因为各向异性而向 对称面平移， 使得与图 8相同的两束电磁波汇聚的点离超材料的距离 小于图 8的汇聚距离 fl。
图 10所述的超材料片层 1 , 其各个超材料单元 2的人造微结构 4均与图 9 所示实施例——对应相同，但 y方向的每列超材料单元的人造微结构 4 , 分别相 对于图 9所示实施例中对应的人造微结构 4旋转了一个角度。 相对于图 9所示 的折射率为 al a2, a3, ... ... , as, bi , b2, b3, ... ... , bq、 且波传播椭球 6的短 轴相对于对称面均顺时针旋转了 Θ角的 s+q个人造微结构， 图 10所示实施例中 相应这 s+q个人造微结构在图 9基础上顺时针旋转的角度依次为 Θ 1 θ 2, θ 3 , ... ... , θ 8, θ 8+1 , ... ... , θ s+q_! , 0 s+q, 且这些旋转角度之间具有如下关系： θ 1 < Θ 2 < Θ 3 < < Θ s < Θ s+1 < < Θ s+q-1 < Θ s+q ( 13 ) 上述关系式（11 ) 中不同时取等号， 且 Θ s+q使得折射率 bq所对应的超材 料单元的波传播椭球 6的短轴垂直于 z方向， 也即其折射率椭球 5的非寻常光 光轴垂直于 z方向， 或者接近垂直于 z方向。
由图 9已知各向异性的超材料单元其波传播椭球 6顺时针旋转 Θ角可以减 小电磁波汇聚点离超材料的距离。 在本实施例中， 由于人造微结构 4 的进一步 依次旋转使得波传播椭球 6也依次沿 y方向继续顺时针旋转。 因此， 电磁波在 超材料内部， 每经过一个超材料单元均会使其再次向对称面偏折， 这些偏折叠 加使得电磁波出射时的等效平移量增大。 因此， 在由折射率非均勾导致的相位 传播偏折角 β 1、 β 2不变的前提下， 电磁波汇聚点的距离将进一步减小为 f2。 则 fl、 £2、 β之间有如下关系： fl>f2>B ( 14 )
由此可见， 在折射率分布相同的条件下， 釆用各向异性的超材料单元 2, 能 够减小电磁波的汇聚点到超材料的距离， 也即减小焦距。
换言之， 当折射率分布相同、 焦距相同的条件下， 釆用各向异性且折射率 椭球 5的非寻常光光轴不垂直且不平行于对称面的超材料片层 1 (例如图 9、 图 10所示实施例）， 其电磁波偏折角将小于图 7所示实施例中的偏折角 β 1、 β 2。 根据关系式（7 ) 可以推知， 此时， 釆用前者制成的超材料片层 1 , 其 ζ方向的 长度 d也将减小。 简言之， 达到相同的汇聚效果， 图 9、 图 10所示的超材料片 层 1 , z方向的长度 d小于图 8所示超材料片层 1或者各向同性的超材料片层 1。 这种特性的好处在于能够减少材料的使用， 使超材料制造得更小， 有利于轻量 化和小型化。
如图 11所示， 本发明的汇聚电磁波的超材料， 是由多个超材料片层 1沿 X 方向堆叠并组装成一体的， 各片超材料片层 1 之间隔有空气或者填充有介电常 数接近 1、对电磁波没有响应的材料。 当超材料片层 1的数量较多使得 X方向的 长度远大于 z方向的长度时，整个超材料可以看做是一个薄片，则 z方向的长度 为该薄片的厚度。 因此， 根据上述结论可知， 釆用各向异性且可以实现电磁波 能量传播方向改变的人造微结构 4 , 可以减小整个汇聚电磁波的超材料的厚度， 从而减少材料的消耗， 实现轻薄、 小型化。
构成超材料的各个超材料片层 1可以完全相同， 则此时对于平面电磁波， 由于每个超材料片层 1 均可将经过该片层的一列电磁波汇聚到一点， 故而沿 X 方向叠加而成的多个超材料片层 1可以将电磁波汇聚成平行于 X方向的一条线。
要实现汇聚成一点， 各个超材料片层的折射率分布将不完全相同。 在 xy平 面上， 由超材料单元以 X方向为堆叠行、 y方向为列构成第二阵列中， 折射率呈 环形分布， 至少包括共圓心的一个圓形分布区和一个环形分布区， 且环形分布 区的内径与圓形分布区的外径基本相同， 相同半径的圓周上的各个超材料单元 的折射率相同， 且自圓形分布区外径所在的超材料单元到圓心所在的超材料单 元沿径向的折射率依次为 bl b2 , b3 , ... ... , bq, 自圓环分布区的外径所在的超 材料单元到圓环分布区的内径所在的超材料单元沿径向的折射率依次为 1 , a2, a3, ... ... , as, 圓心所在的超材料单元为中心超材料单元。
由以上可知， 经过中心超材料单元的一堆叠行和一列超材料单元、 经过中 心超材料单元中心的任意一条直线上的多个超材料单元的中间部分超材料单 元， 它们的折射率均依次为 al a2, a3, ……， as, bi , b2, b3, ……， bm, d , c2, c3, ... ... , cp, 且折射率为对称分布， 即满足公式（8 )至（10 )。
由此得出的折射率分布， 为了更直观的表示， 在第二阵列上， 将折射率相 同的超材料单元连成一条线， 并用线的疏密来表示折射率的大小， 线越密折射 率越大， 则符合以上所有关系式的超材料其折射率分布如图 12所示。
需要说明的是， 由于实际上超材料单元是一个立方体而非一个点， 因此上 述圓形、 环形只是近似描述， 实际上的折射率相同或基本相同的超材料单元是 在一个锯齿形圓周上的。 例如， H没超材料单元为边长为 lmm的立方体， 坐标 原点为中心超材料单元的中心点， 原理上设计认为坐标（X, y )为 （3.2, 5.7 ) 上的折射率为 ηι , 则该折射率！^实际上是坐标为（3 , 5 )、 （3 , 6 )、 （4, 5 )、 （4, 6 )四个点所围成的一个方形超材料单元的折射率。 其具体设计类似于计算机用 方形像素点绘制圓形、 椭圓形等平滑曲线时进行描点的编程模式 （例如 OpenGL ), 其在像素点相对于曲线很小时曲线显示为光滑， 而在像素点相对于 曲线较大时曲线显示有锯齿。
综上所述， 本发明的超材料具有以下特征：
1 )折射率在 xy平面上的分布如图 12、图 13所示，沿 z方向的折射率不变， 可以实现汇聚。 z方向的厚度可以做得非常薄， 已经实现的是在 2~3mm左右。
2 )每个超材料片层 1上的人造微结构 4设计成各向异性， 且其折射率椭球 5不垂直且不平行于 z方向，可以实现电磁波的能量传播方向在超材料内部向中 间偏折， 从而使出射时的电磁波汇聚的焦距减小， 传播范围变窄； 换言之， 实 现相同的汇聚效果， 釆用各向异性的人造微结构 4可以使超材料做得更薄。
3 ) y方向的人造微结构 4依次旋转， 可以进一步增大电磁波在超材料内部 的平移量， 从而减小焦距， 或者同理减薄超材料的厚度 d。 在实际应用中， 对于一个确定的应用环境， 在超材料大小、 位置、 焦距确 定、 入射电磁波的传播特征也确定的情况下， 可以先计算经过超材料上的每个 超材料单元 2的电磁波的偏折角度， 再利用公式（7 )计算相邻两个超材料单元 的折射率差值 Δη, 可以用微分和积分来反求 x、 y方向上各个超材料单元的折射 率 n的分布。
由于折射率是由介电常数和磁导率共同决定的， 因此可以通过改变介电常 数来调整折射率， 实现电磁波在 xy平面上的不同折射率分布。 改变人造微结构 4的形状和尺寸，即可改变其所在的超材料单元 2的介电常数，进而改变折射率。 例如改变图 3、 图 4和图 5中的人造微结构 4的第一、 第二金属丝的长短， 即可 改变其超材料单元 2的介电常数。
对于形状几何相似的人造微结构 4 ,对应的超材料单元 2的折射率随其人造 微结构 4尺寸的增大而增大。 z方向上由于折射率不变， 因此可以设计成沿 z方 向的每行超材料单元的人造微结构 4完全相同。
传统的超材料， 其电磁波的汇聚是通过沿 y方向和 /或 X方向的折射率的逐 渐增大到一个最大值后逐渐减小而实现的。 但是， 由于人造微结构 4 的尺寸受 到基材单元的限制， 而基材单元的尺寸必须在入射电磁波波长的五分之一以内 才能使得超材料单元对电磁波的响应视为连续， 因此人造微结构的最大尺寸只 能为入射电磁波波长的五分之一， 此时其折射率值也是有限的， 当上述折射率 逐渐增大到的最大值大于此时的折射率值， 则无法实现汇聚目的。
由于电磁波的偏折角与超材料沿 y方向的折射率变化量而有关， 而不与折 射率本身的值有关， 因此， 本发明的创新点在于， 釆用折射率值分段的第一至 第四段超材料来实现汇聚， 而各段超材料沿 y方向的折射率变化量使得电磁波 的偏折角满足汇聚功能， 而折射率本身的值是始终保持在一个范围内的， 例如 第一段超材料沿 y方向的折射率 ai , a2 , a3 , ... ... , as和第二段超材料沿 y方向 的折射率 bl b2 , b3 , ... ... , bq, 二者的最大值 as, bq和最小值 1 , ^是分别 相等的， 这就避免了因要满足的折射率值过大而无法制造的问题。
同时， 在超材料尺寸一定、 折射率的最大值和最小值相等的条件下， 本发 明的超材料釆用了四段式超材料、 且每段超材料均可达到最大值和最小值的方 式， 而传统超材料的折射率只有两个变化区段分别依次达到最大值和最小值， 因此本发明的折射率的平均变化率是传统超材料的平均变化率的两倍， 则电磁 波的偏折角要远大于传统超材料， 因此焦距变短。 换言之， 要实现相同的焦距， 则本发明的超材料厚度将减薄， 有利于实现小型化和轻便化。 因此， 上面结合附图对本发明的实施例进行了描述， 但是本发明并不局限 于上述的具体实施方式， 上述的具体实施方式仅仅是示意性的， 而不是限制性 的， 本领域的普通技术人员在本发明的启示下， 在不脱离本发明宗旨和权利要 求所保护的范围情况下， 还可做出很多形式， 这些均属于本发明的保护之内。

Claims

权 利 要求
1、一种汇聚电磁波的超材料，包括沿 X方向堆叠成一体的多个超材料片层， 每个超材料片层包括多个超材料单元， 每个超材料单元具有完全相同的基材单 元和附着在所述基材单元上人造微结构， 所述超材料单元以垂直于 X 方向的 y 方向为列、 以同时垂直于 x、 y方向的 z方向为行排成第一阵列， 其特征在于， 每行的各个超材料单元的折射率相同， 每列所述超材料单元的折射率依次 为 a a2, a3, …… , as, b b2, b3, …… , bm, c c2, c3, …… , cp, 各个折 射率满足：
ai < a2 < a3 < as, Ci > c2 > c3 > cp; 其中 b^as, bm < Ci , 且 s、 p均 为不小于 2的自然数， m为不小于 1的自然数；
所述人造微结构为非 90度旋转对称结构，且其折射率椭球的非寻常光光轴 不垂直且不平行于 y方向。
2、根据权利要求 1所述的汇聚电磁波的超材料， 其特征在于， 所述 ^， b2, b3, ...... , bm之间存在以下关系：
bi < b2 < b3…… <bq, bq > bq+i > bq+2 > bq+3…… >bm, 且 q为小于 m的自然 数。
3、 根据权利要求 2所述的汇聚电磁波的超材料， 其特征在于， 每列所述超 材料单元的折射率还具有如下关系：
(a2-ai) > (a3-a2)…… > (as-as-1) > (b2-bi) > (b3-b2)…… > (bq- bq),
(bq-bq+i) < (bq+i-bq+2) < (bq+2-bq+3)…… < (bm-1-bm) < (ci-c2) < (c2-c3) < (cp-1-cp)。
4、 根据权利要求 3所述的汇聚电磁波的超材料， 其特征在于， 上述折射率 还具有如下关系：
a尸 b尸 bm=cp, as=bq=Ci , s=p, q> s JL q>p, q=[(m+l)/2]„
5、 根据权利要求 4所述的汇聚电磁波的超材料， 其特征在于， 沿 y方向的 每列超材料单元的各个人造微结构其对应的各个折射率椭球的非寻常光光轴依 次顺时针方向旋转， 且折射率为 bq的一行人造微结构的折射率椭球的非寻常光 光轴平行于 y方向。
6、 根据权利要求 5所述的汇聚电磁波的超材料， 其特征在于， 所述多个超 材料片层完全相同且具有相同的折射率分布。
7、 根据权利要求 5所述的汇聚电磁波的超材料， 其特征在于， 所述多个超 材料片层具有不同的折射率分布， 在每个由超材料单元以 X方向为堆叠行、 y方 向为列构成第二阵列中， 以一中心超材料单元为圓心， 经过所述中心超材料单 元的一堆叠行和一列超材料单元其折射率均依次为 al a2, a3 , ... ... , as, bi , b2, b3 , …… , bm, ci , c2, c3 , …… , cp。
8、 根据权利要求 7所述的汇聚电磁波的超材料， 其特征在于， 所述第二阵 列的折射率呈环形分布， 经过所述圓心的任意一条直线上的多个超材料单元至 少部分超材料单元的折射率依次为 al a2, a3 , ... ... , as, bi , b2, b3 , ... ... , bm, c c2, c3 , ……， cp。
9、 根据权利要求 1所述的汇聚电磁波的超材料， 其特征在于， 各人造微结 构形状几何相似但尺寸随折射率的增大或随折射率的减小而减小。
10、 根据权利要求 1 所述的汇聚电磁波的超材料， 其特征在于， 所述人造 微结构为 "工" 字形或雪花形。
11、 根据权利要求 10所述的汇聚电磁波的超材料， 其特征在于， 所述人造 微结构的材料为金属。
12、 根据权利要求 1所述的汇聚电磁波的超材料， 其特征在于， y方向上的
转， 且两端超材料单元上的人造微结构相对于所述中间超材料单元上的人造微 结构的旋转角度不超过 90度。
13、 根据权利要求 12所述的汇聚电磁波的超材料， 其特征在于， y方向上 的每一列上的人造微结构在顺时针旋转的角度依次为 Θ1 θ2, θ3, ... ... , 0q, 且 这些旋转角度之间具有如下关系：
θι 02 Θ3 9q。
14、 根据权利要求 1所述的汇聚电磁波的超材料， 其特征在于， 所述超材 料单元其 x、 y、 z方向的长度在电磁波波长的五十分之一至二分之一之间。
PCT/CN2011/082387 2011-04-12 2011-11-17 一种汇聚电磁波的超材料 WO2012139379A1 (zh)

Priority Applications (2)

Application Number Priority Date Filing Date Title
EP11855252.0A EP2698650B1 (en) 2011-04-12 2011-11-17 A metamaterial enabling electromagnetic wave convergence
US13/522,493 US8681429B2 (en) 2011-04-12 2011-11-17 Metamaterial for converging electromagnetic waves

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN2011100913228A CN102480007B (zh) 2011-04-12 2011-04-12 一种汇聚电磁波的超材料
CN201110091322.8 2011-04-12

Publications (1)

Publication Number Publication Date
WO2012139379A1 true WO2012139379A1 (zh) 2012-10-18

Family

ID=46092544

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2011/082387 WO2012139379A1 (zh) 2011-04-12 2011-11-17 一种汇聚电磁波的超材料

Country Status (4)

Country Link
US (1) US8681429B2 (zh)
EP (1) EP2698650B1 (zh)
CN (1) CN102480007B (zh)
WO (1) WO2012139379A1 (zh)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102480008B (zh) * 2011-04-14 2013-06-12 深圳光启高等理工研究院 汇聚电磁波的超材料
EP2738875B1 (en) * 2011-07-26 2018-09-19 Kuang-Chi Innovative Technology Ltd. Cassegrain microwave antenna
US9697680B2 (en) 2014-08-25 2017-07-04 Skillz Inc. Cooperative gameplay in peer-to-peer wagering platform
JP6676238B2 (ja) * 2016-02-29 2020-04-08 国立大学法人東京農工大学 シート型メタマテリアルおよびシート型レンズ
US20210271000A1 (en) * 2020-02-28 2021-09-02 Samsung Electronics Co., Ltd. Meta-optical device and electronic apparatus including the same
CN113097735B (zh) * 2021-04-06 2022-03-18 南京大学 一种多功能超表面及隐身天线
CN116979235A (zh) * 2023-07-07 2023-10-31 苏州城市学院 一种波导中电磁能流操控装置

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101389998A (zh) * 2004-07-23 2009-03-18 加利福尼亚大学董事会 特异材料
US20090201572A1 (en) * 2008-02-07 2009-08-13 Toyota Motor Engineering & Manufacturing North America, Inc. Metamaterial gradient index lens
WO2010021736A2 (en) * 2008-08-22 2010-02-25 Duke University Metamaterials for surfaces and waveguides
US20110069377A1 (en) * 2009-09-18 2011-03-24 Toyota Motor Engineering & Manufacturing North America, Inc. Planar gradient index optical metamaterials

Family Cites Families (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8207907B2 (en) * 2006-02-16 2012-06-26 The Invention Science Fund I Llc Variable metamaterial apparatus
US7492329B2 (en) * 2006-10-12 2009-02-17 Hewlett-Packard Development Company, L.P. Composite material with chirped resonant cells
US7561320B2 (en) * 2007-10-26 2009-07-14 Hewlett-Packard Development Company, L.P. Modulation of electromagnetic radiation with electrically controllable composite material
US8411375B2 (en) * 2008-01-25 2013-04-02 Aptina Imaging Corporation Method and apparatus providing gradient index of refraction lens for image sensors
KR101472052B1 (ko) * 2008-07-30 2014-12-12 삼성디스플레이 주식회사 표시장치
US8174341B2 (en) * 2008-12-01 2012-05-08 Toyota Motor Engineering & Manufacturing North America, Inc. Thin film based split resonator tunable metamaterial
CN101587990B (zh) * 2009-07-01 2012-09-26 东南大学 基于人工电磁材料的宽带圆柱形透镜天线

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101389998A (zh) * 2004-07-23 2009-03-18 加利福尼亚大学董事会 特异材料
US20090201572A1 (en) * 2008-02-07 2009-08-13 Toyota Motor Engineering & Manufacturing North America, Inc. Metamaterial gradient index lens
WO2010021736A2 (en) * 2008-08-22 2010-02-25 Duke University Metamaterials for surfaces and waveguides
US20110069377A1 (en) * 2009-09-18 2011-03-24 Toyota Motor Engineering & Manufacturing North America, Inc. Planar gradient index optical metamaterials

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
"Metamaterials: Theory, Design, and Applications", SPRINGER, pages: 75 - 76
D. R. SMITH; D. C. VIER; T. KOSCHNY; C. M. SOUKOULIS, PHYSICAL REVIEW, vol. E 71, 2005, pages 036617
LIN, XIAN QI ET AL.: "Metamaterials Realized by Novel Compact Structures.", IEEE, 2006, XP031063750 *
See also references of EP2698650A4
SMITH, D.R. ET AL.: "Electromagnetic parameter retrieval from inhomogeneous metamaterials.", PHYSICAL REVIEW E., vol. 71, no. 3, 2005, pages 036617-1 - 036617-11, XP055128725 *

Also Published As

Publication number Publication date
US8681429B2 (en) 2014-03-25
EP2698650A1 (en) 2014-02-19
EP2698650A4 (en) 2014-08-27
CN102480007B (zh) 2013-06-12
CN102480007A (zh) 2012-05-30
EP2698650B1 (en) 2021-09-08
US20120299670A1 (en) 2012-11-29

Similar Documents

Publication Publication Date Title
WO2012139379A1 (zh) 一种汇聚电磁波的超材料
WO2012139391A1 (zh) 一种偏折电磁波的超材料
CN102480008B (zh) 汇聚电磁波的超材料
CN102891366B (zh) 一种电磁透镜天线
CN102790277B (zh) 定向天线
CN102780096A (zh) 超材料透镜天线
WO2012126249A1 (zh) 一种实现电磁波偏折的超材料
CN102480002B (zh) 电磁波汇聚元件
CN102480005B (zh) 偏折电磁波的超材料
US20140070117A1 (en) Electromagnetic wave beam splitter
CN102800912B (zh) 一种波导功分器
CN102480059B (zh) 基于超材料的天线
WO2012139368A1 (zh) 一种人工电磁材料
CN102478679A (zh) 电磁波分裂元件
CN102790273B (zh) 实现电磁波全方位辐射的超材料
EP2728669A1 (en) Metamaterial and metamaterial antenna
EP2738876A1 (en) Artificial composite material and antenna made of artificial composite material
US9142891B2 (en) Man-made composite material and man-made composite material antenna
US9099788B2 (en) Man-made composite material and man-made composite material antenna
WO2012122837A1 (zh) 一种电磁波元件
EP2731197A1 (en) Artificial composite material and antenna thereof
WO2012122803A1 (zh) 一种人造微结构及其应用的人工电磁材料
CN117317612A (zh) 一种基于超表面的龙伯透镜及其制备方法
CN115877562A (zh) 极化不敏感的超高数值孔径超表面透镜及设计方法
WO2012149824A1 (zh) 基于超材料的天线、微波热疗辐射器及微波热疗装置

Legal Events

Date Code Title Description
WWE Wipo information: entry into national phase

Ref document number: 13522493

Country of ref document: US

WWE Wipo information: entry into national phase

Ref document number: 2011855252

Country of ref document: EP

121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 11855252

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE