A zero-refractive-index metamaterial structure with full angular matching for arbitrary polarization incident waves

Abstract

This invention discloses a zero-refractive-index metamaterial structure that operates with arbitrarily polarized incident waves at all angles. The structure mainly consists of multiple identical subwavelength structural units arranged periodically. Each subwavelength structural unit is a metallic regular triangular prism, with electromagnetic waves propagating along its axial direction. Each subwavelength structural unit has an air aperture penetrating it along its axial direction; the air aperture is a single connecting channel. In cross-section, the connecting channel mainly consists of a "Y"-shaped channel and three "V"-shaped channels. The zero-refractive-index metamaterial achieved by this invention exhibits zero phase accumulation characteristics, full-angle impedance matching in free space, and insensitivity to incident wave polarization, showing broad application prospects in electromagnetic stealth, metalenses, and other fields.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic metamaterials, and specifically relates to a zero-refractive-index metamaterial structure that works for arbitrary polarized incident waves at all angles. Background Technology

[0002] Zero-refractive-index metamaterials are a class of artificial electromagnetic media with a refractive index approaching zero. In such media, the wavelength of electromagnetic waves approaches infinity, and the phase accumulation during propagation is close to zero. This unique electromagnetic modulation property makes zero-refractive-index metamaterials promising for applications in beamforming, highly directional antennas, electromagnetic stealth, and super-resolution imaging.

[0003] Achieving zero refractive index requires the dielectric constant or permeability of a material to approach zero. However, simply achieving zero refractive index does not guarantee efficient transmission of electromagnetic waves. To achieve perfect matching with free space, impedance matching conditions must also be met, meaning that both the dielectric constant and permeability tensors must simultaneously satisfy certain conditions. This material allows electromagnetic waves to pass through without reflection or phase accumulation, as if the space did not exist optically.

[0004] Traditional metamaterial design methods, such as those using resonant units, struggle to independently control electromagnetic parameters in multiple directions at subwavelength scales and often result in high losses and complex structures. Porous metal plate structures offer a pathway to achieve zero-refractive-index characteristics with full-angle matching. However, existing porous metal plate structures typically employ square lattice arrangements, with their first Brillouin zone exhibiting only C4 rotational symmetry. This low symmetry leads to poor electromagnetic isotropy, meaning inconsistent electromagnetic responses along the diagonal and principal axes. This makes the performance of existing structures highly sensitive to the polarization state and incident angle of the incident wave, preventing true full-polarization, full-angle operation. This severely limits the application of zero-refractive-index metamaterials in complex electromagnetic environments. Therefore, there is an urgent need to develop a structural design with higher-order rotational symmetry to ensure excellent macroscopic isotropy of the metamaterial, enabling impedance matching with free space and zero-refractive-index characteristics under arbitrary polarization and full-angle conditions. Summary of the Invention

[0005] To address the problems existing in the background art, this invention provides a zero-refractive-index metamaterial structure that works with arbitrarily polarized incident waves at all angles, solving the technical problems of polarization sensitivity, angle dependence, and impedance mismatch caused by insufficient isotropy in zero-refractive-index materials in the background art.

[0006] The technical solution adopted by the present invention for a zero-refractive-index metamaterial structure with full-angle matching for arbitrary polarization incident waves is as follows:

[0007] The full-angle matching zero-refractive-index metamaterial structure is mainly composed of multiple subwavelength structural units arranged closely and periodically. The main body of each subwavelength structural unit is a regular triangular prism made of metal, and electromagnetic waves propagate along the axial direction of the regular triangular prism. Each subwavelength structural unit has an air aperture penetrating it along the axial direction. The air aperture is a single connecting channel. In the cross-section, the connecting channel is mainly composed of a "Y"-shaped channel and three "V"-shaped channels. The "Y"-shaped channel is arranged at the center of the cross-section, and the three branches of the "Y"-shaped channel extend outward. The distance between each two adjacent branches of the "Y"-shaped channel is 120 degrees. The apex angle formed by the two branches of each "V"-shaped channel is 60 degrees. The apex of each "V"-shaped channel is connected to the end of the corresponding branch of the "Y"-shaped channel, and the apex opening of the "V"-shaped channel faces the center of the "Y"-shaped channel. The two branches of each "V"-shaped channel are parallel to the corresponding adjacent sides of the equilateral triangle.

[0008] The axial direction of the regular triangular prism is perpendicular to the direction of the base of the two equilateral triangles of the regular triangular prism; the cross-section is a plane perpendicular to the direction of electromagnetic wave propagation.

[0009] Multiple subwavelength structural units are arranged periodically in a triangular lattice on the cross-section of the subwavelength structural unit to form a fully angularly matched zero-refractive-index metamaterial structure.

[0010] The first Brillouin zone of the full-angle matched zero-refractive-index metamaterial structure has C6 rotational symmetry.

[0011] The cross-section and air aperture shape of each of the subwavelength structural units have C3 rotational symmetry.

[0012] The three branches of a “Y”-shaped channel are all of equal length; the two branches of a “V”-shaped channel are of equal length.

[0013] Each of the subwavelength structural units is made of a high-conductivity metal material such as copper, silver, gold, aluminum or tungsten, or is implemented by coating a dielectric substrate with a high-conductivity metal material.

[0014] The air aperture is filled with air.

[0015] The beneficial effects of this invention are:

[0016] 1. Fully polarized and operating at all angles (excellent isotropy): By arranging C3 symmetric units into a triangular lattice with C6 symmetry in the Brillouin zone, excellent isotropy is achieved. This metamaterial can achieve a stable and consistent response to incident waves of arbitrary polarization and angle.

[0017] 2. Full-angle matching: The structure of this invention achieves ideal electromagnetic parameters through a fractal-like air aperture design. This ensures that the impedance matches the free space impedance at all incident angles, achieving perfect transmission.

[0018] 3. Zero phase accumulation: When electromagnetic waves pass through the structure of this invention, there is no phase accumulation, which is equivalent to zero on the optical path.

[0019] 4. Low loss: Based on the non-resonant mechanism, it has lower loss compared to traditional resonant metamaterials. Attached Figure Description

[0020] Figure 1 This is a three-dimensional solid model of the subwavelength structural unit of the present invention;

[0021] Figure 2 This is a three-dimensional perspective view of the subwavelength structural unit of the present invention;

[0022] Figure 3 This is a geometric dimensioning diagram of the subwavelength structural unit of the present invention;

[0023] Figure 4 This is a front view of the structure of the present invention;

[0024] Figure 5 This is a schematic diagram illustrating the transmission amplitude and transmission phase at different incident angles in an embodiment.

[0025] Figure 6 A schematic diagram of the equivalent tangential permittivity and permeability for an embodiment;

[0026] Figure 7 This is a schematic diagram illustrating the transmission amplitude and transmission phase under different incident angles and different polarization angles in an embodiment.

[0027] Figure 8 The field distribution diagrams for different incident angles are shown in the example. Detailed Implementation

[0028] The present invention will now be described in more detail with reference to the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

[0029] like Figure 1 and Figure 2As shown, the all-angle matched zero-refractive-index metamaterial structure of this embodiment is mainly composed of multiple subwavelength structural units arranged in a close periodic pattern; each subwavelength structural unit has the same structure; the main body of each subwavelength structural unit is a regular triangular prism made of metal, and electromagnetic waves propagate along the axial direction (Z direction) of the regular triangular prism; each subwavelength structural unit has an air aperture with a specific shape penetrating along the axial direction, thereby forming a waveguide channel; the geometry of the air aperture is specially designed, adopting a fractal design, and is a single connected channel; in the cross-section (XY plane), the connection... The channel mainly consists of a "Y" shaped channel and three "V" shaped channels. The "Y" shaped channel is arranged at the center of the cross-section. The three branches of the "Y" shaped channel extend outward. The distance between each pair of adjacent branches of the "Y" shaped channel is 120 degrees. The apex angle formed by the two branches of each "V" shaped channel is 60 degrees. The vertex of each "V" shaped channel is connected to the outer end of the corresponding branch of the "Y" shaped channel, and the apex opening of the "V" shaped channel faces the center of the "Y" shaped channel. The two branches of each "V" shaped channel are parallel to the sides of the corresponding adjacent equilateral triangles.

[0030] By employing a fractal-like design, the undulating nature of the geometry is increased, which can greatly reduce the overlap integral between the incident wave and the waveguide fundamental mode of the air aperture while maintaining the overall subwavelength size of the unit.

[0031] According to the effective medium theory, when the subwavelength structural unit operates at the cutoff frequency of the waveguide's fundamental mode in the air aperture, the tangential component of its equivalent permittivity tends to zero. Simultaneously, since the overlap integral between the incident wave and the waveguide's fundamental mode in the air aperture is designed to approach zero, the tangential component of its equivalent permeability also tends to zero. Furthermore, due to the presence of the metal wall, the normal components of both the equivalent permittivity and permeability tend to infinity. Therefore, the equivalent parameters of this all-angle matched zero-refractive-index metamaterial structure are achieved. This leads to the realization of a zero-refractive-index metamaterial that works with arbitrarily polarized incident waves at all angles.

[0032] The axial direction of the regular triangular prism is perpendicular to the direction of the base of the two equilateral triangles of the regular triangular prism; the cross-section is a plane perpendicular to the direction of electromagnetic wave propagation.

[0033] like Figure 4 As shown, multiple subwavelength structural units are arranged periodically in a triangular lattice on the cross-section of the subwavelength structural unit to form a fully angularly matched zero-refractive-index metamaterial structure. This periodic arrangement of the triangular lattice ensures that each subwavelength structural unit (regular triangular prism) is tightly and seamlessly arranged periodically on the cross-section. Furthermore, to ensure that each subwavelength structural unit (regular triangular prism) is tightly and seamlessly arranged periodically on the cross-section, it is only possible to... Figure 4This is a method of periodic arrangement according to a triangular lattice.

[0034] In the X-axis direction of the cross-section, the triangular lattice periodic arrangement presents a rhombus shape formed by every two adjacent subwavelength structural units. In the Y-axis direction of the cross-section, the triangular lattice periodic arrangement presents a rhombus shape formed by two adjacent subwavelength structural units, or a centrally symmetrical funnel-like shape formed by one vertex of each of two adjacent subwavelength structural units being closely connected.

[0035] The first Brillouin zone of the full-angle matched zero-refractive-index metamaterial structure has C6 rotational symmetry.

[0036] The first Brillouin zone of the all-angle matched zero-refractive-index metamaterial structure is C6 rotational symmetry due to the periodic arrangement of the triangular lattice. This higher-order C6 symmetry ensures excellent electromagnetic isotropy, thus providing a consistent response to arbitrary polarized incident waves and arbitrary incident angles.

[0037] The cross-section and air aperture shape of each of the subwavelength structural units have C3 rotational symmetry.

[0038] The three branches of a “Y”-shaped channel are all of equal length; the two branches of a “V”-shaped channel are of equal length.

[0039] Each of the subwavelength structural units is made of a high-conductivity metal material such as copper, silver, gold, aluminum or tungsten, or is implemented by coating a dielectric substrate with a high-conductivity metal material.

[0040] The air aperture is filled with air.

[0041] like Figure 3 As shown, in this embodiment, the specific dimensions of the subwavelength structural unit are: the side length of the regular triangular prism. ,thickness Width of air aperture The length of each branch arm of the "Y"-shaped channel The length of each branch arm of the "V" shaped channel .

[0042] like Figure 4 As shown, the periodic arrangement of the basic structural units is illustrated. The overall structure of the metamaterial of this invention is an array composed of basic structural units arranged periodically in a triangular lattice on the XY plane, achieving seamless coverage of the entire plane.

[0043] This triangular lattice arrangement is key to the superior performance of this invention. Although individual regular triangular prism units possess only C3 symmetry, when they form a triangular lattice, their corresponding reciprocal lattice is a regular hexagon, meaning its first Brillouin zone has C6 rotational symmetry. Compared to the C4 symmetry of a square lattice (where the Brillouin zone is square), the C6 symmetry of the regular hexagon is closer to a perfect circle. In electromagnetic wave propagation, this means the metamaterial's iso-frequency dispersion curve is closer to a circle, and the wave propagates more consistently in all directions within the medium (i.e., superior isotropy). This is the fundamental reason why the structure maintains consistent response to arbitrary polarization and incident angles. Therefore, the metamaterial of this invention eliminates sensitivity to polarization and incident angles.

[0044] In the actual fabrication of this embodiment, each of the subwavelength structural units is manufactured using metal 3D printing technology. For example, iron is used as the internal substrate, and a layer of silver is electroplated on its surface (including the inner wall of the air aperture). Utilizing the skin effect, the silver plating layer provides extremely high surface conductivity, effectively reducing ohmic losses, making the structure's performance in the microwave band approach that of an ideal perfect conductor. The air aperture is filled with air.

[0045] At an operating frequency of 6 GHz, such as Figure 5 As shown, regardless of whether it is under TE polarization or TM polarization, when the incident angle changes from 0 degrees to 60 degrees, the transmission amplitude is close to 1 (perfect transmission), and the transmission phase is close to 0 degrees (zero phase accumulation). This fully verifies that the structure proposed in this invention achieves full-angle matching zero refractive index characteristics based on its high-order lattice symmetry.

[0046] At an operating frequency of 6 GHz, such as Figure 6 As shown, the equivalent tangential permittivity of the structure of the present invention ( ) and permeability ( The real and imaginary parts of the α-index both tend to 0, meaning the equivalent refractive index tends to 0.

[0047] At an operating frequency of 6GHz, such as Figure 7 As shown, regardless of whether it is TE polarization or TM polarization, when the incident angle ( The polarization angle changes from 0 degrees to 80 degrees. When the temperature changes from 0 degrees to 45 degrees, the transmission amplitude ( Both are close to 1 (perfect transmission), and the transmission phase ( All of these values ​​are close to 0 degrees (zero phase accumulation). This fully verifies that the structure proposed in this invention, based on its high-order lattice symmetry, achieves full-angle impedance matching, arbitrary polarization operation, and zero refractive index characteristics.

[0048] At an operating frequency of 6GHz, such as Figure 8 As shown, the first row represents the TE-polarized plane wave along the wave vector. The electric field of the metamaterial at incident angles of 0, 30, and 60 degrees. Distribution diagram, the second row shows the TM polarized plane wave along the wave vector. The magnetic field of the metamaterial at the indicated incident angles of 0, 30, and 60 degrees. The distribution diagram shows that this metamaterial achieves arbitrary polarization and exhibits good transmission at all incident angles with zero refractive index.

[0049] The structure in this embodiment operates at a frequency of 6 GHz. To enable the structure to operate at other frequencies, the dimensions of the metal triangular prism and the air aperture need to be adjusted according to the operating wavelength ratio.

[0050] The all-angle matched zero-refractive-index metamaterial structure in this embodiment is designed to operate at the cutoff frequency of the waveguide fundamental mode of the fractal-like air aperture. The air aperture, through a meandering current path, lowers the cutoff frequency while maintaining the overall unit size as subwavelength, and makes the overlap integral between the incident plane wave and the waveguide fundamental mode of the air aperture approach zero. Therefore, at the operating frequency, the parallel component of the equivalent dielectric constant tensor of the all-angle matched zero-refractive-index metamaterial structure approaches zero due to operating at the cutoff frequency, the parallel component of the equivalent permeability tensor approaches zero due to the overlap integral between the incident plane wave and the waveguide fundamental mode of the air aperture, and the perpendicular component approaches infinity, thus achieving equivalent parameters approaching zero. This achieves full-angle impedance matching with free space and zero-refractive index characteristics with zero-phase propagation.

[0051] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A zero-refractive-index metamaterial structure with full-angle matching that works for incident waves of arbitrary polarization, characterized in that: The full-angle matching zero-refractive-index metamaterial structure is composed of multiple subwavelength structural units arranged closely and periodically. The main body of each subwavelength structural unit is a regular triangular prism made of metal, and electromagnetic waves propagate along the axial direction of the regular triangular prism. Each subwavelength structural unit has an air aperture penetrating it along the axial direction. The air aperture is a single connecting channel. In cross-section, the connecting channel consists of a "Y"-shaped channel and three "V"-shaped channels. The "Y"-shaped channel is arranged at the center of the cross-section, and the three branches of the "Y"-shaped channel extend outward. The distance between each two adjacent branches of the "Y"-shaped channel is 120 degrees. The apex angle formed by the two branches of each "V"-shaped channel is 60 degrees. The apex of each "V"-shaped channel is connected to the end of the corresponding branch of the "Y"-shaped channel, and the apex opening of the "V"-shaped channel faces the center of the "Y"-shaped channel. The two branches of each "V"-shaped channel are parallel to the corresponding adjacent sides of the equilateral triangle.

2. The all-angle matching zero-refractive-index metamaterial structure for arbitrary polarization incident waves as described in claim 1, characterized in that: The axial direction of the regular triangular prism is perpendicular to the direction of the base of the two equilateral triangles of the regular triangular prism; the cross-section is a plane perpendicular to the direction of electromagnetic wave propagation.

3. The all-angle matching zero-refractive-index metamaterial structure for arbitrary polarization incident waves as described in claim 1, characterized in that: Multiple subwavelength structural units are arranged periodically in a triangular lattice on the cross-section of the subwavelength structural unit to form a fully angularly matched zero-refractive-index metamaterial structure.

4. The all-angle matching zero-refractive-index metamaterial structure for arbitrary polarization incident waves as described in claim 1, characterized in that: The first Brillouin zone of the full-angle matched zero-refractive-index metamaterial structure has C6 rotational symmetry; The cross-section and air aperture shape of each of the subwavelength structural units have C3 rotational symmetry.

5. The all-angle matching zero-refractive-index metamaterial structure for arbitrary polarization incident waves as described in claim 1, characterized in that: The three branches of a "Y" shaped channel are all of equal length; the two branches of a "V" shaped channel are of equal length.

6. The all-angle matching zero-refractive-index metamaterial structure for arbitrary polarization incident waves according to claim 1, characterized in that: Each of the subwavelength structural units is made of a high-conductivity metal material such as copper, silver, gold, aluminum or tungsten, or is implemented by coating a dielectric substrate with a high-conductivity metal material.

7. The all-angle matching zero-refractive-index metamaterial structure for arbitrary polarization incident waves according to claim 1, characterized in that: The air aperture is filled with air.

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