Meta-structure grating design method and meta-structure grating
By analyzing the electromagnetic field distribution functions of the reflected wave and the excitation wave, a metagrating that can achieve the target absorption rate is designed, which solves the problem that traditional methods cannot be applied to waveguides, and achieves efficient absorption of reflected waves and improved system stability.
Patent Information
- Application Number
- CN202511114047.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-11
- Publication Date
- 2025-09-26
AI Technical Summary
Traditional metagrating design methods cannot be effectively applied to waveguides and cannot effectively absorb the reflected TE10 mode, resulting in signal interference and system instability.
A metagrating design method is provided. By analyzing the electromagnetic field distribution functions of the reflected wave and the excitation wave, a metagrating capable of achieving a target absorption rate is designed. The metagrating includes a dielectric substrate and a metaconductor. The dielectric parameters and the conductor structure parameters are optimized to ensure destructive interference of the reflected wave.
It achieves efficient and accurate absorption of reflected waves, improves system stability and signal integrity, is applicable to various types of waveguides, has a simple design, and can absorb reflected waves over a wider bandwidth.
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Figure CN120703975A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of diffraction optical technology, and in particular to a metagrating design method and a metagrating. Background Art
[0002] In microwave / millimeter wave systems, absorbing reflected waves is a key approach to addressing signal integrity, system stability, and electromagnetic compatibility. For example, the reflected TE10 mode not only interferes with normal signal transmission but can also cause a series of chain reactions, including signal distortion and system errors, electromagnetic interference, and device thermal failure.
[0003] A metagrating is a new type of grating based on metasurface technology. It utilizes artificially designed subwavelength-scale micro-nanostructure units (also known as "metaatoms") arranged periodically or non-periodically on a two-dimensional plane to precisely control the phase, amplitude, polarization and other properties of light waves. Therefore, there have been related studies applying metagratings to absorb reflected waves. However, the field distribution and wave impedance in waveguides are significantly different from those of spatial waves propagating in free space. Therefore, traditional metasurface design methods cannot be directly applied to the design of metagratings in waveguides. Summary of the Invention
[0004] The present invention provides a metagrating design method and a metagrating, which are used to provide a systematic metagrating design method. Through this design method, a metagrating that can absorb the reflected TE10 mode to a target absorption rate can be designed. The metagrating designed based on this method has the advantages of small size and simple processing.
[0005] The present invention provides a metagrating design method, wherein the metagrating includes a dielectric substrate and a metaconductor, which is arranged at the bottom of a waveguide. The method comprises: determining an electromagnetic field distribution function of a reflected wave after reflection from the surface of the dielectric substrate based on an electromagnetic field distribution function of an input wave, dielectric parameters and dimensions of the dielectric substrate, and dimensions of the waveguide; determining an electromagnetic field distribution function of an excitation wave of the metaconductor excited by the input wave and transmitted into the dielectric layer based on the electromagnetic field distribution function of the input wave, dimensions of the waveguide, and dielectric parameters of a dielectric layer in the waveguide, wherein the excitation wave is adapted to destructively interfere with the reflected wave so that the reflected wave reaches a target absorptivity; determining an electromagnetic wave distribution function of a total field in the waveguide based on the electromagnetic field distribution functions of the input wave, the excitation wave, and the reflected wave; determining a target excitation current value in the metaconductor based on the reflected wave, the electromagnetic field distribution functions of the excitation wave, and the target absorptivity; determining a target impedance density of the metaconductor based on the target excitation current value and the electromagnetic wave distribution function of the total field; and determining structural parameters of the metaconductor based on the target impedance density.
[0006] According to the metagrating design method provided by the present invention, the electromagnetic field distribution function of the excitation wave in which the metaconductor is excited by the input wave and transmitted to the dielectric layer is determined based on the electromagnetic field distribution function of the input wave, the size of the waveguide, and the dielectric parameters of the dielectric layer in the waveguide, including: determining the electromagnetic field distribution function of the assumed excitation wave in the metaconductor based on the dielectric parameters of the dielectric layer, the thickness of the dielectric substrate, and the position information of the metaconductor, wherein the assumed excitation wave is the radiation field formed by the metaconductor being excited by the input wave in free space; and determining the electromagnetic field distribution function of the excitation wave based on the electromagnetic field distribution function of the assumed excitation wave and the reflection coefficient of the assumed excitation wave on the surface of the dielectric substrate.
[0007] According to the metagrating design method provided by the present invention, the above-mentioned determination of the structural parameters of the metagrating based on the above-mentioned target impedance density includes: equating the above-mentioned metaconductor to a flat strip structure; determining the number of metaatoms constituting the above-mentioned metaconductor based on the above-mentioned waveguide size; and determining the longitudinal length of the metaatoms along the direction of the above-mentioned metaconductor.
[0008] According to the metagrating design method provided by the present invention, the structural parameters of the metaconductor are determined based on the target impedance density, and further include: constructing a strip capacitor in the metaatom when the target impedance density is determined as a complex number; determining the strip length of the strip capacitor based on the imaginary part of the target impedance density, the longitudinal length of the metaatom, the dielectric parameters of the dielectric layer, and the dielectric parameters of the dielectric substrate; and determining the resistance value of the resistor in the metaatom based on the real part of the target impedance density and the longitudinal length of the metaatom.
[0009] The metagrating design method provided by the present invention also includes: optimizing the strip length and the resistance value of the resistor when the absorption rate of the reflected wave does not reach the target absorption rate, including: substituting the strip length and the resistance value of the resistor into the simulation software to calculate the actual absorption rate; when the actual absorption rate is less than the target absorption rate, determining the strip length as the strip length to be optimized, and determining the resistance value of the resistor as the resistance value to be optimized; adjusting the strip length to be optimized with a first preset step size within a first preset range; adjusting the resistance value to be optimized with a second preset step size within a second preset range; iteratively substituting the strip length to be optimized and the resistance value to be optimized into the simulation software to calculate the calculated absorption rate; when the calculated absorption rate is equal to or greater than the target absorption rate, determining the strip length to be optimized as the target strip length, and determining the resistance value to be optimized as the target resistance value.
[0010] According to the metagrating design method provided by the present invention, the structural parameters of the metaconductor are determined based on the target impedance density, and further include: constructing the metaatom using a conductive optical film when the target impedance density is determined as a real number, including: determining a target width of the conductive optical film based on the target impedance density; determining a target surface resistance value of the conductive optical film based on the target width of the conductive optical film and the target impedance density.
[0011] The present invention also provides a metagrating designed by the above-mentioned metagrating design method, comprising: a dielectric substrate; a metaconductor wire, arranged on the surface of the above-mentioned dielectric substrate, comprising a plurality of metaatoms arranged in series, the above-mentioned metaatoms including edge resistors, and strip capacitors connected in series with the above-mentioned chip resistors.
[0012] The present invention also provides another metagrating designed by the above-mentioned metagrating design method, comprising: a dielectric substrate; a metaconductor wire, arranged on the surface of the above-mentioned dielectric substrate, comprising one or more metaatoms composed of a conductive optical film, wherein, when there are multiple metaatoms, the multiple metaatoms are arranged in series.
[0013] According to the metagrating provided by the present invention, the conductive optical film is an indium tin oxide film.
[0014] According to the metagrating provided by the present invention, the loss tangent value of the dielectric substrate is less than 0.01.
[0015] The metagrating design method provided by the present invention can obtain the electromagnetic field distribution function of the reflected wave and the electromagnetic field distribution function of the excitation wave excited by the input wave in the metagrating conductor based on the electromagnetic field distribution function of the input wave, the dielectric parameters of the dielectric substrate and the size of the waveguide. After determining the target absorptivity, since the electromagnetic field distribution function of the reflected wave is known, the electromagnetic field distribution function of the excitation wave can be designed to cause destructive interference between the excitation wave and the reflected wave, so that the reflected wave can reach the target absorptivity. Since the target absorptivity and the electromagnetic field distribution function of the reflected wave are determined, the determined electromagnetic field distribution function of the excitation wave can naturally be obtained. When the electromagnetic field distribution function of the excitation wave is determined, the target excitation current value in the metagrating conductor and the electromagnetic distribution function of the total field in the waveguide can be obtained. After determining the target excitation current value, Ohm's law can be used to determine the target impedance density required for the metaconductor to achieve the target excitation current value under the electromagnetic distribution function of the total field. After the target impedance density is clear, the structural parameters of the metaconductor can be determined. Since the structural parameters of the metaconductor are clear, a metagrating that can make the reflected wave reach the target absorption rate can naturally be obtained accordingly.
[0016] One or more technical solutions of the present invention have at least the following technical effects or advantages: (1) The metagrating design method provided by the present invention analyzes the electromagnetic field distribution functions of the reflected wave and the excitation wave, and directly analyzes the distribution function of the excitation wave that enables the reflected wave to interfere with each other through mathematical analysis. Then, the structural parameters of the metaconductor are designed accordingly according to the distribution function of the excitation wave, providing a stable and reliable metagrating design method. Compared with the traditional method of numerical simulation of the full wave in the waveguide, it is more efficient and accurate, and the designed metagrating can also be used in various types of waveguides.
[0017] (2) The present invention also provides a method for further optimizing the target strip width and target resistance value of the strip resistor in the meta-atom. By optimizing through simulation software, it can be ensured that the complex conditions in the actual environment are comprehensively considered, and that the meta-grating designed according to the meta-grating design method provided by the present invention can achieve the target absorption rate for the reflected wave.
[0018] (3) The metagrating provided by the present invention can absorb reflected waves over a wider bandwidth than the grating structure in the related art. BRIEF DESCRIPTION OF THE DRAWINGS
[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0020] Figure 1 is a structural diagram of a waveguide provided with a metagrating according to an exemplary embodiment of the present invention; Figure 2 is a flow chart of a metagrating design method according to an exemplary embodiment of the present invention; Figure 3 Schematic diagram showing the metal waveguide cavity ( x 0 , h ) is a schematic diagram of the image source analysis method for the radiation field of the current source at ) being bounced off the electric walls on both sides; Figure 4 (a) shows a schematic diagram of a super-atomic structure according to an exemplary embodiment of the present invention. Figure 4 (b) shows an exemplary embodiment of the present invention. Figure 4 (a) Schematic diagram of the metagrating constructed by metaatoms. Figure 4 (c) shows the Figure 4 (b) is a graph showing the absorptivity of the TE10 mode absorbed by the metagrating. Figure 4(d) shows another exemplary embodiment of the present invention. Figure 4 (a) Schematic diagram of the metagrating constructed by metaatoms. Figure 4 (e) shows the Figure 4 (d) is a graph showing the absorptivity of the TE10 mode absorbed by the metagrating. Figure 5 (a) is a schematic diagram of the meta-atom realized based on indium tin oxide (ITO) thin film; Figure 5 (b) is based on Figure 5 (a) Graph showing the relationship between w and h in the type III metagrating constructed by the metaatom shown; Figure 5 (c) is a schematic diagram of a type III waveguide constructed based on a type III metagrating; Figure 5 (d) is a graph showing the absorptivity of the type III waveguide and the S11 parameter simulation results; Figure 6 is the relationship between the real part of the impedance density R(Z) in the metagrating and the substrate thickness h; Figure 7 is a graph of the simulation results of the metagrating waveguide with a dielectric basic thickness of h = 4.68 mm (corresponding to the maximum value of the real part of the load impedance density), where Figure 7 (a) is the absorption bandwidth simulation curve of type I metagrating waveguide. Figure 7 (b) is a simulated absorption bandwidth curve of the type III metagrating waveguide. DETAILED DESCRIPTION
[0021] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.
[0022] The terms used herein are only for describing specific embodiments and are not intended to limit the present disclosure. The terms "comprise," "include," etc. used herein indicate the presence of the features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.
[0023] All terms used herein, including technical and scientific terms, have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.
[0024] When expressions such as “at least one of A, B, and C, etc.” are used, they should generally be interpreted in accordance with the meaning commonly understood by those skilled in the art. For example, “a system having at least one of A, B, and C” should include but is not limited to systems having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, and C, etc. When expressions such as “at least one of A, B, or C, etc.” are used, they should generally be interpreted in accordance with the meaning commonly understood by those skilled in the art. For example, “a system having at least one of A, B, or C” should include but is not limited to systems having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, and C, etc.
[0025] In related technologies, although metagratings are placed in waveguides in the hope of absorbing reflected waves and reducing interference from reflected waves, the field distribution and wave impedance in the waveguide are significantly different from those of spatial waves propagating in free space, and therefore cannot be well applied in the design of absorption-type metagratings in waveguides.
[0026] In view of this, embodiments of the present invention provide a metagrating design method and a metagrating.
[0027] Figure 1 1 is a structural diagram of a waveguide provided with a metagrating according to an exemplary embodiment of the present invention. Figure 2 4 is a flow chart of a metagrating design method according to an exemplary embodiment of the present invention.
[0028] According to a metagrating design method provided by the present invention, Figure 2 The metagrating design method includes but is not limited to steps S110 to S160.
[0029] The metagrating design method provided in the embodiment of the present invention can be designed for a metagrating disposed in a waveguide. The metagrating includes a dielectric substrate 1 and a metaconductor wire 2 , and is disposed at the bottom of a waveguide 3 .
[0030] Step S110: determining the electromagnetic field distribution function of the reflected wave after being reflected by the surface of the dielectric substrate based on the electromagnetic field distribution function of the input wave, the dielectric parameters and dimensions of the dielectric substrate, and the dimensions of the waveguide.
[0031] According to an embodiment of the present invention, the size of the dielectric substrate 1 includes the thickness of the dielectric substrate 1 .
[0032] According to an embodiment of the present invention, the dielectric parameters of the dielectric substrate 1 and the dielectric layer include relative dielectric constant, wave number and wave impedance. The relative dielectric constants of the dielectric layer and the dielectric substrate 1 are respectively ε0 (vacuum dielectric constant) and ε s = ε r ε0( ε r is the relative dielectric constant of the dielectric substrate). Since both the dielectric layer and the dielectric substrate 1 are non-magnetic media, the wave number and wave impedance of the input wave in the dielectric layer and the dielectric substrate 1 are expressed as , , , , where k0 is the wave number of the input wave in the dielectric layer, ω is the angular frequency of the input wave, is the magnetic permeability of the input wave in vacuum, is the wave number of the input wave in the dielectric layer, is the wave number of the input wave in the dielectric substrate, is the wave number of the input wave in the dielectric substrate.
[0033] Therefore, the electromagnetic field distribution function of the input wave can be expressed as , in is the amplitude of the input wave, is the longitudinal wave number of the TEm0 mode of the incident wave in the dielectric layer, where m is the order of the TE mode, so It represents the longitudinal wave number of TE10 mode, is the width of the waveguide, x is Figure 1 The x-axis coordinate along the waveguide width direction, where x=0 is set to Figure 1 The left edge of the waveguide, z is Figure 1 The coordinate along the z-axis opposite to the incident direction of the input wave, where z=0 is set to Figure 1 When the dielectric substrate is away from the outer edge of the input wave direction, h is the thickness of the dielectric substrate, and j is the imaginary unit. When only the reflection effect of the short-circuited dielectric substrate 1 is considered when the metaconductor 2 is not loaded, the TE10 mode of the incident wave in the waveguide 3 is in the dielectric layer ( z > h ) The electromagnetic wave distribution function generated by can be expressed as: (1) In the dielectric substrate area (0< z < h ), the electromagnetic wave distribution function expression is (2) in R 1 indicates that the TE10 mode of the incident wave is on the surface of the dielectric substrate 1 ( z = h ) reflection coefficient, which can be obtained by the dielectric substrate 1 surface ( z = h ) is derived as follows: (3) ρ 1 is defined as ρ 1= β s1 / β 1, where represents the longitudinal wave number of the TEm0 mode in the dielectric substrate.
[0034] Step S120: Determine the electromagnetic field distribution function of the excitation wave excited by the input wave and transmitted to the dielectric layer of the metaconductor based on the electromagnetic field distribution function of the input wave, the size of the waveguide, and the dielectric parameters of the dielectric layer in the waveguide, wherein the excitation wave is suitable for destructively interfering with the reflected wave so that the reflected wave reaches a target absorption rate.
[0035] According to embodiments of the present invention, the electromagnetic field distribution function of the excitation wave can be calculated by directly inputting relevant parameters of the waveguide 3, dielectric layer, and metagrating (including the shape, dimensions, and material of the metaconductor 2), setting an input wave source, and then numerically calculating the electromagnetic field distribution of the reflected wave within the dielectric layer. Alternatively, the electromagnetic field distribution function of the reflected wave within the dielectric layer can be calculated using methods such as coupled mode theory, Green's function equivalent circuits, or analytical approximation.
[0036] According to an embodiment of the present invention, the electromagnetic field distribution function of the excitation wave in the dielectric layer can be expressed as: (4) Where I is the current value of the excitation current generated by the superconductor, R m is the reflection coefficient of the TEm0 mode in the excitation wave on the surface of the dielectric substrate.
[0037] Step S130: determining the electromagnetic wave distribution function of the total field in the waveguide based on the electromagnetic field distribution functions of the input wave, the excitation wave, and the reflected wave.
[0038] According to the embodiments of the present disclosure, when the electromagnetic field distribution functions of the input wave, the excitation wave, and the reflected wave in the dielectric layer are clear, equations (1), (3), and (4) can be combined to obtain the electromagnetic wave distribution function of the total field in the dielectric layer: (5) Where x0 is the coordinate of the metaconductor on the x-axis.
[0039] Step S140: determining a target excitation current value in the metaconductor based on the electromagnetic field distribution function of the reflected wave and the excitation wave and the target absorptivity.
[0040] According to the embodiments of the present disclosure, if the goal is to completely absorb the TE10 mode, it is necessary to first determine the field component of the TE10 mode. In the dielectric layer, the electromagnetic field distribution function of the superposition field including the reflected wave and the excitation wave can be expressed as: (6) Equation (6) can also be written as , therefore, the field component of the TE10 mode can be written as: (7) Let the equation (7) The required target excitation current is: (8) Step S150: determining a target impedance density of the metaconductor based on the target excitation current value and the electromagnetic wave distribution function of the total field.
[0041] According to the embodiment of the present invention, since the excitation current in the metaconductor is affected by the total field in the waveguide 3, based on Ohm's law, the electromagnetic distribution function of the total field can be used to calculate the excitation current. E tot and target excitation current I Determine the target impedance density of the metaconductor.
[0042] According to an embodiment of the present invention, the target impedance density Z can be obtained by combining equations (5) and (8): (9) in , as well as The expression is (10) in, is the wavelength of the input wave in free space, .
[0043] Step S160: Determine the structural parameters of the metaconductor based on the target impedance density.
[0044] According to an embodiment of the present invention, when the target impedance density to be achieved by the metaconductor is clear, corresponding design can be made around how to achieve the target impedance density. The width, thickness, shape of the metaatoms constituting the metaconductor, and the period of arrangement can be designed to form a complete metaconductor, which can then be designed into a complete metagrating.
[0045] The metagrating design method provided by the embodiment of the present invention converts the size conditions of the waveguide 3 into design constraints. By combining the size of the waveguide 3 with the field distribution function in the waveguide 3, the parameters of the metaconductor that can achieve the target excitation current value can be directly determined, thereby realizing the design of a metagrating that can absorb specific absorption waves. Compared with traditional numerical methods, a clear analytical process is directly given, which has stronger adaptability.
[0046] Figure 3 Schematic diagram showing the metal waveguide cavity ( x 0 , h ) is a schematic diagram of the image source analysis method in which the radiation field of the current source at is bounced off the electric walls on both sides.
[0047] In an exemplary embodiment, step S110 includes determining an electromagnetic field distribution function of a hypothetical excitation wave of the metawire based on dielectric parameters of the dielectric layer, thickness of the dielectric substrate, and location information of the metawire, where the hypothetical excitation wave is a radiation field generated by the metawire in free space when excited by an input wave. The electromagnetic field distribution function of the excitation wave is determined based on the electromagnetic field distribution function of the hypothetical excitation wave and a reflection coefficient of the hypothetical excitation wave on the surface of the dielectric substrate.
[0048] According to an embodiment of the present invention, Figure 3 Shown in ( x 0 , h ) of the current source and its current source in the electric wall 1( x=0 ) and electric wall 2( x=a ) forms an infinite periodic array with a spacing of 2a. Figure 3 In the figure, Electric wall 1 is Electric wall 1, Current source is Current source, Electric wall 2 is Electric wall 2, First-order mirror source 1 is First-order mirror source 1, First-order mirror source 2 is First-order mirror source 2, Second-order mirror source 1 is Second-order mirror source 1, and Second-order mirror source 2 is Second-order mirror source 2. The first-order mirror source (brown) is the primary reflection of the current source on the two electric walls, and the second-order mirror source (purple) is the secondary reflection of the first-order mirror source on the opposite electric wall. This reflection pattern is extended to infinity through iteration. When it is located on a dielectric substrate ( x 0, h ) is irradiated by the total field, it can be equivalent to an infinite periodic source array with a spacing of 2a according to the image source analysis method. For a single current source infinitely extending along the y direction in free space I, which assumes that the electromagnetic field distribution function of the excitation wave can be expressed as , where is the second kind of Hankel function. Therefore, the electromagnetic field distribution function of the assumed excitation wave generated by the current source h in the dielectric layer (z > I ) can be expressed as: (11) where , , n represents the nth periodic source array. Applying Poisson summation and Fourier transform of the Hankel function, equation (11) can be rewritten as (12) Considering that the assumed excitation wave will also be reflected at the dielectric substrate at the waveguide terminal, the assumed excitation wave (the combination of the radiation field and its reflected field) generated by the meta-wire in the dielectric layer (z > h) can be determined as the excitation wave in the dielectric layer, and its electromagnetic distribution function can be expressed by equation (4).
[0049] Similarly, the electromagnetic distribution function of the assumed excitation wave in the dielectric substrate region (0 < z < h) can be expressed as (13) where the reflection coefficient of the assumed excitation wave at the dielectric substrate is: (14) where .
[0050] In a schematic embodiment, the target impedance density Z can be obtained through the following derivation. Based on equation (8) and Ohm's law, substituting the position information of the meta-wire ( x 0 ,h ) into equation (5), when substituting the position information of the meta-wire, a hypothetical divergence term will appear. For this reason, can be used to replace , where r0 is the radius of the meta-wire. Therefore, when substituting the position information of the meta-wire into equation (11), it can be written as (15) It can be further rewritten as (16) where . Similarly, when considering the substrate reflection, the corresponding external field is (17) Thus, by联立 equations (1), equation (8), and equation (17), equation (9) and the expression of the target impedance density can be obtained.
[0051] In an exemplary embodiment, step S160 includes converting the metawire into a flat strip structure, determining the number of metaatoms constituting the metawire based on the waveguide dimensions, and determining the longitudinal length of the metaatoms along the metawire.
[0052] According to an embodiment of the present invention, in order to achieve the uniformity of impedance load as much as possible, the number of metaatoms should be set as much as possible, and the number of metaatoms is positively correlated with the complexity of the structure. Therefore, it is necessary to balance the uniformity of impedance load and the complexity of the structure as much as possible. After determining the number of metaatoms, the longitudinal length of the metaatoms can naturally be determined based on the length of the metawire.
[0053] Through the embodiments of the present invention, by making the metaconductor equivalent to a flat strip structure, it can be compatible with the PCB manufacturing process, ensuring that the metaconductor can be manufactured using a relatively mature process, which can greatly simplify the manufacturing process.
[0054] According to an embodiment of the present invention, a metaconductor is equivalent to a flat strip structure, reducing the electromagnetic field problem from three dimensions to two dimensions. This allows the electric and magnetic fields to vary only along the waveguide cross-section (the xy plane) and remain uniform along the length of the conductor (the z direction). This allows the radiation field to be directly described using two-dimensional Green's functions (such as Hankel functions), avoiding tedious three-dimensional integration.
[0055] In an illustrative embodiment, step S160 further includes: constructing a strip capacitor in the metaatom when the target impedance density is determined as a complex number. Determining a strip length of the strip capacitor based on an imaginary part of the target impedance density, a longitudinal length of the metaatom, dielectric parameters of the dielectric layer, and dielectric parameters of the dielectric substrate. Determining a resistance value of a resistor in the metaatom based on the real part of the target impedance density and the longitudinal length of the metaatom.
[0056] According to an embodiment of the present invention, the target impedance density Z can be written in the form of a complex number: (18) The real part expression for (19) Imaginary part expression for (20) According to an embodiment of the present invention, when the target impedance density is a complex number, the imaginary part of the target impedance density can be realized by setting a capacitor structure in the meta-atom.
[0057] Figure 4(a) shows a schematic diagram of a super-atomic structure according to an exemplary embodiment of the present invention. Figure 4 (b) shows an exemplary embodiment of the present invention. Figure 4 (a) Schematic diagram of the metagrating constructed by metaatoms. Figure 4 (c) shows the Figure 4 (b) is a graph showing the absorptivity of the TE10 mode absorbed by the metagrating. Figure 4 (d) shows another exemplary embodiment of the present invention. Figure 4 (a) Schematic diagram of the metagrating constructed by metaatoms. Figure 4 (e) shows the Figure 4 (d) Graph of the absorptivity of the TE10 mode absorbed by the metagrating.
[0058] Here, transformation is the process of converting a cylindrical conductor into an atom with a strip capacitor structure, Absorbance is the absorption rate of the reflected wave, Frequency is the frequency of the reflected wave, and S-parameter is the S11 parameter, which is used to measure the reflection characteristics of electromagnetic waves at a port or interface.
[0059] An illustrative embodiment is given below to illustrate the process of determining the metaconductor structure parameters based on the target impedance density when the target impedance density is a complex number.
[0060] In this embodiment, the X-band 10 GHz is selected as the operating frequency, the dielectric layer is set to air, and the metagrating medium substrate is RO3003 ( ε r = 3, tan δ = 0.001), the waveguide is standard WR90 type ( a = 22.86 mm, b = 10.16mm). According to equations (18)-(20), the parameters x 0 and h The metagrating design for the absorption waveguide can be freely selected. Considering the structural symmetry, the x 0= a / 2, and select h = λ 0 / 10 = 3 mm, which is the wavelength λ 0 to ensure ultra-thin characteristics. The calculated load impedance density is Z = (1.2411 – j 5.4927) η / λ To achieve this impedance characteristic, PCB technology (copper thickness t= 0.018 mm) with 01005 package resistors (length 0.4 mm, width 0.2 mm) to construct a super atomic structure such as Figure 4 As shown in (a) and (b), the imaginary part of the load impedance is realized by the strip capacitor structure. Since the cylindrical metaconductor is equivalent to a flat strip structure, the conversion relationship between its width w and the cylindrical conductor radius r is w = 4r. In this embodiment, the strip width w = 0.2 mm is selected, and the real part of the load impedance is realized by the surface mount resistor. To ensure the uniformity of the impedance distribution, as shown in Figure 4 As shown in (a), the longitudinal length of the metaatom is set to Λy = b / 4 = 2.54 mm. Based on the imaginary part of the desired target impedance density, the length L of the strip capacitor can be calculated as follows: (twenty one) In the formula ε eff = ( ε 0+ ε s ) / 2 represents the equivalent dielectric constant of the air-substrate interface. The resistance R is determined based on the real part of the target impedance density: (twenty two) The capacitor arm length and resistor value were then calculated to be L = 3.85 mm and R = 39.62 Ω, respectively. Four metaatoms were arranged in series along the y-axis and placed at the center of a dielectric substrate, forming the metagrating structure required for an absorption-type waveguide (Type I waveguide).
[0061] In an illustrative embodiment, the metagrating design method further includes: optimizing the strip length and the resistance value of the resistor when the absorption rate of the reflected wave does not reach the target absorption rate, including: substituting the strip length and the resistance value of the resistor into the simulation software to calculate the actual absorption rate. When the actual absorption rate is less than the target absorption rate, the strip length is determined as the strip length to be optimized, and the resistance value of the resistor is determined as the resistance value to be optimized. Adjusting the strip length to be optimized with a first preset step size within a first preset range. Adjusting the resistance value to be optimized with a second preset step size within a second preset range. Iteratively substituting the strip length to be optimized and the resistance value to be optimized into the simulation software to calculate the calculated absorption rate. When the calculated absorption rate is equal to or greater than the target absorption rate, the strip length to be optimized is determined as the target strip length, and the resistance value to be optimized is determined as the target resistance value.
[0062] According to an embodiment of the present invention, Figure 4 The metagrating structure shown in (b) is substituted into the simulation software for modeling. For example, after modeling and simulation by the simulation software, Figure 4As shown in (c), the dotted and dashed lines represent the simulation results. The results show that the maximum absorption rate of 92% occurs at 9.94 GHz (the absorption rate calculation formula is ), which is slightly lower than the design target of perfect absorption at 10 GHz. This deviation is mainly due to several factors, especially the slight offset between the actual impedance of the meta-atom and the theoretical value - for example, the capacitive structure made of copper with finite thickness will introduce a non-negligible real part of the load impedance. Therefore, it is necessary to further optimize the size of the meta-atom. For example, in this embodiment, the first preset range can be determined as 3.55mm-4.15mm, and the first preset step size can be determined as 0.05mm. In addition, the second preset range can be determined as 15Ω-85Ω, and the second preset step size can be determined as 1Ω. After optimization, the target strip length is 3.45mm, the target resistance is 20Ω, and the optimized results can be seen in Figure 4 (c) 100% perfect absorption of the TE10 mode at 10 GHz is achieved, enabling reflection-free waveguide transmission at the target frequency. Furthermore, the relative bandwidth, defined as an absorption exceeding 90% (S11 < -10 dB), reaches 14.1% of the center frequency.
[0063] In another exemplary embodiment, considering the processing complexity of the metagrating, Figure 4 As shown in (d), the number of metaatoms connected in series on the metawire is set to two, so the longitudinal length of the metaatom is set to Λy = b / 2 = 5.08 mm, thus forming Figure 4 (d) shows the Type II waveguide structure. In this design, the same impedance density as the Type I waveguide in the previous exemplary embodiment is maintained, and the target strip length L = 1.45 mm and the target resistance R = 79 Ω are calculated. After further optimization using simulation software, the structure achieves 100% guided wave absorption at 10 GHz, with the optimized target strip length L = 1.45 mm and the target resistance R = 60 Ω. The initial simulation results based on the calculated parameters and the final results based on the optimized parameters are shown in Figure 3 (e) shows that the difference between the two is very small, which verifies the accuracy of the analytical model and theoretical design method of the present invention. The final measured relative absorption bandwidth of the optimized result reaches 16.8%.
[0064] In an exemplary embodiment, step S160 further includes: constructing meta-atoms using the conductive optical film when the target impedance density is determined as a real number, including: determining a target width of the conductive optical film based on the target impedance density; and determining a target sheet resistance of the conductive optical film based on the target width and the target impedance density of the conductive optical film.
[0065] According to an embodiment of the present invention, metaatoms constructed by conductive optical films can be used to limit the target impedance density of the metaconductor to a pure real number. Since the target impedance density is a pure real number, it is naturally only necessary to design the resistance of the metaatoms. This approach can make the impedance distribution of the metaconductor more uniform, and the larger real part can also correspond to a wider absorption bandwidth, which also overcomes the problem of the narrow working bandwidth of traditional absorption waveguides based on metagratings.
[0066] In order to clearly illustrate how to construct meta-atoms based on conductive optical films, the following examples are given for detailed explanation.
[0067] Figure 5 (a) is a schematic diagram of the meta-atom realized based on indium tin oxide (ITO) thin film; Figure 5 (b) is based on Figure 5 (a) Graph showing the relationship between w and h in the type III metagrating constructed by the metaatom shown; Figure 5 (c) is a schematic diagram of a type III waveguide constructed based on a type III metagrating; Figure 5 (d) is a graph of the simulation results of the absorption rate of the type III waveguide and the S11 parameter.
[0068] In an illustrative embodiment, Figure 5 As shown, ITO thin film is used to construct the meta-atom, and the dimensions of the waveguide and are the same as those in the aforementioned embodiment. In this embodiment, only one meta-atom is set in the meta-conductor, so the longitudinal length of the meta-atom Λy = b = 10.16 mm. It should be noted that in the previous meta-atom design (Type I and Type II) using PCB series chip resistors, the strip width w can be selected arbitrarily; but when the impedance density is a pure real number, the selection of w must be constrained by formula (20). By setting the imaginary part in this formula to 0, the strip width corresponding to the meta-atom can be determined to be (twenty three) In addition, the thickness h of the dielectric substrate can also be freely selected, but care must be taken to avoid causing the line width w to be too large or even exceeding the waveguide width a. According to formula (23), the relationship curve between the strip width w and the thickness h of the dielectric substrate can be obtained, as shown in Figure 5 (b) To ensure that w is always less than a, the value of h must be limited to Figure 5 (b) In the shaded area. To achieve a smaller w value, this study selected a dielectric substrate thickness of h = λ0 / 6 = 5 mm. At the same time, the meta-atom is located at the center of the waveguide along the x-axis (i.e., x0 = b / 2). The corresponding strip width w = 4.99 mm is calculated by equation (23). Substituting these parameters into equation (19) yields the load impedance Z = 3.3036η / λ. At this point, the target surface resistance Zs of the ITO film can be obtained by the following method (twenty four) The target sheet resistance of the ITO film was calculated to be Zs = 475 Ω / sq. The metagrating waveguide structure (Type III waveguide) constructed in this way is shown in the figure. Figure 5 (c) shown. Figure 5 The simulation results shown in (d) are in perfect agreement with the theoretical predictions, achieving 100% absorption of the TE10 mode at 10 GHz, indicating that the type III waveguide design requires no further optimization, and its relative absorption bandwidth reaches 30.5%.
[0069] Figure 6 This is a graph showing the relationship between the real part of the impedance density R(Z) in the metagrating and the substrate thickness h. Figure 7 is a graph of the simulation results of the metagrating waveguide with a dielectric basic thickness of h = 4.68 mm (corresponding to the maximum value of the real part of the load impedance density), where Figure 7 (a) is the absorption bandwidth simulation curve of type I metagrating waveguide. Figure 7 (b) is a simulated absorption bandwidth curve of the type III metagrating waveguide.
[0070] In the design of absorption waveguides, bandwidth is a core consideration. By comparing the aforementioned metagrating waveguide designs, it can be clearly seen that: when the impedance density remains constant (such as type I and type II), although the difference in impedance distribution uniformity will slightly affect the electromagnetic field regulation and cause a slight change in bandwidth, the absorption curves are generally similar; when the impedance density is different (such as type I and type III or type II and type III), the absorption curves show significant differences, and the difference in absorption bandwidth can be nearly twice. This difference is mainly due to the change in the real part of the impedance density - according to formula (19), the real part of the impedance density is only determined by the thickness h of the dielectric substrate. To this end, the applicant conducted a parametric study on the real part of the impedance density and found that a larger real part value corresponds to a wider absorption bandwidth. The relationship curve between the real part of the impedance density and the substrate thickness h based on formula (19) is shown in the figure: Figure 6 As shown, when When (i.e. h=(2n+1)×4.68 mm, n=0,1,2…), the real part of the impedance density reaches its maximum value.
[0071] In an illustrative embodiment, the minimum dielectric substrate thickness (corresponding to h=4.68 mm when n=0) is selected, and type I and type III structures are used to design metagrating waveguides to explore their maximum absorption bandwidth. For the type I waveguide structure, the load impedance density Z=(3.4782-j3.9603)η / λ is calculated, and the corresponding target strip length L=5.34 mm and target resistance R=111 Ω are obtained by formulas (21) and (22). After optimization by simulation software, the optimal parameters L=5.3 mm and R=80 Ω are obtained. Figure 7 (a) The simulation results show that its relative absorption bandwidth reaches 41.4%, which is significantly wider than the previous h=3 mm type I waveguide design. For the type III waveguide structure, the calculated load impedance density Z=3.4782η / λ, and the strip width w=10.49 mm and the target surface resistance Zs=458 Ω / sq of the ITO film are determined according to formulas (23) and (24). It should be noted that the equivalent conversion condition w=4r of the circular wire radius r and the flat line width w requires that both are much smaller than the wavelength λ0, but in this case w≈λ0 / 3, so the surface resistance Zs needs to be further optimized to achieve the ideal absorption effect. The final result after optimization is as follows Figure 7 As shown in (b), the relative absorption bandwidth is 32.2% when the optimal sheet resistance Zs = 400Ω / sq, which is also better than the original type III waveguide design with h = 5 mm.
[0072] In an illustrative embodiment, a metagrating designed using the metagrating design method described above is provided, comprising: a dielectric substrate; a metaconductor disposed on a surface of the dielectric substrate, comprising a plurality of metaatoms connected in series, wherein the metaatoms include edge resistors and strip capacitors connected in series with the chip resistors.
[0073] In an illustrative embodiment, another metagrating designed using the metagrating design method described above is provided, comprising: a dielectric substrate; and a metaconductor disposed on a surface of the dielectric substrate, comprising one or more metaatoms formed from a conductive optical film. If there are multiple metaatoms, the multiple metaatoms are connected in series.
[0074] In an illustrative embodiment, the conductive optical film may include an indium tin oxide film, or a metal film (such as silver, gold, etc.) with a thickness of less than 20 nm, or a MXene film.
[0075] In an exemplary embodiment, the dielectric substrate has a loss tangent value less than 0.01.
[0076] According to the embodiments of the present disclosure, since the loss tangent of the dielectric substrate is less than 0.01, it has fewer restrictions and stronger compatibility in material temperature characterization compared to the metagrating waveguide in related technologies.
[0077] In order to more intuitively describe the characteristics of the metagrating constructed according to the embodiments of the present disclosure, a comparison is made with some absorption waveguides in related technologies through Table 1.
[0078] Table 1 Comparison between the present invention and partially absorbing waveguide
[0079] Wherein, for lossless substrate, tan δ < 0.01; for lossy substrate, tan δ > 0.01; FBW: relative absorption bandwidth corresponding to S11 < -10 dB; η: normalized bandwidth-to-thickness ratio, FBW is relative bandwidth.
[0080] Prior art A is YQHe et al., IEEE Trans.Microwave Theory Techn ., vol.72, no. 6, pp. 3588–3599, Jun. 2024. Prior art B is F. Nazari et al, AEU-International Journal of Electronics and Communications , vol. 137, p. 153820, Jul. 2021. Prior art C is N. Bai et al, IEEE Trans. Electron Devices , vol. 67, no. 3, pp. 1248–1253, Mar. 2020. where, when S11 = -10 dB, the normalized bandwidth-to-thickness ratio is defined as (twenty four) Through comparative analysis, it is clear that the metagrating provided by the embodiment of the present invention shows significant advantages in structural compactness and bandwidth performance, fully demonstrating its superior characteristics.
[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.
Claims
1. A method for designing a metagrating, wherein the metagrating comprises a dielectric substrate and a metaconductor, and is disposed at the bottom of a waveguide, wherein: include: determining an electromagnetic field distribution function of a reflected wave after being reflected by a surface of the dielectric substrate based on the electromagnetic field distribution function of the input wave, dielectric parameters and dimensions of the dielectric substrate, and dimensions of the waveguide; determining an electromagnetic field distribution function of an excitation wave excited by the input wave and transmitted to the dielectric layer by the metaconductor based on the electromagnetic field distribution function of the input wave, the dimensions of the waveguide, and dielectric parameters of a dielectric layer in the waveguide, wherein the excitation wave is adapted to destructively interfere with the reflected wave so that the reflected wave achieves a target absorptivity; determining an electromagnetic wave distribution function of a total field in the waveguide based on the electromagnetic field distribution functions of the input wave, the excitation wave, and the reflected wave; Determining a target excitation current value in the metaconductor based on the reflected wave, the electromagnetic field distribution function of the excitation wave, and the target absorptivity; Determining a target impedance density of the metaconductor based on the target excitation current value and the electromagnetic wave distribution function of the total field; and Structural parameters of the metaconductor are determined based on the target impedance density.
2. The method according to claim 1, characterized in that The determining, based on the electromagnetic field distribution function of the input wave, the size of the waveguide, and the dielectric parameters of the dielectric layer in the waveguide, of the electromagnetic field distribution function of the excitation wave excited by the input wave and transmitted to the dielectric layer by the metaconductor includes: Determining an electromagnetic field distribution function of a hypothetical excitation wave of the metaconductor based on dielectric parameters of the dielectric layer, a thickness of the dielectric substrate, and position information of the metaconductor, wherein the hypothetical excitation wave is a radiation field generated by the metaconductor being excited by the input wave in free space; The electromagnetic field distribution function of the excitation wave is determined based on the electromagnetic field distribution function of the assumed excitation wave and a reflection coefficient of the assumed excitation wave on the surface of the dielectric substrate.
3. The method according to claim 1, characterized in that The determining the structural parameters of the metagrating based on the target impedance density includes: Equivalently converting the metaconductor into a flat strip structure; determining the number of metaatoms constituting the metaconductor wire based on the waveguide size; and The longitudinal length of the metaatom along the metawire is determined.
4. The method according to claim 3, characterized in that The determining of the structural parameters of the metaconductor based on the target impedance density further includes: When the target impedance density is determined as a complex number, constructing a strip capacitance in the metaatom; determining a strip length of the strip capacitor based on an imaginary part of the target impedance density, a longitudinal length of the metaatom, a dielectric parameter of the dielectric layer, and a dielectric parameter of the dielectric substrate; The resistance value of the resistor in the meta-atom is determined based on the real part of the target impedance density and the longitudinal length of the meta-atom.
5. The method according to claim 4, characterized in that Also includes: When the absorption rate of the reflected wave does not reach the target absorption rate, optimizing the strip length and the resistance value of the resistor includes: Substituting the strip length and the resistance value of the resistor into the simulation software to calculate the actual absorption rate; When the actual absorption rate is less than the target absorption rate, the strip length is determined as the strip length to be optimized, and the resistance value of the resistor is determined as the resistance value to be optimized; Adjusting the length of the strip to be optimized within a first preset range with a first preset step size; Adjusting the resistance to be optimized within a second preset range with a second preset step size; Iteratively substituting the strip length to be optimized and the resistance value to be optimized into the simulation software to calculate the absorption rate; When the calculated absorption rate is equal to or greater than the target absorption rate, the strip length to be optimized is determined as the target strip length, and the resistance value to be optimized is determined as the target resistance value.
6. The method according to claim 3, characterized in that The determining of the structural parameters of the metaconductor based on the target impedance density further includes: When the target impedance density is determined to be a real number, constructing the meta-atom using a conductive optical film includes: determining a target width of the conductive optical film based on the target impedance density; A target sheet resistance value of the conductive optical film is determined based on the target width of the conductive optical film and the target impedance density.
7. A metagrating designed by the method according to any one of claims 4 and 5, characterized in that: The metagrating comprises: dielectric substrates; The metaconductor is arranged on the surface of the dielectric substrate and includes a plurality of metaatoms arranged in series. The metaatoms include edge resistors and strip capacitors connected in series with the chip resistors.
8. A metagrating designed by the method according to claim 6, characterized in that: The metagrating comprises: dielectric substrates; The metaconductor is arranged on the surface of the dielectric substrate and includes one or more metaatoms composed of a conductive optical film. When there are multiple metaatoms, the multiple metaatoms are arranged in series.
9. The metagrating according to claim 8, wherein: The conductive optical film is an indium tin oxide film.
10. The metagrating according to claim 9, wherein: The loss tangent value of the dielectric substrate is less than 0.01.