A dual-frequency left-right rotation independent regulation metasurface design method

Abstract

The application discloses a design method of a dual-frequency left-right rotation independent regulation metasurface in artificial electromagnetic material design. The design method combines geometric phase, propagation phase and an optimization algorithm in metasurface design, and can quickly and accurately design a left-right rotation decoupling metasurface unit working in two frequency bands, and can independently control the electromagnetic wave reflection phase of four channels of the dual-frequency left-right rotation. The metasurface is composed of three layers of cross metal structures with independently controllable length and rotation angle, three layers of dielectric layers and a metal back plate. Meanwhile, the application firstly independently describes the correspondence relationship between the propagation phase-unit length of the unit and x polarization and y polarization. The optimized metasurface unit can realize complete decoupling of high and low frequencies and left and right rotations, thereby effectively improving the regulation freedom of the passive metasurface, further improving the channel capacity, being helpful to the integration and miniaturization of equipment, and having wide application prospects in holographic imaging, beam regulation and the like.

Description

Technical fields:

[0001] This invention relates to a novel dual-frequency left- and right-hand independently controllable metasurface design method, belonging to the field of artificial electromagnetic materials. It relates to a dual-frequency metasurface unit optimization method, which is simple, fast, and efficient. At the same time, it can achieve completely independent decoupling of the four channels of left- and right-hand rotation in the designed dual-frequency band. Background technology:

[0002] Metamaterials are a new type of artificial electromagnetic material composed of subwavelength microstructures arranged according to certain rules, and they have attracted widespread attention since their emergence. Unlike natural materials, metamaterials can achieve some unique electromagnetic properties, such as negative refractive index, negative permittivity, and negative permeability. This theoretical concept was first proposed by scientist V.G. Veselago in 1968, but it was not until 1996 that it was experimentally verified by British scientist Sir Pendry. Later, to address the shortcomings of metamaterials, such as complex fabrication, high cost, and high loss, Professor Capasso of Harvard University proposed the concept of metasurfaces in 2011. By reducing three-dimensional metamaterials to two-dimensional form, this further advances the practical application of artificial electromagnetic materials.

[0003] Existing circularly polarized metasurfaces often employ geometric phase units to control left-handed and right-handed circularly polarized electromagnetic waves. While geometric phase metasurfaces can achieve continuous phase control, coupling exists between the two circular polarizations during control, meaning their functions cannot be completely independent. Combining geometric phase (unit rotation angle) with propagation phase (unit size variation) can directly achieve complete decoupling of the two circularly polarized electromagnetic waves. However, this introduces the problem that changes in both rotation angle and size affect the metasurface's operating mode in other frequency bands. The integration and decoupling of multi-frequency circularly polarized metasurfaces has long been limited by crosstalk; however, circularly polarized electromagnetic waves are widely used in satellites and radar, thus remaining a significant research area. This invention designs a dual-frequency, independently controllable left-handed and right-handed circularly polarized metasurface that combines geometric phase, propagation phase, and optimization algorithms. This enables completely independent four functions, such as beam anomalous reflection and beam splitting, at two frequency points (10 GHz and 17.8 GHz) when left-handed and right-handed circularly polarized waves are incident. Summary of the Invention:

[0004] Objective: This invention provides a design method for anisotropic metasurfaces with independent left and right rotation control across dual frequencies. By assigning independent phase distributions to the four channels of the dual-frequency left and right rotations, four independent functions can be achieved, with complete decoupling between the left and right rotations and excellent suppression of crosstalk between high and low frequencies. This polarized, frequency-reused anisotropic metasurface adds another degree of freedom in frequency control on top of the decoupled left and right rotation metasurface, further increasing channel capacity. It also provides insights into crosstalk suppression during the integration and miniaturization of wireless communication devices, and has many potential applications.

[0005] Technical Solution: The dual-frequency left- and right-hand circularly polarized metasurface of this invention combines geometric phase, propagation phase, and optimization algorithm. The purpose of combining geometric phase and propagation phase is to decouple the reflection responses of left-hand and right-hand circularly polarized waves, while the optimization algorithm aims to effectively suppress electromagnetic response crosstalk between the two frequencies. The anisotropic unit structure of this invention includes an upper, middle, and lower three-layer composite metal structure, with dielectric layers of thicknesses h1, h2, and h3 respectively, and a bottom metal backplate. The upper and middle metal layers are uniformly distributed 2×2 arrays of cross-shaped patches, and these eight cross-shaped patches have identical parameters. The third metal layer consists of larger Jerusalem cross-shaped patches. Therefore, each unit structure has a total of nine cross-shaped metal patches. By designing the lengths (L) of these crosses in both directions... x L y , l x , l y The independent control of dual-frequency left- and right-hand circularly polarized electromagnetic waves is achieved using the rotation angles (α, β). Since the frequency of the electromagnetic wave response is related to the size of the metal structure, the eight identical cross-shaped metal patches in the unit represent the high-frequency response, while the larger Jerusalem cross corresponds to the low-frequency response. Due to the larger number of high-frequency cross patches and their double-layer structure, the resonance is stronger. Therefore, the crosstalk between the two frequencies is mainly the crosstalk between the high-frequency and low-frequency operating modes during metasurface operation, while there is no crosstalk between the low-frequency and high-frequency modes. Through specific theoretical analysis and simulation verification, the crosstalk is divided into propagation phase crosstalk between the high-frequency cross and the low-frequency cross, with the former being dominant. To effectively suppress this crosstalk, the high-frequency unit structure is first determined, and the crosstalk caused by the determined high-frequency structure is used as a preset condition for low-frequency operation. Then, the length and rotation angle of the low-frequency structure in both directions are iteratively optimized. Therefore, the combined optimization algorithm of geometric phase and propagation phase can effectively decouple the high and low frequencies, and the left and right-hand circular polarization. The four channels of the designed metasurface can also achieve four completely independent functions based on this.

[0006] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0007] 1. Polarization multiplexing: The dual-frequency left and right independently controllable metasurface described in this invention can achieve completely different functions under the incidence of dual circularly polarized electromagnetic waves, such as anomalous reflection of a left-handed single beam and splitting of a right-handed beam, thus breaking the left-handed coupling effect brought about by traditional geometric phase metasurfaces.

[0008] 2. Frequency reuse: The crosstalk of the dual-frequency left and right independently controllable metasurface described in this invention is effectively suppressed when it operates at high and low frequencies, and different functions can be achieved at the two frequency bands, such as beam splitting in the xoz plane when operating at low frequency and beam splitting in the yoz plane when operating at high frequency.

[0009] 3. Crosstalk Suppression: The optimization algorithm used in the dual-frequency left and right independent control metasurface described in this invention divides the crosstalk between multiple frequencies into geometric phase (rotation angle) crosstalk and propagation phase (length) crosstalk. Furthermore, it independently considers the x-polarization and y-polarization propagation phase-length correspondence under various conditions to solve the phase compensation problem, and finally effectively suppresses the crosstalk between the two frequencies, providing a solution for the integrated design of multi-frequency metasurfaces.

[0010] 4. One-way crosstalk: The cross-shaped metal patch of the dual-frequency left and right independently controllable metasurface unit described in this invention is divided into a single-layer low-frequency structure and a double-layer high-frequency structure. Crosstalk only exists in the crosstalk of the high-frequency structure to the low-frequency working mode, while the low-frequency structure has no effect on the high-frequency working mode. Attached image description:

[0011] Figure 1 This is a schematic diagram of the dual-frequency left and right rotation independently controlled metasurface operation involved in this invention. Linearly polarized electromagnetic waves at two frequency points are incident, and four circularly polarized channels (dual-frequency left and right rotation) can provide four completely independent functions.

[0012] Figure 2 These are the basic unit structure design drawings of the metasurface unit. (a) Overall schematic diagram of the unit, (b) Schematic diagram of the unfolded structure of each layer of the unit, (c) Design drawing of the third layer metal structure, (d) Design drawing of the second layer metal structure, (e) Design drawing of the first layer metal structure.

[0013] Figure 3 These are the amplitude and phase curves of the unit. (a) Phase curves of the unit for different lengths of the high-frequency cross-shaped structure, (b) Amplitude curves of the unit for different lengths of the high-frequency cross-shaped structure, (c) Phase curves of the unit for different lengths of the low-frequency cross-shaped structure, (d) Amplitude curves of the unit for different lengths of the low-frequency cross-shaped structure.

[0014] Figure 4This represents the relationship between the propagation phase and the lengths of the two directions of the low-frequency crosshair under different high-frequency encodings. (a) High-frequency encoding is 00, i.e., when the phase modulation of the high-frequency left-hand circularly polarized electromagnetic wave is 0° and 0° respectively. (b) High-frequency encoding is 06, i.e., when the phase modulation of the high-frequency left-hand circularly polarized electromagnetic wave is 0° and 270° respectively. (c) High-frequency encoding is 26, i.e., when the phase modulation of the high-frequency left-hand circularly polarized electromagnetic wave is 90° and 270° respectively.

[0015] Figure 5 This is an optimized design flowchart of a metasurface unit with independent left and right rotation dual-frequency control. The inset shows the propagation phases of x-polarization and y-polarization as a function of the length of the cross-shaped structure.

[0016] Figure 6 These are schematic diagrams of several optimized dual-frequency left and right independently controllable metasurface unit structures.

[0017] Figure 7 These are far-field scattering diagrams of dual-frequency left- and right-handed rotating beams independently controlled by the metasurface. (a) Low-frequency left-handed incident, (b) Low-frequency right-handed incident, (c) High-frequency left-handed incident, (d) High-frequency right-handed incident.

[0018] Figure 2 In the diagram, 1-first layer high-frequency metal structure; 2-second layer high-frequency metal structure; 3-third layer low-frequency metal structure; 4-first layer dielectric substrate; 5-second layer dielectric substrate; 6-third layer dielectric substrate; 7-metal backplate; Detailed implementation method:

[0019] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments.

[0020] The metasurface described in this invention combines geometric phase, propagation phase, and optimization algorithms to achieve independent control of left- and right-hand circularly polarized waves in two frequency bands. For example... Figure 1 As shown, when x-polarized electromagnetic waves of two frequency bands are incident (x-polarized electromagnetic waves can be decomposed into left-handed and right-handed circularly polarized waves, which is actually equivalent to the incident of left-handed and right-handed circularly polarized waves of two frequency bands), after phase modulation by the reflective metasurface, the circularly polarized electromagnetic waves of the four channels can be independently controlled and deflected in different directions. The anisotropic unit consists of an upper, middle, and lower three-layer composite metal structure ( Figure 2 Structures 1, 2, and 3), with three dielectric layers of thicknesses h1, h2, and h3 respectively. Figure 2 Structures 4, 5, and 6 in the middle and the metal back plate at the bottom ( Figure 2 Structure 7 in the text. Figure 2As shown, the unit employs a multi-layer laminated structure with a unit size of p = 10 mm. The thicknesses of the three dielectric layers are h1 = h2 = 1 mm and h3 = 1.63 mm, respectively. The dielectric material is TRF-43 type substrate with a dielectric constant of 4.3 and a loss tangent of 0.0033. The metal material is copper with a thickness of 0.018 mm. To demonstrate the detailed structure of each layer of this unit, Figure 2 (b) A schematic diagram of the unit unfolding is given. The upper metal structure 1 and the middle metal structure 2 are completely identical, both consisting of four evenly distributed small cross-shaped structures, each with a width of t2 = 0.4 mm, and a length l in both directions. x and l y The variation range is between 3.3 and 4.5 mm. Figure 2 (c)(d)(e) provide more detailed parameters for each structure. Figure 2 (c) shows the Jerusalem cross structure corresponding to the low frequency, with lengths L in both directions. x and L y The range of variation is 2-8.5 mm. The rotation angle of the overall structure is represented by α, which ranges from -90° to 90°. The length of the branch at the tail end of the cross-shaped structure is w = 1 mm, and the width of the overall structure and the branch is t1 = 0.3 mm. Figure 2 (d) and (e) both show small cross-shaped structures corresponding to high frequencies, with lengths of l in the two directions respectively. x and l y The range of variation is 2-8.5 mm. The rotation angle of the overall structure is denoted as β, and its range is also between -90° and 90°. It should be noted that when the high-frequency cross structure rotates, it does not rotate around the center of the unit cell, but rather around its respective geometric center. In the specific design of the metasurface, the lengths and rotation angles of the two directions corresponding to the high and low frequency crosses can be calculated by using the left and right circularly polarized phase modulation targets of the two frequency bands. Therefore, by arranging a series of metasurface units with different parameters according to a certain rule, the circularly polarized waves of the four channels can be independently controlled, achieving four completely decoupled functions.

[0021] Encoded metasurfaces are a concept that has emerged in recent years, representing the modulation phase of a unit cell using simple digital encoding. Typically, 1-bit encoding uses symbols "0" and "1" to represent modulation phases of 0° and 180°, 2-bit encoding uses symbols "00", "01", "10", and "11" to represent modulation phases of 0°, 90°, 180°, and 270°, and 3-bit encoding uses symbols "000" to "111" or "0" to "7" to represent modulation phases from 0° to 315° (with a step size of 360° / 2). NWhere N is the number of bits (e.g., when N=3, the phase modulation step size is 45°). In the dual-frequency left- and right-hand independently controllable metasurface described in this invention, to simplify the representation method, a four-bit digital code is used to represent the modulation phase of high-frequency left-hand rotation, high-frequency right-hand rotation, low-frequency left-hand rotation, and low-frequency right-hand rotation, respectively. For example, "0123" represents the modulation phases of the four channels as 0°, 45°, 90°, and 135°, respectively; and "0246" represents the modulation phases of the four channels as 0°, 90°, 180°, and 270°, respectively.

[0022] Based on the above element design and coding representation, the anisotropic element structure was simulated using the commercial software CST. The simulation boundary conditions were set as periodic boundary conditions in the x and y directions, and as open boundary conditions in the z direction. Figure 3 As shown in (a) and (b), x-polarized incident radiation occurs when the length l of the high-frequency cross structure is set. x When the aperture diameter varies from 3.3 to 4.5 mm, the amplitude of the unit remains above 0.9 at the high frequency of 17.8 GHz, and the phase coverage is close to 360°. As can be seen from the figure, changing the parameters of the high-frequency crosshair has little effect on the low-frequency amplitude curve, but it does introduce significant crosstalk to the low-frequency phase curve. Figure 3 As shown in (c) and (d), under the same x-polarized incident condition, the length L of the low-frequency cross structure is set. x With a variation of 2-8.5mm, the amplitude of the unit remained above 0.9 at a high frequency of 10GHz, and the phase coverage was close to 360°. Figure 3 The difference between (a) and (b) is that changing the parameters of the low-frequency crosshair does not cause crosstalk to the amplitude and phase curves of the high-frequency frequencies. Full-wave simulations have proven that the crosstalk between the two frequencies of the unit described in this invention exists only between the high-frequency structure and the low-frequency structure. Therefore, the structure of the high-frequency crosshair can be determined first, and this can be used as a preset condition to optimize the structural parameters of the low-frequency structure, thereby effectively suppressing crosstalk.

[0023] To suppress crosstalk between the high-frequency structure and the low-frequency structure's operating mode through algorithm optimization, it is first necessary to determine the three parameters l of the high-frequency cross. x , l y From a geometric perspective, when β = 45°, the crosstalk between the eight small cross-shaped metal structures at high frequencies and the Jerusalem cross structure at low frequencies is the same in both the x and y directions. Therefore, the phase-length relationship of the low-frequency propagation is equivalent for both x-polarization and y-polarization at this time, as shown below. Figure 4 As shown in (c). β = 45° is a special case; in most cases, it is as follows. Figure 4As shown in (a) and (b), the propagation phase-length relationship of low frequencies is not equivalent for x-polarization and y-polarization. Therefore, the crosstalk of the high-frequency structure to the low-frequency structure propagation phase manifests in two aspects: firstly, the propagation phase-length relationship of low frequencies is inconsistent under different high-frequency encodings; secondly, when the rotation angle of the high-frequency structure is not 45°, the propagation phase-length relationship of low-frequency x-polarization and y-polarization is inconsistent. To address this, it is necessary to describe the propagation phase-length correspondence of x-polarization and y-polarization separately and independently under different high-frequency encodings.

[0024] Based on the above analysis of the principles of crosstalk, we propose the following... Figure 5 The optimization algorithm shown first determines the target phase modulation for high-frequency left and right rotation. and The propagation phase and rotation angle β that should exist under linearly polarized incident radiation are calculated using the following formulas. Propagation phase combined with... Figure 3 The high-frequency propagation phase-length correspondence in (a) allows us to obtain the lengths l in both directions of the high-frequency cross element. x and l y Since the low-frequency structure does not cause crosstalk to the high-frequency structure's operating mode, the structural parameters calculated theoretically are accurate.

[0025]

[0026] Similarly, the three parameters L of the low-frequency Jerusalem cross structure x L y The initial values ​​for α and y can also be simply given based on the target low-frequency left- or right-hand circular phase modulation. However, due to crosstalk between the high-frequency structure and the low-frequency structure, the low-frequency phase modulation under this initial value setting will generally have a large error compared to the target. This is the purpose of the algorithm optimization here. After obtaining the initial parameter settings for high and low frequencies, they are imported into the commercial software CST to simulate and obtain the modulation phase and amplitude of the unit structure for the low-frequency (10GHz) left-hand and right-hand circularly polarized waves. Next, it is determined whether the current modulation phase and amplitude meet the requirements (phase error within 10°, amplitude above 0.9). If the requirements are met, the structural parameters are output and saved, and the process ends; if the requirements are not met, the program retrieves the propagation phase-length correspondence of x-polarization and y-polarization under the current high-frequency encoding, and modulates the rotation angle α and L according to the error value. x and L yThe algorithm automatically adjusts the parameters, re-imports them into CST for simulation, and iterates repeatedly until the phase error and amplitude meet the requirements. It's important to note that if the absolute value of the rotation angle α of the current low-frequency structure is greater than 45°, the propagation phase-length correspondence between x-polarization and y-polarization needs to be swapped, because in this case, the influence of the high-frequency structure on the low-frequency structure is closer to the situation after rotating the coordinate axes by 90°. If the optimization algorithm fails to converge after several iterations, the parameter adjustments in each iteration can be appropriately reduced to prevent the deviation from the optimization target from increasing, but this will require a longer optimization time.

[0027] Using the optimization method described in this invention, Figure 6 Sixteen unit cells were selected as examples. The four-bit code for phase modulation represents the phase modulation of high-frequency left and right rotations and low-frequency left and right rotations, respectively. "0", "2", "4", and "6" represent modulation phases of 0°, 90°, 180°, and 270°, respectively. To verify the function of this dual-frequency left and right rotation independently controllable metasurface, a... Figure 6 The 16 units shown are arranged in a 4×4 small array as a two-dimensional period, and then 5×5 two-dimensional periods are combined to form a large array, with a total size of 200×200mm. 2 The simulation was also performed using the commercial software CST. During the simulation, the excitation was set to plane wave excitation, and all boundary conditions were set to open boundaries. The element arrangement used in this example creates phase gradients of "0°, 90°, 180°, 270°" for both left and right rotations of the dual-frequency beams. Therefore, the reflected beams of the four channels will undergo completely independent anomalous deflections. The anomalous reflection angle can be obtained using the following generalized Snell's law.

[0028]

[0029] Where θ r Indicates the anomalous reflection angle, θ i Let λ0 represent the incident angle (where the incident angle is 0), and let n represent the wavelength of the incident wave. i The value represents the refractive index of the incident space, and the last term on the right-hand side of the formula represents the phase gradient. For example... Figure 7 As shown, at low frequencies, the left and right circularly polarized waves deflect by 48.6° in the xoz and yoz planes, respectively, and at high frequencies, they deflect by 24.6% in the xoz and yoz planes, respectively. The low-frequency left-handed and right-handed polarizations, and the high-frequency left-handed and right-handed polarizations, are respectively... Figure 7 (a)-(d) correspond one-to-one, and the simulation values ​​match the theoretical calculation values ​​well.

[0030] The embodiments described above merely illustrate implementation methods of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, such as using the structure or optimization algorithm to achieve other functions like vortex wave generation, multifocal lenses, etc., all of which fall within the protection scope of the present invention. Therefore, the protection scope of this invention should be determined by the appended claims.

Claims

1. A design method of dual-frequency left and right-handed independently regulated metasurface, characterized in that, The designed super surface unit is stacked by high-frequency structure and low-frequency structure, including three layers of metal structure, three layers of dielectric layer with thickness of h1, h2 and h3, and a bottom metal back plate, the upper and middle layers of metal structure are high-frequency structure, and the lower layer of metal structure is low-frequency structure, the optimization algorithm is combined in the design, the phase coding of high-frequency and low-frequency is determined first, the initial parameters are set, the electromagnetic simulation is imported, and the iterative optimization is carried out according to the feedback of the current structure electromagnetic response, the left-handed and right-handed circularly polarized electromagnetic waves of two frequency bands can be independently controlled, and four completely decoupled functions can be realized according to the pre-designed phase arrangement.

2. The dual-frequency left-right handed independent tuning metasurface design method of claim 1, wherein, The iterative optimization algorithm is used in the process of mapping the geometric phase and propagation phase of the high-frequency structure and the low-frequency structure into specific structure parameters, wherein the purpose of the geometric phase and the propagation phase is to eliminate the coupling between the left-handed circularly polarized wave and the right-handed circularly polarized wave; the purpose of the iterative optimization algorithm is to suppress the crosstalk between the high-frequency and the low-frequency.

3. The dual-frequency left-right handed independent tuning metasurface design method of claim 1, wherein, The crosstalk of the high-frequency structure and the low-frequency structure only exists in the influence of the high-frequency structure on the low-frequency structure.

4. The dual-frequency left-right handed independent tuning metasurface design method of claim 1, wherein, The upper layer metal structure and the middle layer metal structure of the unit are the same, which are 2*2 uniformly distributed small cross-shaped metal patches.

5. The dual-frequency left-right handed independent tuning metasurface design method of claim 1, wherein, The lower layer metal structure is a single Jerusalem cross-shaped metal patch, and a one-to-many corresponding relationship is maintained between the small cross-shaped metal patch of the high-frequency structure.

6. The dual-frequency left-right handed independent tuning metasurface design method of claim 1, wherein, In the optimization algorithm, the parameters of the high-frequency structure are determined first, which are used as the preset conditions to optimize the parameters of the low-frequency structure, so as to specifically suppress the crosstalk.

7. The dual-frequency left-right handed independent tuning metasurface design method of claim 1, wherein, In the optimization algorithm, the propagation phase-length corresponding relationship of x polarization and y polarization is described separately under different parameters of the high-frequency structure.

8. The dual-frequency left-right circularly independent modulation metasurface design method of claim 1, wherein, When the length of the high-frequency and low-frequency structure of the unit changes within a certain range, the phase coverage of nearly 360° can be realized.

9. The dual-frequency left-right handed independent tuning metasurface design method of claim 1, wherein, The high-frequency and low-frequency structure of the unit is rotated around the geometric center of the cross structure.

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