A Fast Design Method of Metasurface Based on Fibonacci Sequence

Abstract

The present invention relates to the field of aerospace technology, and specifically provides a fast design method for metasurfaces based on the Fibonacci sequence. The present invention combines the Fibonacci sequence with the reflection phase to quickly generate the phase distribution of a diffuse reflection metasurface with discrete phase characteristics, thereby achieving the RCS reduction of the metasurface; and different phase distributions can be obtained by further changing the set initial phase value, so as to obtain different metasurfaces and select the optimal one. It is verified by simulation calculations that the metasurface optimized and designed based on the present invention has good RCS reduction performance in a wide frequency band and a large angle range; the effectiveness of the present invention is also verified through relevant experimental tests, and it can effectively and quickly design a diffuse reflection metasurface for RCS reduction, providing a new design optimization idea for the design of diffuse reflection metasurfaces; moreover, the present invention has strong operability and is easy to implement, and is worthy of popularization.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and specifically to a fast design method of metasurface based on the Fibonacci sequence. Background Technique

[0002] The metasurface is a new type of material with many excellent properties. By adjusting the unit size and shape of the metasurface structure, precise control and regulation of the reflection, transmission, and scattering of electromagnetic waves on the metasurface can be achieved, so that it has unique optical properties at different wavelengths such as visible light, infrared, and microwave. Currently, there are many design methods for metasurfaces, including compact arrays of absorbing metasurfaces, phase gradient metasurfaces, polarization conversion metasurfaces, diffuse reflection metasurfaces, etc. Without considering the absorption performance, appropriately designing the phase gradient of the metasurface array can scatter the incident wave in other directions, so as to achieve the purpose of reducing the radar cross section (RCS).

[0003] Random distribution and coding methods are often used to design diffuse reflection metasurfaces. The uncertainty brought by the random method is disadvantageous for design, and the coded metasurface can obtain metasurfaces with different characteristics through coding optimization. However, with the increase in the number of basic cells on the metasurface and the increase in the area of the metasurface itself, resulting in an increase in the total number of required cells, the overall computational complexity of the coded metasurface will increase exponentially. When only considering diffuse reflection metasurfaces, the increase in the overall coding amount will instead reduce the design efficiency. In many existing optimization algorithms, such as genetic algorithms, simulated annealing algorithms, ant colony algorithms, etc., in the presence of algorithms such as particle swarm optimization, the explosive growth of computational complexity caused by this exponential growth will also consume a large amount of computational resources, including computational memory and time. When large-scale diffuse scattering discrete phase metasurface design is required, adopting a design strategy that saves more computational resources will significantly improve the design efficiency. Summary of the Invention

[0004] Aiming at the above existing problems or deficiencies, to solve the problem of fast and accurate design of existing diffuse reflection discrete phase metasurfaces, the present invention provides a fast design method of metasurface based on the Fibonacci sequence. In the case that many types of metasurfaces currently have a set of fast design concepts and methods, this method gives a fast design method by combining the Fibonacci sequence and reflection phase, including a phase design formula and an optimization design process. Finally, basic phase units are designed through the proposed method, and performance optimization is carried out within the desired frequency band. According to the final optimization results, physical objects are manufactured and the effectiveness of the design method is verified. It is verified that the design method can quickly design metasurfaces with desired performance and has good RCS reduction performance within a certain angle range. The present invention provides a new fast design method for diffuse scattering discrete phase gradient metasurfaces.

[0005] The technical solution of the present invention is as follows:

[0006] A fast metasurface design method based on the Fibonacci sequence, comprising the following steps:

[0007] Step 1: First, give the recurrence formula of the Fibonacci sequence:

[0008]

[0009] where F(0), F(1) are the initial terms of the Fibonacci sequence, F(n) is the nth term of the Fibonacci sequence when n≥2, and n∈N * , N * represents the set of natural numbers.

[0010] Step 2: Combine the original Fibonacci sequence with the reflection phase to obtain the one-dimensional Fibonacci phase gradient calculation formula:

[0011] To combine the sequence and the reflection phase, set the initial phase as:

[0012]

[0013] where φ1, φ2 represent the values of the initial phase.

[0014] After determining the initial phase, the subsequent phases are obtained by the following formula:

[0015] F(n) = (F(n - 1)+F(n - 1))mod 360 (3)

[0016] where mod represents the modulo operation.

[0017] Step 3: Generalize the one-dimensional Fibonacci gradient in Step 2 to a two-dimensional plane to obtain the recurrence formula for the Fibonacci phase distribution in the two-dimensional plane, as follows:

[0018]

[0019] where F(1, 1), F(1, 2), F(2, 1), F(2, 2) represent the initial terms at the corners of the metasurface phase distribution; φ1, φ2, φ3, φ4 respectively correspond to the actual phase values of the initial terms at the corners of the metasurface; F(i, j) represents the term in the i-th row and j-th column of the metasurface phase distribution matrix, where in the fourth row formula of (4), i, j satisfy i∈(1, 2), j>2, and in the fifth row formula of (4), i, j satisfy i>2.

[0020] Step 4: According to the two-dimensional recurrence formula in Step 3, by setting the initial phase value, a set of phase distributions in the two-dimensional plane can be obtained.

[0021] Step 5: For the two-dimensional planar phase distribution obtained in Step 4, replace the corresponding positions with phase units that meet the requirements. The metasurface thus formed is the designed metasurface.

[0022] Furthermore, after Step 5, the following steps are included: By changing the initial phase value set in Step 4, different phase distributions are obtained, and thus different metasurfaces are obtained; finally, according to the actual design requirements, the desired metasurface parameters are selected preferentially, thereby completing the final design. The essence of this step is to map the phase distribution of the entire complete surface through the corner initial units, so as to greatly reduce the coding data volume, realize the metasurface design faster, and then select preferentially according to the requirements.

[0023] In summary, the present invention proposes a fast design method for a metasurface based on the Fibonacci sequence, which combines the Fibonacci sequence with the reflection phase to quickly generate the phase distribution of a diffusive metasurface with discrete phase characteristics. Through simulation and application measurement, it can be seen that the metasurface designed and optimized by using this method can effectively reduce the radar cross section (RCS) under two polarizations. The present invention provides a new fast design method for a diffusive discrete phase gradient metasurface. Description of the Drawings

[0024] Figure 1 is the design and optimization flow chart of the present invention;

[0025] Figure 2 is the schematic diagram of the one-dimensional Fibonacci phase gradient generated when the initial phase in the embodiment is 30°;

[0026] Figure 3 is the topological structure diagram of the phase unit designed in the embodiment;

[0027] Figure 4 is Figure 3 the corresponding diagram of the size parameters of each unit in

[0028] Figure 5 is the dB value diagram of the reflectivity of each phase unit under co-polarization;

[0029] Figure 6 is the linear value diagram of the reflectivity of each unit under cross-polarization;

[0030] Figure 7 is the reflection phase curve diagram of each phase unit varying with frequency under cross-polarization;

[0031] Figure 8 is the phase distribution diagram of the metasurface during the design and optimization process;

[0032] Figure 9 is Figure 8The RCS reduction curve diagrams corresponding to the metasurfaces under different phase distributions;

[0033] Figure 10 is the finally optimized model ( Figure 8 j) The physical object made and the test environment diagram;

[0034] Figure 11 is the comparison curve diagram of the simulation and experiment of the finally optimized metasurface;

[0035] Figure 12 is the RCS reduction curve diagram of the two polarizations of the finally optimized metasurface at 0-40°;

[0036] Figure 13 is the far-field scattering diagram corresponding to the finally optimized metasurface at different frequencies;

[0037] Figure 14 is the comparison diagram of the coding data volume between the embodiment of the present invention and the conventional 1-bit coded metasurface. Detailed implementation mode

[0038] The technical solution of the present invention will be described in detail below in conjunction with the drawings and examples.

[0039] A fast design method of a metasurface based on the Fibonacci sequence, comprising the following steps:

[0040] Step 1. According to the technical solution, the recurrence formula for generating the two-dimensional Fibonacci phase gradient is:

[0041]

[0042] Among them, F(1, 1), F(1, 2), F(2, 1), F(2, 2) represent the initial terms at the corners of the metasurface phase distribution, φ1, φ2, φ3, φ4 respectively correspond to the actual phase values of the initial terms at the corners of the metasurface, F(i, j) represents the term in the i-th row and j-th column of the metasurface phase distribution matrix, where in the fourth row formula of formula (4), i, j satisfy i ∈ (1, 2), j > 2; in the fifth row formula of formula (4), i, j satisfy i > 2;

[0043] Step 2. An example of generating a one-dimensional phase gradient with an initial phase of 30° is Figure 2 As shown, according to the example, it can be seen that the design needs to use basic phase units at intervals of 30° to complete the model construction. The topological structure of the required phase units is as Figure 3As shown in the figure, the letters in the figure represent the dimensions at the corresponding positions indicated by the black lines. From a to f are the 0° phase unit, 30° phase unit, 60° phase unit, 90° phase unit, 120° phase unit, and 150° phase unit in sequence; from g to I are the mirror units of a to f, and their phases correspond to 180° to 330°, with an interval of 30°. Where p = 10 mm is the side length of the unit, h1 = 1 mm is the medium thickness, h2 = 4 mm is the air layer thickness, and the other parameters refer to Figure 4 .

[0044] Step 3: Simulate each designed phase unit to obtain its co-polarization reflectivity as Figure 5 shown, and the cross-polarization reflectivity as Figure 6 shown, and the corresponding reflection phase under cross-polarization as Figure 7 shown.

[0045] Step 4: According to the design and optimization process shown in Figure 1 , conduct the metasurface phase distribution design, where f L is the lower limit of the desired frequency band, and f U is the upper limit of the desired frequency band. Here, the RCS reduction within the 6 - 18 GHz frequency band is taken as the design goal, and the obtained phase distributions are as Figure 8 shown; Figure 8 The RCS reduction curves corresponding to the phase distributions in are as Figure 9 shown, and the phase distribution corresponding to Figure 8 (j) can be obtained, that is, the metasurface corresponding to IP = [210, 30; 60, 90] in Figure 9 satisfies that its RCS reduction is below -10 dB within the 6 - 18 GHz frequency band.

[0046] Step 5: According to the optimization results obtained in Step 4, manufacture a physical object, as Figure 10 (b) shown, and conduct tests in the test environment shown in Figure 10 (a), and the results are as Figure 11 shown; the peak values of the test results and the simulation results curves correspond, and the curve trends are the same, which proves the effectiveness of the design of the present invention; further, test the oblique incidence performance of the sample, and the results are as Figure 12 shown. It can be seen that within the 6 - 18 GHz frequency band and within the 0 - 30° incidence range, the sample in this embodiment can maintain a good RCS reduction performance, Figure 13 indicating that the designed sample is indeed a diffuse reflection type metasurface (corresponding to the frequency points 6 GHz, 12 GHz, and 18 GHz from left to right).

[0047] As can be seen from the above embodiments, the present invention combines the Fibonacci sequence with the reflection phase, and realizes the reduction of RCS under TE and TM polarizations of electromagnetic waves by designing and optimizing the phase distribution of the metasurface. Through theoretical derivation and simulation verification, it is proved that the design method of the present invention can effectively reduce the RCS under TE and TM polarizations of electromagnetic waves, and provides a new design idea for the rapid design of the diffuse reflection type discrete phase distribution metasurface. Moreover, the computational resources required by the design and optimization method of the present invention are small ( Figure 14 as compared with those already given), and it has broad application prospects in the field of metasurface design.

Claims

1. A fast design method for metasurfaces based on the Fibonacci sequence, characterized in that, It includes the following steps: Step 1: First, give the recurrence formula of the Fibonacci sequence: Where F(0) and F(1) are the initial terms of the Fibonacci sequence, and F(n) is the nth term of the Fibonacci sequence when n ≥ 2, where n ∈ N * , N * represents the set of natural numbers; Step 2: Combine the original Fibonacci sequence with the reflection phase to obtain the calculation formula for the one-dimensional Fibonacci phase gradient: Let the initial phase be: where φ1 and φ2 represent the values of the initial phase; After determining the initial phase, the subsequent phases are obtained from the following formula: F(n) = (F(n - 1)+F(n - 2))mod 360 (3) where mod represents the modulo operation; Step 3: Generalize the one-dimensional Fibonacci gradient in Step 2 to a two-dimensional plane to obtain the recurrence formula for the Fibonacci phase distribution in the two-dimensional plane, as follows: where F(1, 1), F(1, 2), F(2, 1), F(2, 2) represent the initial terms at the corners of the metasurface phase distribution; φ1, φ2, φ3, φ4 respectively correspond to the actual phase values of the initial terms at the corners of the metasurface; F(i, j) represents the term in the i-th row and j-th column of the metasurface phase distribution matrix, where in the fourth row formula of (4), i, j satisfy i ∈ (1, 2), j > 2, and in the fifth row formula of (4), i, j satisfy i > 2; Step 4: According to the two-dimensional recurrence formula in Step 3, by setting the initial phase value, a set of phase distributions in the two-dimensional plane can be obtained; Step 5: Replace the corresponding positions in the two-dimensional plane phase distribution obtained in Step 4 with phase units that meet the requirements. The metasurface thus formed is the designed metasurface.

2. The rapid design method of the metasurface based on the Fibonacci sequence according to claim 1, characterized in that After the above Step 5, it further includes: By changing the initial phase value set in Step 4, different phase distributions are obtained, and thus different metasurfaces are obtained; finally, the desired metasurface parameters are preferentially selected according to the actual design requirements, and the final design is completed.

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