CN104931818B - Extraction Method of Equivalent Electromagnetic Parameters of Asymmetric Artificial Electromagnetic Materials - Google Patents

Abstract

The invention proposes a method for extracting electromagnetic parameters of asymmetric artificial electromagnetic materials to solve the problem that the electromagnetic parameters of materials cannot be extracted due to structural asymmetry. The implementation steps of the extraction method are: separately simulate the scattering parameter S of the first layer of materials '; use S' and the symmetric structure algorithm to calculate the electromagnetic parameters of the first layer material; simulate the external scattering parameter S of the asymmetric artificial electromagnetic material; obtain the electromagnetic parameters of the second layer based on S and the electromagnetic parameters of the first layer; use S and The electromagnetic parameters of the second layer re-correct the electromagnetic parameters of the first layer; the above steps are repeated until the electromagnetic parameters of the two layers after correction do not change significantly in the entire frequency band, and this is taken as the final electromagnetic parameter; the final parameter is simulated to obtain Scattering parameter S ", completely coincides with the S parameter of actual structure, has verified the accuracy of the present invention, feasibility and practicality, has realized the process of extracting the equivalent electromagnetic parameter of asymmetrical artificial electromagnetic material with symmetrical method.

Description

Extraction Method of Equivalent Electromagnetic Parameters of Asymmetric Artificial Electromagnetic Materials

technical field

The invention belongs to the technical field of electromagnetic fields and electromagnetic materials, and further relates to an electromagnetic parameter extraction method, which uses an analytical method combined with a numerical iteration method to extract equivalent electromagnetic parameters of artificial electromagnetic materials; the method solves the problem of extracting electromagnetic parameters of asymmetric artificial electromagnetic materials.

Background technique

New artificial electromagnetic materials (metamaterials) are artificial composite structures or composite materials that are different from natural ones, and have extraordinary physical properties such as negative refraction effect, abnormal Doppler effect, abnormal Cerenkov effect, and perfect lens;

In 1967, Veselago, a former Soviet scientist, made a theoretical study on the propagation characteristics of electromagnetic waves in a medium with negative permittivity and magnetic permeability. In 1996 and 1999, Pendry et al. in the United Kingdom successively proposed to use thin metal wire arrays to achieve negative permittivity, and split ring resonator (Splitring Resonator) arrays to achieve negative magnetic permeability. In order to realize the medium with negative dielectric constant and magnetic permeability at the same time, in 2000, Smith et al. of Duke University in the United States designed a left-handed material composed of a split resonator ring and a wire array according to the theoretical model proposed by Pendry, and passed Prism experiments have verified the negative refractive index characteristics of this left-handed material; the "artificial electromagnetic materials" developed so far include: "left-handed materials", "photonic crystals", and "supermagnetic materials"; artificial electromagnetic materials (metamaterial) are important The three important characteristics of are:

(1) metamaterial is usually a composite material with a novel artificial structure;

(2) Metamaterial has extraordinary physical properties, which are often not available in natural materials;

(3) The nature of metamaterial is often not determined by the intrinsic properties of the constituent materials, but by the artificial structure in it;

In the past ten years, artificial electromagnetic materials have become the frontier development direction of materials science, physics, chemistry and engineering. It provides a new idea and method that allows people to manufacture many special physical properties as they like; The equivalent electromagnetic parameters of electromagnetic materials include four parameters: equivalent wave impedance, equivalent refractive index, equivalent permittivity, and equivalent magnetic permeability. The extraction of equivalent electromagnetic parameters of artificial electromagnetic materials has become a One of the research directions of materials, by studying the equivalent electromagnetic parameters of artificial electromagnetic materials, we can better understand their electromagnetic properties; in 2005, Smith et al proposed a method to extract the equivalent electromagnetic parameters of artificial electromagnetic materials by using method, this method can well extract the equivalent electromagnetic parameters of electrically small-sized artificial electromagnetic materials, but it cannot extract the electromagnetic parameters of asymmetric artificial electromagnetic materials and electrically large-sized artificial electromagnetic materials. In 2010, a method based on K-K The method of extracting the equivalent electromagnetic parameters of the relationship is proposed, which can better solve the shortcoming of ambiguous branches, but requires a generalized integral, which is cumbersome and inefficient in actual engineering. The method of equivalent electromagnetic parameters of artificial electromagnetic materials has not been mentioned for the situation of asymmetric artificial electromagnetic materials, so it is very important to extract the equivalent electromagnetic parameters of asymmetric artificial electromagnetic materials;

Contents of the invention

The present invention proposes a method for extracting equivalent electromagnetic parameters of asymmetric artificial electromagnetic materials, adopts a layered method to extract equivalent electromagnetic parameters, and realizes the extraction of equivalent electromagnetic parameters of asymmetric artificial electromagnetic materials through multiple iterations. Solve the problem of extracting equivalent electromagnetic parameters of asymmetric artificial electromagnetic materials existing in the technical field;

The technical idea of this method is: divide the asymmetric artificial electromagnetic material into two layers of symmetrical structures in the propagation direction of electromagnetic waves, and make each layer of symmetrical structures equivalent to a uniform medium, and set them as medium II and medium respectively along the propagation direction of electromagnetic waves. Ⅲ, the two sides of the asymmetric artificial electromagnetic material are the test environment, let the test environment adjacent to the medium Ⅱ be the medium Ⅰ, and the test environment adjacent to the medium Ⅲ is the medium Ⅳ; the interface between the medium Ⅰ and the medium Ⅱ is regarded as the boundary 1, The interface between medium Ⅱ and medium Ⅲ is regarded as boundary 2, and the interface between medium Ⅲ and medium Ⅳ is regarded as boundary 3. Then, the electromagnetic field in each layer of equivalent medium is theoretically analyzed, and the electromagnetic parameters of medium Ⅱ and Ⅲ are obtained. Analytical form, and then by determining the electromagnetic parameters of medium II as the initial value of the solution, using an iterative method to correct the electromagnetic parameters of medium II and medium III during the solution process, and finally obtain the final values of the electromagnetic parameters of medium II and medium III, And this final value is used as the equivalent electromagnetic parameters of the first-layer structure and the second-layer structure respectively, and these two sets of parameters are used to describe the electromagnetic characteristics of the entire asymmetric artificial electromagnetic material; by combining the electromagnetic parameters of medium II and medium III Bring the final value of the final value into the full-wave simulation software for modeling and simulation again to obtain the external scattering parameter S", and compare whether the external scattering parameter S" obtained by the simulation is consistent with the external scattering parameter S of the actual artificial electromagnetic material, so as to verify the extracted Accuracy of equivalent electromagnetic parameters;

The steps of the technical method for realizing the object of the present invention are as follows:

(1) Use the full-wave simulation software HFSS to simulate the first layer structure separately to obtain its external scattering parameter S′;

(2) Using the equivalent electromagnetic parameter extraction method of the symmetrical structure, using the scattering parameter S′ obtained in step (1) to calculate the relative equivalent wave impedance and relative equivalent refractive index of the first layer structure, the obtained relative The equivalent wave impedance and relative equivalent refractive index are used as the relative wave impedance and relative refractive index of medium II, and these two values are used as the iterative initial value of the equivalent electromagnetic parameter extraction method of the two-layer structure;

(3) Use the full-wave simulation software HFSS to simulate the asymmetric artificial electromagnetic material to obtain the external scattering parameter S of the two-layer structure, and the S includes four parameters of S11, S21, S12, and S22;

Assuming that the electromagnetic wave is incident from the medium Ⅰ and emerges from the medium Ⅳ through the medium Ⅱ and Ⅲ, theoretically analyze the expression form of the electromagnetic field of the four-layer equivalent medium, and get the following relationship:

【1】

in,

【2】

In formula [1] and formula [2], S11 is the reflection coefficient of electromagnetic wave on boundary 1, S21 is the transmission coefficient of electromagnetic wave from medium _I to medium IV, Z1 is the relative wave impedance of medium I, and Z2 is medium _II Z ₃ is the relative wave impedance of medium Ⅲ, Z ₄ is the relative wave impedance of medium Ⅳ, n ₂ is the relative refractive index of medium Ⅱ, n ₃ is the relative refractive index of medium Ⅲ, k ₀ is the electromagnetic wave at The wave number of free space, d2 is the thickness of medium II along the direction of electromagnetic wave propagation, d3 is the thickness of medium III along the direction of electromagnetic wave propagation, A and B are the transition variables of formula [1] operation;

Similarly, if the incident wave enters from medium IV and exits from medium I through medium III and medium II, the other two scattering parameters S22 and S12 can be expressed as follows:

【3】

in,

【4】

S22 in formula [3] and formula [4] is the reflection coefficient of electromagnetic wave on boundary 3, S12 is the transmission coefficient of electromagnetic wave from medium IV to medium I, and C and D are the transition variables for the operation of formula [3];

(4) Finally, the method of numerical iteration is used to use the relative wave impedance and relative refractive index obtained in step (2) as the initial value of the iteration to perform iterative calculations to determine the final equivalent electromagnetic parameter values of the two layers of artificial electromagnetic materials. The specific implementation steps are as follows :

(4.1) Using formulas [3] and [4], based on the relative wave impedance Z ₂ ⁽⁰⁾ and relative refractive index n ₂ ⁽⁰⁾ of medium II obtained in step (2), calculate the relative wave impedance of medium III Impedance Z ₃ ⁽⁰⁾ , relative refractive index n ₃ ⁽⁰⁾ ;

(4.2) Using formulas [1] and [2], based on the relative wave impedance Z ₃ ⁽⁰⁾ and relative refractive index n ₃ ⁽⁰⁾ of medium III obtained in step (1), calculate the first time of medium II Corrected relative wave impedance Z ₂ ⁽¹⁾ , relative refractive index n ₂ ⁽¹⁾ ;

(4.3) Next, using expressions [3] and [4], based on the relative wave impedance Z ₂ ⁽¹⁾ and relative refractive index n ₂ ⁽¹⁾ obtained in step (4.2) after the first correction of medium II, calculate Obtain the relative wave impedance Z ₃ ⁽¹⁾ and relative refractive index n ₃ ⁽¹⁾ of medium III after the first correction;

(4.4) Using expressions [1] and [2] again, based on the relative wave impedance Z ₃ ⁽¹⁾ and relative refractive index n ₃ ⁽¹⁾ of medium III obtained in step (4.3) after the first correction, calculate Obtain the relative wave impedance Z ₂ ⁽²⁾ and relative refractive index n ₂ ⁽²⁾ of medium II after the second correction;

(4.5) Repeat the process in steps (4.3) and (4.4) until the values of the relative wave impedance and relative refractive index of medium II and medium III after multiple corrections do not change significantly in the entire frequency band, then repeat the correction The final relative wave impedance and relative refractive index are the final relative wave impedance and relative refractive index, and these two sets of final relative wave impedance and relative refractive index are respectively used as the relative equivalent wave impedance and relative equivalent refraction corresponding to the two-layer structure The relative equivalent wave impedance and the relative equivalent refractive index of the two-layer symmetrical structure are used to describe the electromagnetic characteristics of the asymmetric artificial electromagnetic material. The relative equivalent dielectric constant and relative The equivalent magnetic permeability calculation formula is as follows:

【5】

【6】

In formula [5] and formula [6], ε ₂ is the relative equivalent permittivity of the first layer structure, μ ₂ is the relative equivalent magnetic permeability of the first layer structure, ε ₃ is the relative equivalent permeability of the second layer structure Equivalent permittivity, μ ₃ is the relative equivalent magnetic permeability of the second layer structure, n is the final number of corrections.

The advantages that the present invention has compared with prior art are as follows:

The present invention adopts the method of combining theoretical analysis and numerical iteration to divide the asymmetric artificial electromagnetic material into two layers of symmetrical structures in the propagation direction of electromagnetic waves, and repeatedly corrects the equivalent electromagnetic parameters of the two-layer structure by using iterative methods. The equivalent electromagnetic parameters of the symmetrical structure jointly describe the electromagnetic characteristics of the asymmetric artificial electromagnetic material, thereby realizing the extraction of the equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material; changing the existing technology that can only extract the equivalent electromagnetic parameters of the symmetrical structure, But can not extract the current situation of the equivalent electromagnetic parameters of the asymmetric structure.

The present invention adopts full-wave simulation software HFSS to simulate the equivalent model with equivalent electromagnetic parameters, and obtains the external scattering parameter S" of the equivalent model, and the obtained S" is completely consistent with the scattering parameter S of the actual structure, which verifies the present invention Accuracy, feasibility and effectiveness of the method in extracting equivalent electromagnetic parameters of asymmetric artificial electromagnetic materials; it can be extended to extract equivalent electromagnetic parameters of asymmetric artificial electromagnetic materials.

Below in conjunction with accompanying drawing and embodiment the present invention will be further described:

Description of drawings

Fig. 1 is a unit structure diagram of an asymmetric artificial electromagnetic material;

Fig. 2 is the flow chart of the present invention extracting the electromagnetic parameter of asymmetric artificial electromagnetic material;

Fig. 3 is the relative equivalent wave impedance diagram of the first layer structure;

Fig. 4 is the relative equivalent wave impedance diagram of the second layer structure;

Fig. 5 is the relative equivalent refractive index diagram of the first layer structure;

Fig. 6 is the relative equivalent refractive index diagram of the second layer structure;

Fig. 7 is the relative equivalent dielectric constant diagram of the first layer structure;

Fig. 8 is the relative equivalent dielectric constant diagram of the second layer structure;

Fig. 9 is a relative equivalent magnetic permeability diagram of the first layer structure;

Fig. 10 is the relative equivalent magnetic permeability diagram of the second layer structure;

Fig. 11 is the comparison chart of the amplitude of the S11 " of inversion and the amplitude of actual S11;

Fig. 12 is the contrast figure of the amplitude of the S21 " of inversion and the amplitude of actual S21;

Fig. 13 is the contrast figure of the amplitude of the S12 " of inversion and the amplitude of actual S12;

Fig. 14 is the contrast figure of the amplitude of the S22 " of inversion and the amplitude of actual S22;

Fig. 15 is the contrast figure of the phase of the S11 " of inversion and the phase of actual S11;

Fig. 16 is the contrast figure of the phase of the S21 " of inversion and the phase of actual S21;

Fig. 17 is the contrast figure of the phase of the S12 " of inversion and the phase of actual S12;

Fig. 18 is the contrast figure of the phase of the S22 " of inversion and the phase of actual S22;

detailed description:

The present invention provides a specific asymmetric artificial electromagnetic material as an example

As shown in Figure 1, the asymmetric artificial electromagnetic material unit is divided into two layers, and each layer is a symmetrical structure. The two-layer structure is composed of a dielectric substrate and metal pattern layers printed on both sides of the dielectric substrate. Among them, the dielectric substrate The length and width are both 2.5mm, and the thickness is 0.25mm. The outside is wrapped by an air box with a length, width, and height of 2.5mm. The dielectric substrate is located in the center of the air box; the material property of the two-layer dielectric substrate is FR4; The width of the printed metal strip on the back of the one-layer structure is 0.14mm, and the length is 2.5mm. 0.15mm, the entire printed pattern is arranged in the center; the printed metal pattern in the second layer structure is to move the metal inner ring on the front of the first layer to the back and the metal strip on the back to the top surface, and move the metal strip It is formed by subtracting the part of the outer ring at the bottom; the material property of the metal pattern on the surface of the dielectric substrate is set as an ideal conductor; the port type is set as a wave port, the frequency sweep type is discrete frequency sweep, and the waveguide method is used to simulate its scattering parameters ; The first layer structure is equivalent to medium II, and the second layer structure is equivalent to medium III;

Referring to Figure 2, the equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material in Figure 1 are extracted. The equivalent electromagnetic parameters are divided into two groups, which are the equivalent electromagnetic parameters of the first layer structure and the equivalent electromagnetic parameters of the second layer structure. Effective electromagnetic parameters, the extracted equivalent electromagnetic parameters are four physical quantities of equivalent wave impedance, equivalent refractive index, equivalent dielectric constant, and equivalent magnetic permeability. The specific implementation steps are as follows:

Step 1. Let the electromagnetic wave propagate from left to right. The asymmetric artificial electromagnetic material is regarded as composed of two layers of uniform media along the propagation direction of the electromagnetic wave, which are respectively set as medium II and medium III. The two sides of the asymmetric artificial electromagnetic material are The test environment, assuming that the test environment adjacent to medium II is medium I, and the test environment adjacent to medium III is medium IV, both medium I and medium IV are air; the interface between medium I and medium II is taken as boundary one, medium The interface between Ⅱ and medium Ⅲ is regarded as boundary 2, and the interface between medium Ⅲ and medium Ⅳ is regarded as boundary 3;

(1) Assuming that the electromagnetic wave is incident from the medium Ⅰ and emerges from the medium Ⅳ through the medium Ⅱ and Ⅲ, the Cartesian coordinate system is adopted, and the boundary 1 is located on the plane of z=0 in the coordinate system. The expression of the electromagnetic field is as follows:

Medium Ⅰ:

【7】

In formula [7] is the total electric field vector in medium Ⅰ; is the total magnetic field vector in medium I; is the unit direction vector of the direction of the electric field vector; is the unit direction vector of the direction of the magnetic field vector; E _i1 is the amplitude of the incident electric field in the medium Ⅰ; H _i1 is the amplitude of the incident magnetic field in the medium Ⅰ; E _r1 is the amplitude of the reflected electric field _in the medium Ⅰ; The amplitude of the reflected magnetic field; k ₁ is the wave number of the electromagnetic wave in the medium I; z is the position of the field point on the z coordinate axis;

Medium II:

【8】

In formula [8] is the total electric field vector in medium II; is the total magnetic field vector in medium II; E _i2 is the incident electric field amplitude in medium II; H _i2 is the incident magnetic field amplitude in medium II; E _r2 is the reflected electric field amplitude in medium II; H _r2 is the reflection in medium II Magnetic field amplitude; k ₀ is the wave number of electromagnetic wave in air; n ₂ is the relative refractive index of medium II;

Medium III:

【9】

In formula [9] is the total electric field vector in medium III; is the total magnetic field vector in medium III; E _i3 is the incident electric field amplitude in medium III; H _i3 is the incident magnetic field amplitude in medium III; E _r3 is the reflected electric field amplitude in medium III; H _r3 is the reflected electric field in medium III Magnetic field amplitude; n ₃ is the relative refractive index of medium III; d2 is the thickness of medium II along the direction of electromagnetic wave propagation; d3 is the thickness of medium III along the direction of electromagnetic wave propagation;

Medium IV:

【10】

In formula [10] is the total electric field vector in medium IV; is the total magnetic field vector in medium IV; E _i4 is the transmitted electric field amplitude in medium IV; H _i4 is the transmitted magnetic field amplitude in medium IV; k ₄ is the wave number in medium IV;

(2) Consider the electromagnetic fields at the three interfaces as follows:

Boundary one left:

【11】

In formula [11] is the total electric field intensity on the left side of boundary one; is the total magnetic field intensity on the left side of boundary one; Z ₁ is the relative wave impedance of medium I;

Right side of boundary one:

【12】

In formula [12] is the total electric field intensity on the right side of boundary one; is the total magnetic field intensity on the right side of boundary one; Z2 is the relative wave impedance of medium _II ;

On the left side of boundary two:

【13】

In formula [13] is the total electric field intensity on the left side of boundary 2; is the total magnetic field intensity on the left side of boundary 2;

On the right side of boundary two:

【14】

In formula [14] is the total electric field intensity on the right side of boundary 2; is the total magnetic field intensity on the right side of boundary 2; Z ₃ is the relative wave impedance in medium Ⅲ;

Left side of boundary three:

【15】

In formula [15] is the total electric field intensity on the left side of boundary 3; is the total magnetic field intensity on the left side of boundary 3;

On the right side of boundary three:

【16】

In formula [16] is the total electric field intensity on the right side of boundary 3; is the total magnetic field intensity on the right side of boundary three; Z ₄ is the relative wave impedance of medium IV;

(3) Boundary conditions are applied at the three boundaries, namely: the electric field and magnetic field on both sides of boundary 1, boundary 2, and boundary 3 are equal, and the following relationship is obtained:

One border:

【17】

Boundary two:

【18】

At border three:

【19】

(4) Combining the above boundary conditions and scattering parameter S, the following expression can be obtained:

【1】

in,

【2】

In formula [1], S11 in formula [2] is the reflection coefficient on the left side of boundary one; S21 is the transmission coefficient from the left side of boundary one to the right side of boundary three; A and B are intermediate variables, which have no actual physical meaning;

In the same way, if the incident wave enters from medium IV and exits from medium I through medium III and medium II, the other two scattering parameters S22 and S12 can be obtained, and their expressions are as follows:

【3】

in,

【4】

S22 in Equation [3] and Equation [4] is the reflection coefficient on the right side of boundary three; S12 is the transmission coefficient from the right side of boundary three to the left side of boundary one; C and D are intermediate variables and have no actual physical meaning; the rest Variables have the same physical meaning as in equations [1], [2];

(5) Solve the equations [1], [2] and [3], [4] to obtain the expressions of the equivalent electromagnetic parameters Z ₂ , n ₂ and Z ₃ , n ₃ respectively;

Step 2, using the mature equivalent electromagnetic parameter extraction method for symmetrical structures, by separately simulating the external scattering parameter S′ of the first layer structure, to obtain the equivalent electromagnetic parameter Z ₂ of the first layer structure without the influence of the second layer structure ⁽⁰⁾ and n ₂ ⁽⁰⁾ , take these two equivalent electromagnetic parameters as the electromagnetic parameters of medium II;

Step 3, use the full-wave simulation software HFSS to simulate the asymmetric artificial electromagnetic material to obtain its external scattering parameter S, and use the expressions [3] and [4] in step 1, based on the electromagnetic properties of medium II obtained in step 2 parameters to obtain the relative wave impedance Z ₃ ⁽⁰⁾ and relative refractive index n ₃ ⁽⁰⁾ of the medium III;

Step 4, using the expressions [1] and [2] in step 1, based on the relative wave impedance Z ₃ ⁽⁰⁾ and relative refractive index n ₃ ⁽⁰⁾ of medium III obtained in step 3, the first Relative wave impedance Z ₂ ⁽¹⁾ and relative refractive index n ₂ ⁽¹⁾ after the second correction;

Step 5, using the expressions [3] and [4] in step 1 again, based on the first corrected relative wave impedance Z ₂ ⁽¹⁾ and relative refractive index n ₂ ⁽¹⁾ of medium II obtained in step 4 , to obtain the relative wave impedance Z ₃ ⁽¹⁾ and relative refractive index n ₃ ⁽¹⁾ of medium III after the first correction;

Step 6, using the expressions [1] and [2] in step 1, based on the first corrected relative wave impedance Z ₃ ⁽¹⁾ and relative refractive index n ₃ ⁽¹⁾ of medium III obtained in step 5, Obtain the relative wave impedance Z ₂ ⁽²⁾ and relative refractive index n ₂ ⁽²⁾ of medium II after the second correction;

Step 7, repeat the above steps 5 and 6, until the values of the relative equivalent wave impedance and relative equivalent refractive index of medium II and medium III after repeated iterations do not change significantly in the whole frequency band, the iteration is selected here The number of steps is 50. At this time, the relative equivalent wave impedance and relative equivalent refractive index after repeated corrections can be seen to be the final relative equivalent wave impedance and relative equivalent refractive index, and the two sets of final relative wave impedance and the relative refractive index are respectively used as the relative equivalent wave impedance and relative equivalent refractive index corresponding to the two-layer symmetrical structure, and finally the relative equivalent permittivity and relative equivalent magnetic permeability are obtained by the following expressions:

【5】

【6】

In formula [5] and formula [6], ε ₂ is the relative equivalent permittivity of the first layer structure, μ ₂ is the relative equivalent magnetic permeability of the first layer structure, ε ₃ is the relative equivalent permeability of the second layer structure Equivalent permittivity, μ ₃ is the relative equivalent magnetic permeability of the second layer structure, Z ₂ ⁽⁵⁰⁾ is the relative equivalent wave impedance when the first layer structure is corrected 50 times, n ₂ ⁽⁵⁰⁾ is the first The relative equivalent refractive index when the layer structure is modified 50 times, Z ₃ ⁽⁵⁰⁾ is the relative equivalent wave impedance when the second layer structure is modified 50 times, n ₃ ⁽⁵⁰⁾ is the relative equivalent wave impedance when the second layer structure is modified 50 times equivalent refractive index.

The relative equivalent permittivity and relative equivalent permeability curves are shown in Figures 7 to 10;

Step 7: In the full-wave simulation software HFSS, two cube models without material properties with the same size as the air box in the original model are established to simulate the equivalent medium II and the equivalent medium III. The effective electromagnetic parameters are brought into the two established models as material parameters for full-wave simulation, and other settings are kept unchanged, and the external scattering parameter S" is obtained, and this scattering parameter is compared with the scattering S of the actual structure, As shown in Figure 11 to Figure 18.

Describe the effect that the equivalent electromagnetic parameter of the present invention extracts below in conjunction with accompanying drawing:

Figure 3 shows the real part and imaginary part of the final relative equivalent wave impedance of the first layer structure in the asymmetric artificial electromagnetic material; Figure 4 shows the final relative equivalent wave impedance of the second layer structure in the asymmetric artificial electromagnetic material Real part and imaginary part; Figure 5 shows the real part and imaginary part of the final relative equivalent refractive index of the first layer structure in the asymmetric artificial electromagnetic material; Figure 6 shows the final result of the second layer structure in the asymmetric artificial electromagnetic material The real and imaginary parts of the relative equivalent refractive index; Figure 7 shows the real and imaginary parts of the final relative equivalent dielectric constant of the first layer structure in the asymmetric artificial electromagnetic material; Figure 8 shows the asymmetric artificial electromagnetic material The real part and the imaginary part of the final relative equivalent permittivity of the second layer structure in the middle; Fig. 9 has shown the real part and the imaginary part of the final relative equivalent magnetic permeability of the first layer structure in the asymmetric artificial electromagnetic material; Fig. 10 represents the real part and the imaginary part of the final relative equivalent magnetic permeability of the second layer structure in the asymmetric artificial electromagnetic material;

The present invention uses full-wave simulation software HFSS to model and simulate the equivalent electromagnetic parameters extracted at last; firstly, two cube models without material attributes with the same size as the air box in the actual material structure in Fig. 1 are established, and then the obtained The extracted two sets of equivalent electromagnetic parameters are respectively assigned to the corresponding cube model as material parameters, and the waveguide method is used to perform full-wave simulation on it to obtain the external scattering parameter S". As shown in Figures 11 to 18: Figure 11 shows the comparison between the S11" amplitude obtained by simulation using the extracted equivalent electromagnetic parameters and the S11 amplitude of the actual structure, and the two curves are completely consistent; Figure 12 shows the obtained by using the extracted The comparison chart of the S21" amplitude obtained by the simulation of the equivalent electromagnetic parameters and the S21 amplitude of the actual structure, the two curves are completely consistent; Figure 13 shows the S12" amplitude obtained by the simulation using the extracted equivalent electromagnetic parameters and the actual structure. The comparison diagram of the S12 amplitude, the two curves are completely consistent; Figure 14 shows the comparison diagram between the S22 "amplitude obtained by the simulation using the extracted equivalent electromagnetic parameters and the S22 amplitude of the actual structure, and the two curves are completely consistent; Fig. 15 shows Figure 16 shows the S21" phase obtained by simulation using the extracted equivalent electromagnetic parameters and the S11 phase of the actual structure. The comparison diagram of the phase and the S21 phase of the actual structure, the two curves are completely consistent; Figure 17 shows the comparison diagram of the S12" phase obtained by using the extracted equivalent electromagnetic parameters for simulation and the S12 phase of the actual structure, the two curves are completely consistent coincide; Fig. 18 shows the comparison diagram between the S22" phase obtained by the simulation using the extracted equivalent electromagnetic parameters and the S22 phase of the actual structure, and the two curves are completely consistent;

In summary, the present invention can accurately extract its equivalent electromagnetic parameters for asymmetric artificial electromagnetic materials, and the extracted two sets of equivalent electromagnetic parameters can accurately describe the electromagnetic characteristics of asymmetric artificial electromagnetic materials, and it has been verified by simulation that the extracted equivalent electromagnetic parameters have The accuracy of the external scattering parameter S" of the model of the effective electromagnetic parameter, the result is in full agreement with the external S parameter of the actual structure, further confirming the feasibility and practicability of the present invention.

Claims (1)

1. A method for extracting equivalent electromagnetic parameters of an asymmetric artificial electromagnetic material comprises the following steps of dividing the asymmetric artificial electromagnetic material into two layers of symmetrical structures in the propagation direction of electromagnetic waves, equivalently forming two layers of uniform media II and media III by using an equivalent medium theory, wherein the outer side of the media II is a testing environment medium I, the outer side of the media III is a testing environment medium IV, in general, the media I and the media IV are both free spaces, the interface of the media I and the media II is used as a boundary I, the interface of the media III and the media IV is used as a boundary III, forming an equivalent model by the asymmetric artificial electromagnetic material, and extracting the electromagnetic parameters of the media II and the media III from the equivalent model:

(1) simulating the first layer of symmetrical structure by using full-wave simulation software HFSS to obtain an external scattering parameter S';

(2) calculating to obtain the relative equivalent wave impedance Z of the first layer structure by using the scattering parameter S' obtained in the step (1) by adopting an equivalent electromagnetic parameter extraction method of a symmetrical structure₂ ⁽⁰⁾Relative equivalent refractive index n₂ ⁽⁰⁾Taking the two values as the relative wave impedance and the relative refractive index in the electromagnetic parameters of a medium II in an equivalent medium model, and taking the two values as iteration initial values of an equivalent electromagnetic parameter extraction method of a two-layer structure;

(3) simulating the asymmetric artificial electromagnetic material by using full-wave simulation software HFSS to obtain external scattering parameters S of the asymmetric artificial electromagnetic material, wherein the S comprises four parameters of S11, S21, S12 and S22;

assuming that electromagnetic waves are vertically incident from a medium I and are emitted from a medium IV through a medium II and a medium III, a Cartesian rectangular coordinate system is adopted, a boundary I is superposed with a plane with a coordinate system z being 0, and the expression form of the electromagnetic fields in four layers of equivalent media is theoretically analyzed, so that the following relation is obtained:

wherein,

s11 in the formulas (1) and (2) is the reflection coefficient of the electromagnetic wave on the boundary I, S21 is the transmission coefficient of the electromagnetic wave from the medium I to the medium IV, and Z₁Is the relative equivalent wave impedance of medium I, Z₂Is the relative equivalent wave impedance of medium II, Z₃Is the relative equivalent wave impedance of medium III, Z₄Is the relative equivalent wave impedance of the medium IV, n₂Is the relative equivalent refractive index of medium II, n₃Is the relative equivalent refractive index of medium III, k₀The wave number of the electromagnetic wave in the free space, d2, d3, A and B are transition variables calculated by the formula (1), wherein d2 is the thickness of a medium II in the electromagnetic wave propagation direction, d3 is the thickness of a medium III in the electromagnetic wave propagation direction;

similarly, if the incident wave is vertically incident from the medium iv and exits from the medium i through the medium iii and the medium ii, two other scattering parameters S22 can be obtained, and the expression of S12 is as follows:

wherein,

s22 of the formulas (3) and (4) is the reflection coefficient of the electromagnetic wave on the boundary III, S12 is the transmission coefficient of the electromagnetic wave from the medium IV to the medium I, and C and D are transition variables of the formula (3) operation;

(4) and finally, carrying out iterative operation by using the relative wave impedance and the relative refractive index obtained in the step (2) as iterative initial values by adopting a numerical iteration method to determine final equivalent electromagnetic parameter values of the two layers of artificial electromagnetic materials, wherein the specific implementation steps are as follows:

(4.1) calculating the relative wave impedance Z of the medium II obtained in the step (2) by adopting the formulas (3) and (4)₂ ⁽⁰⁾Relative refractive index n₂ ⁽⁰⁾Calculating to obtain the relative wave impedance Z of the medium III₃ ⁽⁰⁾Relative refractive index n₃ ⁽⁰⁾；

(4.2) calculating the relative wave impedance Z of the medium III obtained in the step (4.1) by using the formulas (1) and (2)₃ ⁽⁰⁾Relative refractive index n₃ ⁽⁰⁾Calculating to obtain the relative wave impedance Z of the medium II after the first correction₂ ⁽¹⁾Relative refractive index n₂ ⁽¹⁾；

(4.3) secondly adopting the expressions [ 3 ] and [ 4 ] after the first correction based on the medium II obtained in the step (4.2)Relative wave impedance Z of₂ ⁽¹⁾Relative refractive index n₂ ⁽¹⁾Calculating to obtain the relative wave impedance Z of the medium III after the first correction₃ ⁽¹⁾Relative refractive index n₃ ⁽¹⁾；

(4.4) adopting the expressions [ 1 ] and [ 2 ] again, and based on the relative wave impedance Z obtained in the step (4.3) after the medium III is corrected for the first time₃ ⁽¹⁾Relative refractive index n₃ ⁽¹⁾Calculating to obtain the relative wave impedance Z of the medium II after the second correction₂ ⁽²⁾Relative refractive index n₂ ⁽²⁾；

(4.5) the process in the steps (4.3) and (4.4) is circulated until the values of the relative wave impedance and the relative refractive index of the medium II and the medium III after multiple corrections do not change obviously in the whole frequency band any more, the relative wave impedance and the relative refractive index after repeated corrections are regarded as the final relative wave impedance and the final relative refractive index, the two groups of final relative wave impedance and the final relative refractive index are respectively used as the relative equivalent wave impedance and the relative equivalent refractive index corresponding to the two-layer structure, the relative equivalent wave impedance and the relative equivalent refractive index of the two-layer structure are used for describing the electromagnetic property of the asymmetric artificial electromagnetic material together, and the relative equivalent dielectric constant and the relative equivalent magnetic permeability in the equivalent electromagnetic parameters of the two-layer structure are calculated as follows:

in the formula (5) or (6)₂Is the relative equivalent dielectric constant, mu, of the first layer structure₂Is the relative equivalent permeability of the first layer structure,₃is the relative equivalent dielectric constant, mu, of the second layer structure₃Is the relative equivalent permeability of the second layer structure, and n is the final correction number.