CN104931818B - The effective electromagnetic parameter extracting method of asymmetric artificial electromagnetic material - Google Patents
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Abstract
The present invention proposes a kind of extracting method of asymmetric electromagnetic parameters of artificial electromagnetic material parameter, and the problem of asymmetry to solve due to structure leads to not extract material electromagnetic parameter, extracting method implementation steps are：Individually emulate the scattering parameter S ' of the first layer material；The electromagnetic parameter of the first layer material is calculated using S ' and symmetrical structure algorithm；Emulate the externals stray parameter S of asymmetric artificial electromagnetic material；Electromagnetic parameter based on S and first layer obtains the electromagnetic parameter of the second layer；Correct the electromagnetic parameter of first layer again using S and second layer electromagnetic parameter；Above-mentioned steps are circulated, until electromagnetic parameter no longer significant change in whole frequency range in revised two layers, regard this as final electromagnetic parameter；Final argument emulate to obtain scattering parameter S ", is fitted like a glove with the S parameter of practical structures, it was confirmed that accuracy of the invention, feasibility and practicality, realizes the process that asymmetric artificial electromagnetic material effective electromagnetic parameter is extracted with symmetrical method.
Description
Technical Field
The invention belongs to the technical field of electromagnetic fields and electromagnetic materials, and further relates to an electromagnetic parameter extraction method, wherein equivalent electromagnetic parameters of an artificial electromagnetic material are extracted by using an analytical method in combination with a numerical iteration method; the method solves the problem of extracting the electromagnetic parameters of the asymmetric artificial electromagnetic material.
Background
The novel artificial electromagnetic material (metamaterials) is an artificial composite structure or composite material different from natural materials, and has extraordinary physical properties such as negative refraction effect, abnormal Doppler effect, abnormal Cerenkov effect, perfect lens and the like;
in 1967, the former soviet union scientist Veselago conducted theoretical research on the propagation characteristics of electromagnetic waves in a medium with negative dielectric constant and magnetic permeability, in the 80 th 19 th century, chiral media with dielectric constant and magnetic permeability smaller than 1 in a microwave frequency band were found in experiments, in 1996 and 1999, Pendry et al in the uk proposed a thin metal wire array to realize the negative dielectric constant, and an open resonance ring (split resonance) array to realize the negative magnetic permeability, so as to realize the medium with the dielectric constant and the magnetic permeability simultaneously being negative values, in 2000, Smith et al in the university of duck designed a left-handed material consisting of the open resonance ring and a wire array according to a theoretical model proposed by Pendry, and verified the negative refractive index characteristic of the left-handed material through a prism experiment; "artificial electromagnetic materials" developed so far include: "left-handed material", "photonic crystal", "super-magnetic material", and the like; three important features of artificial electromagnetic materials (metamaterials) are:
(1) metamaterials are typically composite materials with novel artificial structures;
(2) metamaterials have exceptional physical properties often not found in natural materials;
(3) the properties of metamaterials are often not determined by the intrinsic properties of the constituent materials, but rather by the artificial structure therein;
in the last decade, artificial electromagnetic materials have become the leading development direction of the subjects of material science, physics, chemistry, engineering and the like, and provide a brand new thought and method which can make people have many special physical properties at will; the extraction of the equivalent electromagnetic parameters of the artificial electromagnetic material becomes one of the research directions of the artificial electromagnetic material, and the electromagnetic characteristics of the artificial electromagnetic material can be better known by researching the equivalent electromagnetic parameters of the artificial electromagnetic material; in 2005, Smith et al proposed a method for extracting equivalent electromagnetic parameters of an artificial electromagnetic material using scattering parameters S, which can extract equivalent electromagnetic parameters of an electrically small-sized artificial electromagnetic material well, but could not extract electromagnetic parameters of an asymmetric artificial electromagnetic material and an electrically large-sized artificial electromagnetic material, in 2010, an equivalent electromagnetic parameter extraction method based on a K-K relationship was proposed, which can solve the disadvantage of ambiguous branch well, but requires a generalized integral, which is heavy and inefficient in practical engineering, which is a method for extracting equivalent electromagnetic parameters of a symmetric artificial electromagnetic material, and is not mentioned at present for the case of an asymmetric artificial electromagnetic material, and thus, it is very important for extracting equivalent electromagnetic parameters of an asymmetric artificial electromagnetic material;
disclosure of Invention
The invention provides a method for extracting equivalent electromagnetic parameters of an asymmetric artificial electromagnetic material, which adopts a layering method to extract the equivalent electromagnetic parameters, realizes the extraction of the equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material through multiple iterations, and solves the extraction problem of the equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material in the technical field;
the technical idea of the method is as follows: dividing the asymmetric artificial electromagnetic material into two layers of symmetrical structures in the propagation direction of electromagnetic waves, enabling each layer of symmetrical structure to be equivalent to a uniform medium, respectively setting the symmetrical structures as a medium II and a medium III along the propagation direction of the electromagnetic waves, setting the two sides of the asymmetric artificial electromagnetic material as test environments, setting the test environment adjacent to the medium II as a medium I, and setting the test environment adjacent to the medium III as a medium IV; the interface of a medium I and a medium II is used as a boundary I, the interface of a medium II and a medium III is used as a boundary II, the interface of a medium III and a medium IV is used as a boundary III, then, the electromagnetic field in each layer of equivalent medium is theoretically analyzed to obtain the analysis form of the electromagnetic parameters of the medium II and the medium III, then, the electromagnetic parameters of the medium II are determined as the initial value for solving, the electromagnetic parameters of the medium II and the medium III in the solving process are corrected by adopting an iterative method, the final values of the electromagnetic parameters of the medium II and the medium III are finally obtained, the final values are respectively used as the equivalent electromagnetic parameters of a first layer structure and a second layer structure, and the two groups of parameters are used for describing the electromagnetic characteristics of the whole artificial asymmetric electromagnetic material together; introducing the final values of the electromagnetic parameters of the medium II and the medium III into full-wave simulation software for modeling simulation again to obtain external scattering parameters S, and comparing whether the external scattering parameters S' obtained by simulation are consistent with the external scattering parameters S of the actual artificial electromagnetic material or not to verify the accuracy of the extracted equivalent electromagnetic parameters;
the technical method for realizing the purpose of the invention comprises the following steps:
(1) simulating the first layer structure by full-wave simulation software HFSS to obtain an external scattering parameter S';
(2) calculating to obtain the relative equivalent wave impedance and the relative equivalent refractive index 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 structure, taking the obtained relative equivalent wave impedance and the obtained relative equivalent refractive index as the relative wave impedance and the relative refractive index of a medium II, and taking the two values as iteration initial values of the equivalent electromagnetic parameter extraction method of the two-layer structure;
(3) simulating the asymmetric artificial electromagnetic material by using full-wave simulation software HFSS to obtain external scattering parameters S of a two-layer structure, wherein the S comprises four parameters of S11, S21, S12 and S22;
assuming that electromagnetic waves enter from a medium I and exit from a medium IV through a medium II and a medium III, the expression form of the electromagnetic field of the four layers of equivalent media is theoretically analyzed, and the following relation is obtained:
【1】
wherein,
【2】
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 wave impedance of medium I, Z2Is the relative wave impedance of medium II, Z3Is the relative wave impedance of medium III, Z4Is the relative wave impedance of the medium IV, n2Is the relative refractive index of medium II, n3Is the relative 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 an incident wave enters 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:
【3】
wherein,
【4】
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 (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 ] based on the relative wave impedance Z obtained after the medium II obtained in the step (4.2) is firstly corrected2 (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:
【5】
【6】
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.
Compared with the prior art, the invention has the following advantages:
the invention adopts a 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, repeatedly corrects equivalent electromagnetic parameters of the two layers of structures by using the iterative method, and describes the electromagnetic characteristics of the asymmetric artificial electromagnetic material by using the equivalent electromagnetic parameters of the two layers of symmetrical structures together, thereby realizing the problem of extracting the equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material; the current situation that only equivalent electromagnetic parameters of a symmetrical structure can be extracted but equivalent electromagnetic parameters of an asymmetrical structure cannot be extracted in the prior art is changed.
The method adopts full-wave simulation software HFSS to simulate the equivalent model with equivalent electromagnetic parameters to obtain external scattering parameters S of the equivalent model, and the obtained S is completely consistent with the scattering parameters S of the actual structure, so that the accuracy, feasibility and effectiveness of the method in extracting the equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material are verified; the method can be popularized and applied to the extraction of equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material.
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
drawings
FIG. 1 is a block diagram of an asymmetric artificial electromagnetic material;
FIG. 2 is a flow chart of the present invention for extracting electromagnetic parameters of an asymmetric artificial electromagnetic material;
FIG. 3 is a graph of relative equivalent wave impedance of a first layer structure;
FIG. 4 is a graph of relative equivalent wave impedance of the second layer structure;
FIG. 5 is a graph of relative equivalent refractive index of a first layer structure;
FIG. 6 is a graph of relative equivalent refractive index of a second layer structure;
FIG. 7 is a graph of relative equivalent dielectric constant of a first layer structure;
FIG. 8 is a graph of relative equivalent dielectric constant of a second layer structure;
FIG. 9 is a graph of relative equivalent permeability of a first layer structure;
FIG. 10 is a graph of the relative equivalent permeability of the second layer structure;
FIG. 11 is a graph comparing the amplitude of the inverted S11' with the amplitude of the actual S11;
FIG. 12 is a graph comparing the amplitude of the inverted S21' with the amplitude of the actual S21;
FIG. 13 is a graph comparing the amplitude of the inverted S12' with the amplitude of the actual S12;
FIG. 14 is a graph comparing the amplitude of the inverted S22' with the amplitude of the actual S22;
FIG. 15 is a graph comparing the inverted S11' phase with the actual S11 phase;
FIG. 16 is a graph comparing the inverted S21' phase with the actual S21 phase;
FIG. 17 is a graph comparing the inverted S12' phase with the actual S12 phase;
FIG. 18 is a graph comparing the inverted S22' phase with the actual S22 phase;
the specific implementation mode is as follows:
the invention provides a specific asymmetric artificial electromagnetic material as an embodiment
As shown in fig. 1, the asymmetric artificial electromagnetic material unit is divided into two layers, each layer is a symmetric structure, and the two layers of structures are composed of a medium substrate and metal pattern layers printed on two sides of the medium substrate, wherein the length and width of the medium substrate are both 2.5mm, the thickness is 0.25mm, the outside of the medium substrate is wrapped by an air box with the length, width and height of 2.5mm, and the medium substrate is positioned at the center of the air box; the material property of the two-layer dielectric substrate is FR 4; the width of a printed metal strip on the back of the first layer structure is 0.14mm, the length of the printed metal strip is 2.5mm, the side length of the outer ring of the metal opening resonance ring on the front side is 2.2mm, the line width of the metal opening resonance ring is 0.2mm, the gap of each ring opening is 0.3mm, the distance between the inner ring and the outer ring is 0.15mm, and the whole printed pattern is arranged in the middle; the printed metal pattern in the second layer structure is formed by moving the metal inner ring on the front surface of the first layer to the back surface and moving the metal strip on the back surface to the top surface, and reducing the part of the moved metal strip, the bottom of which extends out of the outer ring; setting the material property of the metal pattern on the surface of the dielectric substrate as an ideal conductor; the port type is set as a wave port, the sweep frequency type is discrete sweep frequency, and a waveguide method is adopted to carry out scattering parameter simulation on the sweep frequency type; the first layer structure is equivalent to a medium II, and the second layer structure is equivalent to a medium III;
referring to fig. 2, the asymmetric artificial electromagnetic material in fig. 1 is subjected to extraction of equivalent electromagnetic parameters, the equivalent electromagnetic parameters are divided into two groups in total, the two groups are respectively equivalent electromagnetic parameters of a first layer structure and equivalent electromagnetic parameters of a second layer structure, the extracted equivalent electromagnetic parameters are four physical quantities of equivalent wave impedance, equivalent refractive index, equivalent dielectric constant and equivalent magnetic permeability, and the specific implementation steps are as follows:
step 1, enabling electromagnetic waves to propagate from left to right, regarding an asymmetric artificial electromagnetic material as being composed of two layers of uniform media along the propagation direction of the electromagnetic waves, wherein the two layers of uniform media are respectively set as a medium II and a medium III, two sides of the asymmetric artificial electromagnetic material are testing environments, the testing environment adjacent to the medium II is set as a medium I, the testing environment adjacent to the medium III is set as a medium IV, and the medium I and the medium IV are both air; the interface of the medium I and the medium II is used as a first boundary, the interface of the medium II and the medium III is used as a second boundary, and the interface of the medium III and the medium IV is used as a third boundary;
(1) assuming that electromagnetic waves are 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, and a boundary is a plane with z being 0 in the coordinate system, firstly, the electromagnetic field expression form in each layer of medium is analyzed by adopting an electromagnetic field theory as follows:
medium I:
【7】
in the formula [ 7 ]Is the total electric field vector in the medium I;is the total magnetic field vector in the medium I;a unit direction vector which is the direction in which the electric field vector is located;a unit direction vector which is the direction in which the magnetic field vector is located; ei1The amplitude of an incident electric field in a medium I; hi1The amplitude of an incident magnetic field in a medium I; er1Is the amplitude of the reflected electric field in medium I; hr1The amplitude of the reflected magnetic field in the medium I; k is a radical of1The 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 the formula [ 8 ]Is the total electric field vector in medium II;is the total magnetic field vector in medium II; ei2The amplitude of the incident electric field in medium II; hi2Is the amplitude of the incident magnetic field in medium II; er2Is the amplitude of the reflected electric field in medium II; hr2As a mediumThe amplitude of the reflected magnetic field in II; k is a radical of0The wave number of the electromagnetic wave in the air; n is2Relative refractive index of medium II;
medium III:
【9】
in the formula [ 9 ]Is the total electric field vector in medium III;is the total magnetic field vector in medium III; ei3Is the amplitude of the incident electric field in medium III; hi3Is the amplitude of the incident magnetic field in medium III; er3Is the reflected electric field amplitude in medium III; hr3Is the reflected magnetic field amplitude in medium III; n is3Is the relative refractive index of medium III; d2 is the thickness of medium II along the electromagnetic wave propagation direction; d3 is the thickness of medium III along the electromagnetic wave propagation direction;
medium IV:
【10】
in the formula [ 10 ]Is the total electric field vector in the medium IV;is the total magnetic field vector in the medium IV; ei4Is the amplitude of the transmitted electric field in the medium IV; hi4Is the amplitude of the transmission magnetic field in the medium IV; k is a radical of4The wave number in the medium IV;
(2) the electromagnetic fields at the three interfaces are considered to be expressed as follows:
boundary one left side:
【11】
in the formula (11)Total electric field strength to the left of boundary one;total magnetic field strength to the left of boundary one; z1Is the relative wave impedance of medium I;
boundary one, right:
【12】
in the formula [ 12 ]The total electric field strength to the right of boundary one;the total magnetic field strength to the right of boundary one; z2Is the relative wave impedance of medium II;
left side of boundary two:
【13】
in the formula [ 13 ]Total electric field strength of the left side of the boundaryDegree;the total magnetic field strength to the left of boundary two;
right of boundary two:
【14】
in the formula [ 14 ]The total electric field strength on the right side of the boundary II;the total magnetic field strength on the right side of the boundary II; z3Is the relative wave impedance in medium III;
left side of boundary three:
【15】
in the formula [ 15 ]The total electric field strength to the left of boundary three;the total magnetic field strength to the left of boundary three;
boundary three right:
【16】
in the formula [ 16 ]The total electric field strength to the right of boundary three;the total magnetic field strength to the right of boundary three; z4Is the relative wave impedance of the medium IV;
(3) boundary conditions are applied at three boundaries, namely: the electric field and the magnetic field on the two sides of the boundary I, the boundary II and the boundary III are equal to obtain the following relational expression:
at the first boundary:
【17】
and the second boundary is as follows:
【18】
at boundary three:
【19】
(4) combining the boundary condition and the scattering parameter S, the following expression can be obtained:
【1】
wherein,
【2】
in the formula (1), S11 in the formula (2) is a reflection coefficient on the left side of the boundary I; 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 and have no actual physical significance;
similarly, if an incident wave is incident from the medium iv and exits from the medium i via the medium iii and the medium ii, two other scattering parameters S22 and S12 can be obtained, which are expressed as follows:
【3】
wherein,
【4】
in the formula (3), S22 in the formula (4) is the reflection coefficient on the right side of the 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 significance; the other variables have the same physical meanings as those in equation sets (1) and (2);
(5) solving equation sets (1), (2) and (3) and (4) to obtain equivalent electromagnetic parameters Z2,n2And Z3,n3The expression of (1);
step 2, obtaining the equivalent electromagnetic parameters Z of the first layer structure without the influence of the second layer structure by independently simulating the external scattering parameters S' of the first layer structure by utilizing a mature equivalent electromagnetic parameter extraction method of the symmetrical structure2 (0)And n2 (0)Taking the two equivalent electromagnetic parameters as electromagnetic parameters of a medium II;
and 3, simulating the asymmetric artificial electromagnetic material by full-wave simulation software HFSS to obtain an external scattering parameter S of the asymmetric artificial electromagnetic material, and obtaining the relative wave impedance Z of the medium III based on the electromagnetic parameter of the medium II obtained in the step 2 by adopting the expressions (3) and (4) in the step 13 (0)And relative refractive index n3 (0)；
And 4, adopting the expressions [ 1 ] and [ 2 ] in the step 1, and based on the relative wave impedance Z of the medium III obtained in the step 33 (0)And relative refractive index n3 (0)Obtaining the relative wave impedance Z of the medium II after the first correction2 (1)And relative refractive index n2 (1)；
And 5, adopting the expressions [ 3 ] and [ 4 ] in the step 1 again, and based on the relative wave impedance Z obtained in the step 4 after the medium II is corrected for the first time2 (1)And relative refractive index n2 (1)Obtaining the relative wave impedance Z of the medium III after the first correction3 (1)And relative refractive index n3 (1)；
And 6, adopting the expressions [ 1 ] and [ 2 ] in the step 1, and based on the relative wave impedance Z obtained in the step 5 after the medium III is corrected for the first time3 (1)And relative refractive index n3 (1)Obtaining the relative wave impedance Z after the second correction of the medium II2 (2)And relative refractive index n2 (2)；
And 7, circulating the step 5 and the step 6 until the values of the relative equivalent wave impedance and the relative equivalent refractive index of the medium II and the medium III after repeated correction do not obviously change in the whole frequency band after continuous iteration, wherein the iteration step number is 50, at the moment, the relative equivalent wave impedance and the relative equivalent refractive index after repeated correction are considered as the final relative equivalent wave impedance and the final relative equivalent refractive index, the two groups of final relative wave impedance and the final relative equivalent refractive index are respectively used as the relative equivalent wave impedance and the relative equivalent refractive index corresponding to the two-layer symmetrical structure, and finally, the relative equivalent dielectric constant and the relative equivalent magnetic permeability are obtained through the following expressions:
【5】
【6】
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, Z, of the second layer structure2 (50)Correcting the relative equivalent wave impedance n for the first layer structure 50 times2 (50)Relative equivalent refractive index, Z, at 50 modifications to the first layer structure3 (50)Correcting the relative equivalent wave impedance of the second layer structure 50 times, n3 (50)The relative equivalent refractive index at 50 times was corrected for the second layer structure.
The relative equivalent dielectric constant and relative equivalent permeability curves are shown in fig. 7 to 10;
and 7, establishing two cubic models without material attributes, which have the same size as an air box in the original model, in full-wave simulation software HFSS (high frequency synchronous satellite system) for simulating an equivalent medium II and an equivalent medium III, respectively taking two sets of finally obtained equivalent electromagnetic parameters as material parameters into the two established models for full-wave simulation, keeping the other settings unchanged, obtaining external scattering parameters S ", and comparing the scattering parameters with scattering S of an actual structure, as shown in FIGS. 11-18.
The effect of the equivalent electromagnetic parameter extraction of the present invention is described below with reference to the accompanying drawings:
FIG. 3 illustrates the real and imaginary parts of the resulting relative equivalent wave impedance of a first layer structure in an asymmetric artificial electromagnetic material; FIG. 4 shows the real and imaginary parts of the resulting relative equivalent wave impedance of the second layer structure in an asymmetric artificial electromagnetic material; FIG. 5 shows the real and imaginary parts of the resulting relative equivalent refractive index of a first layer structure in an asymmetric artificial electromagnetic material; FIG. 6 shows the real and imaginary parts of the resulting relative equivalent refractive index of the second layer structure in an asymmetric artificial electromagnetic material; FIG. 7 shows the real and imaginary parts of the resulting relative equivalent permittivity of a first layer structure in an asymmetric artificial electromagnetic material; FIG. 8 shows the real and imaginary parts of the resulting relative equivalent permittivity of the second layer structure in an asymmetric artificial electromagnetic material; FIG. 9 shows real and imaginary parts of the resulting relative equivalent permeability of a first layer structure in an asymmetric artificial electromagnetic material; FIG. 10 shows the real and imaginary parts of the resulting relative equivalent permeability of the second layer structure in an asymmetric artificial electromagnetic material;
modeling and simulating equivalent electromagnetic parameters obtained by final extraction by using full-wave simulation software HFSS; firstly, establishing two cube models without material attributes, which have the same size as an air box in the actual material structure in fig. 1, then respectively giving the two groups of extracted equivalent electromagnetic parameters to the corresponding cube models as material parameters, and performing full-wave simulation on the cube models by adopting a waveguide method to obtain external scattering parameters S ", wherein the comparison result of the simulation result and the scattering parameters S of the actual structure is shown in fig. 11-18: FIG. 11 is a graph showing the comparison of the S11 "amplitude obtained by simulation using the extracted equivalent electromagnetic parameters with the S11 amplitude of the actual structure, wherein the two curves are completely coincident; FIG. 12 is a graph showing the comparison of the S21 "amplitude obtained by simulation using the extracted equivalent electromagnetic parameters with the S21 amplitude of the actual structure, the two curves being completely coincident; FIG. 13 is a graph showing the comparison of the S12 "amplitude obtained by simulation using the extracted equivalent electromagnetic parameters with the S12 amplitude of the actual structure, the two curves being completely coincident; FIG. 14 is a graph showing the comparison of the S22 "amplitude obtained by simulation using the extracted equivalent electromagnetic parameters with the S22 amplitude of the actual structure, the two curves being in full agreement; FIG. 15 is a graph showing the comparison of the S11' phase obtained by simulation using the extracted equivalent electromagnetic parameters and the S11 phase of the actual structure, wherein the two curves are completely coincident; FIG. 16 is a graph showing the comparison of the S21' phase obtained by simulation using the extracted equivalent electromagnetic parameters and the S21 phase of an actual structure, wherein the two curves are completely coincident; FIG. 17 is a graph showing the comparison of the S12' phase obtained by simulation using the extracted equivalent electromagnetic parameters and the S12 phase of an actual structure, wherein the two curves are completely coincident; FIG. 18 is a graph showing the comparison of the S22' phase obtained by simulation using the extracted equivalent electromagnetic parameters and the S22 phase of an actual structure, wherein the two curves are completely coincident;
in conclusion, the equivalent electromagnetic parameters of the asymmetric artificial electromagnetic material can be accurately extracted by the method, the electromagnetic characteristics of the asymmetric artificial electromagnetic material can be accurately described by the two groups of extracted equivalent electromagnetic parameters, the accuracy of the external scattering parameters S' of the model with the extracted equivalent electromagnetic parameters is verified through simulation, the result is completely consistent with the external S parameters of the actual structure, and the feasibility and the practicability of the method are further verified.
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.
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