Method for designing illusion of large-scale complex shape target
By covering the outside of electrically large-scale complex-shaped targets with an electric scale conversion coating and an illusion coating, and by utilizing the formal invariance of Maxwell's equations and spatial mapping techniques, the illusion design problem of electrically large-scale complex-shaped targets is solved, and the same scattering mode as the equivalent electrically small-scale target is achieved. This method is applicable to isotropic and uniaxial anisotropic targets.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-11-22
- Publication Date
- 2026-03-27
AI Technical Summary
Existing technologies struggle to effectively achieve the illusion design of electrically large-scale complex-shaped targets, especially due to the challenges in scattering analysis and control caused by the increased geometric scale and shape complexity of the targets.
By covering a target with a complex shape at a large electrical scale with two layers of uniform dielectric material, including an electrical scale conversion coating and an illusion coating, and by utilizing the formal invariance of Maxwell's equations and spatial mapping techniques, the dielectric constant and permeability are calculated to achieve the same scattering mode as the equivalent small electrical scale target, thereby producing an illusion effect.
It achieves the illusion effect of electrically large-scale complex-shaped targets, overcomes the limitations of existing methods in terms of scale and shape, and is applicable to isotropic and uniaxial anisotropic targets. Simulation results show good illusion effect.
Smart Images
Figure CN115828560B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of electromagnetic technology, in particular to a method for designing an illusion of an electrically large and complexly shaped target, which can be used to control the electromagnetic scattering of the electrically large and complexly shaped target to produce an illusion effect. BACKGROUND
[0002] With the rapid development of new generation of weapon equipment and detection control technology in various countries, stealth technology is not only the key technology to seize the initiative in war and improve the survivability on the battlefield, but also an important technical index for measuring new generation of weapon equipment. Stealth technology, also known as low detectability technology, reduces the detectability of a target to radar by reducing the electromagnetic scattering characteristics of the target, so that the target is difficult to be discovered, identified, tracked and attacked. The main threat to the stealth of an aircraft in medium and long distance air combat comes from electromagnetic detectors. Radar Cross Section (RCS) is a main index for characterizing the scattering ability of a stealth target to incident waves, but in the engineering radar stealth test, the background noise caused by the carrier of the target can seriously affect the test accuracy, and reducing the electromagnetic scattering of the carrier on the basis of reasonable shape design can further reduce the stray interference. The illusion of a target is a special stealth technology, which makes the electromagnetic scattering mode of the original target the same as that of another object through certain control means, so as to achieve the purpose of camouflage. Traditional stealth and illusion technologies mainly have two means of shape and material, which use various wave-absorbing and wave-transmitting materials to absorb energy or reflect incident wave energy to an unimportant direction through appropriate shape design to realize the stealth of the target. However, the wave-absorbing materials at home and abroad have the disadvantages of narrow frequency band and low efficiency, which limits their application range.
[0003] The carrier with shape design is usually complex in shape and larger in geometric size than the wavelength of incident electromagnetic waves, i.e. an electrically large and complexly shaped target. New type of electromagnetic metamaterials (EMM) have become a subject widely concerned in the fields of physics, optics, materials science and electromagnetism due to their unique physical properties. Professor R.M.Walser first proposed the new type of electromagnetic metamaterials in 1999, and they were listed as one of the top ten important scientific advances in this century by the American Science magazine. The new type of electromagnetic metamaterials refers to some artificially designed composite structures, which have physical properties that do not exist in natural materials and do not conform to conventional cognition. The physical properties and electromagnetic properties are not determined by the properties of the materials, but by the resonant characteristics of the artificially designed unit structure. By artificially changing the unit structure and distribution mode, electromagnetic waves can produce special responses completely different from natural materials, so as to realize the control of electromagnetic waves.
[0004] In July 2006, J.B.Pendry, D.Schurig and D.R.Smith proposed a coordinate transformation theory, which designed the medium electromagnetic parameters of the invisibility cloak as a function of the spatial position, regulated the electromagnetic wave to bypass the target and return to the original propagation path, so as to achieve perfect invisibility, and even the experimental verification at microwave frequency or optical frequency was confirmed in the same year. Thus, the invisibility cloak based on optical transformation provides a new idea for the design of invisibility cloak. However, the parameters of the invisibility cloak designed by the coordinate transformation are non-uniform and anisotropic, which does not exist in nature, and need to be realized by the design of metamaterial structure.
[0005] In addition to the space transformation, Alu et al. proposed a three-dimensional spherical invisibility cloak based on scattering cancellation in 2005. This cloak is to cover a layer of uniform material with complementary polarizability outside the target to cancel or regulate the scattering field of the spherical target, and finally achieve the effect of invisibility or illusion. When designing the “scattering cancellation cloak”, the scattering coefficient of the spherical target object is calculated first, and then the scattering coefficient of the whole target is set to 0 or equal to the scattering coefficient of the illusion target, so that the relationship between the size and the electromagnetic parameters of the target when the target produces invisibility or illusion can be obtained. However, in practice, the target such as the carrier in the radar scattering characteristic test is an electrically large scale complex shape. However, the existing “scattering cancellation cloak” is for simple and analytical solution targets such as columns and spheres. On the one hand, due to the increase of the electric scale of the target, the quasi-static, small-zone approximation in the plane wave expansion function does not hold, which leads to the fact that it cannot be directly used for scattering analysis of electrically large scale targets. On the other hand, although the Mie scattering invisibility theory can be extended to cylindrical and spherical targets, it is currently only applicable to specific regular shape targets with the same dipole moment as the cylindrical and spherical targets, and there is a limitation on the shape of the target to be hidden. In addition, for complex shape targets, some documents report that on the basis of Mie scattering, the discrete dipole approximation and characteristic mode theory are used to design the invisibility or illusion coating for electrically small scale targets, to solve the problem of invisibility or illusion design for complex shape targets, but it is only applicable to electrically small size and difficult to apply to the invisibility design of other complex shape targets. Therefore, for electrically large scale complex shape targets, whether in size or shape, the existing method has the problem of scattering analysis and regulation. SUMMARY
[0006] In order to overcome the defect that the “scattering cancellation cloak” cannot make the electrically large scale complex shape target such as the carrier produce the illusion effect, the present application provides a method for designing the illusion of an electrically large scale complex shape target.
[0007] The technical scheme adopted by the present application to solve the technical problem is:
[0008] A method for designing the illusion of an electrically large scale complex shape target, comprising the following steps:
[0009] Step 1, obtaining the permittivity ε3' and permeability μ3' of the electric scale conversion coating
[0010] Taking an electrically large scale complex shape target as the research object, a layer of electric scale conversion coating is covered outside the electrically large scale complex shape target, so that it has the same scattering mode as the equivalent electrically small scale complex shape target with unchanged shape; thus, the spatial mapping of electric scale conversion is constructed. According to the formal invariance of Maxwell's equations, the permittivity ε3' and permeability μ3' of the electric scale conversion coating are calculated.
[0011] At a distance a1 from the surface of the electrically large scale complex shape target, an electric scale conversion coating with a size of b, a permittivity of ε3' and a permeability of μ3' is covered, and the electrically large scale complex shape target covered with the electric scale conversion coating forms an electrically large scale complex shape target covered with the electric scale conversion coating. The electrically large scale complex shape target covered with the electric scale conversion coating has the same electromagnetic scattering mode as the equivalent electrically small scale complex shape target with a size of c0, a permittivity of ε1 and a permeability of μ1. The permittivity ε3' and permeability μ3' of the electric scale conversion coating are calculated.
[0012] Step 2, obtaining the permittivity ε1 and permeability μ1 of the equivalent electrically small scale complex shape target
[0013] The electric scale conversion mapping between the electrically large scale complex shape target and the equivalent electrically small scale complex shape target is established, and the permittivity ε1 and permeability μ1 of the equivalent electrically small scale complex shape target are calculated according to the formal invariance of Maxwell's equations.
[0014] Step 3, obtaining the permittivity ε2 and permeability μ2 of the illusion coating of the equivalent electrically small scale complex shape target
[0015] In the virtual conversion space, an illusion coating is covered on the surface of the equivalent electrically small scale complex shape target, and the permittivity and permeability of the illusion coating of the equivalent electrically small scale complex shape target are calculated.
[0016] An illusion coating is covered outside the equivalent electrically small scale complex shape target, so that the whole after the equivalent electrically small scale complex shape target covered with the illusion coating has the same scattering mode as the illusion target. A unit amplitude plane wave is vertically incident on the equivalent electrically small scale complex shape target covered with the illusion coating. According to the stealth and illusion conditions of the electrically small scale complex shape target, the permittivity ε2 and permeability μ2 of the illusion coating of the equivalent electrically small scale complex shape target are calculated.
[0017] Step 4, obtaining the permittivity ε2' and permeability μ2' of the illusion coating of the electrically large scale complex shape target
[0018] According to the target electric size transformation of step 2 and the dielectric constant and magnetic permeability of the illusion coating of the equivalent electric small scale complex shape target of step 3, the dielectric constant and magnetic permeability of the illusion coating of the electric large scale complex shape target are derived.
[0019] In the actual physical space, the illusion coating is covered outside the electric large scale complex shape target, and the dielectric constant ε2' and the magnetic permeability μ2' of the illusion coating of the electric large scale complex shape target are calculated according to the size relationship between the electric large scale complex shape target and the equivalent electric small scale complex shape target.
[0020] Step 5, the illusion coating and the electric scale conversion coating are covered on the electric large scale complex shape target in sequence
[0021] According to the dielectric constant and magnetic permeability of the electric scale conversion coating and the illusion coating obtained in steps 2 and 4, the illusion coating and the electric scale conversion coating are covered on the surface of the electric large scale complex shape target in sequence, and the illusion effect is generated.
[0022] Thus, the illusion effect of the electric large scale complex shape target is realized.
[0023] In step 1 of the above illusion design method, the process of obtaining the dielectric constant ε3' and the magnetic permeability μ3' of the electric scale conversion coating is as follows:
[0024] The electric large scale complex shape target composed of uniform isotropic or anisotropic materials has a geometric size c1, a dielectric constant ε1', and a magnetic permeability μ1'. An electric scale conversion coating with a size b, a dielectric constant ε3', and a magnetic permeability μ3' is covered outside the electric large scale complex shape target at a1. According to the electric size transformation requirement, virtual-actual space transformation is performed, that is, the actual physical space a1 < r' < b is compressed to the virtual transformation space a0 < r < b. The point in the actual physical space is represented by (r', θ', φ'), the point in the virtual transformation space is represented by (r, θ, φ), and a linear function is used to construct the space mapping as follows:
[0025]
[0026] θ' = θ (2)
[0027]
[0028] In formulas (1), (2), and (3), a1(θ) is the inner boundary function of the conversion coating of the electric large scale complex shape target in the actual physical space, b(θ) is the outer boundary function of the conversion coating of the electric large scale complex shape target in the actual physical space, and a0(θ) is the boundary function of the equivalent electric small scale complex shape target in the virtual transformation space.
[0029] According to the space mapping, the corresponding Jacobian matrix Λ is calculated as follows:
[0030]
[0031] In combination with the form invariance of Maxwell equations, the permittivity ε3' and permeability μ3' of the electric scale conversion coating are calculated as follows:
[0032]
[0033]
[0034] In formula (5) (6), A is B is
[0035] In the above illusion design method, in step 2, the process of calculating the permittivity ε1 and permeability μ1 of the equivalent electric small scale complex shape target is as follows:
[0036] Through the transformation of virtual-real space, the electric large scale complex shape target with size c1, permittivity ε1' and permeability μ1' covered by the electric scale conversion coating has the same scattering mode as the equivalent electric small scale complex shape target with size c0, permittivity ε1 and permeability μ1, and the size of the equivalent electric small scale complex shape target is c1c0 times smaller than that of the electric large scale complex shape target:
[0037]
[0038] Correspondingly, the permittivity ε1 and permeability μ1 of the equivalent electric small scale complex shape target are
[0039]
[0040]
[0041] In the above illusion design method of the electric large scale complex shape target, in step 3, the process of calculating the permittivity ε2 and permeability μ2 of the illusion coating of the equivalent electric small scale complex shape target is as follows:
[0042] First, a series of dipoles characterized by polarizability are used to establish a discrete dipole model of the equivalent electric small scale complex shape target.
[0043] The equivalent electric small scale complex shape target is discretized and simulated by N1 discrete cubic lattices, each of which is replaced by a dipole with a permittivity of ε i characterized by polarizability α i :
[0044]
[0045] In formula (10), the constant terms are b1=-1.8915316, b2=0.1648469, b3=-1.7700004, respectively, and and are the components of the incident wave vector and the polarization vector in the rectangular coordinate system, respectively, k is the wave number of the incident electromagnetic wave, d is the distance between the dipoles, is the Clausius-Mossotti polarizability, is calculated by the following formula:
[0046]
[0047] In formula (11), i=1, 2, …, N1.
[0048] Secondly, the dielectric constant ε2 and the magnetic permeability μ2 of the illusion coating of the equivalent electric small-scale complex-shaped target are calculated
[0049] The illusion coating of the non-magnetic equivalent electric small-scale complex-shaped target is simulated by N2 discrete dipoles, the dielectric constant of the illusion coating is ε2, the magnetic permeability μ2=1; the size of the illusion target of the non-magnetic equivalent electric small-scale complex-shaped target is a0, the dielectric constant is ε e , and the magnetic permeability is μ e =1. Assuming that the equivalent electric small-scale complex-shaped target with the illusion coating is equal in size to the illusion target, the size is a0, the number of dipoles satisfies N=N1+N2. According to the stealth and illusion conditions of the equivalent electric small-scale complex-shaped target, the dielectric constant ε2 of the illusion coating of the equivalent electric small-scale complex-shaped target is obtained as follows:
[0050]
[0051] In formula (12), α2 is the polarizability of the equivalent electric small-scale complex-shaped target and its illusion coating, is the real part of .
[0052] According to the stealth and illusion conditions of the equivalent electric small-scale complex-shaped target, the magnetic permeability μ2 of the illusion coating of the equivalent electric small-scale complex-shaped target is obtained as follows:
[0053] μ2=1(13)
[0054] In the above illusion design method, in step 4, the process of calculating the dielectric constant ε2′ and the magnetic permeability μ2′ of the illusion coating of the electric large-scale complex-shaped target is as follows:
[0055] The surface of the electrically large complex shape target with size c1 is covered with an illusion coating with size a1, dielectric constant ε2', and magnetic permeability μ2', which has the same scattering pattern as an illusion target with size a0, dielectric constant ε e , and magnetic permeability μ e . According to the target electric size transformation formula (7) and the illusion condition formulas (12) and (13), the dielectric constant ε2' and the magnetic permeability μ2' of the illusion coating of the electrically large complex shape target in the actual physical space are calculated as follows:
[0056]
[0057]
[0058] The above-mentioned illusion design method further comprises the following step 5:
[0059] The surface of the electrically large complex shape target is sequentially covered with the illusion coating and the electric scale conversion coating to form an illusion target. If the dielectric constant ε e and the magnetic permeability μ e of the illusion target are the same as air, i.e., both equal to 1, then the stealth effect of the electrically large complex shape target can be achieved.
[0060] The present application has the following advantages:
[0061] An illusion design method for an electrically large complex shape target is provided based on the existing stealth design method for an electrically small complex shape target. The design condition for the electrically large complex shape target to produce an illusion effect by covering two layers of uniform media is proposed. The electrically large complex shape target can produce an illusion effect by covering the uniform media satisfying the design condition.
[0062] An illusion design method for an electrically large complex shape target is provided. A general expression for the electrically large complex shape target to produce an illusion effect by covering uniform media is given. The expression is not only applicable to isotropic targets but also to targets with uniaxial anisotropy.
[0063] Simulation results show that the electrically medium-scale complex shape target covered with the uniform media satisfying the above-mentioned design condition can produce the same scattering field distribution as the illusion target, and has good illusion effect. Compared with the existing scattering regulation method, the method not only solves the problem of inapplicability of the existing method caused by the increase of the geometric size of the target, but also solves the problem of scattering regulation of anisotropic targets. BRIEF DESCRIPTION OF DRAWINGS
[0064] Figure 1 is a schematic diagram of the design principle of the illusion effect of the electrically large complex shape target;
[0065] Figure 2is the cross section of electromagnetic scattering simulation effect of hat-shaped target in the middle of electricity after adding illusion coating and electric scale conversion coating in turn;
[0066] Figure 3 is the cross section of equivalent illusion sphere electromagnetic scattering simulation effect of hat-shaped target in the middle of electricity after adding illusion coating and electric scale conversion coating in turn.
[0067] In the figure, 1. electric large scale complex shape target; 2. illusion coating of electric large scale complex shape target; 3. electric scale conversion coating; 4. equivalent electric small scale complex shape target; 5. illusion coating of equivalent electric small scale complex shape target; Hz represents the magnetic field intensity in z direction, unit: A / m. DETAILED DESCRIPTION
[0068] EMBODIMENT
[0069] An illusion design method of electric large scale complex shape target, which is suitable for electric middle scale complex shape target and electric large scale complex shape target, and the specific method comprises the following steps:
[0070] Step 1, calculating the dielectric constant ε3' and magnetic permeability μ3' of electric scale conversion coating
[0071] Taking electric large scale complex shape target as the research object, a layer of electric scale conversion coating is covered outside the electric large scale complex shape target, so that it has the same scattering mode as the equivalent electric small scale complex shape target with unchanged shape; thus, the spatial mapping of electric scale conversion is constructed. According to the form invariance of Maxwell equations, the dielectric constant ε3' and magnetic permeability μ3' of electric scale conversion coating are calculated.
[0072] At a distance a1 from the surface of electric large scale complex shape target, an electric scale conversion coating with size b, dielectric constant ε3' and magnetic permeability μ3' is covered, and the electric large scale complex shape target is covered with a layer of electric scale conversion coating to form an electric large scale complex shape target covered with electric scale conversion coating. The electric large scale complex shape target covered with electric scale conversion coating has the same electromagnetic scattering mode as the equivalent electric small scale complex shape target with size c0, dielectric constant ε1 and magnetic permeability μ1. The dielectric constant ε3' and magnetic permeability μ3' of electric scale conversion coating are calculated.
[0073] The specific process of calculating the dielectric constant ε3' and magnetic permeability μ3' of electric scale conversion coating is as follows:
[0074] As Figure 1As shown, the electrically large complex shape target 1 composed of uniform isotropic or anisotropic material with geometric size c1, dielectric constant ε1', and magnetic permeability μ1', covers the electric scale conversion coating 3 with size b, dielectric constant ε3', and magnetic permeability μ3' at a1 outside the electrically large complex shape target, so that the electrically large complex shape target 1 covered with the electric scale conversion coating 3 has the same electromagnetic scattering mode as the equivalent electrically small complex shape target 4; the illusion coating 5 is covered outside the equivalent electrically small complex shape target 4, so that the whole of the equivalent electrically small complex shape target 4 covered with the illusion coating 5 of the equivalent electrically small complex shape target has the same electromagnetic scattering mode as the illusion target; according to the electric size transformation, the illusion coating 2 of the electrically large complex shape target is covered outside the electrically large complex shape target 1, so that the electrically large complex shape target 1 produces an illusion.
[0075] According to the requirement of the electric size transformation, the virtual-actual space transformation is performed, i.e. the actual physical space a1 < r' < b is compressed to the virtual transformation space a0 < r < b, the point in the actual physical space is represented by (r', θ', φ'), the point in the virtual transformation space is represented by (r, θ, φ), and a linear function is used to construct the space mapping as follows:
[0076] θ' = θ (2)
[0077]
[0078]
[0079] In the formula (1), (2), and (3), a1(θ) is the inner boundary function of the conversion coating of the electrically large complex shape target in the actual physical space, b(θ) is the outer boundary function of the conversion coating of the electrically large complex shape target in the actual physical space, and a0(θ) is the boundary function of the equivalent electrically small complex shape target in the virtual transformation space.
[0080] According to the space mapping, the corresponding Jacobian matrix Λ is calculated as follows:
[0081]
[0082] In combination with the form invariance of the Maxwell equation set, the dielectric constant ε3' and the magnetic permeability μ3' of the electric scale conversion coating are calculated as follows:
[0083]
[0084]
[0085] In the formula (5) and (6), A is B is
[0086] Thus, the permittivity ε3' and permeability μ3' of the electric scale conversion coating are obtained.
[0087] For example, when the target is an electric mesoscale hat-shaped target, the conditions of the electric mesoscale hat-shaped target are: the hat mouth length and width are equal to λ0, the hat height is equal to 2λ0, the hat brim radius is equal to 1.5λ0, the permittivity ε1' is equal to 1, and the permeability μ1' is equal to 110. A plane wave with a wavelength of 3GHz is vertically incident on the electric mesoscale hat-shaped target, the wavelength of the plane wave in air is λ0, a spherical electric scale conversion coating with a radius of b = 4λ0 is covered at a distance of 2λ0 from the hat outer edge, and the permittivity ε3' and permeability μ3' of the electric scale conversion coating are calculated according to formula (5) (6) by using the calculation method of step 1:
[0088]
[0089]
[0090] Step 2, calculating the permittivity ε1 and permeability μ1 of the equivalent electric small scale complex shape target;
[0091] According to the virtual-actual space transformation of step 1, the electric scale transformation mapping between the electric large scale complex shape target and the equivalent electric small scale complex shape target is established, and the permittivity ε1 and permeability μ1 of the equivalent electric small scale complex shape target are calculated according to the form invariance of Maxwell's equations.
[0092] The specific process of calculating the permittivity ε1 and permeability μ1 of the equivalent electric small scale complex shape target is as follows:
[0093] Through the virtual-actual space transformation, the electric large scale complex shape target with a size of c1, a permittivity of ε1' and a permeability of μ1' has the same scattering mode as the equivalent electric small scale complex shape target with a size of c0, a permittivity of ε1 and a permeability of μ1 after covering the electric scale conversion coating, and the size of the equivalent electric small scale complex shape target is c1c0 times smaller than that of the electric large scale complex shape target:
[0094]
[0095] Correspondingly, the permittivity ε1 and permeability μ1 of the equivalent electric small scale complex shape target are
[0096]
[0097]
[0098] Thus, the permittivity ε1 and permeability μ1 of the equivalent electric small scale complex shape target are obtained.
[0099] For example, for the electrically mesoscale hat-shaped target given in step 1, according to equations (8) and (9), the equivalent electrically small-scale hat-shaped target permittivity and permeability are respectively...
[0100] Step 3: Calculate the dielectric constant ε2 and magnetic permeability μ2 of the illusory coating of the equivalent small-scale complex-shaped target.
[0101] In the virtual transformation space, an illusory coating is applied to the surface of an equivalent electrically small complex-shaped target, and the dielectric constant and permeability of the illusory coating of the equivalent electrically small complex-shaped target are calculated.
[0102] An illusion coating is applied to the outside of an equivalent small-scale complex-shaped target, so that the overall equivalent small-scale complex-shaped target after being covered with the illusion coating produces the same scattering mode as the illusion target. A plane wave of unit amplitude is perpendicularly incident on the equivalent small-scale complex-shaped target covered with the illusion coating. Based on the stealth and illusion conditions of the small-scale complex-shaped target, the dielectric constant ε2 and magnetic permeability μ2 of the illusion coating of the equivalent small-scale complex-shaped target are calculated.
[0103] The specific process for calculating the dielectric constant ε2 and magnetic permeability μ2 of the illusory coating of an equivalent small-scale complex-shaped target is as follows:
[0104] The first step is to establish a discrete dipole model of an equivalent small-scale complex-shaped target using a series of dipoles characterized by polarizability.
[0105] The equivalent small-scale complex shape target is discretized and simulated using N1 discrete cubic lattices, with each cubic lattice using a dielectric constant ε″. i The dipole is replaced by a polarizability α related to the dielectric constant. i Characterization:
[0106]
[0107] In equation (10), the constant terms are b1 = -1.8915316, b2 = 0.1648469, and b3 = -1.7700004, respectively. and These are the components of the incident wave vector and polarization vector in a rectangular coordinate system, respectively; k is the incident electromagnetic wave number; and d is the dipole spacing. For Clausius-Mosso polarization, Calculate using the following formula:
[0108]
[0109] In formula (11), i = 1, 2, … N1.
[0110] Second step, calculating the dielectric constant ε2 and the magnetic permeability μ2 of the illusion coating of the equivalent electric small-scale complex-shaped target
[0111] The illusion coating of the non-magnetic equivalent electric small-scale complex-shaped target is simulated by N2 discrete dipoles, the dielectric constant of the illusion coating is ε2, and the magnetic permeability μ2 = 1; the size of the illusion target of the non-magnetic equivalent electric small-scale complex-shaped target is a0, the dielectric constant is ε e , and the magnetic permeability is μ e = 1. Assuming that the equivalent electric small-scale complex-shaped target with the illusion coating is equal in size to the illusion target, the size is a0, then the number of dipoles satisfies N = N1 + N2. According to the stealth and illusion conditions of the equivalent electric small-scale complex-shaped target, the dielectric constant ε2 of the illusion coating of the equivalent electric small-scale complex-shaped target is obtained as follows:
[0112]
[0113] In formula (12), α2 is the polarizability of the illusion coating of the equivalent electric small-scale complex-shaped target, is the real part of .
[0114] Similarly, the magnetic permeability μ2 of the illusion coating of the equivalent electric small-scale complex-shaped target is obtained as follows:
[0115] μ2 = 1 (13)
[0116] Thus, the dielectric constant ε2 and the magnetic permeability μ2 of the illusion coating of the equivalent electric small-scale complex-shaped target are obtained.
[0117] For example, for the electrically medium-sized hat-shaped target given in step 1, when its equivalent electric small-scale hat-shaped target is added with an illusion coating, it has the same scattering mode as a non-magnetic spherical illusion target with a radius of 0.3 λ0 and a dielectric constant of 6ε0. According to formula (12) (13), the dielectric constant and the magnetic permeability of the illusion coating of the equivalent electric small-scale hat-shaped target are ε2 = 6.2 and μ2 = 1, respectively.
[0118] Step 4, calculating the dielectric constant ε2' and the magnetic permeability μ2' of the illusion coating of the electrically large-scale complex-shaped target.
[0119] According to the target electric size transformation in step 2 and the dielectric constant and the magnetic permeability of the illusion coating of the equivalent electric small-scale complex-shaped target in step 3, the dielectric constant and the magnetic permeability of the illusion coating of the electrically large-scale complex-shaped target are derived.
[0120] In the actual physical space, the illusion coating is covered outside the electrically large scale complex shape target, and the permittivity ε2' and the permeability μ2' of the illusion coating of the electrically large scale complex shape target are calculated according to the size relationship between the electrically large scale complex shape target and the equivalent electrically small scale complex shape target.
[0121] The specific process of calculating the permittivity ε2' and the permeability μ2' of the illusion coating of the electrically large scale complex shape target is as follows:
[0122] The size of the electrically large scale complex shape target is c1, and the illusion coating with the size a1, the permittivity ε2' and the permeability μ2' is covered outside the surface of the electrically large scale complex shape target, which has the same scattering mode as the illusion target with the size a0, the permittivity ε e and the permeability μ e According to the target electric size transformation formula (7) and the illusion condition formula (12) and formula (13), the permittivity ε2' and the permeability μ2' of the illusion coating of the electrically large scale complex shape target in the actual physical space are calculated as follows:
[0123]
[0124]
[0125] Thus, the permittivity ε2' and the permeability μ2' of the illusion coating of the electrically large scale complex shape target are obtained.
[0126] For example, for the electrically medium scale hat-shaped target given in step 1, according to formula (14) (15), the permittivity and the permeability of the illusion coating of the electrically medium scale hat-shaped target are respectively: ε2' = 6.210, μ2' = 110.
[0127] Step 5, the illusion coating and the electric scale conversion coating are covered on the electrically large scale complex shape target in sequence.
[0128] According to the permittivity and the permeability of the electric scale conversion coating and the illusion coating obtained in step 2 and step 4, the illusion coating and the electric scale conversion coating are covered on the surface of the electrically large scale complex shape target in sequence, so as to produce the illusion effect.
[0129] The size parameters b-a1 of the known electric scale conversion coating, b-a1 is the thickness, and the size parameters a0 of the equivalent electrically small scale complex shape target are substituted into formula (5) and formula (6), so as to obtain the permittivity ε3' and the permeability μ3' of the electric scale conversion coating.
[0130] Substituting the known dimensions c1, dielectric constant ε1′, and permeability μ1′ of the electrically large-scale complex-shaped target, and the dimension parameter c0 of the equivalent electrically small-scale complex-shaped target, into equations (7) and (8), we obtain the dielectric constant ε1 and permeability μ1 of the equivalent electrically small-scale complex-shaped target.
[0131] The equivalent small-scale complex-shaped target's dimensions c0, dielectric constant ε1, and permeability μ1=1 are given, along with the illusory target's dimensions a0 and dielectric constant ε. e Magnetic permeability μ e Substituting the discrete dipole numbers N, N1, and N2 into equations (10), (11), (12), and (13), we obtain the dielectric constant ε2 and permeability μ2 of the illusory coating of the equivalent electrically small-scale complex-shaped target. Substituting ε2 and μ2 into equations (14) and (15), we obtain the dielectric constant ε2′ and permeability μ2′ of the illusory coating of the electrically large-scale complex-shaped target.
[0132] An illusion target is formed by sequentially covering the surface of a target with a complex shape at a large electrical scale with an illusion coating and an electrical scale conversion coating. If the dielectric constant ε of the illusion target is... e and permeability μ e When both the number of elements in the atmosphere and the number of elements in the atmosphere are equal to 1, an invisibility effect can be achieved, creating an illusion.
[0133] Thus, the illusion effect of large-scale, complex-shaped targets is achieved.
[0134] For example, for the electric mesoscale hat-shaped target given in step 1, an illusion coating with a dielectric constant of ε2′ and a permeability of μ2′, and an electric scale conversion coating with a dielectric constant of ε3′ and a permeability of μ3′ are sequentially applied to the surface of the electric mesoscale hat-shaped target. After a plane wave with a wavelength of 3 GHz is incident perpendicularly on the electric mesoscale hat-shaped target covered with both the illusion coating and the electric scale conversion coating, the resulting cross-sectional diagram of the magnetic field distribution is shown below. Figure 2 As shown, the dielectric constant is ε e , with a permeability of μ e The cross-sectional effect diagram of the magnetic field distribution of the illusion target is as follows: Figure 3 As shown. Comparison Figure 2 and Figure 3 It is evident that the distribution of the scattering magnetic field of the hat-shaped target at the electrical mesoscale is the same as that of the spherical illusion after being covered with the illusion coating and the electrical scale conversion coating. This indicates that the illusion coating and the electrical scale conversion coating designed in this invention can enable targets with complex shapes at electrical large or even electrical mesoscale to achieve an illusion effect.
Claims
1. A method for designing illusions around electrically large-scale complex-shaped targets, characterized in that, Includes the following steps: Step 1: Calculate the dielectric constant ε′3 and magnetic permeability μ′3 of the electrical scale conversion coating: Taking electrically large-scale complex-shaped targets as the research object, an electric scale transformation coating is applied to the outside of the electrically large-scale complex-shaped targets to make them have the same scattering mode as the equivalent electrically small-scale complex-shaped targets with unchanged shape; thus, a spatial mapping of electric scale transformation is constructed; based on the formal invariance of Maxwell's equations, the permittivity ε′3 and permeability μ′3 of the electric scale transformation coating are calculated. At a distance a1 from the surface of an electrically large-scale complex-shaped target, an electrically large-scale conversion coating with size b, dielectric constant ε′3, and permeability μ′3 is applied. After the electrically large-scale complex-shaped target is covered with an electrically large-scale complex-shaped target, an electrically large-scale complex-shaped target covered with an electrically large-scale conversion coating is formed. The electromagnetic scattering mode of the electrically large-scale complex-shaped target covered with the electrically large-scale conversion coating is the same as that of the equivalent electrically small-scale complex-shaped target with size c0, dielectric constant ε1, and permeability μ1. The dielectric constant ε′3 and permeability μ′3 of the electrically large-scale conversion coating are calculated. Step 2, determine the dielectric constant ε1 and permeability μ1 of the equivalent small-scale complex-shaped target: Establish an electric scale transformation mapping between electrically large-scale complex-shaped targets and equivalent electrically small-scale complex-shaped targets. Based on the formal invariance of Maxwell's equations, calculate the dielectric constant ε1 and magnetic permeability μ1 of the equivalent electrically small-scale complex-shaped targets. Step 3, determine the dielectric constant ε2 and permeability μ2 of the illusory coating of the equivalent small-scale complex-shaped target: In the virtual transformation space, an illusory coating is applied to the surface of an equivalent small-scale complex-shaped target, and the dielectric constant and permeability of the illusory coating of the equivalent small-scale complex-shaped target are calculated. An illusion coating is applied to the outside of an equivalent small-scale complex-shaped target, so that the overall equivalent small-scale complex-shaped target after being covered with the illusion coating produces the same scattering mode as the illusion target. A plane wave of unit amplitude is perpendicularly incident on the equivalent small-scale complex-shaped target covered with the illusion coating. Based on the stealth and illusion conditions of the small-scale complex-shaped target, the dielectric constant ε2 and magnetic permeability μ2 of the illusion coating of the equivalent small-scale complex-shaped target are calculated. Step 4: Calculate the dielectric constant ε′2 and magnetic permeability μ′2 of the illusory coating of the electrically large-scale complex-shaped target: Based on the target electrical size transformation in step 2 and the dielectric constant and permeability of the illusory coating of the equivalent small-scale complex-shaped target in step 3, the dielectric constant and permeability of the illusory coating of the large-scale complex-shaped target are derived. In actual physical space, an illusion coating is applied to the outside of an electrically large-scale complex-shaped target. Based on the size relationship between the electrically large-scale complex-shaped target and the equivalent electrically small-scale complex-shaped target, the dielectric constant ε′2 and magnetic permeability μ′2 of the illusion coating of the electrically large-scale complex-shaped target are calculated. Step 5: Apply the illusion coating and the electrical scale conversion coating sequentially to the electrically large-scale complex-shaped target: Based on the dielectric constant and magnetic permeability of the electrical scale conversion coating and the illusion coating obtained in steps 2 and 4, the illusion coating and the electrical scale conversion coating are sequentially applied to the surface of the electrically large-scale complex-shaped target to produce an illusion effect; thus, the illusion effect of the electrically large-scale complex-shaped target is achieved.
2. The method for designing illusions of electrically large-scale complex-shaped targets according to claim 1, characterized in that, The process for determining the dielectric constant ε′3 and magnetic permeability μ′3 of the electrical scale conversion coating is as follows: An electrically large-scale complex-shaped target, composed of homogeneous isotropic or anisotropic materials, has geometric dimensions c1, dielectric constant ε′1, and magnetic permeability μ′1. An electrically large-scale conversion coating with dimensions b, dielectric constant ε′3, and magnetic permeability μ′3 is covered at a1 on the outside of the electrically large-scale complex-shaped target. According to the electrical dimension transformation requirements, a virtual-to-real space transformation is performed, that is, the actual physical space a1 < r′ < b is compressed into the virtual transformation space a0 < r < b. The points in the actual physical space are represented by... Points in virtual transformation space are represented by The space mapping is constructed using a linear function as follows: θ′=θ (2) In equations (1), (2), and (3), a1(θ) is the inner boundary function of the transformation coating of the electrically large-scale complex-shaped target in the actual physical space, b(θ) is the outer boundary function of the transformation coating of the electrically large-scale complex-shaped target in the actual physical space, and a0(θ) is the boundary function of the equivalent electrically small-scale complex-shaped target in the virtual transformation space. Based on the spatial mapping, the corresponding Jacobian matrix Λ is calculated as follows: Based on the formal invariance of Maxwell's equations, the dielectric constant ε′3 and magnetic permeability μ′3 of the electrical scale conversion cladding are calculated as follows: In equations (5) and (6), A is B is 3. The method for designing illusions of electrically large-scale complex-shaped targets according to claim 1, characterized in that, The process for obtaining the dielectric constant ε1 and permeability μ1 of the equivalent small-scale complex-shaped target is as follows: Through virtual-to-real space transformation, an electrically large-scale complex-shaped target with size c1, dielectric constant ε′1, and permeability μ′1, after being covered with an electrically scale transformation coating, exhibits the same scattering mode as an equivalent electrically small-scale complex-shaped target with size c0, dielectric constant ε1, and permeability μ1. The size of the equivalent electrically small-scale complex-shaped target is reduced by a factor of c1 / c0 compared to the electrically large-scale complex-shaped target. Correspondingly, the dielectric constant ε1 and magnetic permeability μ1 of the equivalent small-scale complex-shaped target are respectively 4. The method for designing illusions of electrically large-scale complex-shaped targets according to claim 3, characterized in that, The process for determining the dielectric constant ε2 and magnetic permeability μ2 of the illusory coating of an equivalent small-scale complex-shaped target is as follows: The first step is to establish a discrete dipole model of an equivalent small-scale complex-shaped target using a series of dipoles characterized by polarizability. The equivalent small-scale complex-shaped target is discretized and simulated using N1 discrete cubic lattices, with each cubic lattice using a dielectric constant ε″. i The dipole is replaced by a polarizability α related to the dielectric constant. i Characterization: In equation (10), the constant terms are b1 = -1.8915316, b2 = 0.1648469, and b3 = -1.7700004, respectively. and These are the components of the incident wave vector and polarization vector in a Cartesian coordinate system, respectively; k is the incident electromagnetic wave number; and d is the dipole spacing. For Clausius-Mosso polarization, Calculate using the following formula: In equation (11), i = 1, 2, ... N1; The second step involves calculating the dielectric constant ε2 and magnetic permeability μ2 of the illusory coating of the equivalent small-scale complex-shaped target. The illusion coating of a nonmagnetic equivalent small-scale complex-shaped target is simulated using N2 discrete dipoles. The dielectric constant of the illusion coating is ε2, and the permeability is μ2 = 1. The size of the illusion target of the nonmagnetic equivalent small-scale complex-shaped target is a0, and the dielectric constant is ε. e The permeability is μ e =1; Assuming the equivalent small-scale complex-shaped target, after being coated with an illusion layer, is the same size as the illusion target, with dimensions a0, then the number of dipoles satisfies N = N1 + N2; Based on the stealth and illusion conditions of the equivalent small-scale complex-shaped target, the dielectric constant ε2 of the illusion coating of the equivalent small-scale complex-shaped target is obtained as follows: In equation (12), α2 is the polarizability of the equivalent small-scale complex-shaped target and its illusory coating. for The real part; Based on the stealth and illusion conditions of an equivalent small-scale complex-shaped target, the magnetic permeability μ2 of the illusion coating of the equivalent small-scale complex-shaped target is obtained as follows: μ2=1 (13).
5. The method for designing illusions of electrically large-scale complex-shaped targets according to claim 4, characterized in that, The process for calculating the dielectric constant ε′2 and magnetic permeability μ′2 of the illusory coating of electrically large-scale complex-shaped targets is as follows: Outside the surface of a target with an electrically large-scale complex shape of size c1, an illusion coating with size a1, dielectric constant ε′2, and magnetic permeability μ′2 is applied, along with a coating with size a0 and dielectric constant ε′2. e , with a permeability of μ e The scattering pattern of the illusory target is the same; according to the target electric size transformation equation (7) and the illusion conditions equations (12) and (13), the dielectric constant ε′2 and magnetic permeability μ′2 of the illusory coating of the electrically large-scale complex-shaped target in the actual physical space are calculated as follows:
6. The method for designing illusions of electrically large-scale complex-shaped targets according to claim 1, characterized in that, Step 5 further includes: An illusion target is formed by sequentially covering the surface of the electrically large-scale complex-shaped target with an illusion coating and an electrical-scale conversion coating. If the dielectric constant ε of the illusion target... e and permeability μ e When the value is the same as that of air, i.e., equal to 1, the stealth effect of large-scale complex-shaped targets can be achieved.