KR101509301B1 - Invisiblization Method - Google Patents

Abstract

A transparency method is disclosed. A method of transparency according to an exemplary embodiment of the present invention is a method for inspecting a shielding object to cover a surface of an object to be shielded in bipolar cylindrical coordinates determined by coordinate axes of (?,?, Z; a) Determining σ _1, which is a σ value for half the length (a) of the object, determining the meta materials for shielding the shielding object, and then using the determined permittivity of the meta material, σ ₂ A condition in which the Maxwell's equations are covariant in a general relativity is defined by defining a time-space matrix tensor such that there is no space-time in the space in the range of? ₁ and? ₂ in order to determine the permittivity and the permeability, Expressed as a function of the matrix tensor, and the above-mentioned? ₂ is determined from the expression thus expressed.

Description

{Invisiblization Method}

The present invention relates to a transparency method, and more particularly to a transparency method using a meta material.

Recent work on meta-materials has enabled microscopic and macroscopic control of electromagnetic fields [Phys.Rev.Lett. 85, 3966 (2000); Science 312,1777 (2006); Science 312, 1780 (2006)). A metamaterial is an artificial method that can not be obtained in a normal natural state. An unusual point of a metamaterial is that it has a negative refractive index, so that the light in the metamaterial warps in a direction opposite to the direction .

Using these metamaterials, it was possible to adjust the direction of the electromagnetic field freely irrespective of the source of the electromagnetic field, and to guide the object as if there were no objects [Science 312, 1777 (2006); Science 312, 1780 (2006)). This can potentially be applied to electromagnetic shielding from strong electromagnetic field pulses (EMP) or directional electromagnetic energy.

The present invention provides a general method for electromagnetic wave radiation or shielding of electromagnetic waves of arbitrary intensity, for parabolic objects, using a general transformation method based on general theory of relativity. The present invention can also be applied to an object to be shielded having a shape of an anode cylindrical coordinate system such as a wing of a flight body.

In order to solve such a problem, a method of transparency according to an exemplary embodiment of the present invention is a method of interpolating a surface of an object to be shielded in bipolar cylindrical coordinates determined by coordinate axes of (?,?, Z; a) and determining a σ value, σ ₁ for the half (a) the length of the shielding object so as to cover the step of determining the meta-material for shielding the shielded object, and by the dielectric constant of the determined meta-material, In order to determine σ _2, which is the σ value for the thickness of the meta-materials, a time-space matrix tensor is defined such that space-time does not exist in the space within the above-mentioned σ ₁ and σ ₂ ranges so that the Maxwell equations in the general relativity are covariant The step of expressing the permittivity and the permeability as a function of the space-time matrix tensor in the state where the condition is made, and determining the σ ₂ from the expression And a transparency method comprising:

In this case, the value σ ₂ is the dielectric constant of the metamaterial ^{_{ε σ σ = (σ 2 -σ}} 1) / (σ 2 -π), ε τ τ = (σ 2 -π) / (σ 2 -σ 1) _{^{, ε z z = [(σ}} 2 -π) (cosσ-coshτ) 2] / [(σ 2 -σ 1) (cos [(σ 2 -π) (σ-σ 1) / (σ 2 -σ 1 ) + π] -coshτ) ² ].

In order to solve such a problem, the transparency method according to another exemplary embodiment of the present invention is characterized in that in the bipolar cylindrical coordinates determined by the coordinate axes of (?,?, Z; a), the surface of the object to be shielded corresponding to the stage, and σ ₂ values determined for determining a σ value σ ₂ of the stage and, the dimensions of the metamaterial to determine the σ value, σ ₁ for the length of a half (a) of the shielding object to cover In order to select the meta-materials, a condition in which a space-time matrix is defined such that space-time does not exist in the space within the range of? ₁ and? ₂ is defined so that Maxwell's equations in the general relativity are covariant, As a function of the space-time matrix tensor, and selecting the meta material satisfying the dielectric constant and the permeability expressed in this manner.

At this time, the meta-material corresponding to the determined value of σ ₂ are the dielectric constant ^{_{ε σ σ = (σ 2 -σ}} 1) / (σ 2 -π), ε τ τ = (σ 2 -π) / (σ 2 -σ 1 _{^{), ε z z = [(}} σ 2 -π) (cosσ-coshτ) 2] / [(σ 2 -σ 1) (cos [(σ 2 -π) (σ-σ 1) / (σ 2 -σ ₁ ) +?] -Coshτ) ² ].

According to the present invention, it is possible not only to achieve transparency by cloaking an arbitrary object with a meta-material, but also to prevent it from being caught by an external radar or the like.

BRIEF DESCRIPTION OF DRAWINGS FIG. 1 is a diagram showing the relationship between each axis of bipolar cylindrical coordinates and a Cartesian coordinate system. FIG.
FIG. 2 is a diagram showing a result of calculating a dielectric constant or a permeability using a resultant expression of the present invention. FIG.

BRIEF DESCRIPTION OF THE DRAWINGS The above and other features and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings, It will be possible. The present invention is not limited to the following embodiments and may be embodied in other forms. The embodiments disclosed herein are provided so that the disclosure may be more complete and that those skilled in the art will be able to convey the spirit and scope of the present invention. In the drawings, the thickness of each device or film (layer) and regions is exaggerated for clarity of the present invention, and each device may have various additional devices not described herein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

Electromagnetic wave propagating in the in the basic concept of the present invention, space-time (curved spacetime) bent (propagation) is a non-homogeneous inhomogeneous valid pair anisotropic medium propagation of light in a (inhomogeneous effective bi-anisotropic medium) which parameters are described as space-time metrics Can be described [Phys. Rev. 118, 1396 (1960)]. Accordingly, specific conditions for radiation shielding and cloaking can be found.

(A)For electromagnetic waves, time and space of vacuum Heterogeneity Effective pair anisotropic medium ( inhomogeneous effective bi - anisotropic medium ) Equivalence of

To determine the effect of gravity or warped space time on the general physics system, we replace all Lorentz tensors described by special relativity equations in Minkowski space and time with moving objects like tensors under general coordinate transformations Rev. 130, 800 (1963)]. Also, all derivative functions can be transformed into covariant derivatives (covariant derivatives) ) substituted and also replacing the Minkowski metric tensor in metric tensor g _ab η _μν. here, the Minkowski metric tensor _ab η is expressed by the following equation (1).

The equation is then generally covariant. The general covariance Maxwell's equation is expressed by the following equation (2).

In the implantation, g is a determinant of the metric tensor g [ _mu ] _v .

Further, the covariance tensor F _? ^V of the contravariant tensor F? _N satisfies the following equation (3).

On the other hand, in the equation (3), the electromagnetic field tensor F? _V is expressed by the following equation (4).

In addition, the new ^transverse tensor H? ^V is defined by the following equation (5).

In this equation, the ^transverse tensor H? ^V can be expressed by the following Equation (6).

From Equations (2) to (6), the following Equations (7) and (8) can be obtained.

In Equation (7) and Equation (8), [ijk] is an anti-symmetric permutation symbol with [xyz] = 1. That is, when ijk is exchanged evenly in [ijk], it gives a value of 1, and when exchanged odd times, it gives a value of -1.

From the equations (7) and (8), the following equations (9) and (10) can be obtained.

And

및

고, 벡터

는 각각 다음의 수학식 11 및 수학식 12로 주어진다.In equations (9) and (10), the symmetric tensor

And

High, vector

Are given by the following equations (11) and (12), respectively.

From this, the warped spacetime of a vacuum can be viewed as an effective bipyropic medium, where the electric permittivity tensor and the magnetic permeability tensor can be described as space-time metrics.

Conversely, a dielectric medium can be described by a coordinate space transformed space of vacuum or a coordinate system.

On the other hand, the transverse metric tensor is transformed as shown in Equation (13) below, and the covariance matrix tensor is transformed as shown in Equation (14) below.

Suppose that the physical medium is described by a spatial coordinate system x _i having a spatial metric y _ij and a determinant y. The spatial metric y _ij should be different from the spatial part of the effective spatial metric g _{alpha beta} generated by the physical medium. Since? _Ij describes the actual space-time coordinate system, while the spatial metric g? _Beta describes the effective geometry corresponding to the original bivariate anisotropy medium rather than describing the actual space-time.

Taking into account the spatial covariance of divergence in the Maxwell equation, the contitutive parameters are described by the following mathematical equations (15) and (16).

(B) Radiation shielding  And Cloaking ( cloaking ) Design of devices

Suppose that the space transformed from the initial vacuum space-time does not cover the entire physical space for the entire medium, and that the medium excludes the electromagnetic field in a particular area but is smoothly fitted outside the device. Thus, the electromagnetic radiation is guided avoiding the sparse area. As a result, the medium clogs the region so that no object in the region appears outside. The cloaking device should include anisotropic media. This is because the problem of reverse scattering of waves in isotropic media has a single solution. The implementation of the cloaking device or radiation shielding employs the coordinate transformation of the hole.

In the following description, a bipolar cylindrical cloak of an anode cylindrical coordinate is designed by using the equivalence of the inhomogeneous effective bipyotropic medium and the space time of vacuum for the above-mentioned electromagnetic wave.

First, the coordinate system x, y, z of the right handed Cartesian coordinate system is in the relationship of the following equation (17): curvilinear coordinate x ¹ , y ¹ , z ¹ Let's assume.

Then, the metric is given by the following equation (18).

On the other hand, the material we want to shield occupies a space in the range represented by the following equation (19) of the curved coordinate system x ¹ , y ¹ , z ¹ .

In order to shield the material represented by the above equation (19), a meta material is attached so as to have the following range of the following expression (20).

A coordinate system to which a prime is attached is used for a space-time coordinate system in a vacuum, and a physical system is defined as the following equation (21).

Then, the effective geometry corresponding to the first bi-anisotropic medium is defined by the following equations (22) and (23).

In the above equation (23),? = Det (? _Ij ) and? ^Kk = 1 /? _Kk .

On the other hand, a conversion formula for calculating the dielectric constant tensor and the permeability tensor can be obtained from the above formula (17). Considering the form of covariant forms of divergences in the Maxwell equations, the following equations can be obtained.

In the above equations, [ijk] is an anti-symmetric permutation symbol with [xyz] = 1. That is, when ijk is exchanged evenly in [ijk], it gives a value of 1, and when exchanged odd times, it gives a value of -1.

g _μλ g ^λν = δ _μ ^ν , the above dielectric constant tensor and permeability tensor can be briefly expressed by the following equation (26).

The negative sign in the above equation indicates that the medium has a negative refractive index.

The bipolar cylindrical coordinates shown in Fig. 1 have axes of (?,?, Z; a), which is a Cartesian coordinate system with (x, y, z) .

In the above equation (27), a value of a (> 0) has a range of 0≤σ <2π, -∞ <τ <∞ and -∞ <z <∞, to be.

Then, the metric is expressed by the following equation (28).

Referring to Fig. 1, the shield and the object, and places the characters on _{σ 1 <σ <2π-σ} 1 which, the meta-material having a refractive index of the negative _{{σ 2 ≤σ≤σ 1} ∪ {} 2π-σ 1 ≤σ ₂ &amp; le; ₂ &amp; circ &amp; ₂ }. As a result, the map is defined by the following equation (29).

In the above equation (29), the coordinate system to which the prime is attached is the coordinate system in vacuum, and the coordinate system to which the prime is not attached represents the actual physical system.

From the above equation (29), the following equation (30) can be obtained.

Then, ε ^ij = μ ^ij , and these values are expressed by the following equation (31).

From the equation (31), the mixed tensor is expressed by the following equation (32).

If the prime coordinate system of Equation (29) is removed, Equation (32) can be expressed as Equation (33).

From the above equation (33), it can be seen that ε ^σ _σ and ε ^τ _τ are constants, and ε ^z _z is as shown in FIG. Equation (33) represents the relationship between the refractive index of the corresponding meta material and the thickness of the meta material when the size of the object to be shielded is determined.

More specifically, the relationship between the refractive indices of the meta-material filling the space between? ₁ and? ₂ when the shielding object is disposed within the space defined by a and? ₁ in FIG. 1 is shown. Therefore, when the meta materials for shielding are determined, the value of the refractive index tensor (? ^I _j ) of these materials is a fixed value, so that the value of? ₂ , which is the thickness of the meta material, can be determined. Conversely, If the value of? ₂ is determined, the value of the refractive index tensor (? ^I _j ) of the meta-materials for shielding can be determined. Fig. 2 is a calculation result of ε ^z _z value by substituting σ ₁ = 0.75π, σ ₂ = 0.5π, and a = 0.3m.

That is, the transparency method according to an exemplary embodiment of the present invention is characterized in that in the bipolar cylindrical coordinates determined by the coordinate axes of (?,?, Z; a), in order to cover the surface of the object to be shielded after determining the σ value, σ ₁ for the half (a) the length of the shielded object, and determining a meta-material for shielding the shielded object, by using the refractive index of the determined meta-material, σ a value for the thickness of the metamaterial ₂ &lt; / RTI &gt;

In this case, the value σ ₂ is the dielectric constant of the metamaterial ^{_{ε σ σ = (σ 2 -σ}} 1) / (σ 2 -π), ε τ τ = (σ 2 -π) / (σ 2 -σ 1) _{^{, ε z z = [(σ}} 2 -π) (cosσ-coshτ) 2] / [(σ 2 -σ 1) (cos [(σ 2 -π) (σ-σ 1) / (σ 2 -σ 1 ) + π] -coshτ) ² ].

A method of transparency according to another exemplary embodiment of the present invention is a method of shielding an object to be shielded in order to cover a surface of an object to be shielded in bipolar cylindrical coordinates determined by coordinate axes of (?,?, Z; ₁ &quot;, which is the sigma value for the half value (a) of the length of the meta material, determines the sigma value ₂ for the thickness of the meta materials, and then selects the meta materials corresponding to the determined sigma ₂ value.

At this time, the meta-material corresponding to the determined value of σ ₂ are the dielectric constant ^{_{ε σ σ = (σ 2 -σ}} 1) / (σ 2 -π), ε τ τ = (σ 2 -π) / (σ 2 -σ 1 _{^{), ε z z = [(}} σ 2 -π) (cosσ-coshτ) 2] / [(σ 2 -σ 1) (cos [(σ 2 -π) (σ-σ 1) / (σ 2 -σ ₁ ) +?] -Coshτ) ² ].

According to the present invention, it is possible not only to realize transparency by cloaking an arbitrary object with a meta-material but also to prevent it from being caught by an external radar or the like.

While the present invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (4)

(σ, τ, z; a) the positive cylindrical coordinate system (bipolar cylindrical coordinates) is determined by the coordinate axes in order to cover the surface of the shielding object σ a value for the length of a half (a) of the shielding object σ ₁ ;
Determining meta-materials for shielding the shielding object; And
In order to determine σ _2, which is the σ value of the thickness of the meta-materials, using the permittivity of the determined meta-material, a space-time matrix tensor is defined such that space-time does not exist in the space within the range of σ ₁ and σ _2, And expressing the permittivity and the permeability as a function of the space-time matrix tensor with the condition that the Maxwell's equations are covariant, and determining the σ ₂ from the expressions thus expressed. The method according to claim 1,
The value of &lt; ₂ &gt;
The permittivity ε ^σ _σ = (σ ₂ -σ ₁ ) / (σ ₂ -π), ε ^τ _τ = (σ ₂ -π) / (σ ₂ -σ ₁ ) and ∈ ^z _z = _{2 -π) (cosσ-coshτ)} 2] / [(σ 2 -σ 1) (cos [(σ 2 -π) (σ-σ 1) / (σ 2 -σ 1) + π] -coshτ) 2 Is satisfied. &Lt; / RTI &gt; (σ, τ, z; a) the positive cylindrical coordinate system (bipolar cylindrical coordinates) is determined by the coordinate axes in order to cover the surface of the shielding object σ a value for the length of a half (a) of the shielding object σ ₁ ;
Determining σ _2, which is a σ value for the thickness of the metamaterials; And
In order to select the meta-materials corresponding to the determined σ ₂ values, a condition in which the Maxwell's equations are covariant in a general relativity is defined by defining a time-space matrix tensor such that space-time does not exist in the space in the range of σ ₁ and σ ₂ And expressing the permittivity and the permeability as a function of the space-time matrix tensor, and selecting the meta material satisfying the permittivity and the permeability expressed in this manner. The method of claim 3,
The meta-materials corresponding to the determined sigma ₂ value,
The dielectric constant ^{_{ε σ σ = (σ 2 -σ}} 1) / (σ 2 -π), ε τ τ = (σ 2 -π) / (σ 2 -σ 1), ε z z = [(σ 2 -π) ^{(cosσ-coshτ) 2] /} [(σ 2 -σ 1) (cos [(σ 2 -π) (σ-σ 1) / (σ 2 -σ 1) + π] -coshτ) so as to satisfy the ^2] . &Lt; / RTI &gt;

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