Abstract

A multi-physics null medium that performs as a perfect endoscope for both electromagnetic and acoustic waves is designed by transformation optics, which opens a new way to control electromagnetic and acoustic waves simultaneously. Surface transformation multi-physics, which is a novel graphical method to design multi-physics devices, is proposed based on the directional projecting feature of a multi-physics null medium. Many multi-physics devices, including beam shifters, scattering reduction, imaging devices and beam steering devices, for both electromagnetic and acoustic waves can be simply designed in a surface-corresponding manner. All devices designed by surface transformation multi-physics only need one homogeneous anisotropic medium (null medium) to realize, which can be approximately implemented by a brass plate array without any artificial sub-wavelength structures. Numerical simulations are given to verify the performances of the designed multi-physics devices made of brass plate array.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Since the theory of transformation optics was proposed in 2006 [1,2], it has been successfully applied to manipulate various physical fields including electromagnetic fields [35], acoustic fields [6,7], thermal fields [811], water waves [12], and magnetostatics [13,14]. These coordinate-transformation-based methods are based on the formality-invariance of physical equations for various physical phenomena (e.g. fields, waves, fluxes) under coordinate transformations [15,16]. Meta-materials with artificial subwavelength units can provide unique properties that cannot be found in natural materials, which have been widely applied to realize novel devices designed by coordinate-transformation-based methods [17,18].

In recent years, “transformation multi-physics”, i.e. controlling more than one physical wave/field by a single device simultaneously, has become an important branch of transformation optics and meta-materials [1928]. For example, bi-functional cloak for both DC electric field and thermal field has been theoretically designed and experimentally demonstrated by bi-functional meta-materials [1924]. However, limited by the current bi-functional meta-materials, most studies on bi-functional devices with some coordinate-transformation-based methods are mainly focused on tailoring DC electric field and thermal field [1928]. Although there are some studies on bi-functional meta-materials for other kinds of physical waves/fields [2934], it still lacks some general theory and systematical studies on controlling electromagnetic waves and acoustic waves simultaneously by a single device. In this study, a general designing and realization method, “surface transformation multi-physics”, is proposed to tailor both electromagnetic waves and acoustic waves simultaneously in a graphical way with some naturally available materials. Surface transformation multi-physics can be derived from coordinate-transformation-based methods. In previous studies, we have introduced optical surface transformation and acoustic surface transformation for EM waves [35] and acoustic waves [36] separately. Optic-null medium and acoustic-null medium are essential materials to realize devices designed by optical surface transformation and acoustic surface transformation, respectively. Transmission metallic gratings used for extraordinary optical transmission (EOT) can be treated as a reduced null-medium for both EM waves and acoustic waves [3744], which pave the way for the surface transformation multi-physics method.

2. Theoretical method

The transformed material parameters in transformation optics and transformation acoustics can be summarized by [1,6]:

$$\left\{ \begin{array}{l} \varepsilon ' = \frac{{J\varepsilon {J^T}}}{{\det (J)}}\\ \mu ' = \frac{{J\mu {J^T}}}{{\det (J)}} \end{array} \right.,\ \left\{ \begin{array}{l} \rho {'^{ - 1}} = \frac{{J{\rho ^{ - 1}}{J^T}}}{{\det (J)}}\\ \kappa ' = \det (J)\kappa \end{array} \right..$$
Here ɛ, μ, ρ, к are permittivity, permeability, mass density and modulus of a medium in the reference space. Quantities with superscript prime are corresponding physical quantities in the real space. J=∂(x’, y’, z’)/∂(x, y, z) is Jacobian matrix whose determinant is det(J). Next, we will introduce the key element ‘null medium’ in our surface transformation multi-physics method by applying an extremely spatial compression transformation. As shown in Fig. 1, the yellow region between two surfaces of arbitrary shapes S1 and S2 in the real space is greatly compressed into an extremely thin strip of thickness Δ in the reference space. If Δ→0, the volume between two surfaces S1 and S2 in the real space is reduced into a surface in the reference space. That is the reason why the medium between two surfaces S1 and S2 in the real space is referred to as ‘null medium’ (its corresponding region in the reference space is a surface but not an area/volume [35,36]). Assuming the reference space is air, the required material parameters of the null medium can be calculated by dividing the yellow regions in the real space and in the reference space into many small trapezoid regions of height hi by inserting infinite parallel lines (parallel to the x’ axis indicated by the dashed blue lines in Figs. 1(a) and 1(b)). The curved surfaces S1 and S2 are divided into many small elements ΔS1i and ΔS2i. When hi is small enough, the elements on curved surfaces ΔS1i and ΔS2i can be treated as planes. We can use the following coordinate transformation to relate each trapezoid region in the real space (see Fig. 1(c)) with the corresponding thin trapezoid in the reference space (see Fig. 1(d)):
$$x^{\prime} = \left\{ {\begin{array}{{c}} {{d_1}/({\Delta /2} )x,x^{\prime} \in [0,{d_1}]}\\ {\tan (\pi - {\alpha_1})(x - \frac{\Delta }{2})/\tan (\pi - {\theta_1}) + {d_1},x^{\prime} \in [{d_1},{d_1} + {h_i}/\tan (\pi - {\theta_1})]}\\ {{d_2}/({\Delta /2} )x,x^{\prime} \in [ - {d_2},0)}\\ {\tan {\alpha_2}(x + \frac{\Delta }{2})/\tan {\theta_2} - {d_2},x^{\prime} \in [ - {d_2} - {h_i}/\tan {\theta_2}, - {d_2}]}\\ {x,else} \end{array}} \right.;y^{\prime} = y;z^{\prime} = z.$$

 figure: Fig. 1.

Fig. 1. The coordinate transformation relation between the real space (a) and the reference space (b). The yellow region between surfaces S1 and S2 of arbitrarily shapes is compressed into a thin yellow slab of thickness Δ in the reference space. The yellow regions in the real space and in the reference space are divided into many small trapezoid regions of height hi. Representative small trapezoid regions in the real space (c) and in the reference space (d).

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With the help of material parameter relations given by Eq. (1), we can calculate the required materials for coordinate transformation in Eq. (2):

$$\frac{{\varepsilon '}}{{{\varepsilon _0}}} = \frac{{\mu '}}{{{\mu _0}}} = \frac{{{\rho _0}}}{{\rho '}} = \left\{ {\begin{array}{{c}} {diag(2{d_1}/\Delta ,\Delta /2{d_1},\Delta /2{d_1}),x' \in [0,{d_1}]}\\ {\begin{array}{{c}} diag(\tan (\pi - {\alpha _1})/\tan (\pi - {\theta _1}),\tan (\pi - {\theta _1})/\tan (\pi - {\alpha _1}),\tan (\pi - {\theta _1})/\tan (\pi - {\alpha _1})),\\ x' \in [{d_1},{d_1} + {h_i}/\tan (\pi - {\theta _1})]\end{array}}\\ \begin{array}{l} diag(2{d_2}/\Delta ,\Delta /2{d_2},\Delta /2{d_2}),x' \in [ - {d_2},0)\\ diag(\tan {\alpha _2}/\tan {\theta _2},\tan {\theta _2}/\tan {\alpha _2},\tan {\theta _2}/\tan {\alpha _2}),x' \in [ - {d_2} - {h_i}/\tan {\theta _2}, - {d_2}]\\ 1,esle \end{array} \end{array}} \right..$$
$$ \kappa '/{\kappa _0} = \left\{ {\begin{array}{*{20}{c}} {2{d_1}/\Delta ,x' \in [0,{d_1}]}\\ {\tan (\pi - {\alpha _1})/\tan (\pi - {\theta _1}),x' \in [{d_1},{d_1} + {h_i}/\tan (\pi - {\theta _1})]}\\ \begin{array}{l} 2{d_2}/\Delta ,x' \in [ - {d_2},0)\\ \tan {\alpha _2}/\tan {\theta _2},x' \in [ - {d_2} - {h_i}/\tan {\theta _2}, - {d_2}]\\ 1,esle \end{array} \end{array}} \right..$$
θ1, θ2, d1 and d2 can take arbitrary values, which are related with trapezoid shapes formed by surfaces S1 and S2. If α1→π/2, α2→π/2 and Δ→0, the small trapezoid region in the reference space will be reduced to a small surface element. In this case, the medium in the trapezoid region of the real space is the null medium, which can be obtained by taking α1→π/2, α2→π/2 and Δ→0 in Eqs. (3) and (4):
$$\frac{{\varepsilon '}}{{{\varepsilon _0}}} = \frac{{\mu '}}{{{\mu _0}}} = \frac{{{\rho _0}}}{{\rho '}}\mathop \to \limits^{\scriptstyle{\alpha _1} \to \pi /2\atop {\scriptstyle{\alpha _2} \to \pi /2\atop \scriptstyle{\Delta } \to 0}} \left\{ {\begin{array}{c} {diag(\infty ,0,0), - {d_1} \le x' \le {d_2}}\\ {1,else} \end{array}} \right..$$
$$\frac{{\kappa '}}{{{\kappa _0}}}\mathop \to \limits^{\scriptstyle{\alpha _1} \to \pi /2\atop {\scriptstyle{\alpha _2} \to \pi /2\atop \scriptstyle{\Delta } \to 0}} \left\{ {\begin{array}{c} {\infty , - {d_1} \le x' \le {d_2}}\\ {1,else} \end{array}} \right..$$
When each small trapezoid region (see Fig. 1(c)) in the real space is filled with the null medium given by Eqs. (5) and (6), the corresponding region in the reference space is a small surface (α1→π/2, α2→π/2 and Δ→0 in Fig. 1(d)). This means that small plane elements ΔS1i and ΔS2i are equivalent surfaces for both electromagnetic wave and acoustic wave when they are linked by the multi-physics null medium given by Eqs. (5) and (6). We can summarize the null medium in the reference space given by Eqs. (5) and (6) as:
$$\left\{ \begin{array}{l} \varepsilon^{\prime} = \mu^{\prime} = diag(\infty ,0,0)\\ \rho^{\prime} = diag(0,\infty ,\infty )\\ \kappa^{\prime} = \infty \end{array} \right., - {d_1} \le x^{\prime} \le {d_2}.$$
From Eq. (7), we can see the permittivity and permeability of the ideal null medium in the real space are extremely anisotropic tensors, whose values approach infinity along their main axis (x’ direction here) and are close to zero in other orthogonal directions. The mass density is also extremely anisotropic tensor, whose value approaches zero along its main axis and infinity in other orthogonal directions. The modulus of the ideal null medium is infinitely large. Once each plane element pair ΔS1i and ΔS2i in the small trapezoid region in the real space is linked by the null medium in Eq. (7), they are equivalent surfaces (they correspond to the same surface in the reference space: electromagnetic/acoustic field on one point of surface element ΔS1i will be identically projected to its corresponding point on surface element ΔS2i). As surfaces S1 and S2 in the real space can be treated as the superposition of infinite small planes ΔS1i and ΔS2i, surfaces S1 and S2 are also equivalent surfaces (they correspond to the same surface in the reference space). Since S1 and S2 are equivalent surfaces (any point on S1 has one corresponding point on S2), the electromagnetic/acoustic field on one point of surface S1 can be identically projected onto its corresponding point on surface S2 along the null medium’s main axis (the x’ direction here). Although in the above calculations we assumed the main axis of the null medium in Eq. (7) is along the x’ direction, the directional projecting feature of the multi-physics null medium also works when the null medium’s main axis is along other directions. Similar calculations can be made by setting a local Cartesian coordinate system with the x’ axis along the null medium’s main axis to obtain the same required material parameters. This corresponding relation between two equivalent surfaces can also be transmitted to more surfaces by introducing null media of various main axes to connect these surfaces.

In summary, the ideal null medium described in Eq. (7) performs like a perfect endoscope, which can identically project electromagnetic/acoustic field distribution from one surface it linked to another surface it linked along its main axis. From the perspective of transformation optics, all surfaces linked by the ideal null medium are equivalent surfaces, which correspond to the same surface in the reference space. In practice, the ideal null medium in Eq. (7) does not exist. However, the reduced multi-physics null medium (permittivity and permeability are very large along its main axis and very small in other orthogonal directions, mass density is very small along its main axis and very large in other orthogonal directions, and modulus is very large) can still keep a certain directional projecting property (e.g. a reduced endoscope) for both electromagnetic and acoustic waves. Before we show how to design novel multi-physics devices in a graphical way with the help of multi-physics null medium’s directional projection feature, we need to introduce how to realize the reduced multi-physics null medium by natural materials.

When the wavelength is much larger than the periodicity of a metal plate array in Fig. 2(a) (i.e. λ0>>d > a) and satisfies the Fabry-Pérot resonance condition (i.e. h =mλ0, m = 1, 2, 3…), this structure can perform as perfect endoscope for both electromagnetic waves [3742] and acoustic waves [43,44], which can be utilized to realize the 2D reduced null medium. For electromagnetic waves in the microwave frequencies, the metal can be modeled as perfect electric conductor (PEC), the effective electromagnetic parameters of the metal plate array in Fig. 2(a) can be expressed by [40,42]:

$$\left\{ \begin{array}{l} {\varepsilon_y} = \frac{d}{a}{\varepsilon_h},{\varepsilon_x} = {\varepsilon_z} \to \infty \\ {\mu_y} = {\mu_h},{\mu_x} = {\mu_z} = \frac{a}{d}{\mu_h} \end{array} \right..$$
For TM polarization waves (magnetic field only contains z component), Eq. (8) reduced to:
$${\varepsilon _y} = \frac{d}{a}{\varepsilon _h},{\mu _z} = \frac{a}{d}{\mu _h},{\varepsilon _x} \to \infty .$$

 figure: Fig. 2.

Fig. 2. The structures of metal plate array (a) and a metal plate with periodic sub-wavelength square holes (b) to effectively realize the 2D and 3D reduced null media, respectively. The metals are indicated by the blue color. d is the lattice constant. a is the height of the air gaps in (a) and side length of square air cylinders.

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Here ɛh and µh are permittivity and permeability of the host medium inside the metal plate array in Fig. 2(a). As shown in Eq. (9), we can achieve a reduced null medium of the main axis along the x direction by choosing appropriate geometrical parameters (a and d) and the host medium (ɛh and µh). The best choice is to use some near-zero refractive index materials as the host medium [45]. Some studies show the metal plate array in Fig. 2(a) can still perform as a reduced optic-null medium for electromagnetic wave even if the host medium is air (e.g. d = 2a, ɛy=2ɛ0, µz=0.5μ0, ɛx→∞) [38].

For acoustic waves, the effective modulus and mass density for the metal plate array in Fig. 2(a) can be calculated with the help of the effective medium theory [43]:

$$\frac{1}{{{\rho _x}}} = \frac{{{f_h}}}{{{\rho _h}}} + \frac{{{f_m}}}{{{\rho _m}}},\textrm{ }{\rho _y} = {f_h}{\rho _h} + {f_m}{\rho _m},\textrm{ }\frac{1}{\kappa } = \frac{{{f_h}}}{{{\kappa _h}}} + \frac{{{f_m}}}{{{\kappa _m}}}.$$
The subscripts h and m means host medium and metal, respectively. fh=a/d and fm=(d-a)/d are the filling factors of the host medium and metal, respectively. We also choose air as the host medium (ρh=1.29 kg/m3, кh=0.15MPa), brass as the metal (ρm=8500 kg/m3, кm=104GPa), and geometrical parameter d = 2a (i.e., fh=fm=0.5). In this case, the effective modulus and mass density of the metal plate array in Fig. 2(a) can be calculated by Eq. (10): ρx=2.58kg/m3, ρy=4250.6kg/m3, к=0.3MPa, which can be treated as a reduced 2D null medium for an acoustic wave. There have also been some separate studies on the structure in Fig. 2(b) for electromagnetic waves [46] and acoustic waves [47]. Actually, the structure in Fig. 2(b) can perform as a perfect endoscope for both electromagnetic wave and acoustic wave simultaneously, and thus it is possible to realize 3D reduced multi-physics null medium. For convenience of simulations, we only consider 2D reduced multi-physics null medium in this study. As previously analyzed, the metal plate array by layered brass and air can perform as a 2D reduced multi-physics null medium for both electromagnetic waves and acoustic waves when both the effective medium approximation (λ0>>d > a) and the Fabry-Pérot resonance condition (i.e. h =mλ0, m = 1, 2, 3…) are satisfied. If the geometrical parameters of the brass plate array satisfy d = 2a, the effective parameters of the metal plate array by layered brass and air can be summarized by:
$$ \left\{ \begin{array}{l} {\varepsilon _y} = 2{\varepsilon _0},{\mu _z} = 0.5{\mu _0},{\varepsilon _x} \to \infty \\ {\rho _x} = 2.58kg/{m^3},{\rho _y} = 4250.6kg/{m^3}, = 0.3MPa \end{array} \right..$$

From Eq. (11), the effective permittivity is infinitely large and very small along x and y directions, respectively. The permeability is also very small in z direction, which can be treated as a reduced null medium with the main axis along the x direction for TM polarized electromagnetic wave. The mass density is extremely large and very small in y and x direction, respectively. At the same time, its modulus is very large, which can be treated as a reduced null medium for acoustic waves. In summary, the metal plate array by layered brass and air of size d = 2a performs as a reduced 2D multi-physics null medium with the main axis along the orientation of metallic plates for both TM polarized electromagnetic waves and acoustic waves when the effective medium approximation and the Fabry-Pérot resonance condition are satisfied. It means that the metal plate array by layered brass and air can perform as a reduced multi-physics endoscope, which can one-to-one correspondingly project TM polarized electromagnetic fields and acoustics fields from one surface it linked to another surface it linked along the direction of the orientation of metallic plates. Next, we will show how to design some novel multi-physics devices based on the directional projecting feature of this reduced 2D multi-physics null medium.

3. Design examples and numerical simulations

The first example is the multi-physics beam shifter in Fig. 3(a), which can shift electromagnetic wave and acoustic wave simultaneously by a fixed pre-defined displacement. The input surface and output surface of the shifter are S1 and S2, respectively, which are connected by the brass plate array. The direction of the brass plane is the main axis of the reduced multi-physics null medium, which can project both electromagnetic field and acoustic field distribution from the input surface to the output surface. Figures 3(b)–3(e) show that the shifter can shift the position of the incident beam along y direction by a fixed pre-defined displacement h sinα without changing its wave-front. The multi-physical beam shifter can steer electromagnetic wave and acoustic wave simultaneously, which can work as a building block to achieve many other multi-physics illusions (e.g., imaging and scattering reduction). Multi-physics shifter can work not only for normal incidence but also oblique incidence (see Visualization 1 and Visualization 2).

 figure: Fig. 3.

Fig. 3. (a) Structure of the brass plate array used to achieve a multi-physics shifter for both electromagnetic wave and acoustic wave simultaneously (the thick black lines are brass and all other white regions are air). The length of each brass plate is h =mλ0 (the Fabry-Pérot resonance condition) and m = 2 here. The thickness of brass plate and air gap are both λ0/10, which means the filling factor of brass and air is 0.5. The angle between the brass plates and x axis is α=30 degree. The structure is designed at working wavelength λ0=3cm: corresponding frequencies are 10 GHz for electromagnetic wave and 11.433kHz for acoustic wave, respectively. (b) and (c) are distributions of normalized magnetic field’s z component for the TM polarized waves when a Gaussian electromagnetic beam incidents onto the brass plate array by 0 degree and -30 degree, respectively (see Visualization 1). (d) and (e) are normalized acoustic pressure distributions when a Gaussian acoustic beam incidents onto the brass plate array by 0 degree and -30 degree, respectively (see Visualization 2). (e) and (f) show the reflectivity of the multi-physics shifter in (a) when the wavelength deviates from the designed value λ0=3 cm for EM wave and acoustic wave, respectively (see Visualization 3 and Visualization 4).

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The reduced null medium by brass plate array may introduce some reflections when the Fabry-Pérot condition is not satisfied. The reflectivity of the multi-physics shifter changes as the wavelength deviates from the designed value λ0=3cm in Figs. 3(f) and 3(g) for EM wave and acoustic wave, respectively (see Visualization 3 and Visualization 4). If the thickness of the device does not satisfy the Fabry-Pérot condition, the multi-physics shifter can still maintain its multi-physical shifting effect, while some unexpected reflections may appear.

Next, we can use the above designed multi-physics shifter as the building block to create a scattering reduction device that can simultaneously guide both the electromagnetic wave and acoustic wave smoothly around the strongly scattering object and restore the wave-front. We can use four shifters of Fig. 3(a) with the configuration shown in Fig. 4(a) to achieve a scattering reduction device. The detecting beam from the left is firstly split by the front two shifters, and then combined by the two rear shifters. In the central red region we put some strongly scattering object (e.g. PEC boundary for electromagnetic waves and hard wall boundary for acoustic waves). Figures 4(b)–4(g) shows the good scattering reduction performance of the device by the brass plate array for the electromagnetic wave and acoustic wave simultaneously. If we remove the scattering reduction device (i.e., only the central strongly scattering object is left in air), the scattering is obvious (see Fig. 5 for comparison). There were some separate studies on invisibility cloaking to achieve scattering reduction for electromagnetic waves by transformation optics [15,4850] and acoustic waves by transformation acoustic [6,5153]. However, previous studies can work only for electromagnetic waves or acoustic waves. Our scattering reduction device can effectively reduce the scattering cross section for both the electromagnetic wave and acoustic wave (not only for normal incidence but also oblique incidence; see Visualization 5 and Visualization 6), which may have some potential applications in stealth technology for both radar and sonar. The multi-physical scattering reduction device can still show good scattering reduction effect for both EM wave and acoustic wave when the working wavelength is scanned to some frequencies at which the Fabry-Pérot condition is not satisfied (see Visualization 7 and Visualization 8), compared with the cases when the scattering reduction device is removed (see Visualization 9 and Visualization 10).

 figure: Fig. 4.

Fig. 4. (a) The structure of the brass plate array for multi-physics scattering reduction. The thick black lines are brass plates of thickness λ0/10 and length h= 2λ0. (b)-(d) The normalized magnetic field’s z component for the TM polarized waves when a Gaussian electromagnetic beam incidents onto the brass plate array by 0, 20 and 40 degrees (see Visualization 5). (e)-(g) The normalized acoustic pressure when a Gaussian acoustic beam incidents onto the brass plate array by 0, 20 and 40 degrees (see Visualization 6). The boundaries of the central object of strong scattering are set as PEC and hard walls for electromagnetic wave and acoustic wave, respectively. All other parameters are the same as those in Fig. 3. Visualization 7 and Visualization 8 show Gaussian beam normally incidents onto the multi-physics scattering reduction device in Fig. 4(a) when the wavelength of incident Gaussian beam changes from λ0/3 to 2λ0 for electromagnetic case and acoustic case, respectively.

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 figure: Fig. 5.

Fig. 5. Scattering when a Gaussian beam incidents onto the strongly scattering object by 0, 20 and 40 degrees. (a)-(c) The corresponding normalized magnetic field’s z component when the brass plates are removed from Figs. 4(b)–4(d) (only the central object of strong scattering is left in air). (d)-(f) The corresponding normalized acoustic pressure when the brass plates are removed from Figs. 4(e)–4(g). Other parameters are the same as those in Fig. 3. Visualization 9 and Visualization 10 show Gaussian beam normally incidents onto the strongly scattering object in the center of Fig. 4(a) (scattering reduction device is removed) when the wavelength of incident Gaussian beam changes from λ0/3 to 2λ0 for electromagnetic case and acoustic case, respectively.

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Since the multi-physics null medium (e.g., brass plate array) can guide both electromagnetic wave and acoustic wave along its main axis, we can gradually change the main axis of the brass plate array to steer the propagation or radiation for both the electromagnetic wave and acoustic wave simultaneously. As shown in Fig. 6(a), two cascaded brass plate arrays indicated in green and black with the length L10 and L2=2λ0, respectively, can steer the incident electromagnetic wave and acoustic wave by a pre-defined angle. The inner brass plates (colored green) and outer brass plates (colored black) are rotated by 10 degrees and 20 degrees from the radical direction, respectively. If the acoustic beam and electromagnetic wave incident onto the beam steering device from the right, the output beams are steered by 20 degrees in Figs. 6(b) and 6(c). There were some separate studies on how to steer electromagnetic waves by transformation optics [5456] and acoustic waves by transformation acoustic [57,58]. With the help of the present surface transformation multi-physics, we can easily design the orientation of the brass plate arrays to achieve a desired beam steering effect for both the electromagnetic wave and acoustic wave simultaneously.

 figure: Fig. 6.

Fig. 6. (a) Structure of the beam steering device. (b) and (c) are normalized amplitude of acoustic pressure and z component of the magnetic field in 2D numerical simulations when acoustic wave and TM polarized electromagnetic wave incident onto the beam steering device, respectively.

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Numerical simulations in Figs. 36 are made by commercial software COMSOL Multiphysics 5.0 based on the finite element method (wave optics package for electromagnetic wave and acoustic package for acoustic wave).

4. Discussion

The filling factor of brass and air for the brass plate array in Figs. 3 and 4 are fh=fm=0.5, whose effective material parameters are given in Eq. (11). Compared with the ideal null medium whose material parameters are given in Eq. (7), the brass plate array performs as a reduced null medium. In addition, the degrees of reduction are different for acoustic wave and EM wave, and this is the reason why the performance of the devices in Figs. 3 and 4 appears to be poorer for the case of acoustic waves as compared with the case of electromagnetic waves.

There are also some other ways to design multi-physical devices [31,32]. A homogenization method [32] can be used to achieve a carpet cloak [31] and full space cloak [32] working for microwave, acoustic wave and water wave if the aluminum cloak can be designed for one kind of these waves, as aluminum cloak provides the same mathematical model (Helmholtz equation with Neumann boundary conditions) for transverse magnetic EM wave (perfect electric conductors in microwave frequencies), acoustic wave (rigid inclusions in air) and water wave (no flow conditions). However, we still need to design first a cloak or devices of other functions before we extend these devices to multi-physical fields by the homogenization method. The homogenization method provides a way to extend the designed device for one physical field to multi-physical fields, but not a general design method as the transformation optics and surface transformation multi-physics proposed in this study. Surface transformation multi-physics can be utilized directly to design multi-physical devices of various functions in a surface-mapping way. Another important difference between the surface transformation multi-physics and the homogenization method is that all multi-physical devices of various functions designed by our method only require one same material (i.e., null medium), which is homogenous (no gradient control is required). The same structure of metal plate array given in Fig. 2 can be utilized to realize all devices designed by our surface transformation multi-physics no matter how functions, geometrical shapes and sizes of these devices would change. However, devices designed by the homogenization method require different aluminum units when the function or geometrical shapes change. For example, full space cloak [32] and carpet cloak [31] are both designed by the homogenization method, but using different aluminum structures (perforated rotating aluminum disc with gradient small air tubes and aluminum meta-surfaces).

5. Summary

The designing process in surface transformation multi-physics is very simple. The first step is to choose the proper geometrical shapes of the input/output surfaces. The second step is to fill the brass plate array of the proper orientations that can link the input and output surfaces. The period of the brass plate array should be much smaller than the working wavelength and the length of each brass plate satisfies the Fabry-Pérot condition. Compared with coordinate-transformation-based methods, our surface transformation multi-physics method has many advantages, which can be summarized as: 1) the designing process is very simple. We only need to design the geometrical shapes of the input/output surfaces and the orientations of the brass plate array between them. There are no complex mathematical calculations during the whole designing process. 2) All devices of various functions designed by our method only require one natural material, e.g. the brass plate array, to realize, while conventional coordinate-transformation-based methods requires different materials for various devices. Note that some devices designed by coordinate-transformation-based methods can be implemented with the same materials by applying effective medium theories [48]. 3) All devices designed by our method can always work for both electromagnetic waves and acoustic waves simultaneously. The method (surface transformation multi-physics) proposed in this study is derived from the transformation optics, which is a more general method. Only a subset of devices of novel functions designed by the transformation optics can be achieved by the surface transformation method.

Exploring and designing functional devices of multi-physics is an interesting topic for transformation optics and artificial metamaterials. Controlling electromagnetic waves and acoustic waves simultaneously will promote the development of multi-physics technology. The present surface transformation multi-physics provides an effective, simple and realizable way to design novel multi-physics devices. Multi-physics devices that can control electromagnetic wave and acoustic wave simultaneously will have important applications in various fields (e.g., composite stealth technology and multi-physics biomedical imaging).

Funding

National Natural Science Foundation of China (11604292, 11621101, 11674239, 60990322, 61905208, 61971300, 91233208, 91833303); Scientific and Technological Innovation Programs (STIP) of Higher Education Institutions in Shanxi (2019L0146, 2019L0159); he National Key Research and Development Program of China (2017YFA0205700); the Program of Zhejiang Leading Team of Science and Technology Innovation.

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7. F. Sun, S. Li, and S. He, “Translational illusion of acoustic sources by transformation acoustics,” J. Acoust. Soc. Am. 142(3), 1213–1218 (2017). [CrossRef]  

8. S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012). [CrossRef]  

9. F. Sun and S. He, “Remote cooling by a novel thermal lens with anisotropic positive thermal conductivity,” Sci. Rep. 7(1), 40949 (2017). [CrossRef]  

10. M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016). [CrossRef]  

11. T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016). [CrossRef]  

12. C. Li, L. Xu, L. Zhu, S. Zou, Q. H. Liu, Z. Wang, and H. Chen, “Concentrators for Water Waves,” Phys. Rev. Lett. 121(10), 104501 (2018). [CrossRef]  

13. F. Sun and S. He, “Transformation magneto-statics and illusions for magnets,” Sci. Rep. 4(1), 6593 (2015). [CrossRef]  

14. C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012). [CrossRef]  

15. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006). [CrossRef]  

16. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, 1999).

17. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef]  

18. N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12(1), 25–28 (2013). [CrossRef]  

19. Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014). [CrossRef]  

20. M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys. 117(2), 024502 (2015). [CrossRef]  

21. C. Lan, K. Bi, Z. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016). [CrossRef]  

22. T. Stedman and L. M. Woods, “Cloaking of Thermoelectric Transport,” Sci. Rep. 7(1), 6988 (2017). [CrossRef]  

23. J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010). [CrossRef]  

24. L. Zhang and Y. Shi, “Bifunctional arbitrarily-shaped cloak for thermal and electric manipulations,” Opt. Mater. Express 8(9), 2600–2613 (2018). [CrossRef]  

25. M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014). [CrossRef]  

26. C. Lan, K. Bi, X. Fu, B. Li, and J. Zhou, “Bifunctional metamaterials with simultaneous and independent manipulation of thermal and electric fields,” Opt. Express 24(20), 23072–23080 (2016). [CrossRef]  

27. G. Xu, X. Zhou, H. Zhang, and H. P. Tan, “Creating illusion of discrete source array by simultaneously allocating thermal and DC fields with homogeneous media,” Energy Convers. Manage. 187, 546–553 (2019). [CrossRef]  

28. C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015). [CrossRef]  

29. C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019). [CrossRef]  

30. G. Song, C. Zhang, Q. Cheng, Y. Jing, C. Qiu, and T. Cui, “Transparent coupled membrane metamaterials with simultaneous microwave absorption and sound reduction,” Opt. Express 26(18), 22916–22925 (2018). [CrossRef]  

31. Y. Yang, H. Wang, F. Yu, Z. Xu, and H. Chen, “A metasurface carpet cloak for electromagnetic, acoustic and water waves,” Sci. Rep. 6(1), 20219 (2016). [CrossRef]  

32. J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015). [CrossRef]  

33. M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013). [CrossRef]  

34. J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013). [CrossRef]  

35. F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5(1), 16032 (2015). [CrossRef]  

36. B. Li, F. Sun, and S. He, “Acoustic surface transformation realized by acoustic-null materials using bilayer natural materials,” Appl. Phys. Express 10(11), 114001 (2017). [CrossRef]  

37. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002). [CrossRef]  

38. M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry-Pérot resonances,” Sci. Rep. 5(1), 8680 (2015). [CrossRef]  

39. J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009). [CrossRef]  

40. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]  

41. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002). [CrossRef]  

42. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]  

43. J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. Mater. 8(12), 931–934 (2009). [CrossRef]  

44. Z. M. Gu, B. Liang, Y. Li, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Experimental realization of broadband acoustic omnidirectional absorber by homogeneous anisotropic metamaterials,” J. Appl. Phys. 117(7), 074502 (2015). [CrossRef]  

45. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017). [CrossRef]  

46. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef]  

47. J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011). [CrossRef]  

48. B. Zheng, Y. Yang, Z. Shao, Q. Yan, N. H. Shen, L. Shen, H. Wang, E. Li, C. M. Soukoulis, and H. Chen, “Experimental Realization of an Extreme-Parameter Omnidirectional Cloak,” Research 2019, 1–8 (2019). [CrossRef]  

49. Y. Zhang, Y. Luo, J. B. Pendry, and B. Zhang, “Transformation-Invariant Metamaterials,” Phys. Rev. Lett. 123(6), 067701 (2019). [CrossRef]  

50. F. Sun, Y. Zhang, J. Evans, and S. He, “A Camouflage Device Without Metamaterials,” Prog. Electromagn. Res. 165, 107–117 (2019). [CrossRef]  

51. S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011). [CrossRef]  

52. L. Sanchis, V. M. García-Chocano, R. Llopis-Pontiveros, A. Climente, J. Martínez-Pastor, F. Cervera, and J. Sánchez-Dehesa, “Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere,” Phys. Rev. Lett. 110(12), 124301 (2013). [CrossRef]  

53. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008). [CrossRef]  

54. F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4(1), 6832 (2015). [CrossRef]  

55. J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015). [CrossRef]  

56. J. Lei, J. Yang, X. Chen, Z. Zhang, G. Fu, and Y. Hao, “Experimental demonstration of conformal phased array antenna via transformation optics,” Sci. Rep. 8(1), 3807 (2018). [CrossRef]  

57. P. Wei, F. Liu, Z. Liang, Y. Xu, S. T. Chu, and J. Li, “An acoustic beam shifter with enhanced transmission using perforated metamaterials,” Europhys. Lett. 109(1), 14004 (2015). [CrossRef]  

58. X. Jiang, B. Liang, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Broadband field rotator based on acoustic metamaterials,” Appl. Phys. Lett. 104(8), 083510 (2014). [CrossRef]  

References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref]
  3. J. B. Pendry, Y. Luo, and R. Zhao, “Transforming the optical landscape,” Science 348(6234), 521–524 (2015).
    [Crossref]
  4. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
    [Crossref]
  5. F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation Optics: From Classic Theory and Applications to its New Branches,” Laser Photonics Rev. 11(6), 1700034 (2017).
    [Crossref]
  6. H. Chen and C. T. Chan, “Acoustic cloaking and transformation acoustics,” J. Phys. D: Appl. Phys. 43(11), 113001 (2010).
    [Crossref]
  7. F. Sun, S. Li, and S. He, “Translational illusion of acoustic sources by transformation acoustics,” J. Acoust. Soc. Am. 142(3), 1213–1218 (2017).
    [Crossref]
  8. S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
    [Crossref]
  9. F. Sun and S. He, “Remote cooling by a novel thermal lens with anisotropic positive thermal conductivity,” Sci. Rep. 7(1), 40949 (2017).
    [Crossref]
  10. M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
    [Crossref]
  11. T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
    [Crossref]
  12. C. Li, L. Xu, L. Zhu, S. Zou, Q. H. Liu, Z. Wang, and H. Chen, “Concentrators for Water Waves,” Phys. Rev. Lett. 121(10), 104501 (2018).
    [Crossref]
  13. F. Sun and S. He, “Transformation magneto-statics and illusions for magnets,” Sci. Rep. 4(1), 6593 (2015).
    [Crossref]
  14. C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
    [Crossref]
  15. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006).
    [Crossref]
  16. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, 1999).
  17. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
    [Crossref]
  18. N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12(1), 25–28 (2013).
    [Crossref]
  19. Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
    [Crossref]
  20. M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys. 117(2), 024502 (2015).
    [Crossref]
  21. C. Lan, K. Bi, Z. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
    [Crossref]
  22. T. Stedman and L. M. Woods, “Cloaking of Thermoelectric Transport,” Sci. Rep. 7(1), 6988 (2017).
    [Crossref]
  23. J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
    [Crossref]
  24. L. Zhang and Y. Shi, “Bifunctional arbitrarily-shaped cloak for thermal and electric manipulations,” Opt. Mater. Express 8(9), 2600–2613 (2018).
    [Crossref]
  25. M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
    [Crossref]
  26. C. Lan, K. Bi, X. Fu, B. Li, and J. Zhou, “Bifunctional metamaterials with simultaneous and independent manipulation of thermal and electric fields,” Opt. Express 24(20), 23072–23080 (2016).
    [Crossref]
  27. G. Xu, X. Zhou, H. Zhang, and H. P. Tan, “Creating illusion of discrete source array by simultaneously allocating thermal and DC fields with homogeneous media,” Energy Convers. Manage. 187, 546–553 (2019).
    [Crossref]
  28. C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015).
    [Crossref]
  29. C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
    [Crossref]
  30. G. Song, C. Zhang, Q. Cheng, Y. Jing, C. Qiu, and T. Cui, “Transparent coupled membrane metamaterials with simultaneous microwave absorption and sound reduction,” Opt. Express 26(18), 22916–22925 (2018).
    [Crossref]
  31. Y. Yang, H. Wang, F. Yu, Z. Xu, and H. Chen, “A metasurface carpet cloak for electromagnetic, acoustic and water waves,” Sci. Rep. 6(1), 20219 (2016).
    [Crossref]
  32. J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
    [Crossref]
  33. M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
    [Crossref]
  34. J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013).
    [Crossref]
  35. F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5(1), 16032 (2015).
    [Crossref]
  36. B. Li, F. Sun, and S. He, “Acoustic surface transformation realized by acoustic-null materials using bilayer natural materials,” Appl. Phys. Express 10(11), 114001 (2017).
    [Crossref]
  37. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002).
    [Crossref]
  38. M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry-Pérot resonances,” Sci. Rep. 5(1), 8680 (2015).
    [Crossref]
  39. J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
    [Crossref]
  40. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7(2), S97–S101 (2005).
    [Crossref]
  41. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002).
    [Crossref]
  42. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
    [Crossref]
  43. J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. Mater. 8(12), 931–934 (2009).
    [Crossref]
  44. Z. M. Gu, B. Liang, Y. Li, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Experimental realization of broadband acoustic omnidirectional absorber by homogeneous anisotropic metamaterials,” J. Appl. Phys. 117(7), 074502 (2015).
    [Crossref]
  45. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
    [Crossref]
  46. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
    [Crossref]
  47. J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011).
    [Crossref]
  48. B. Zheng, Y. Yang, Z. Shao, Q. Yan, N. H. Shen, L. Shen, H. Wang, E. Li, C. M. Soukoulis, and H. Chen, “Experimental Realization of an Extreme-Parameter Omnidirectional Cloak,” Research 2019, 1–8 (2019).
    [Crossref]
  49. Y. Zhang, Y. Luo, J. B. Pendry, and B. Zhang, “Transformation-Invariant Metamaterials,” Phys. Rev. Lett. 123(6), 067701 (2019).
    [Crossref]
  50. F. Sun, Y. Zhang, J. Evans, and S. He, “A Camouflage Device Without Metamaterials,” Prog. Electromagn. Res. 165, 107–117 (2019).
    [Crossref]
  51. S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
    [Crossref]
  52. L. Sanchis, V. M. García-Chocano, R. Llopis-Pontiveros, A. Climente, J. Martínez-Pastor, F. Cervera, and J. Sánchez-Dehesa, “Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere,” Phys. Rev. Lett. 110(12), 124301 (2013).
    [Crossref]
  53. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
    [Crossref]
  54. F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4(1), 6832 (2015).
    [Crossref]
  55. J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015).
    [Crossref]
  56. J. Lei, J. Yang, X. Chen, Z. Zhang, G. Fu, and Y. Hao, “Experimental demonstration of conformal phased array antenna via transformation optics,” Sci. Rep. 8(1), 3807 (2018).
    [Crossref]
  57. P. Wei, F. Liu, Z. Liang, Y. Xu, S. T. Chu, and J. Li, “An acoustic beam shifter with enhanced transmission using perforated metamaterials,” Europhys. Lett. 109(1), 14004 (2015).
    [Crossref]
  58. X. Jiang, B. Liang, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Broadband field rotator based on acoustic metamaterials,” Appl. Phys. Lett. 104(8), 083510 (2014).
    [Crossref]

2019 (5)

G. Xu, X. Zhou, H. Zhang, and H. P. Tan, “Creating illusion of discrete source array by simultaneously allocating thermal and DC fields with homogeneous media,” Energy Convers. Manage. 187, 546–553 (2019).
[Crossref]

C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
[Crossref]

B. Zheng, Y. Yang, Z. Shao, Q. Yan, N. H. Shen, L. Shen, H. Wang, E. Li, C. M. Soukoulis, and H. Chen, “Experimental Realization of an Extreme-Parameter Omnidirectional Cloak,” Research 2019, 1–8 (2019).
[Crossref]

Y. Zhang, Y. Luo, J. B. Pendry, and B. Zhang, “Transformation-Invariant Metamaterials,” Phys. Rev. Lett. 123(6), 067701 (2019).
[Crossref]

F. Sun, Y. Zhang, J. Evans, and S. He, “A Camouflage Device Without Metamaterials,” Prog. Electromagn. Res. 165, 107–117 (2019).
[Crossref]

2018 (4)

J. Lei, J. Yang, X. Chen, Z. Zhang, G. Fu, and Y. Hao, “Experimental demonstration of conformal phased array antenna via transformation optics,” Sci. Rep. 8(1), 3807 (2018).
[Crossref]

G. Song, C. Zhang, Q. Cheng, Y. Jing, C. Qiu, and T. Cui, “Transparent coupled membrane metamaterials with simultaneous microwave absorption and sound reduction,” Opt. Express 26(18), 22916–22925 (2018).
[Crossref]

L. Zhang and Y. Shi, “Bifunctional arbitrarily-shaped cloak for thermal and electric manipulations,” Opt. Mater. Express 8(9), 2600–2613 (2018).
[Crossref]

C. Li, L. Xu, L. Zhu, S. Zou, Q. H. Liu, Z. Wang, and H. Chen, “Concentrators for Water Waves,” Phys. Rev. Lett. 121(10), 104501 (2018).
[Crossref]

2017 (6)

F. Sun and S. He, “Remote cooling by a novel thermal lens with anisotropic positive thermal conductivity,” Sci. Rep. 7(1), 40949 (2017).
[Crossref]

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation Optics: From Classic Theory and Applications to its New Branches,” Laser Photonics Rev. 11(6), 1700034 (2017).
[Crossref]

F. Sun, S. Li, and S. He, “Translational illusion of acoustic sources by transformation acoustics,” J. Acoust. Soc. Am. 142(3), 1213–1218 (2017).
[Crossref]

T. Stedman and L. M. Woods, “Cloaking of Thermoelectric Transport,” Sci. Rep. 7(1), 6988 (2017).
[Crossref]

B. Li, F. Sun, and S. He, “Acoustic surface transformation realized by acoustic-null materials using bilayer natural materials,” Appl. Phys. Express 10(11), 114001 (2017).
[Crossref]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

2016 (5)

C. Lan, K. Bi, X. Fu, B. Li, and J. Zhou, “Bifunctional metamaterials with simultaneous and independent manipulation of thermal and electric fields,” Opt. Express 24(20), 23072–23080 (2016).
[Crossref]

Y. Yang, H. Wang, F. Yu, Z. Xu, and H. Chen, “A metasurface carpet cloak for electromagnetic, acoustic and water waves,” Sci. Rep. 6(1), 20219 (2016).
[Crossref]

C. Lan, K. Bi, Z. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
[Crossref]

T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

2015 (11)

F. Sun and S. He, “Transformation magneto-statics and illusions for magnets,” Sci. Rep. 4(1), 6593 (2015).
[Crossref]

J. B. Pendry, Y. Luo, and R. Zhao, “Transforming the optical landscape,” Science 348(6234), 521–524 (2015).
[Crossref]

M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys. 117(2), 024502 (2015).
[Crossref]

C. Lan, B. Li, and J. Zhou, “Simultaneously concentrated electric and thermal fields using fan-shaped structure,” Opt. Express 23(19), 24475–24483 (2015).
[Crossref]

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5(1), 16032 (2015).
[Crossref]

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry-Pérot resonances,” Sci. Rep. 5(1), 8680 (2015).
[Crossref]

Z. M. Gu, B. Liang, Y. Li, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Experimental realization of broadband acoustic omnidirectional absorber by homogeneous anisotropic metamaterials,” J. Appl. Phys. 117(7), 074502 (2015).
[Crossref]

P. Wei, F. Liu, Z. Liang, Y. Xu, S. T. Chu, and J. Li, “An acoustic beam shifter with enhanced transmission using perforated metamaterials,” Europhys. Lett. 109(1), 14004 (2015).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4(1), 6832 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015).
[Crossref]

2014 (3)

X. Jiang, B. Liang, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Broadband field rotator based on acoustic metamaterials,” Appl. Phys. Lett. 104(8), 083510 (2014).
[Crossref]

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref]

2013 (4)

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12(1), 25–28 (2013).
[Crossref]

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013).
[Crossref]

L. Sanchis, V. M. García-Chocano, R. Llopis-Pontiveros, A. Climente, J. Martínez-Pastor, F. Cervera, and J. Sánchez-Dehesa, “Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere,” Phys. Rev. Lett. 110(12), 124301 (2013).
[Crossref]

2012 (2)

C. Navau, J. Prat-Camps, and A. Sanchez, “Magnetic energy harvesting and concentration at a distance by transformation optics,” Phys. Rev. Lett. 109(26), 263903 (2012).
[Crossref]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref]

2011 (2)

J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011).
[Crossref]

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref]

2010 (4)

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking and transformation acoustics,” J. Phys. D: Appl. Phys. 43(11), 113001 (2010).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref]

J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
[Crossref]

2009 (2)

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. Mater. 8(12), 931–934 (2009).
[Crossref]

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

2008 (1)

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref]

2006 (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

2005 (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

2004 (1)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref]

2002 (2)

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002).
[Crossref]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002).
[Crossref]

Abdeddaim, R.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

Amra, C.

Bagci, H.

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

Bartal, G.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. Mater. 8(12), 931–934 (2009).
[Crossref]

Bi, K.

C. Lan, K. Bi, Z. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

C. Lan, K. Bi, X. Fu, B. Li, and J. Zhou, “Bifunctional metamaterials with simultaneous and independent manipulation of thermal and electric fields,” Opt. Express 24(20), 23072–23080 (2016).
[Crossref]

Burokur, S. N.

Calle, F.

J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013).
[Crossref]

Cao, W. K.

C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
[Crossref]

Castaldi, G.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Cervera, F.

L. Sanchis, V. M. García-Chocano, R. Llopis-Pontiveros, A. Climente, J. Martínez-Pastor, F. Cervera, and J. Sánchez-Dehesa, “Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere,” Phys. Rev. Lett. 110(12), 124301 (2013).
[Crossref]

Chan, C. T.

H. Chen and C. T. Chan, “Acoustic cloaking and transformation acoustics,” J. Phys. D: Appl. Phys. 43(11), 113001 (2010).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref]

Chen, H.

B. Zheng, Y. Yang, Z. Shao, Q. Yan, N. H. Shen, L. Shen, H. Wang, E. Li, C. M. Soukoulis, and H. Chen, “Experimental Realization of an Extreme-Parameter Omnidirectional Cloak,” Research 2019, 1–8 (2019).
[Crossref]

C. Li, L. Xu, L. Zhu, S. Zou, Q. H. Liu, Z. Wang, and H. Chen, “Concentrators for Water Waves,” Phys. Rev. Lett. 121(10), 104501 (2018).
[Crossref]

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation Optics: From Classic Theory and Applications to its New Branches,” Laser Photonics Rev. 11(6), 1700034 (2017).
[Crossref]

Y. Yang, H. Wang, F. Yu, Z. Xu, and H. Chen, “A metasurface carpet cloak for electromagnetic, acoustic and water waves,” Sci. Rep. 6(1), 20219 (2016).
[Crossref]

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry-Pérot resonances,” Sci. Rep. 5(1), 8680 (2015).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking and transformation acoustics,” J. Phys. D: Appl. Phys. 43(11), 113001 (2010).
[Crossref]

Chen, M. Z.

C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
[Crossref]

Chen, X.

J. Lei, J. Yang, X. Chen, Z. Zhang, G. Fu, and Y. Hao, “Experimental demonstration of conformal phased array antenna via transformation optics,” Sci. Rep. 8(1), 3807 (2018).
[Crossref]

Cheng, J. C.

Z. M. Gu, B. Liang, Y. Li, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Experimental realization of broadband acoustic omnidirectional absorber by homogeneous anisotropic metamaterials,” J. Appl. Phys. 117(7), 074502 (2015).
[Crossref]

X. Jiang, B. Liang, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Broadband field rotator based on acoustic metamaterials,” Appl. Phys. Lett. 104(8), 083510 (2014).
[Crossref]

Cheng, Q.

C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
[Crossref]

G. Song, C. Zhang, Q. Cheng, Y. Jing, C. Qiu, and T. Cui, “Transparent coupled membrane metamaterials with simultaneous microwave absorption and sound reduction,” Opt. Express 26(18), 22916–22925 (2018).
[Crossref]

Christensen, J.

J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011).
[Crossref]

Chu, S. T.

P. Wei, F. Liu, Z. Liang, Y. Xu, S. T. Chu, and J. Li, “An acoustic beam shifter with enhanced transmission using perforated metamaterials,” Europhys. Lett. 109(1), 14004 (2015).
[Crossref]

Climente, A.

L. Sanchis, V. M. García-Chocano, R. Llopis-Pontiveros, A. Climente, J. Martínez-Pastor, F. Cervera, and J. Sánchez-Dehesa, “Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere,” Phys. Rev. Lett. 110(12), 124301 (2013).
[Crossref]

Cui, T.

Cui, T. J.

C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
[Crossref]

Cummer, S. A.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

de Lustrac, A.

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[Crossref]

Engheta, N.

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

Enoch, S.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

Evans, J.

F. Sun, Y. Zhang, J. Evans, and S. He, “A Camouflage Device Without Metamaterials,” Prog. Electromagn. Res. 165, 107–117 (2019).
[Crossref]

Fang, N.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref]

Farhat, M.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

Fok, L.

J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011).
[Crossref]

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. Mater. 8(12), 931–934 (2009).
[Crossref]

Fu, G.

J. Lei, J. Yang, X. Chen, Z. Zhang, G. Fu, and Y. Hao, “Experimental demonstration of conformal phased array antenna via transformation optics,” Sci. Rep. 8(1), 3807 (2018).
[Crossref]

Fu, X.

Galdi, V.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Gao, Y.

J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
[Crossref]

Gao, Z.

C. Lan, K. Bi, Z. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

García-Chocano, V. M.

L. Sanchis, V. M. García-Chocano, R. Llopis-Pontiveros, A. Climente, J. Martínez-Pastor, F. Cervera, and J. Sánchez-Dehesa, “Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere,” Phys. Rev. Lett. 110(12), 124301 (2013).
[Crossref]

Garcia-Vidal, F. J.

J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[Crossref]

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A: Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002).
[Crossref]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66(15), 155412 (2002).
[Crossref]

Geffrin, J. M.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

Georget, E.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

Gu, Z. M.

Z. M. Gu, B. Liang, Y. Li, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Experimental realization of broadband acoustic omnidirectional absorber by homogeneous anisotropic metamaterials,” J. Appl. Phys. 117(7), 074502 (2015).
[Crossref]

Guenneau, S.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref]

Guinea, F.

J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013).
[Crossref]

Guo, S.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation Optics: From Classic Theory and Applications to its New Branches,” Laser Photonics Rev. 11(6), 1700034 (2017).
[Crossref]

Han, T.

T. Han and C. W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

Hao, Y.

J. Lei, J. Yang, X. Chen, Z. Zhang, G. Fu, and Y. Hao, “Experimental demonstration of conformal phased array antenna via transformation optics,” Sci. Rep. 8(1), 3807 (2018).
[Crossref]

He, S.

F. Sun, Y. Zhang, J. Evans, and S. He, “A Camouflage Device Without Metamaterials,” Prog. Electromagn. Res. 165, 107–117 (2019).
[Crossref]

B. Li, F. Sun, and S. He, “Acoustic surface transformation realized by acoustic-null materials using bilayer natural materials,” Appl. Phys. Express 10(11), 114001 (2017).
[Crossref]

F. Sun and S. He, “Remote cooling by a novel thermal lens with anisotropic positive thermal conductivity,” Sci. Rep. 7(1), 40949 (2017).
[Crossref]

F. Sun, S. Li, and S. He, “Translational illusion of acoustic sources by transformation acoustics,” J. Acoust. Soc. Am. 142(3), 1213–1218 (2017).
[Crossref]

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation Optics: From Classic Theory and Applications to its New Branches,” Laser Photonics Rev. 11(6), 1700034 (2017).
[Crossref]

F. Sun and S. He, “Transformation magneto-statics and illusions for magnets,” Sci. Rep. 4(1), 6593 (2015).
[Crossref]

F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5(1), 16032 (2015).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4(1), 6832 (2015).
[Crossref]

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref]

Hou, B.

M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Chen, “Transformation optics with Fabry-Pérot resonances,” Sci. Rep. 5(1), 8680 (2015).
[Crossref]

Huang, J. P.

J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
[Crossref]

Jiang, W.

F. Sun, B. Zheng, H. Chen, W. Jiang, S. Guo, Y. Liu, Y. Ma, and S. He, “Transformation Optics: From Classic Theory and Applications to its New Branches,” Laser Photonics Rev. 11(6), 1700034 (2017).
[Crossref]

Jiang, X.

J. Xu, X. Jiang, N. Fang, E. Georget, R. Abdeddaim, J. M. Geffrin, M. Farhat, P. Sabouroux, S. Enoch, and S. Guenneau, “Molding acoustic, electromagnetic and water waves with a single cloak,” Sci. Rep. 5(1), 10678 (2015).
[Crossref]

X. Jiang, B. Liang, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Broadband field rotator based on acoustic metamaterials,” Appl. Phys. Lett. 104(8), 083510 (2014).
[Crossref]

Jing, Y.

Jung, J.

J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011).
[Crossref]

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Holey metal films make perfect endoscopes,” Phys. Rev. B 79(15), 153407 (2009).
[Crossref]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref]

Ke, J. C.

C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111(23), 237405 (2013).
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Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
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C. Li, L. Xu, L. Zhu, S. Zou, Q. H. Liu, Z. Wang, and H. Chen, “Concentrators for Water Waves,” Phys. Rev. Lett. 121(10), 104501 (2018).
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P. Wei, F. Liu, Z. Liang, Y. Xu, S. T. Chu, and J. Li, “An acoustic beam shifter with enhanced transmission using perforated metamaterials,” Europhys. Lett. 109(1), 14004 (2015).
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C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, 1999).

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P. Wei, F. Liu, Z. Liang, Y. Xu, S. T. Chu, and J. Li, “An acoustic beam shifter with enhanced transmission using perforated metamaterials,” Europhys. Lett. 109(1), 14004 (2015).
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J. Lei, J. Yang, X. Chen, Z. Zhang, G. Fu, and Y. Hao, “Experimental demonstration of conformal phased array antenna via transformation optics,” Sci. Rep. 8(1), 3807 (2018).
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Yin, L. L.

Z. M. Gu, B. Liang, Y. Li, X. Y. Zou, L. L. Yin, and J. C. Cheng, “Experimental realization of broadband acoustic omnidirectional absorber by homogeneous anisotropic metamaterials,” J. Appl. Phys. 117(7), 074502 (2015).
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Yin, X.

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Y. Yang, H. Wang, F. Yu, Z. Xu, and H. Chen, “A metasurface carpet cloak for electromagnetic, acoustic and water waves,” Sci. Rep. 6(1), 20219 (2016).
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Y. Zhang, Y. Luo, J. B. Pendry, and B. Zhang, “Transformation-Invariant Metamaterials,” Phys. Rev. Lett. 123(6), 067701 (2019).
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S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
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J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, and F. J. Garcia-Vidal, “A holey-structured metamaterial for acoustic deep-subwavelength imaging,” Nat. Phys. 7(1), 52–55 (2011).
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F. Sun, Y. Zhang, J. Evans, and S. He, “A Camouflage Device Without Metamaterials,” Prog. Electromagn. Res. 165, 107–117 (2019).
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Y. Zhang, Y. Luo, J. B. Pendry, and B. Zhang, “Transformation-Invariant Metamaterials,” Phys. Rev. Lett. 123(6), 067701 (2019).
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J. B. Pendry, Y. Luo, and R. Zhao, “Transforming the optical landscape,” Science 348(6234), 521–524 (2015).
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B. Zheng, Y. Yang, Z. Shao, Q. Yan, N. H. Shen, L. Shen, H. Wang, E. Li, C. M. Soukoulis, and H. Chen, “Experimental Realization of an Extreme-Parameter Omnidirectional Cloak,” Research 2019, 1–8 (2019).
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C. Zhang, W. K. Cao, J. Yang, J. C. Ke, M. Z. Chen, L. T. Wu, Q. Cheng, and T. J. Cui, “A Multiphysical Digital Coding Metamaterial for Independent Controls of Broadband Electromagnetic and Acoustic Waves with Large Variety of Functions,” ACS Appl. Mater. Interfaces 11(18), 17050–17055 (2019).
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Y. Zhang, Y. Luo, J. B. Pendry, and B. Zhang, “Transformation-Invariant Metamaterials,” Phys. Rev. Lett. 123(6), 067701 (2019).
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S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
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Supplementary Material (10)

NameDescription
» Visualization 1       Visualization 1
» Visualization 2       Visualization 2
» Visualization 3       Visualization 3
» Visualization 4       Visualization 4
» Visualization 5       Visualization 5
» Visualization 6       Visualization 6
» Visualization 7       Visualization 7
» Visualization 8       Visualization 8
» Visualization 9       Visualization 9
» Visualization 10       Visualization 10

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Figures (6)

Fig. 1.
Fig. 1. The coordinate transformation relation between the real space (a) and the reference space (b). The yellow region between surfaces S1 and S2 of arbitrarily shapes is compressed into a thin yellow slab of thickness Δ in the reference space. The yellow regions in the real space and in the reference space are divided into many small trapezoid regions of height hi. Representative small trapezoid regions in the real space (c) and in the reference space (d).
Fig. 2.
Fig. 2. The structures of metal plate array (a) and a metal plate with periodic sub-wavelength square holes (b) to effectively realize the 2D and 3D reduced null media, respectively. The metals are indicated by the blue color. d is the lattice constant. a is the height of the air gaps in (a) and side length of square air cylinders.
Fig. 3.
Fig. 3. (a) Structure of the brass plate array used to achieve a multi-physics shifter for both electromagnetic wave and acoustic wave simultaneously (the thick black lines are brass and all other white regions are air). The length of each brass plate is h =mλ0 (the Fabry-Pérot resonance condition) and m = 2 here. The thickness of brass plate and air gap are both λ0/10, which means the filling factor of brass and air is 0.5. The angle between the brass plates and x axis is α=30 degree. The structure is designed at working wavelength λ0=3cm: corresponding frequencies are 10 GHz for electromagnetic wave and 11.433kHz for acoustic wave, respectively. (b) and (c) are distributions of normalized magnetic field’s z component for the TM polarized waves when a Gaussian electromagnetic beam incidents onto the brass plate array by 0 degree and -30 degree, respectively (see Visualization 1). (d) and (e) are normalized acoustic pressure distributions when a Gaussian acoustic beam incidents onto the brass plate array by 0 degree and -30 degree, respectively (see Visualization 2). (e) and (f) show the reflectivity of the multi-physics shifter in (a) when the wavelength deviates from the designed value λ0=3 cm for EM wave and acoustic wave, respectively (see Visualization 3 and Visualization 4).
Fig. 4.
Fig. 4. (a) The structure of the brass plate array for multi-physics scattering reduction. The thick black lines are brass plates of thickness λ0/10 and length h= 2λ0. (b)-(d) The normalized magnetic field’s z component for the TM polarized waves when a Gaussian electromagnetic beam incidents onto the brass plate array by 0, 20 and 40 degrees (see Visualization 5). (e)-(g) The normalized acoustic pressure when a Gaussian acoustic beam incidents onto the brass plate array by 0, 20 and 40 degrees (see Visualization 6). The boundaries of the central object of strong scattering are set as PEC and hard walls for electromagnetic wave and acoustic wave, respectively. All other parameters are the same as those in Fig. 3. Visualization 7 and Visualization 8 show Gaussian beam normally incidents onto the multi-physics scattering reduction device in Fig. 4(a) when the wavelength of incident Gaussian beam changes from λ0/3 to 2λ0 for electromagnetic case and acoustic case, respectively.
Fig. 5.
Fig. 5. Scattering when a Gaussian beam incidents onto the strongly scattering object by 0, 20 and 40 degrees. (a)-(c) The corresponding normalized magnetic field’s z component when the brass plates are removed from Figs. 4(b)–4(d) (only the central object of strong scattering is left in air). (d)-(f) The corresponding normalized acoustic pressure when the brass plates are removed from Figs. 4(e)–4(g). Other parameters are the same as those in Fig. 3. Visualization 9 and Visualization 10 show Gaussian beam normally incidents onto the strongly scattering object in the center of Fig. 4(a) (scattering reduction device is removed) when the wavelength of incident Gaussian beam changes from λ0/3 to 2λ0 for electromagnetic case and acoustic case, respectively.
Fig. 6.
Fig. 6. (a) Structure of the beam steering device. (b) and (c) are normalized amplitude of acoustic pressure and z component of the magnetic field in 2D numerical simulations when acoustic wave and TM polarized electromagnetic wave incident onto the beam steering device, respectively.

Equations (11)

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{ ε = J ε J T det ( J ) μ = J μ J T det ( J ) ,   { ρ 1 = J ρ 1 J T det ( J ) κ = det ( J ) κ .
x = { d 1 / ( Δ / 2 ) x , x [ 0 , d 1 ] tan ( π α 1 ) ( x Δ 2 ) / tan ( π θ 1 ) + d 1 , x [ d 1 , d 1 + h i / tan ( π θ 1 ) ] d 2 / ( Δ / 2 ) x , x [ d 2 , 0 ) tan α 2 ( x + Δ 2 ) / tan θ 2 d 2 , x [ d 2 h i / tan θ 2 , d 2 ] x , e l s e ; y = y ; z = z .
ε ε 0 = μ μ 0 = ρ 0 ρ = { d i a g ( 2 d 1 / Δ , Δ / 2 d 1 , Δ / 2 d 1 ) , x [ 0 , d 1 ] d i a g ( tan ( π α 1 ) / tan ( π θ 1 ) , tan ( π θ 1 ) / tan ( π α 1 ) , tan ( π θ 1 ) / tan ( π α 1 ) ) , x [ d 1 , d 1 + h i / tan ( π θ 1 ) ] d i a g ( 2 d 2 / Δ , Δ / 2 d 2 , Δ / 2 d 2 ) , x [ d 2 , 0 ) d i a g ( tan α 2 / tan θ 2 , tan θ 2 / tan α 2 , tan θ 2 / tan α 2 ) , x [ d 2 h i / tan θ 2 , d 2 ] 1 , e s l e .
κ / κ 0 = { 2 d 1 / Δ , x [ 0 , d 1 ] tan ( π α 1 ) / tan ( π θ 1 ) , x [ d 1 , d 1 + h i / tan ( π θ 1 ) ] 2 d 2 / Δ , x [ d 2 , 0 ) tan α 2 / tan θ 2 , x [ d 2 h i / tan θ 2 , d 2 ] 1 , e s l e .
ε ε 0 = μ μ 0 = ρ 0 ρ α 1 π / 2 α 2 π / 2 Δ 0 { d i a g ( , 0 , 0 ) , d 1 x d 2 1 , e l s e .
κ κ 0 α 1 π / 2 α 2 π / 2 Δ 0 { , d 1 x d 2 1 , e l s e .
{ ε = μ = d i a g ( , 0 , 0 ) ρ = d i a g ( 0 , , ) κ = , d 1 x d 2 .
{ ε y = d a ε h , ε x = ε z μ y = μ h , μ x = μ z = a d μ h .
ε y = d a ε h , μ z = a d μ h , ε x .
1 ρ x = f h ρ h + f m ρ m ,   ρ y = f h ρ h + f m ρ m ,   1 κ = f h κ h + f m κ m .
{ ε y = 2 ε 0 , μ z = 0.5 μ 0 , ε x ρ x = 2.58 k g / m 3 , ρ y = 4250.6 k g / m 3 , = 0.3 M P a .

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