Abstract

Remote thermal focusing/refrigeration by suppressing thermal diffusion can be achieved with the help of the novel thermal lens proposed in this paper. Our thermal lens is designed using transformation optics, and has several advantages. Firstly, it is a remote controlling device, i.e. the temperature is increased or decreased only in the heat/cold source and the target points, and the temperature in the area between the source and target points is not influenced. Secondly, the heat/cold sources can move freely inside the lens, and hence the focused points outside the lens can be adjusted dynamically. Numerical simulations are given to verify the novel properties (such as thermal focusing effect, remote refrigeration and remote thermal diffusion suppressing) of the proposed device, which cannot be achieved by any other traditional method.

© 2016 Optical Society of America

1. Introduction

Optical/electromagnetic energy can be collected by an optical lens, which can focus a light beam to a point. However, it is still challenging to focus thermal energy down to a spot with high temperature by some thermal lens. In this paper we study whether some special anisotropic thermal materials that can change the direction of the heat flux in a pre-designed manner are able to focus the thermal energy to a spot.

The conventional method for thermal focusing/refrigeration is using thermal materials with high thermal conductivity or fluidity. For example, heat pipes are used in the Qinghai-Tibet Railway to solve the frozen soil problem [1]. A heat pipe is a vertically placed hollow metal pipe with liquid that can easily be evaporated. Heat from the earth will make the liquid in the lower end of the heat pipe to become vapor, and the vapor will be condensed into a liquid when it reaches the upper end of the heat pipe as it releases heat in a lower temperature environment. Therefore, heat will be easily transmitted to the outside with the heat pipe, which is equivalent to a natural “refrigerator”. Another example is the thermal concentrator [2], which is a circular device designed by transformation optics. It has high radial thermal conductivity and low tangential thermal conductivity, which can be realized by an alternating arrangement of metal and thermal insulator. The thermal concentrator can guide thermal energy along the radial direction to the central part of the device. However, all these thermal focusing/refrigeration devices have a major problem, that is, they can neither focus the thermal energy to a spot nor make the temperature of a spot lower than its surrounding region. The conventional thermal focusing/refrigeration device is, in a sense, just a thermal guiding device, and they can neither force heat flux flow to a high temperature spot nor prevent heat flux flow to a low temperature spot.

Transformation optics (TO) is a novel mathematical tool that can associate a coordinate transformation with a change in material parameters. TO has two spaces. One is the real space and the other is the virtual space. Materials and fields in the two spaces are connected to each other through a mapping (transformation) between the two spaces. TO was first developed for invisibility cloaks [3, 4 ], and was widely used to create novel optical devices with special functions such as perfect lenses [5–8 ], wave front reshapers [9, 10 ], field concentrators [11, 12 ], field rotators [13–15 ], beam splitters [16], antenna shells [17–19 ] and optical illusion devices [20–24 ]. Meanwhile, the same technique was theoretically generalized and applied to different physical equations. In recent years, the idea of TO was extended to acoustic waves [25–28 ], heat flux [2, 29–31 ], mechanical waves [32–34 ] and even matter waves [35]. Thermal cloaks [36–38 ] were a brilliant idea showing the artificial control of heat flux by TO. Recently, TO has also been used in the controlling of multiphysics. A bifunctional cloak was theoretically proposed [39] and even experimentally realized [40]. As a result of the development of metamaterials [41] and TO theory, more and more new devices deemed impossible have been designed and realized.

In the present paper, we use this powerful tool to design a thermal lens. The basic idea of the thermal lens originated from the idea of a spatial translational transformation used in illusion optics. In illusion optics, an object is translated to a new place to form an image. In this paper we translate a heat/cold source to a place far away from the heat/cold source to achieve thermal focusing/refrigeration. One characteristic of the spatial translation is that the center region of the lens is free space without any filling materials. Therefore, for illusion optics, objects can move freely in the lens; for thermal applications, no guiding materials are needed to connect the thermal source to the target point. Another characteristic of the spatial translation is that the region inside the lens is actually the same as its corresponding region outside the lens for an external observer because they are the same place in the virtual space. In real space, they are just spatially separated, but they have no difference for an external observer in the presence of a carefully designed lens. Therefore, for illusion optics, an object can have an image outside the lens; for thermal application, the target point can achieve thermal focusing/refrigeration without heating/cooling its surrounding region.

2. Design method and simulation results

The transformation we use here is a spatial translational transformation. Figure 1 shows the basic idea of the thermal lens by this coordinate transformation. In the virtual space, the heat source is placed at point (d, 0) outside of the empty shell. Note that it is free space in the reference space (the empty shell just indicates the corresponding location in the real space). In the real space, the small square including the heat source is moved inside the lens with anisotropic thermal materials, and there will be an image of the heat source outside the thermal lens. The transformation formula is given below,

x'={badb+axddb+ay+ddb+ab,forregionIbad+bax+ddb+aydd+bab,forregionIIbad+baxdd+baydd+bab,forregionIIIbadb+ax+ddb+ay+ddb+ab,forregionIVy'=y,z'=z,
where (x’, y’, z’) and (x, y, z) are the coordinates in the real space and the virtual space, respectively. Parameters a and b indicate the size of the inner and outer boundaries of the lens, respectively. d is the distance between the thermal source and its image. Given the transformation formula, we can get the thermal conductivity of the lens by the TO method used in the thermal conduction equation [2]. Therefore, the material parameter of the lens we required is:

 

Fig. 1 The basic scheme of the thermal lens by transformation optics. The blue lines form squares with the size denoted by the length of their diagonal lines: 2a and 2b. The yellow suns in the blue line squares denote the thermal sources in the virtual space (a) and the real space (b), respectively. (a) The whole virtual space is the free space (i.e. no thermal materials are utilized). (b) The sun in the dotted line square is the image of the real heat source in the green thermal lens in the real space. The green shell is the proposed thermal lens that can transform the thermal source in real space to its image position, which is consistent with the same position in the virtual space outside the shell.

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κ'=[(P2+Q2)PQPQP1P]κ,

with P=sign(x')Δdsign(x')Δ, Q=sign(x')sign(y')ddsign(x')Δ, Δ=ba and the constant value κ is the thermal conductivity of the background material, which has been assumed to be an isotropic material. Sign is a sign function, which is defined by:

sign(x)={1x>00x=0-1x<0.

The thermal lens designed by the spatial translational transformation has many novel functions. The first function is thermal focusing, which can be used for gathering thermal energy to a small area. The second is remote refrigeration, which is used for cooling a specific area while the low temperature source is far away from that area. The third is suppressing thermal diffusion (i.e. to remotely reduce the temperature around the high temperature heat source). This means that even if the medium between a heat source and a cold source has low thermal conductivity (e.g. vacuum), we can cool down the heat source by the cold source that is far away from the heat source by the proposed thermal lens, which cannot be achieved by any traditional methods.

For a perspective of TO, we can describe the functions of the thermal lens. In this way, we can easily understand why our thermal lens can achieve these novel functions which cannot be achieved by traditional methods. Suppose the whole real space is filled with an elastic surface. Any stretching, squeezing or folding manipulations without splitting are permitted. First we fix the outer boundary of the lens, leaving the elastic surface outside the lens undistorted. Then we pull the small square with its center coordinate (0, 0) out of the lens while keeping the small square undistorted. Noting that, in the whole process, the small square and the region outside the lens are not distorted. In Fig. 1, region II and III experienced a squeezing manipulation; region I and IV experienced a folding manipulation. Therefore, the only distorted part of the elastic surface is the part of the lens. Similarly, we can move a square (out of the lens) to the center of the lens with the distortion part only in the lens region. This illustrates the novel functions and characteristics of our lens, and we know why the lens can make a complete copy of the region inside the lens.

Numerical simulations based on COMSOL Multiphysics software were run to verify the performance of these three functions. In the thermal focusing simulation, we choose b = 3m, a = 2m, and d = 3.2m; the outer boundaries are set at a constant temperature 0°C; the thermal source at 100°C is in the center of the thermal lens. Figure 2 shows the simulation result of the thermal focusing effect of the proposed thermal lens. We can see that the temperature reduces gradually before the heat flux touches the inner boundary of the thermal lens. As soon as the heat flux flows into the thermal lens, heat will gather together, and after it goes through the thermal lens, the thermal energy will converge to a small area (as if a heat source inside the thermal lens forms a real image out of the thermal lens). We should note that our thermal lens has two prominent features. Firstly, unlike a heat pipe with high thermal conductivity (or fluidity) linking the heat source and the focus area to achieve a thermal focusing effect, our thermal lens still works if another object with different thermal conductivity (e.g. some thermal insulator that can cut off the heat flow for a heat pipe) is inserted between the heat source and the focus area (i.e. the heat flow will not be cut off even if some other object with low thermal conductivity is inserted). Secondly, it is a thermal focus lens in every sense, and different from a thermal concentrator. A thermal concentrator [2] can only guide heat flux flowing into a small area, but the temperature in the small area is lower than the temperature along the path of the heat flux. However, in our thermal lens, the temperature of the passing area is lower than that of the focusing area. In this way, we can heat up a specific area without burning out the material between the heat source and the heat-focused area.

 

Fig. 2 Simulation result of the thermal focusing effect, represented by a plot of the temperature distribution. The two arrows point to the thermal source and the focusing point, respectively.

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Figure 3 shows the remote refrigeration function of the proposed thermal lens. The simulation setup is the same as the thermal lens in Fig. 2; the only difference is that the heat source with a high temperature is replaced by a cold source with a low temperature. The temperature in the area between the source and the refrigeration point is much higher than the temperature in the source and the area of refrigeration. Thus, the low temperature source just cools the refrigeration area without affecting the other areas including the area between the source and the refrigeration point, which is a novel function of our lens that cannot be achieved by other traditional cooling methods.

 

Fig. 3 Simulation result of the remote refrigeration effect, represented by a plot of the temperature distribution. The two arrows point to the cold source and the refrigeration point, respectively.

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Figure 4 shows the effect of remotely suppressing the thermal diffusion. Figure 4(a) is the temperature distribution of a point thermal source with only background material. Figure 4(b) is the temperature distribution when we place a low temperature source and a thermal lens near the thermal source. We can see that the temperature is reduced dramatically. Figure 4(c) gives the temperature distribution on a line along the y-direction near the thermal source. We can see that the temperature increase is reduced to 16% of the original case without the thermal lens, which verifies the fact that a cold source with our thermal lens can be utilized to remotely suppress the thermal diffusion produced by a heat source.

 

Fig. 4 Numerical simulation results for remotely suppressing thermal diffusion: (a) with the thermal lens and a source with low temperature; (b) without the lens and the cold source; (c) temperature distribution on the line that has been marked in (a) and (b) along the y-direction near the thermal source.

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3. Discussion

Next we consider how to fabricate the proposed thermal lens. For the thermal lens with the size shown in Fig. 2 (b = 3m, a = 2m, and d = 3.2m), we could calculate the value of the thermal conductivity tensor of the lens using Eq. (2). Figure 5 shows the value of three components of the thermal conductivity tensor, here we choose the thermal conductivity of the background material κ = 1. From Fig. 5, we could see that, in the squeezing parts (regions II & III), κxx and κyy have positive values. However, in the folding parts (regions I & IV), κxx and κyy have negative values due to the space folding transformation. In order to examine it more clearly, we diagnose the materials of the lens in the principle axis system. We use κ// and κ to denote the thermal conductivities of the two directions (parallel and perpendicular to the principle axis) in the principle coordinate system. These two values can be obtained by a coordinate rotation transformation,

[κ00κ]=[cos(θ)sin(θ)sin(θ)cos(θ)][κxxκxyκxyκyy][cos(θ)sin(θ)sin(θ)cos(θ)],
where θ is the angle between the principal coordinate system and the original coordinate system. Solving Eq. (4), we could obtain the directions of the principle axes and the two thermal conductivity values along the two principle axis directions:

 

Fig. 5 Thermal conductivity distribution of the thermal lens. (a), (b) and (c) denote three components of the thermal conductivity tensor. (a) shows the x-x component, κxx = −5.11 for regions I & IV, and κxx = 2.68 for regions II & III. (b) shows the x-y component, κxy = 3.20 for regions I & II, and κxy = −3.20 for regions III & IV. (c) shows the y-y component, κyy = −2.20 for regions I & IV, and κyy = 4.20 for regions II & III.

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θ=12arctan(2κxyκxxκyy),
{κ=cos2θκxx+sin2θκyy+2sinθcosθκxyκ=sin2θκxx+cos2θκyy2sinθcosθκxy.

Substituting the thermal conductivity tensor of the original coordinate system to Eq. (6), we obtain κ// = −7.17, κ = −0.14 for regions I & IV, and κ// = 0.15, κ = 6.73 for regions II & III. With the help of effective medium theory, we can realize the required anisotropic medium in each region by two layered isotropic materials [36]. What we should notice here is that some negative thermal materials are required to achieve the proposed thermal lens with these novel functions, and this is a major restriction for the realization of our device. Although it is challenging, there are still some feasible schemes to achieve negative thermal materials. In a previously published paper [42], the authors used a model of rotor chains with mechanical forcing to show that when the mechanical forcing is strong enough, the energy flow can be increased by an inverse temperature gradient. In this case, the energy flow is in the opposite direction of the temperature gradient, and a negative thermal conductivity can be observed. In a recent paper [43], the authors used active thermoelectric components to “pump” heat from one side to the other side of a hidden object to achieve an active thermal cloak. In fact, a normal material with active components acts as a negative thermal material. Therefore, a negative thermal material is achievable.

4. Conclusions

In this paper, we have designed a thermal lens with three novel functions (a thermal focusing effect, remote refrigeration and remote thermal diffusion suppressing) by TO. All these novel functions of the proposed thermal lens cannot be achieved by any traditional method. The proposed thermal lens allows for some novel and important applications for controlling heat flux in the future. Even if the medium between the source and the targeted region is of low thermal conductivity (e.g. vacuum), we can still cool down or heat up the targeted region by a remote cold/heat source with the help of the proposed thermal lens. With the development of active thermal metamaterials, we believe our muti-functional thermal lens can be realized and widely used in a smart thermal control system.

Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Nos. 91233208 and 61178062), the National High Technology Research and Development Program (863 Program) of China (No. 2012AA030402), the Program of Zhejiang Leading Team of Science and Technology Innovation, the Postdoctoral Science Foundation of China (No. 2013M541774), the Preferred Postdoctoral Research Project Funded by Zhejiang Province (No. BSH1301016), Swedish VR grant (# 621-2011-4620) and AOARD.

References and links

1. L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

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

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

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

5. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef]   [PubMed]  

6. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef]   [PubMed]  

7. W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, “Design of oblate cylindrical perfect lens using coordinate transformation,” Opt. Express 16(11), 8094–8105 (2008). [CrossRef]   [PubMed]  

8. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef]   [PubMed]  

9. F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015). [CrossRef]  

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

11. F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013). [CrossRef]  

12. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008). [CrossRef]  

13. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008). [CrossRef]  

14. H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009). [CrossRef]   [PubMed]  

15. H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007). [CrossRef]  

16. D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008). [CrossRef]   [PubMed]  

17. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009). [CrossRef]  

18. F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014). [CrossRef]  

19. F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014). [CrossRef]   [PubMed]  

20. Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009). [CrossRef]   [PubMed]  

21. C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010). [CrossRef]   [PubMed]  

22. X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” J. Opt. Soc. Am. B 28(8), 1994–2000 (2011). [CrossRef]  

23. Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013). [CrossRef]  

24. F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016). [CrossRef]   [PubMed]  

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

26. H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007). [CrossRef]  

27. M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008). [CrossRef]   [PubMed]  

28. 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]   [PubMed]  

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30. R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013). [CrossRef]   [PubMed]  

31. M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015). [CrossRef]   [PubMed]  

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33. N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012). [CrossRef]   [PubMed]  

34. M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012). [CrossRef]  

35. S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008). [CrossRef]   [PubMed]  

36. Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

37. T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013). [PubMed]  

38. H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014). [CrossRef]   [PubMed]  

39. 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]  

40. 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]   [PubMed]  

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42. A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011). [CrossRef]   [PubMed]  

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References

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  1. L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).
  2. S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
    [Crossref] [PubMed]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  4. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref] [PubMed]
  5. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [Crossref] [PubMed]
  6. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
    [Crossref] [PubMed]
  7. W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, “Design of oblate cylindrical perfect lens using coordinate transformation,” Opt. Express 16(11), 8094–8105 (2008).
    [Crossref] [PubMed]
  8. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
    [Crossref] [PubMed]
  9. F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
    [Crossref]
  10. F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
    [Crossref] [PubMed]
  11. F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
    [Crossref]
  12. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
    [Crossref]
  13. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
    [Crossref]
  14. H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
    [Crossref] [PubMed]
  15. H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
    [Crossref]
  16. D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
    [Crossref] [PubMed]
  17. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
    [Crossref]
  18. F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
    [Crossref]
  19. F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
    [Crossref] [PubMed]
  20. Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
    [Crossref] [PubMed]
  21. C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
    [Crossref] [PubMed]
  22. X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” J. Opt. Soc. Am. B 28(8), 1994–2000 (2011).
    [Crossref]
  23. Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
    [Crossref]
  24. F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
    [Crossref] [PubMed]
  25. S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
    [Crossref] [PubMed]
  26. H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
    [Crossref]
  27. M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
    [Crossref] [PubMed]
  28. 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] [PubMed]
  29. S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
    [Crossref] [PubMed]
  30. R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
    [Crossref] [PubMed]
  31. M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
    [Crossref] [PubMed]
  32. M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
    [Crossref]
  33. N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
    [Crossref] [PubMed]
  34. M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
    [Crossref]
  35. S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
    [Crossref] [PubMed]
  36. Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).
  37. T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
    [PubMed]
  38. H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
    [Crossref] [PubMed]
  39. 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]
  40. 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] [PubMed]
  41. V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [Crossref]
  42. A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
    [Crossref] [PubMed]
  43. D. Nguyen, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 121901 (2015).
    [Crossref]

2016 (1)

F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
[Crossref] [PubMed]

2015 (4)

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
[Crossref]

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

D. Nguyen, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 121901 (2015).
[Crossref]

2014 (5)

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

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] [PubMed]

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
[Crossref] [PubMed]

2013 (5)

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
[Crossref]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

2012 (4)

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

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

2011 (3)

X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” J. Opt. Soc. Am. B 28(8), 1994–2000 (2011).
[Crossref]

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

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

2010 (1)

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

2009 (4)

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

2008 (7)

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, “Design of oblate cylindrical perfect lens using coordinate transformation,” Opt. Express 16(11), 8094–8105 (2008).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

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] [PubMed]

2007 (3)

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

2006 (3)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

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

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

2004 (2)

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Alekseyev, L. V.

Alù, A.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

Amra, C.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

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

Ao, X.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Bagci, H.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

Bao, L.

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

Brun, M.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

Burokur, S. N.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

Cai, B.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[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]

Chan, C.

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Chan, C. T.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

Chen, H.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

Chen, P. Y.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

Chen, S.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Cui, J.

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

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] [PubMed]

de Lustrac, A.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

Du, C.

Enoch, S.

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

Fang, G.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Fang, N.

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

Farhat, M.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

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, F.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Guenneau, S.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

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

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

Han, D.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Han, T.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

He, S.

F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
[Crossref] [PubMed]

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
[Crossref]

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

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
[Crossref] [PubMed]

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] [PubMed]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
[Crossref]

Hou, B.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Iacobucci, A.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Jacob, Z.

Jiang, C.

Jiang, W.

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Kadic, M.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Kong, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Kwon, D. H.

Lai, Y.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Lan, L.

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Legoll, F.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Leonhardt, U.

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

Li, B.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

Li, C.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Li, F.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Li, Z.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Lin, L.

Liu, X.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Liu, Y.

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] [PubMed]

Luo, X.

Luo, Y.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Ma, Y.

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] [PubMed]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Meng, X.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Moccia, M.

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]

Movchan, A. B.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

Narayana, S.

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

Narimanov, E.

Ng, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Nguyen, D.

D. Nguyen, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 121901 (2015).
[Crossref]

Olla, S.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Pendry, J.

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] [PubMed]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

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

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Popa, B. I.

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] [PubMed]

Qiu, C. W.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

Rahm, M.

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] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Ran, L.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

Raza, M.

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] [PubMed]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Sato, Y.

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]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

Savo, S.

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]

Schittny, R.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Schurig, D.

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] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

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

Shalaev, V.

V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

Shi, C.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Shi, X.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Smith, D. R.

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] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

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

Starr, 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] [PubMed]

Stenger, N.

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

Stoltz, G.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Sun, C.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Sun, F.

F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
[Crossref] [PubMed]

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
[Crossref]

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

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
[Crossref] [PubMed]

F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
[Crossref]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Sun, H.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Tichit, P.-H.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

Veynante, D.

Wang, W.

Wang, Y.

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] [PubMed]

Wegener, M.

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

Wen, W.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Werner, D. H.

Wilhelm, M.

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

Xia, C.

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

Xiao, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Xu, H.

D. Nguyen, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 121901 (2015).
[Crossref]

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Xue, X.

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

Yang, X.

Yuan, T.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

Zang, X.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” J. Opt. Soc. Am. B 28(8), 1994–2000 (2011).
[Crossref]

Zhang, B.

D. Nguyen, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 121901 (2015).
[Crossref]

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Zhang, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Zhang, S.

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

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

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Zhang, Y.

D. Nguyen, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 121901 (2015).
[Crossref]

Zhang, Z. Q.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Zhu, Y.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

D. Nguyen, H. Xu, Y. Zhang, and B. Zhang, “Active thermal cloak,” Appl. Phys. Lett. 107(12), 121901 (2015).
[Crossref]

J. Appl. Phys. (1)

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

J. Glaciology Geocryology (1)

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

NPG Asia Mater. (1)

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Opt. Commun. (1)

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Opt. Express (4)

Photonics Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Phys. Rev. B (2)

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Phys. Rev. Lett. (13)

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

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] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

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] [PubMed]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108(21), 214303 (2012).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110(19), 195901 (2013).
[Crossref] [PubMed]

Phys. Rev. X (1)

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]

Prog. Electromagnetics Res. (3)

F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
[Crossref]

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
[Crossref]

Sci. Rep. (5)

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

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
[Crossref] [PubMed]

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

F. Sun and S. He, “Overlapping illusions by transformation optics without any negative refraction material,” Sci. Rep. 6, 19130 (2016).
[Crossref] [PubMed]

Science (2)

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

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

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Figures (5)

Fig. 1
Fig. 1 The basic scheme of the thermal lens by transformation optics. The blue lines form squares with the size denoted by the length of their diagonal lines: 2a and 2b. The yellow suns in the blue line squares denote the thermal sources in the virtual space (a) and the real space (b), respectively. (a) The whole virtual space is the free space (i.e. no thermal materials are utilized). (b) The sun in the dotted line square is the image of the real heat source in the green thermal lens in the real space. The green shell is the proposed thermal lens that can transform the thermal source in real space to its image position, which is consistent with the same position in the virtual space outside the shell.
Fig. 2
Fig. 2 Simulation result of the thermal focusing effect, represented by a plot of the temperature distribution. The two arrows point to the thermal source and the focusing point, respectively.
Fig. 3
Fig. 3 Simulation result of the remote refrigeration effect, represented by a plot of the temperature distribution. The two arrows point to the cold source and the refrigeration point, respectively.
Fig. 4
Fig. 4 Numerical simulation results for remotely suppressing thermal diffusion: (a) with the thermal lens and a source with low temperature; (b) without the lens and the cold source; (c) temperature distribution on the line that has been marked in (a) and (b) along the y-direction near the thermal source.
Fig. 5
Fig. 5 Thermal conductivity distribution of the thermal lens. (a), (b) and (c) denote three components of the thermal conductivity tensor. (a) shows the x-x component, κxx = −5.11 for regions I & IV, and κxx = 2.68 for regions II & III. (b) shows the x-y component, κxy = 3.20 for regions I & II, and κxy = −3.20 for regions III & IV. (c) shows the y-y component, κyy = −2.20 for regions I & IV, and κyy = 4.20 for regions II & III.

Equations (6)

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x ' = { b a d b + a x d d b + a y + d d b + a b ,for region I b a d + b a x + d d b + a y d d + b a b ,for region II b a d + b a x d d + b a y d d + b a b ,for region III b a d b + a x + d d b + a y + d d b + a b ,for region IV y ' = y , z ' = z ,
κ ' = [ ( P 2 + Q 2 ) P Q P Q P 1 P ] κ ,
s i g n ( x ) = { 1 x > 0 0 x = 0 - 1 x < 0 .
[ κ 0 0 κ ] = [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] [ κ x x κ x y κ x y κ y y ] [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] ,
θ = 1 2 arc tan ( 2 κ x y κ x x κ y y ) ,
{ κ = cos 2 θ κ x x + sin 2 θ κ y y + 2 sin θ cos θ κ x y κ = sin 2 θ κ x x + cos 2 θ κ y y 2 sin θ cos θ κ x y .

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