Invisibility Cloak Goes Three-Dimensional for Heat

Authors: Hongyi Xu¹, Xihang Shi¹, Fei Gao¹, Handong Sun^1,2, Baile Zhang^1,2

Affiliation:
¹Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore.
²Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore.

While the topic of invisibility has long been investigated in optics-related topics, it is for the first time that invisibility cloaking is realized for heat in a three-dimensional (3D) thermal space, according to a recent research result[1] published by our group at Nanyang Technological University, Singapore.

Thermal invisibility was initially inspired by the concept of Transformation Optics [2, 3], a method that can control light propagation with a coordinate transformation in a 3D optical space, which in general requires optical metamaterials with exotic constitutive parameters (e.g. extremely large or extremely small anisotropic permittivity and permeability). Despite the inspiring elegance of 3D optical invisibility cloaking theory, its experimental realizations have been mainly limited to two dimensions (2D), because of the widely acknowledged tremendous difficulties in constructing optical metamaterials with stringent parameters in 3D.

Similarly, the recent development of thermal invisibility cloaking based on transformation thermodynamics were firstly demonstrated in 2D [4, 5]. The method, similar to transformation optics, requires thermal metamaterials with anisotropy and inhomogeneity, being difficult in 3D.

Researchers in Nanyang Technological University successfully bypassed the problem by taking advantage of the difference between heat (a diffusion phenomenon) and light (a wave phenomenon), and experimentally demonstrated the world’s first ultra-thin 3D thermal cloak that shields an air bubble in a stainless steel from external conductive heat flux [1]. The technology can protect a 3D object from heat flux without distorting the external temperature distribution by simply using an ultra-thin layer of thermal metamaterial made of copper with carefully designed thickness.

The implementation process of thermal cloak is illustrated in Fig.1. A hemi-spherical hole with radius of 0.51 cm was drilled by electrical discharge machining in a half stainless steel block with dimension of 2×2×1 cm. A thin disk of copper was punched into the hemi-spherical hole by a molding rod (Fig 1a), to form a copper shell (Fig. 1b) with homogeneous thickness of 100 μm. Two identical half blocks were further combined together to form a complete 3D thermal cloak (Fig. 1c), with dimension of 0.5/0.51 cm for the inner/outer radius of the copper spherical layer, and 2×2×2 cm for the complete stainless steel block.

Figure 1. Illustration of the Fabrication of a 3D thermal cloak. a, Molding process of half of the 3D thermal cloak: (a) Thin copper disk is punched into the hemispherical hole in the stainless steel block. (b) Illustration and snapshot of half of the thermal cloak after molding. (c) Illustration and snapshot of the full cloak by combining two half blocks. The red/blue plate represents high/low temperature at the bottom/top surface [1].

In the experimental characterization, a hot plate (red color, Fig. 1c) and an ice tank (blue color, Fig. 1c) were closely attached to the bottom and top surface of the thermal cloak. When heat diffused from bottom to top, the temperature at the cross-section surface was captured by a thermal camera. The dynamic process of heat transfer from the beginning to the moment near thermal equilibrium was recorded in a movie clip:
 

The temperature distributions at the beginning time and at the moment near thermal equilibrium are shown in Fig. 2. In Fig. 2a and 2d (cases of background), the temperature distribution is homogeneous across the entire surface, indicating that heat diffuses through the stainless steel smoothly. In Fig. 2b and 2e (cases without thermal cloak), the distribution of temperature is distorted (being ‘bent’ towards the air bubble) and a relatively cool region is left behind the air bubble, indicating that part of heat flux has been blocked by the air bubble. In Fig. 2c and Fig. 2f (cases with thermal cloak), the temperature distribution outside the air bubble is restored to norm, as if the air bubble did not exist, indicating the cloaking effect for heat flux.

Figure 2. Characterization of conductive thermal cloaking for transient homogeneous thermal flux. (a-c) Temperature distributions for the moment of 0.5 min at the beginning of heat transfer. (d-f) Temperature distributions for the moment of 4.5 min close to thermal equilibrium. (a&d) Temperature distributions in the pure background without any air bubble or cloak. (b&e) Temperature distributions when an air bubble without the cloak is present. (c&f) Temperature distributions when the air bubble is cloaked by the ultra-thin cloak. In b-c and e-f, the dotted circles indicate the position of the air bubble, while the dotted circles in a and d are merely for comparison [1].

This thermal invisibility cloak is the first demonstration in 3D that heat flux can be effectively controlled by thermal metamaterials. Application wise, effective control of heat is an important subject in modern semiconductor industries, where the exponential increase of package density is generating more and more heat in a unit space. The heat generated jeopardized the performance and lifetime of semiconductor devices, accounting for over 50 percent of electronic failures [6]. With effective heat control technologies based on thermal metamaterials, it is possible to develop efficient heat dissipation solutions to thermal problems in semiconductor industries.

References: 
[1] Hongyi Xu, Xihang Shi, Fei Gao, Handong Sun, Baile Zhang, "Ultrathin Three-Dimensional Thermal Cloak", Physical Review Letters, 112, 054301 (2014). Abstract.
[2] Ulf Leonhardt, "Optical Conformal Mapping", Science, 312, 1777-1780 (2006). Abstract.
[3] J. B. Pendry, D. Schurig, D. R. Smith, "Controlling Electromagnetic Fields", Science, 312, 1780-1782 (2006). Abstract.
[4] Supradeep Narayana, Yuki Sato, "Heat Flux Manipulation with Engineered Thermal Materials", Physical Review Letters, 108, 214303 (2012). Abstract.
[5] Robert Schittny, Muamer Kadic, Sebastien Guenneau, Martin Wegener, "Experiments on Transformation Thermodynamics: Molding the Flow of Heat", Physical Review Letters, 110, 195901 (2013). Abstract.
[6] Shanmuga Sundaram Anandan, and Velraj Ramalingam, "Thermal Management of Electronics: A Review of Literature," Thermal Science, 12, 5-26 (2008). Full Article.

Acoustically Invisible Walls

(left) Oliver Wright
(right) Sam Lee

Authors: Oliver B. Wright¹ and Sam Hyeon Lee²

Affiliation:
¹Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan
²Institute of Physics and Applied Physics, Yonsei University, Seoul, South Korea

Physicists in a Korea-Japan collaboration have devised a way to make hard walls transmit sound almost perfectly[1], which could prove useful for developing new types of windows or acoustic concentrators. Based on solid walls of metal or plastic perforated by small holes containing stretched membranes made of humble kitchen cling film, the collaboration have imaged sound travelling unimpeded through them. Sound in such structures, known as metamaterials, resonates strongly with the structure at certain frequencies, allowing counterintuitive effects such as zero sonic reflection. This is an example of a phenomenon known as extraordinary transmission, first demonstrated in the field of optics, whereby light waves are squeezed through sub-wavelength holes more efficiently than expected [2,3].

In the design presented, a tiny force from the sound wave is sufficient to launch a large motion of the membranes, a situation that mimics the air in the hole moving as if with zero mass. Sam Lee of Yonsei University, Kong-ju Bok Lee of Ehwa Women’s University and Oliver Wright of Hokkaido University speculate that this sonic invisible wall could be used for security glass, for example in banks or taxis, that allows you to talk across it, but protects you from any mechanical intrusion.

Figure 1: (left) Single hole with membrane in a cylindrical duct; (right) metamaterial wall consisting of an array of holes containing membranes.

In the first experiments done, sound was incident in a cylindrical tube of diameter 100 mm on a wall blocking the tube containing a single hole of diameter 17 mm mounted with a tight membrane, as shown in Figure 1. It was found that 90% of the acoustic amplitude was transmitted at the audio frequency of 1.2 kHz, in spite of only 3% of the area of the wall being open.

The team also demonstrated a giant concentration up to a factor of 5700 with smaller holes, and that the acoustic energy is effectively transmitted for any angle of incidence, as shown in the example of Figure 2. Figure 1 also shows an example of how a wall of membrane-covered holes could be constructed, effectively constituting a metamaterial wall that transmits sound effectively. This “extraordinary-transmission” phenomenon can be used over a wide range of frequencies. So the method would work equally well for ultrasound, for which preliminary experiments have been reported at lower efficiencies using resonances in bare holes [4]; this could be exploited to concentrate ultrasonic energy through tiny holes, forming novel lenses useful for high resolution ultrasonic imaging.

Figure 2: (Bottom image) Pressure map obtained in the audio-frequency extraordinary-acoustic transmission experiment at 1.2 kHz on an acoustic metamaterial consisting of tight membranes in 4 tiny holes, showing a giant acoustic concentration of 5700 in intensity with an areal coverage ratio of only 0.03. (Top image) Image for holes with no membranes.

References:
[1] Jong Jin Park, K. J. B. Lee, Oliver B. Wright, Myoung Ki Jung, and Sam H. Lee, "Giant Acoustic Concentration by Extraordinary Transmission in Zero-Mass Metamaterials", Physical Review Letters, 110, 244302 (2013). Abstract.
[2] R. Ulrich, in Optical and Acoustical Microelectronics, edited by J. Fox, page 359 (Polytechnic, New York, 1974).
[3] T.W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays", Nature, 391, 667 (1998). Abstract.
[4] Bo Hou, Jun Mei, Manzhu Ke, Weijia Wen, Zhengyou Liu, Jing Shi, and Ping Sheng, "Tuning Fabry-Perot resonances via diffraction evanescent waves", Physical Review B, 76, 054303 (2007). Abstract.

Transformational Thermodynamics: Cloaks to Keep You Cool

Sébastien Guenneau (left) and Claude Amra (right)












Authors: Sebastien Guenneau and Claude Amra

Affiliation: Institut Fresnel, Centre National Recherche Scientifique, Aix-Marseille University and Ecole Centrale Marseille, France

 In 2006, two papers -- published in the same issue of 'Science' -- revolutionized the world of classical optics with the concept of transformation optics (TO). One was by Ulf Leonhardt of University of St Andrews, Scotland, UK [1] and the other was by John Pendry of Imperial College, London, UK and David Schurig and David Smith of Duke University, USA [2]. The concept of transformation optics allows coordinate changes in an isotropic homogeneous dielectric medium that can lead to a anisotropic heterogeneous metamaterial described by tensors of permittivity and permeability, a fact foreseen twenty years ago in two visionary papers on computational electromagnetic [3,4].

The conceptual breakthrough in 2006 was to note that one can blow-up a point into a finite region using a change of coordinates known from mathematicians working on inverse problems [5], in order to conceal this region from electromagnetic waves, and to demonstrate the feasibility of an invisibility cloak for microwaves [6], thereby bringing perhaps the most stunning electromagnetic paradigm of all times into reality!

However, similar changes of coordinates can also be applied to other wave equations, such as linear water waves propagating at the surface of a fluid [7], pressure waves propagating in a fluid [8], coupled pressure and shear waves propagating in a solid material [9,10], or flexural waves in thin elastic plates [11,12]. Such metamaterials designed using transformation acoustics (TA) could be used to protect regions from tsunamis (in general from ocean waves) or earthquakes (especially from surface elastic waves known as Rayleigh waves) on a larger scale! They could also be used to improve sound in opera theaters or to hide submarines from sonars (silence cloak).

But that’s not the end of the invisible story, as one can also leave the world of TO and TA and enter the brave new world of transformation thermodynamics (TT, or T²), whereby one now wishes to control diffusion processes, such as heat. Some precursory theoretical and numerical studies on the conduction equation in anisotropic media [5,13,14] have shown that one can control the diffusive heat flow in new ways in the static limit, a fact experimentally demonstrated this year [15].

Figure 1: [Click on the image to view high resolution version] Numerical simulation showing the distribution of temperature in a region heated from the left (temperature=100 degrees Celsius, red color). The temperature gradually decreases away from the source, until it reaches a temperature of 0 degree Celsius on the left hand side (blue color). Importantly, one sees that the temperature vanishes inside the inner disc of the thermal cloak (annulus containing an anisotropic heterogeneous conductivity). This thermal protection is achieved by curving the isothermal curves (black lines).

Our group at the Fresnel Institute in Marseille and the Ecole Centrale in Paris has shown, under the umbrella of the French National Center for Scientific Research (CNRS), that TT is a valid concept: one can control the flow of heat when time flows [16], and it is enough to use concentric layers with isotropic homogeneous conductivity to design invisibility cloaks (to protect a region from heat, see figure 1) and concentrators (to enhance heat exchange in a region). This opens unprecedented routes towards heat insulators -- for instance, for Green houses and also for heat harvesting in photovoltaics.

References:
[1] U. Leonhardt, “Optical Conformal Mapping”, Science 312, 1777 (2006). Abstract.
[2] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields”, Science, 312, 1780 (2006). Abstract. 
[3] A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, “Transformation methods in computational electromagnetic“, Journal of Applied Physics, 75, 6036-6038 (1994). Abstract.
[4] A.J. Ward and J.B. Pendry, “Refraction and geometry in Maxwell’s equations“, Journal of Modern Optics, 43, 773-793 (1996). Abstract.
[5] A Greenleaf, M Lassas and G Uhlmann, “On nonuniqueness for Calderon’s inverse problem“, Mathematical Research Letters, 10, 685–693 (2003). Full Article.
[6] 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, 977 (2006). Abstract.
[7] M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband Cylindrical Acoustic Cloak for Linear Surface Waves in Fluid”, Physical Review Letters, 101, 134501 (2008). Abstract.
[8] S. Zhang, C. Xia, and N. Fang, “Broadband Acoustic Cloak for Ultrasound Waves”, Physical Review Letters, 106, 024301 (2011). Abstract.
[9] G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant from”, New Journal of Physics, 8, 248 (2006). Abstract.
[10] M. Brun, S. Guenneau and A.B. Movchan, "Achieving control of in-plane elastic waves". Applied Physics Letters, 94, 061903 (2009). Abstract.
[11] M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Ultrabroadband Elastic Cloaking in thin Plates”, Physical Review Letters, 103, 024301 (2009). Abstract.
[12] N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on Elastic Cloaking in Thin Plates”, Physical Review Letters, 108, 014301 (2012). Full Article. 2Physics Article.
[13] C. Z. Fan, Y. Gao, and J. P. Huang, “Shaped graded materials with an apparent negative thermal conductivity", Applied Physics Letters, 92, 251907 (2008). Abstract.
[14] T. Chen, C. N. Weng, and J. S. Chen, “Cloak for curvilinearly anisotropic media in conduction", Applied Physics Letters, 93, 114103 (2008). Abstract.
[15] Supradeep Narayan and Yuki Sato, “Heat flux manipulation with engineered thermal materials", Physical Review Letters 108, 214303 (2012). Abstract.
[16] S. Guenneau, C. Amra, and D. Veynante, ‘’Transformation thermodynamics: cloaking and concentrating heat flux’’, Optics Express, 20, 8207 (2012). Abstract.

Broadband Array of Invisibility Cloaks in the Visible Frequency Range

Author: Vera Smolyaninova 

Affiliation: Dept. of Physics Astronomy and Geosciences, Towson University, MD, USA

Ever since the first experimental demonstrations in the microwave and visible ranges [1,2], invisibility cloaks have stimulated progress in the fields of metamaterials and transformation optics. Very recently, Farhat and co-workers [3] suggested that arrays of invisibility cloaks may have interesting electromagnetic properties, and suggested some potential applications in noninvasive probing, sensing and communication. Our team, Vera Smolyaninova and Kurt Ermer from Towson University, and Igor Smolyaninov from the University of Maryland demonstrated the first experimental realization of an invisibility cloak array.

Our experiment is based on the recent demonstration of broadband invisibility cloak, which relies on a curved waveguide mimicking the metamaterial properties necessary for cloaking [4]. Since a gap between a gold-coated spherical lens touching a gold-coated planar glass slide provides a good approximation of the required waveguide shape, such geometry can be easily transformed into a large array of broadband invisibility cloaks using commercially available microlens arrays. This work is reported in the May issue of the New Journal of Physics [5]. In the experiments, conducted at Towson University, very large arrays of roughly 25000 cloaks were used to “hide” approximately 20% of the surface area. This is the first experimental arrangement which lets you study mutual interactions of a very large number of invisibility cloaks.

Past 2Physics article by Vera Smolyaninova:
June 06, 2009: "Large Broadband Invisibility Cloak for Visible Light"
by Vera Smolyaninova and Vlad Shalaev

Igor Smolyaninov of University of Maryland

Unlike the so-called “carpet cloaks” which hide objects on the metallic mirror background, every cloak in our array guides light around the cloaked area. While the former approach is akin to rendering bumps on a carpet invisible by allowing them to blend in with the carpet, classical cloaking concentrates on enabling light to flow around an object. Typically, such classical cloaks [1,2] require sophisticated metamaterial nanofabrication. Each material has its own refractive index, which describes how much light will bend in that particular material and defines how much the speed of light slows down while passing through a material. Natural materials typically have refractive indices greater than one. Refraction occurs as electromagnetic waves bend when passing from one material into another. It causes the bent-stick-in-water effect, which occurs when a stick placed in a glass of water appears bent when viewed from the outside.

Kurt Ermer of Towson University

Unlike natural materials, metamaterials are able to produce the index of refraction ranging from very large positive values of the order of 100 to less than zero. In particular, artificial metamaterials needed for cloaking must have the index of refraction, which varies from zero to one. Unfortunately, such artificial metamaterials have very large losses. In our cloak array the precisely tapered shape of the waveguide around each cloak alters the refractive index in the same way as in metamaterials, gradually increasing the index from zero to 1 along the curved surface of each microlens. Since light propagates mainly through the air gap, losses in this design are very low, and the resulting structure is broadband. It works across the whole visible light spectrum.

Theoretical work for the design was led by the University of Maryland, with Towson University leading work to fabricate the device and demonstrate its cloaking properties. The cloaking array device is formed by two gold-coated surfaces, one surface being a commercially available microlens array, and the other a flat glass slide. Individual cloaks in the array were separated by about 30 microns, or roughly the width of a human hair, so that a 5 by 5 millimeter squared microlens array would make approximately 25000 individual invisibility cloaks. Instead of being reflected as normally would happen, the light flows around each cloak and shows up on the other side, like water flowing around an array of stones.

[Click on image to see a higher resolution version]

Building and studying the arrays of invisibility cloaks offers more refined experimental tools to test individual cloak performance. Compared to the characterization of individual cloaks, the angular performance of cloak arrays appears to be more sensitive to cloak imperfections. For example, cloak arrays perform better when light is sent in along the row directions. These findings may be useful in such related areas as acoustic and surface-wave cloaking, as well as in the potential practical applications listed above.

On the other hand, since light is “stopped” near each cloak, and the cloak radius depends on the light wavelength, the cloak array produced in our study may be used in the spectrometer on the chip applications. The “trapped rainbow” effect observed near each cloak [6] may find applications in such fields as biosensing and testing for genetic decease. Stopping light at the cloak boundary leads to considerable enhancement of fluorescence near each cloak in the array [6].

The work was funded by the National Science Foundation.

References
[1] “Metamaterial electromagnetic cloak at microwave frequencies”, D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr, D.R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies”, Science 314, 977-980 (2006). Abstract.
[2] “Two-dimensional metamaterial structure exhibiting reduced visibility at 500 nm”, I.I. Smolyaninov, Y.J. Hung, and C.C. Davis, Optics Letters 33, 1342-1344 (2008). Abstract.
[3] “Understanding the functionality of an array of invisibility cloaks”, M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran,C. Rockstuhl, and F. Lederer, Phys. Rev. B 84 235105 (2011). Abstract.
[4] “Anisotropic metamaterials emulated by tapered waveguides: application to electromagnetic cloaking”, I.I. Smolyaninov, V.N. Smolyaninova, A.V. Kildishev, and V.M. Shalaev, Phys. Rev. Letters 103, 213901 (2009). Abstract. 2Physics Article.
[5] “Experimental demonstration of a broadband array of invisibility cloaks in the visible frequency range”, V.N. Smolyaninova, I.I. Smolyaninov, and H.K. Ermer, New J. Phys. 14, 053029 (2012). Full Article.
[6] “Trapped rainbow techniques for spectroscopy on a chip and fluorescence enhancement” V.N. Smolyaninova, I.I. Smolyaninov, A.V. Kildishev, and V.M. Shalaev, Applied Physics B 106, 577-581 (2012).Abstract. arXiv:1101.336.

Near-Infrared Metamaterials Go Beyond Metals

Gururaj V. Naik (left) and Alexandra Boltasseva (right)











Authors: Gururaj V. Naik and Alexandra Boltasseva 

Affiliation: School of Electrical and Computer Engineering and Birck Nanotechnology Center, Purdue University, USA

Engineering the flow of light at the nanoscale is enabled by plasmonics and metamaterials. Research in metamaterials has progressed rapidly in the past decade, producing many breakthroughs that have changed our fundamental understanding of light propagation and interactions and pushed the frontiers of possible applications. The enormous potential of metamaterials is clogged by the limitations arising from the materials, particularly metals that constitute these metamaterials. These limitations of metal building blocks are particular detrimental to the operation of metamaterial devices in the optical range [1].

Past 2Physics article by Alexandra Boltasseva:
February 27, 2011: "New Materials Could Turn Near-Fantastic Devices like Invisibility Cloaks and Hyperlenses into Reality"
by Alexandra Boltasseva and Harry A. Atwater

Metals are the bottleneck of performance in many classes of optical metamaterials. The limitations arise from undesirable properties of metals such as high losses, large magnitude of permittivity, lack of tunability of optical properties, and challenges associated with nanofabrication and integration [2]. A possible alternative to metals that overcomes most of these problems is a semiconductor-based metal. It is well known that heavily doping semiconductors can exhibit metal-like optical properties. GaAs was demonstrated to work as a metal substitute in the mid-IR range when heavily doped (about 10^18-19 cm^-3) [3].

However, achieving metal-like optical properties in semiconductors in the near-infrared range is a tough challenge. The required very high doping (up to 10²¹ cm^-3) can hardly be accomplished in conventional semiconductors. However, some semiconductors such as zinc oxide allow ultra-high doping. Heavily doped zinc oxide for example aluminum-zinc-oxide (Al:ZnO ) belong to the class of materials called transparent conducting oxides (TCOs) that show metal-like optical properties in the near-infrared range [2].

Figure 1. Field map obtained from simulations showing negative refraction occurring in a metamaterial built by stacking sixteen alternating layers of Al:ZnO and ZnO. The incident beam is TM-polarized and impinges the sample at an angle 40 degrees away from normal incidence.

Recently, we showed that Al:ZnO can be utilized as a metal substitute in a near-infrared metamaterial device and demonstrated negative refraction in this device [4]. The device consisted a stack of sixteen alternating layers of ZnO and Al:ZnO. The thickness of each layer was much smaller than the incident wavelength. Such a metamaterial produces extreme anisotropy in its dispersion, which can lead to negative refraction of the incident light. Simulations showed that the light should bend on the ‘wrong’ side of the sample normal for TM-polarized incident light. An experimental set-up was built to verify this phenomenon. The transmittance of light through the sample was measured with a blade blocking half of the transmitted beam. When negative refraction occurred, the beam shifted such that more of the beam was blocked by the blade, which led to a dip in the transmitted light intensity. This observation not only confirmed negative refraction, but it also allowed us to assess the performance of this metamaterial. We found that the performance of this metamaterial device is three orders of magnitude higher than metal-based designs.

Figure 2. a) The experiment schematic used to observe negative refraction. A blade blocks the transmitted beam partially such that the lateral shift of the beam due to refraction modulates the intensity of unblocked portion of the beam. b) The relative transmittance measured for different angles of incidence from the Al:ZnO/ZnO metamaterial. In the wavelength range 1.8-2.4 μm, the metamaterial shows negative refraction, which results in the dips in the curves.

The demonstration of a metal-free plasmonic metamaterial in the near-infrared range with super-high performance is a technologically important step. The transition from metals to doped semiconductor materials enables the efficient and practical implementation of metamaterial devices for applications such as light concentrators for solar cells, optical invisibility cloaks and super-resolution lenses. This demonstration heralds the field of metal-free optical metamaterials.

References:
[1] A. Boltasseva and H. A. Atwater, "Low-loss plasmonic metamaterials," Science 331, 290-291 (2011). Abstract. 2Physics Article.
[2] Gururaj V. Naik, Jongbum Kim and Alexandra Boltasseva, “Oxides and nitrides as alternative plasmonic materials in the optical range,” Optical Material Express, 1, 1090-1099 (2011). Abstract.
[3] Anthony J. Hoffman, Leonid Alekseyev, Scott S. Howard, Kale J. Franz, Dan Wasserman, Viktor A. Podolskiy, Evgenii E. Narimanov, Deborah L. Sivco & Claire Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Materials, 6, 946-950 (2007). Abstract.
[4] Gururaj V. Naik, Jingjing Liua, Alexander V. Kildishev, Vladimir M. Shalaev and Alexandra Boltasseva, “Demonstration of Al:ZnO as a plasmonic component of near-infrared metamaterials,” Proceedings of the National Academy of Sciences of the United States of America,(published online May 16, 2012) DOI: 10.1073/pnas.112151710. Abstract.

A Cloak for Elastic Waves in Thin Polymer Plates

[From Left to Right]  Nicolas Stenger, Manfred Wilhelm and Martin Wegener

Authors: Nicolas Stenger¹, Manfred Wilhelm² and Martin Wegener<sup>1

1</sup>Institute of Applied Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
²Institute for Technical Chemistry and Polymer Chemistry, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany  

 Since the 2006 pioneering theoretical works of Sir John Pendry et al [1] and Ulf Leonhardt [2], the ideas of transformation optics (TO) have been experimentally realized into new optical elements [3-5]. Among all the possible elements predicted by TO, the most demanding one in terms of fabrication is the cylindrical cloak or also called the free space cloak [6]. This device guides an impinging electromagnetic (EM) wave around an object without interacting with it, thus making the object and the cloak itself completely invisible to an external observer. The optical parameter (electric permittivity and magnetic permeability) values needed to guide EM waves in this manner are extreme and normally not available in Nature. To obtain such extreme values, we need to fabricate small resonant metallic elements, or “meta-atoms” which are much smaller than the wavelength of the impinging wave in order to act as an effective medium. This requires engineering meta-atoms with tens of nanometers sizes for visible EM waves and this is still difficult to reach with modern electron beam lithography. Moreover these resonant meta-atoms absorb a non-negligible part of the impinging light because they are usually dispersive, i.e., their optical response changes with frequency, thus strongly limiting the efficiency of the cloak.

Past 2Physics article by this Group:
June 19, 2011: "3D Polarization-Independent Invisibility Cloak at Visible Wavelengths" by Tolga Ergin, Joachim Fischer, Martin Wegener
April 11, 2010: "3D Invisibility Cloaking Device at Optical Wavelengths"
by Tolga Ergin, Nicolas Stenger, Martin Wegener

 Nevertheless David Shurig et al [6] fabricated such a structure for microwave frequencies (the wavelength is here of the order of a few millimeters) by using tailored U-shaped resonant meta-atoms also called split-ring-resonators (SRR). Since they used SRR, the efficiency of their cloaking device is restrained to a very narrow band of frequencies. However, this has been the only demonstration of a free-space cloak for EM waves so far.

 However, the ideas of TO are not restricted to EM waves and other groups have started to adapt TO to waves propagating in matter [7]. This led to two first experimental realizations of cloaking for acoustic waves propagating at the surface of a fluid [8] and for ultrasound pressure waves propagating in water [9]. These two cylindrical cloaks were working in a broader band of frequencies because the constituting elements and the meta-atoms used where less dispersive in comparison with their EM counterparts.

 Our group decided to investigate the possibility to fabricate a cylindrical cloak for waves propagating in elastic materials like waves propagating in guitar strings or at the surface of a drum. The main advantage of elastic materials lies in the fact that their properties, i.e., elastic modulus and the density, can show a very large contrast without frequency dependence for a broad range of frequencies. For example polyvinyl chloride (PVC) has an elastic modulus three orders of magnitude higher than polydimethylsiloxane (PDMS), a silicon rubber, and their densities are almost the same. This eliminates the need for resonant meta-atoms.

 Mohamed Farhat et al [10] showed theoretically the possibility to apply the ideas of TO to flexural waves propagating in thin elastic plates for frequencies of a few hundreds of Hertz. A flexural wave is a vertical displacement propagating in a thin plate or in an elastic membrane. The original design proposed by Mohamed Farhat et al for a cylindrical cloak consists of ten concentric rings made of six different materials. “Gluing” six different materials together still remains a technical challenge because polymer materials are usually repelling each others. We therefore decided to simplify the design by using 16 composites made only out of two materials [11], i.e., a hard material (PVC) and a very soft one (PDMS) (respectively white and black parts in Fig. 1a). By changing the PVC filling fraction from 0% to 100%, the effective elastic modulus can be tuned from the small PDMS value to the large PVC value (Fig. 1a). We then mapped the effective elastic moduli profile computed theoretically onto a local PVC filling fraction in our structure [11].

 To fabricate our cloak we mechanically machined small holes into a thin PVC plate with different volume filling fractions for each of the 20 concentric rings (Fig. 1b) [11] and then filled the holes with PDMS (not shown on Fig. 1b). Here the holes in the composite and the relative thicknesses of the concentric rings are much smaller than the wavelength of the impinging wave because we want our structure to appear as an effective material. The central region of the cloak was then clamped to zero amplitude and was used as the scattering object we want to hide.

Fig. 1: a) Blueprint of the free space cloak. The yellow color corresponds to the outside PVC part of the cloak with a constant filling fraction; the black (PDMS) and white (PVC) circular structure in the middle represents the cloak with 20 rings made of 16 different composites. The object we want to make invisible is symbolized by the red circle in the middle. b) Oblique view of our cloak after drilling holes in a PVC plate and before filling them with PDMS.

 We characterized our cloaking device with a home-built setup. We excited flexural waves with two loudspeakers attached to one end of the plate. A camera was placed vertically above the plate and recorded the vertical displacement created by the flexural wave. A diffuse stroboscopic illumination is then used to follow step by step the propagation of the wave in our structure. Unwanted reflections were reduced by placing absorbing foam material against the other end and the two sides of the plate.

 Figure 2 shows snapshots taken from the reference plate (column a) and the plate with the cloaking structure (column b) for two different frequencies (see also [11] for more frequencies and corresponding movies). The former plate is used as a baseline to quantify the scattering effect of the object on the impinging wave. The filling fraction of this plate is the same as the plate outside the cloaking structure in Fig. 1. For 200Hz (Fig. 2a top row) we can clearly see the effect of the central region leading to strong scattering in front of the object (standing wave) and to shadowing effect behind it. Furthermore the wave front is strongly distorted after the object. With the presence of the cloaking structure (Fig. 2b top row), symbolized by the black dashed circle, the scattering and distortion effects are strongly suppressed. We even recover a plane wave after the clamped region; an external observer will not be able to make the difference between a plane wave propagating in the reference plate without the object and another plate with a cylindrical cloak and the object in its center. The object is thus invisible.

Fig. 2: Measurement snapshots of the propagation of a flexural wave on a thin plate. A monochromatic wave is injected from the left side and propagates to the right. The left column (a) corresponds to the reference plate with a homogeneous filling fraction. The region clamped to zero amplitude (object) is represented by black circles. The right column (b) corresponds to the object plus the cloak. The dashed circles illustrate the outer radius of the cloak. The white scale bar in each image is 5 cm.

 Since our structure consists of non resonant elements we therefore expect our structure to be efficient on a wide range of frequency. This is indeed the case as shown for 400Hz (Fig. 2 bottom row), one octave above, where the cloak is still strongly reducing the scattering of the object. However increasing imperfections are visible with increasing frequency. Here the wavelength is small enough to see the cloak as a discrete structure and the continuous approximation made at the beginning is no more valid. Conceptually, our cloak should also work for frequencies below 200Hz down to 0Hz, however, we were not able to perform measurements in this range.

 To conclude, we have fabricated and characterized a broadband cylindrical cloak for elastic waves and its effect spans more than one octave. To our knowledge this is the largest bandwidth observed in any free-space cloaking device [11]. It is interesting to note this structure is rather easy to fabricate and quite inexpensive. Thus, it is perfectly well suited to convey the ideas of transformation optics. This structure can also be seen as a model experiment for seismic cloaks as discussed in [10].

References: 
[1] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields”, Science 312, 1780 (2006). Abstract.
[2] U. Leonhardt, “Optical Conformal Mapping”, Science 312, 1777 (2006). Abstract.
[3] H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials”, Nature Materials 9, 387 (2010). Abstract.
[4] T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, ”Three-Dimensional Invisibility Cloaking at Optical Wavelengths”, Science 328, 337 (2010). Abstract. 2Physics Post.
 [5] J. Fischer, T. Ergin, and M. Wegener, “Three-dimensional polarization-independent visible-frequency carpet invisibility cloak”, Optics Express 36, 2059 (2011). Abstract. 2Physics Post.
[6] 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, 977 (2006). Abstract.
[7] G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant from”, New Journal of Physics 8, 248 (2006). Abstract.
[8] M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband Cylindrical Acoustic Cloak for Linear Surface Waves in Fluid”, Physical Review Letters 101, 134501 (2008). Abstract.
[9] S. Zhang, C. Xia, and N. Fang, “Broadband Acoustic Cloak for Ultrasound Waves”, Physical Review Letters 106, 024301 (2011). Abstract.
[10] M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Ultrabroadband Elastic Cloaking in thin Plates”, Physical Review Letters 103, 024301 (2009). Abstract.
[11] N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on Elastic Cloaking in Thin Plates”, Physical Review Letters 108, 014301 (2012).Full Paper.

Gradient Birefringent Lenses: A New Degree of Freedom in Optics

Aaron Danner

Author: Aaron Danner

Affiliation: Department of Electrical and Computer Engineering, National University of Singapore, Singapore

Birefringence refers to the fact that some materials have more than one refractive index, causing light beams hitting a birefringent material to split into two parts. Since such materials are uncommon, at first glance this may appear to be a rather startling phenomenon. What we have shown in recent work is that birefringent materials that have gradient indices of refraction -- meaning they are a function of position inside a material -- can do even more surprising things.

Why do some natural materials have two refractive indices (one for each polarization)?

The refractive index of a material comes from the way light interacts with electrons inside a material. Because different materials have their atoms packed together in different arrangements, their electronic structures are different. In many materials, like glass or water, those electronic structures look more or less the same when viewed from any direction or along any angle. Such materials are isotropic and have just one refractive index. Other materials, such as calcite or lithium niobate, however, have crystalline structures where the electronic configuration is different along some directions compared to others. It’s thus natural that some materials would have more than one index of refraction, depending on the polarization direction of the light. When light containing a mixture of randomly polarized photons strikes such a material, it exhibits double refraction.

Birefringence is important for metamaterials researchers because it is often something that pops up where it is unwanted. One doesn’t want to design a new and exciting lens only to see that half of the light isn’t going where you want it to go, but in fact this is exactly what happens in a lot of cases. Many exciting and astonishing devices designed in recent years, such as cloaking devices, depend on a technique in optics called transformation optics [2-7]. It is a toolset that allows researchers to determine what refractive index profile will allow light to behave in a predefined way. Normally, such devices have gradient indices of refraction and require materials that have properties that are not commonly found in nature (or are even impossible or unfeasible to ever build). Transformation optics, for instance, requires the magnetic permeability tensor to equal the permittivity tensor. Since this is unworkable in real materials, a compromise is commonly made in order to actually build some of the amazing devices that researchers have designed: one polarization is sacrificed [8-9] to ease material property constraints. This is the origin of the “unwanted” birefringence.

Figure 1: Computer-generated image of a spherical device that functions as an invisible sphere for one polarization, and as a Luneburg lens for the other polarization [Image reproduced from Ref [1]. Thanks to 'Nature Photonics']

What we have discovered is that the “unwanted” birefringence can do useful things. We can actually design devices that are fully dielectric (removing the most onerous requirement of transformation optics) and have two unique functions, one for each polarization. Figure 1, for example, shows a spherical device that is invisible for one polarization, but acts like a so-called Luneburg lens for another. Without careful consideration, it may seem obvious that such devices are possible – why not just pick each of the two constituent refractive indices in a gradient birefringent device to each perform its own function? The reason why it is not so simple is because as light propagates through a structure, especially a structure with a graded index tensor, the polarization direction itself will rotate. Thus a light beam’s trajectory depends on each of the two indices in a complicated way, and before now, it was not clear whether the two trajectories of a single incident beam could be independently designed except in a few circumstances [10].

Figure 2: Four examples of birefringent dielectric devices designed with the methods described: (a) Invisible for one polarization, a Luneburg lens for the other as shown on the cover art, (b) a Luneburg lens for one polarization, and a ring focuser for the other, (c) Invisible but with a polarization-dependent phase slip, and (d) an interior-focusing potential for one polarization and a Maxwell fisheye for the other [Image reproduced from Ref [1]. Thanks to 'Nature Photonics'].

What we have shown is that, in fact, for all intents and purposes, they can be. This means that a design scheme now exists whereby lenses with multiple functions can be designed (two simultaneous focal lengths in a spherical lens, for example, one for each polarization). It also means that researchers working on unusual devices such as optical cloaks that must be designed with transformation optics need not sacrifice one polarization to make their devices work. They can “save” the other polarization, and at least make it do something useful. Thus, a cloaking device can cloak for one polarization, and perform some other interesting function with the other polarization. Various examples of such devices with dual functionality are shown in Figure 2. With the methods developed, birefringence can be fully controlled in dielectrics and useful optical devices designed that have either two functions, or that have identical functionality for each polarization but with different ray trajectories.

Acknowledgments: I would like to thank my co-authors on the Nature Photonics paper [1], Prof. Tomas Tyc of Masaryk University and Prof. Ulf Leonhardt of the University of St. Andrews. Funding from the Singapore Ministy of Education Tier II Academic Research Fund under grant MOE2009-T2-1-086 is acknowledged.

References:
[1] Danner A.J., Tyc T., and Leonhardt U., "Controlling birefringence in dielectrics," Nature Photonics 5, 357 (2011). Abstract.
[2] Service, R. F. & Cho, A. "Strange New Tricks with Light", Science, 330, 1622 (2010). Abstract.
[3] Leonhardt, U. "Optical Conformal Mapping". Science, 312, 1777-1780 (2006). Abstract.
[4] Pendry, J. B., Schurig, D. & Smith, D. R. "Controlling Electromagnetic Fields". Science, 312, 1780-1782 (2006). Abstract.
[5] Shalaev, V. M. "Transforming Light". Science, 322, 384-386 (2008). Abstract.
[6] Chen, H. Y., Chan, C. T. & Sheng, P. "Transformation Optics and Metamaterials". Naure Materials, 9, 387-396 (2010). Abstract.
[7] Leonhardt, U. & Philbin, T. G. "Geometry and Light: The Science of Invisibility" (Dover, 2010).
[8] 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, 977-980 (2006). Abstract.
[9] Ma, Y. G., Ong, C. K., Tyc, T. & Leonhardt, U. "An Omnidirectional Retroreflector Based on the Transmutation of Dielectric Singularities". Nature Materials, 8, 639-642 (2009). Abstract.
[10] Kwon, D. H. & Werner, D. H. "Polarization Splitter and Polarization Rotator Designs Based on Transformation Optics." Opt. Express, 16, 18731-18738 (2008). Abstract.