Zahra Khwaja

Invisibility Cloaks: Fact or Fiction?

‘So-wI yICHU!’1 As any trekkie2 fluent in Klingon will recognise, the command to engage a Bird-of-Prey’s cloaking device provides tactical advantage in evading an attack or preparing for one. Clearly a handy trick, invisibility has featured heavily in fiction3, but proven elusive in reality. In the last decade however, remarkable progress has been made in the field of invisibility science.4 Although scientists are not at the stage where they can render a spaceship invisible, in this essay I will show that enough has been accomplished through experimental realisation of invisibility theory to recognise it as a definite fact of reality.

Traditionally, invisibility is defined as the state of being imperceptible to the eye. Light that is reflected off the multiple facets of a complex object is interpreted by the brain to form an image. It follows that to conquer invisibility, one must become master of this scattered light. While the eye can be tricked, in certain conditions, using optical illusions and camouflage, a true and perfect invisibility cloak should not reflect light or absorb energy, it should be insensitive to the polarisation and colour of visible light and the angle of observation. 5 Theoretical models present this ideal of ‘pure’ invisibility, but most experimental realisations are subject to the practical limitations of current manufacturing technology which means that the demonstration cannot always be performed with ideal parameters. However, these experiments are undeniable proof of the theory and can be expanded as engineering catches up.

Harry Potter6 style fiction suggests that to render an object invisible, one must cover it with a magical material. Obligingly, scientists have developed metamaterials.7 These materials are artificially engineered to possess micro-structures that produce optical properties not found in nature, such as negative refraction.8 The material needed to make an ideal invisibility cloak should be inhomogeneous (sensitive to light polarisation), anisotropic (speed of light passing through is different in different directions) and magnetically active.9 Using a mathematical tool called transformation optics,10 metamaterials to be used in cloaking, can be specifically designed to manipulate electromagnetic waves with respect to these ideals. Fabrication technology is

advancing rapidly11 and armed with metamaterials, invisibility scientists have finally become masters of light.

In 2006, Pendry, Schurig and Smith presented a theoretical methodology12 from which a number of groundbreaking cloaks were realised. Their approach is based on the principal of guiding light around an object so there is no opportunity for reflection or absorption (Fig.1). This light flow control or ‘bending’

of light is achieved by engineering a metamaterial shell with a suitably designed gradient refractive index, that is, where the refractive index changes continuously as a function of position, and so the direction of the light travelling through also continuously changes (Fig.2).

By placing a spatially varying refractive material around the object, that area is effectively ‘warped’ to light, so light will not travel in a straight line through it and will instead follow the prescribed path.

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Transformation optics is used to calculate coordinate transformations from normal Euclidean space (Fig.3) where light travels in a straight line, to the distorted coordinate system, a stretched and compressed or warped space (Fig.4). Spatially varying material parameters, including electric permittivity and magnetic permeability, required to

make light follow the desired path, are then derived.

There were several successful cloaks based on this model. The first was built by Shurig et al.,13 a two-dimensional cloak which concealed a copper cylinder about 1.4λ (where λ is the operational wavelength) and elegantly accommodated the three ideals of cloaking materials. About 24%14 of the incident microwaves were successfully guided around the cylinder. The electric field strength results from the experiment are shown in

5 http://download.iop.org/pw/PW_jul11_sample_issue.pdf

6 Rowling J.K, “Harry Potter and the Philosophers Stone.” (1997)

1 https://www.youtube.com/watch?v=BpdgUluBJOQ

2 https://en.wikipedia.org/wiki/Star_Trek

3 Beech. M, “The Physics of Invisibility: A Story of Light and Deception.” (2012)

4 Shchelokova. A.V et al. “Experimental realization of invisibility cloaking.” (2015)

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the figures below; Fig.5 shows simulated ideal results, Fig.6 shows the uncloaked object and Fig.7 the actual cloaked object. The scattering from the object is significantly reduced due to the cloak in Fig.7.

7 http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/metamaterials.html

8 Padilla. W.J, Basov. D.N, Smith. D.R, “Negative refractive index metamaterials.” (2006) http://infrared.ucsd.edu/basov_pubs/mt9-28-2006.pdf

9 http://download.iop.org/pw/PW_jul11_sample_issue.pdf

10 http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/TransOptics.html

11 https://www.kit.edu/kit/english/pi_2016_015_nature-materials-smallest-lattice-structure- worldwide.php

12 Pendry. J, Shurig. D, Smith. D “Controlling Electromagnetic Fields” 2006 http://www.ece.utah.edu/~dschurig/Site/Recognition_files/1780.pdf

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A succession of experiments followed5 each making improvements on the last, each demonstrated that the theory behind invisibility modelling was sound.

A derivative method called ‘carpet-cloaking’ was postulated by Pendry and Li in 2008.15 A carpet-cloak is a layer of material that sits above a gap where an object can be placed. By bending light away from the gap, it makes the gap appear flat (Fig.8). As shown in Fig. 9, the warping is much reduced in this model making it easier to implement.

Results

published in April 2009 by Valentine et al.,16 in July 2009 by Gabrielli et al.17 and in 2010 by Ergin et al.18 successfully demonstrated carpet cloaks which functioned for near-infrared wavelengths with a nanoscale cloaked region. The first carpet cloak to conceal an object from nearly the whole visible light range (400-700nm) was demonstrated by Gharghi et al. in 2011.19 This was a major step in invisibility science as it actually rendered objects invisible to the human eye. It consisted of a silicon-nitride waveguide deposited on a low refractive index substrate. The waveguide contained a multitude of etched holes throughout. The variety of differently sized holes altered the way in which light was refracted through the waveguide, allowing its interaction with the substrate to cloak the small gap where the object is situated.

13 D. Schurig et al., “Metamaterial Electromagnetic Cloak at Microwave Frequencies.” 2006http://www.ece.utah.edu/~dschurig/Site/Publications_files/977.pdf

14 N. Kundtz, D. Gaultney, D.R Smith, “Scattering cross-section of a transformation optics-based metamaterial cloak.” (2010)

15 J. Li & J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking.” (2008)

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Representation of a carpet cloak with reduced anisotropy and

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Warping could be reduced further using a technique called ‘conformal mapping’20 which allowed 90°angles between virtual grid lines to be preserved (Fig.10).

In 2011 Baile Zhang et al.2122 created a carpet cloak by gluing two transparent prisms of optical calcite together. It was the first cloak to hide a paper-clip sized macroscopic object. This cloak exploited the natural birefrigence (a varying refractive index depending on the direction of light) of calcite crystals and was not metamaterial-based. It was a great success and was demonstrated at TED23 cloaking a cylinder (Fig. 11).

16 J. Valentine et al., “An optical cloak made of dielectrics.” (2009)

17 L.H. Gabrielli et al., “Silicon nanostructure cloak operating at optical frequencies,” (2009)

18 Y. Ergin et al., “Three-dimensional invisibility cloak at optical wavelengths,” (2010)

19 M. Gharghi et al., “A carpet cloak for visible light.” (2011)

20 Leonhardt. U, “Optical Conformal Mapping and Dielectric Invisibility Devices.” 2008http://arxiv.org/pdf/physics/0602092.pdf

21 Zhang, B., Luo, Y., Liu, X. & Barbastathis, G, “Macroscopic invisible cloak for visible light.” (2010)

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A major breakthrough came in September 2015 when a team at University of California, Berkeley, led by Xiang Zhang, successfully demonstrated an ultra-thin, tight fitting, flexible cloak that perfectly concealed a 3D arbitrarily shaped object24 using the method of scatter cancellation. This ‘skin-cloak’ could be tuned to match it’s background or to create an illusion of what's there.

For experimental realisation, Zhang’s team carved out an object with several bumps and dents (Fig. 12), measuring about 36µm across (just over 1/1000th of an inch or the size of a few biological cells) using a focused ion beam (FIB). The height profile was then mapped out by an atomic force microscope (AFM).24

Using electron beam lithography, a metasurface skin-cloak was then designed on the basis of the height profile. Zhang’s team fabricated a cloak 80nm thick consisting of a 50nm transparent, insulating layer of magnesium fluoride covered in millions of gold brick-shaped nanoantennae, each about 30nm thick (about 1/1000th of a human hair)25 (Fig.13).

Shining a light, with a wavelength of 730nm (near-infrared) they found that the objects became almost perfectly invisible to optical and even to phase-sensitive detection.

http://arxiv4.library.cornell.edu/abs/1012.2238

22 http://www.nature.com/news/2010/101215/full/news.2010.678.html

23 https://www.youtube.com/watch?v=SSVBJ2kf-0w

24 Zhang. X et al. “An ultrathin invisibility skin cloak for visible light.” (2015) http://xlab.me.berkeley.edu/pdf/10.1126_science.aac9411.pdf

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Fig. 12

Fig. 13

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The antennae act as phase-shifting resonant elements on the cloak surface. Using mathematics, the phase shifts of the antennae could be pre-determined. The pattern and sizes of the antennae was precisely tailored to the shape of the object so that exactly the desired phase shift would be produced at each location. The antennae absorbed light, realigned and reradiated it. The metasurface skin-cloak fully restored both the wavefront and the phase of the scattered light as if the incident light had encountered a flat mirror. As shown Fig. 14, light (red solid lines) incident at an oblique angle (θ,Φ) at the point h from a flat reference plane will scatter as if it were reflected by the reference plane (orange dashed lines). The nanoantenna at that point provides a phase shift which compensates the phase difference between the solid and dashed lines creating

the illusion of a flat mirror surface instead of the actual object's shape thereby cloaking it. 24

Testing was very thorough. A scanning electron microscope (SEM) was used to observe the results and a customised Mach-Zehnder interferometer was built for phase measurements; it was shown that no additional phase was introduced by the cloak. Fig. 15 shows the extracted height profile from the interference measurement (▵for cloak off and ○ for cloak on) together with that from the original AFM measurement (solid line) before fabrication of the cloak. When the cloak was on, the extracted height from the interference measurement dropped to zero over the entire area, proving that invisibility was achieved.24 Matching height profiles with the cloak off and the AFM

readings prove experimental integrity.

Pictures from the laboratory demonstration (Fig.16) also show experimental success; the object is invisible when the cloak is on and then visible when the cloak is switched off.

Zhang’s achievement was widely reported and he elegantly summarises his team’s work to various magazines:

25 http://www.livescience.com/52216-ultrathin-invisibility-cloak.html?li_source=LI&li_medium=most-popular

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“You could cover a tank with it and make it look like a bicycle,”26 livescience.com

“This is the first time a 3D object of arbitrary shape has been cloaked from visible light. … It is easy to design and implement, and is potentially scalable for hiding macroscopic objects, ”27 theengineer.co.uk

“It’s good enough, from a scientific point of view, as a proof of principle. The rest is all engineering group.” 28 thewashingtonpost.com

While scientists like Zhang pursue the dream of true invisibility, other very different approaches to achieving invisibility, more akin to camouflage, have also made successful attempts at

tricking the human eye.

A team led by Susumu Tachi29 created a ‘transparent’ cloak in 2003 using retro-reflective projection technology or optical camouflage. It uses a computer, video camera and projector to shine background images onto the front of a subject wearing specialised clothing, creating the illusion of invisibility. The fabric is made of glass beads 50µm wide, which can reflect light directly back at the source and allow you to see a 3D image. Viable applications for this technology, such as a ‘transparent cockpit’ which would improve visibility, are being pioneered.

26 http://www.livescience.com/52216-ultrathin-invisibility-cloak.html?li_source=LI&li_medium=most-popular

27 http://www.theengineer.co.uk/microscopic-invisibility-cloak-has-potential-for-scalability/

28 https://www.washingtonpost.com/news/speaking-of-science/wp/2015/09/17/this-skintight-invisibility-cloak-is-able-to-hide-3-d-objects-as-long-as-theyre-super-tiny/

29 Inami. M, Kawakami. N, Tachi. S “Optical Camouflage Using Retro-reflective Projection Technology” 2003

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The ideas of optical camouflage and projection technology have also been applied to the Tower of Infinity to be constructed in Seoul.30 The background scene of the tower is recorded and projected onto LED screens on the skyscraper in real time, so it has the ability to ‘disappear’. The illusion is intended to be for tourism and a demonstration of Korean technology. On a lower budget, scientists at the University of Rochester have created an invisibility device using inexpensive and readily available equipment.31 The device operates in the whole visible light spectrum, for objects in motion and for a range of viewing angles. The set up comprises an arrangement of standard lenses in such a way that the lenses bend light around the object to be cloaked. The team successfully demonstrated their cloaking device in the lab; their device may be used to help truck drivers see through their ‘blind spots’ on their vehicles and allow surgeons to operate more easily without their view being obstructed by their hands,32 a similar application as the Tachi cloak.

Temporal cloaking or space-time cloaking is an exciting new field.33 It has been theorised34 and successfully realised on two main accounts35 36. Rather than concealing objects, temporal cloaks conceal events in time, rendering them invisible to all but the intended audience. This type of cloaking is used to conceal data events in optical fibres for security purposes. The cloak works by manipulating the speed of light in optical fibres which creates a moving ‘time hole’ or gap where a data event can occur, after which the beam is flawlessly closed back up, leaving the observer with no indication that an event took place or that the light was tampered with. A space-time cloak could potentially conceal real events in time, such as a bank robbery!30 It is metamaterial-based and uses transformation optics to manipulate light.

Looking to the future, the ultimate goal of scientists would be to achieve pure undetectability. As well as visual cloaking, an object may have to be shielded from radar, infra-red sensors and sonar. Scientists continue to innovate independently in anti-radar ‘stealth’ technology and camouflage. BAE systems ADAPTIV37 panels and a new transparent adhesive material based on the skin of cuttlefish3 both cloak objects and clothing

30 http://www.e-architect.co.uk/korea/tower-infinity

31 J. Choi & J. C. Howell, “Paraxial ray optics cloaking.” (2014)http://arxiv.org/pdf/1409.4705.pdf

32 http://www.rochester.edu/newscenter/watch-rochester-cloak-uses-ordinary-lenses-to-hide-objects-across-continuous-range-of-angles-70592/

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against infrared detection by changing temperature rapidly to match the background. The latest stealth aircraft are coated with radiowave absorbative paint and have specially shaped bodies which reflect the remaining radiowaves in a way which can give an aircraft the radar cross-section of large insect. However, it has been reported that advances in sensors and surface-to-air missiles may reduce the advantage of stealth technology38 and that these aircraft may not be as effective in one-on-one combat as older models.39 This illustrates the need for combined cloaking. A metasurface skin-cloak for electromagnetic, acoustic and water waves has been proposed by Yang et al.40 in a paper published in January 2016. Simulations show how a multi-wave single metasurface cloak can potentially hide objects of an arbitrary shape.

35 Fridman, M., Farsi, A., Okawachi, Y. & Gaeta, A. L, “Demonstration of temporal cloaking.” (2012)

36 Lukens, J. M., Leaird, D. E. & Weiner, A. M, “A temporal cloak at telecommunication data rates.” (2013).

33 http://download.iop.org/pw/PW_jul11_sample_issue.pdf

34 McCall, M. W., Favaro, A., Kinsler, P. & Boardman, “A space-time cloak or history editor.” (2011)

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Invisibility science has become a viable frontier field in the last decade. Transformation optics, used by scientists to design unique optical properties into artificially engineered metamaterials, has given them control over light. Pendry’s theory of 2006 inspired a generation of scientists to make true invisibility a reality using the method of guiding light around an object. The success of early experiments such as carpet cloaking laid the important groundwork for Zhang’s skin-cloak, which achieved perfect invisibility using the scatter cancellation method. Additionally, the skin-cloak research may prove useful in the development of high-resolution optical microscopes and superfast optical computers and to hide details on a microscopic scale such as the layout of microelectronic components.41 Other successful approaches to invisibility such as Tachi’s transparent cloak are being applied to improve vehicle safety. These important and practical spin-off uses for invisibility

37http://www.baesystems.com/cs/Satellite?c=BAEFeature_C&childpagename=UK %2FBAELayout&cid=1434567247185&pagename=UKWrapper

38 http://www.wired.com/2011/06/stealth-tech-obsolete/

39 https://www.rt.com/usa/333663-f35-f22-radar-missiles/

40 Yang. Y, Wang. H, Yu. F, Xu. Z, Chen. H, “A metasurface carpet cloak for electromagnetic, acoustic and water waves” (2016)http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4731745/

41 http://newscenter.lbl.gov/2015/09/17/making-3d-objects-disappear/

Figure References

Fig 1: Pendry. J, Shurig. D, Smith. D “Controlling Electromagnetic Fields” 2006 http://www.ece.utah.edu/~dschurig/Site/Recognition_files/1780.pdf

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research will undoubtedly keep up industrial interest and defence departments will be looking to new technologies to maintain their military superiority. We must accept that scientists are yet unable to produce a cloak that can turn a would-be assassin into a ghost, or hide a warplane in plain sight. However, it must also be accepted that invisibility has been demonstrated successfully in the lab and if invisibility science continues on its current trajectory with ample interest and funding, a practical invisibility cloaking device for macroscopic objects will be developed in the not too distant future. Breakthroughs in science can come at any time, and with exciting new theories such as temporal cloaking on the horizon, I certainly believe that determined researchers can quickly build on the successes of the past to achieve their goals. Who knows, perhaps one day soon, we will engage a cloaking device aboard a spacecraft which uses gravitons to distort space–time so that light is directed around it, just like the Klingons.

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Bibliography

Fig 2, 3, 4, 8, 9, 10: http://skullsinthestars.com/2013/03/02/how-to-become-invisible-by-hiding-under-the-carpet/ Fig 5, 6, 7: Shchelokova. A.V et al. “Experimental realization of invisibility cloaking.” (2015)Fig 12, 13, 14, 15, 16: Zhang. X et al. “An ultrathin invisibility skin cloak for visible light.” (2015)Fig 11, 17: http://download.iop.org/pw/PW_jul11_sample_issue.pdf

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