View source for Physics:Metamaterial cloaking

{{Short description|Shielding an object from view using materials made to redirect light}}
{{electromagnetism}}

'''Metamaterial cloaking''' is the usage of metamaterials in an [[Physics:Cloaking device|invisibility cloak]]. This is accomplished by manipulating the paths traversed by light through a novel optical material. Metamaterials direct and control the [[Physics:Wave propagation|propagation]] and transmission of specified parts of the light spectrum and demonstrate the potential to render an object seemingly  invisible. Metamaterial cloaking, based on [[Physics:Transformation optics|transformation optics]], describes the process of shielding something from view by controlling [[Physics:Electromagnetic radiation|electromagnetic radiation]]. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.<ref name=AAAS-322/><ref name=AAAS4/><ref name=AAAS6/><ref name=Duke2009>{{cite web|last1=Merritt |first1=Richard |first2=DavidR. |last2=Smith |first3=Ruopeng |last3=Liu |first4=Chunlin |last4=Ji |title=Summary: New algorithms developed to guide manufacture of metamaterials |publisher=Office of News & Communications, Duke University |date=2009-01-16 |url=http://news.duke.edu/2009/01/invis09.html |access-date=2009-08-06 |url-status=dead |archive-url=https://web.archive.org/web/20090220020959/http://news.duke.edu/2009/01/invis09.html |archive-date=February 20, 2009 }}</ref><ref name=Eng-space/>

==Electromagnetic metamaterials==
''Electromagnetic metamaterials'' respond to chosen parts of radiated light, also known as the  [[Physics:Electromagnetic spectrum|electromagnetic spectrum]], in a manner that is difficult or impossible to achieve with [[Chemistry:Natural material|natural material]]s. In other words, these metamaterials can be further defined as artificially structured [[Chemistry:Composite material|composite material]]s, which exhibit interaction with light usually not available in nature ([[Physics:Electromagnetic interaction|electromagnetic interaction]]s). At the same time, metamaterials have the potential to be engineered and constructed with desirable properties that fit a specific need. That need will be determined by the particular application.<ref name=AAAS4/><ref name=physicsengineering1/><ref name=nat-trans-opt/>

The artificial structure for cloaking applications is a [[Chemistry:Crystal structure|lattice]] design – a sequentially repeating network – of identical elements. Additionally, for [[Physics:Microwave|microwave]] frequencies, these materials are analogous to [[Chemistry:Crystal structure|crystal]]s for [[Physics:Optics|optics]]. Also, a metamaterial is composed of a sequence of elements and spacings, which are much smaller than the selected wavelength of light. The selected wavelength could be [[Engineering:Radio frequency|radio frequency]], microwave, or other radiations, now just beginning to reach into the visible frequencies. [[Physics:Macroscopic|Macroscopic]] properties can be directly controlled by adjusting characteristics of the rudimentary [[Physics:Split-ring resonator|elements]], and their arrangement on, or throughout the material. Moreover, these metamaterials are a basis for building very small cloaking devices in anticipation of larger devices, adaptable to a broad spectrum of radiated light.<ref name=AAAS4/><ref name=physicsengineering1/><ref name=waves-metas/>

Hence, although light consists of an [[Physics:Electric field|electric field]] and a [[Physics:Magnetic field|magnetic field]], ordinary optical materials, such as [[Engineering:Optical microscope|optical microscope]] lenses, have a strong reaction only to the electric field. The corresponding magnetic interaction is essentially nil. This results in only the most common optical effects, such as ordinary [[Physics:Refraction|refraction]] with common diffraction limitations in lenses and [[Physics:Optical resolution|imaging]].<ref name=AAAS4/><ref name=physicsengineering1/><ref name=waves-metas/>

Since the [[Physics:History of optics|beginning of optical sciences]], centuries ago, the ability to control the [[Physics:Light|light]] with materials has been limited to these common optical effects. Metamaterials, on the other hand, are capable of a very strong interaction, or coupling, with the magnetic component of light. Therefore, the range of response to [[Physics:Light|radiated light]] is expanded beyond the ordinary optical limitations that are described by the sciences of [[Physics:Physical optics|physical optics]] and optical physics. In addition, as artificially constructed materials, both the magnetic and electric components of the radiated light can be controlled at will, in any desired fashion as it travels, or more accurately [[Physics:Wave propagation|propagates]], through the material. This is because a metamaterial's behavior is typically formed from individual components, and each component responds independently to a radiated spectrum of light. At this time, however, metamaterials are limited. Cloaking across a broad [[Physics:Frequency spectrum|spectrum of frequencies]] has not been achieved, including the [[Physics:Visible spectrum|visible spectrum]]. [[Dissipation]], [[Physics:Absorption (electromagnetic radiation)|absorption]], and [[Physics:Dispersion relation|dispersion]] are also current drawbacks, but this field is still in its optimistic infancy.<ref name=AAAS4/><ref name=physicsengineering1/><ref name=waves-metas>
{{cite web
  | title =Waves & Metamaterials
  | work = Research & Faculty
  | publisher =Duke University – Pratt School of Engineering
  | date =December 3, 2010
  | url =http://www.ee.duke.edu/waves-metamaterials
  | access-date =2011-01-10}}</ref>

===Metamaterials and transformation optics===
[[File:Circular EM cloak using transformation optics.svg|thumbnail|320px|Left:The cross section of a PEC cylinder subject to a plane wave (only the electric field component of the wave is shown). The field is scattered. Right: a circular cloak, designed using transformation optics methods, is used to cloak the cylinder. In this case the field remains unchanged outside the cloak and the cylinder is invisible electromagnetically. Note the special distortion pattern of the field inside the cloak.]]
{{main|Physics:Transformation optics}}
The field of [[Physics:Transformation optics|transformation optics]] is founded on the effects produced by metamaterials.<ref name=AAAS-322>
{{cite journal
|doi=10.1126/science.1166079
|url=https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1106&context=nanopub
|title=PHYSICS: Transforming Light
|year=2008
|last1=Shalaev
|first1=V. M.
|journal=Science
|volume=322
|issue=5900
|pages=384–386
|pmid=18927379|s2cid = 206516379}}</ref>

Transformation optics has its beginnings in the conclusions of two research endeavors.  They were published on May 25, 2006, in the same issue of ''Science'', a peer-reviewed journal. The two papers are tenable theories on bending or distorting [[Physics:Light|light]] to [[Physics:Electromagnetic field|electromagnetically]] conceal an object. Both papers notably map the initial configuration of the [[Physics:Electromagnetic field|electromagnetic field]]s on to a [[Cartesian coordinate system|Cartesian]] mesh. Twisting the Cartesian mesh, in essence,  transforms the coordinates of the electromagnetic fields, which in turn conceal a given object. Hence, with these two papers, transformation optics is born.<ref name=AAAS4>{{cite journal|last1=Pendry|first1=J.B.|author2=Schurig, D.|author3=Smith, D. R.|title=Controlling Electromagnetic Fields|journal=Science|year=2006|volume=312|issue=5514|pages=1780–1782|url=http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/CloakPap100406.pdf|format=Free PDF download|doi=10.1126/science.1125907|pmid=16728597|bibcode=2006Sci...312.1780P|s2cid=7967675|access-date=2010-12-08|archive-url=https://web.archive.org/web/20160304000453/http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/CloakPap100406.pdf|archive-date=2016-03-04|url-status=dead}}</ref><ref name=AAAS5>{{cite journal|last=Leonhardt|first=Ulf|title=Optical Conformal Mapping|url=http://www-circa.mcs.st-and.ac.uk/Preprints/opticonform.pdf|format=Free PDF download|date=Jun 2006|volume=312|issue=5781|pages=1777–1780|doi=10.1126/science.1126493|pmid=16728596|journal=Science|bibcode=2006Sci...312.1777L|s2cid=8334444|access-date=2010-12-08|archive-url=https://web.archive.org/web/20160304121002/http://www-circa.mcs.st-and.ac.uk/Preprints/opticonform.pdf|archive-date=2016-03-04|url-status=dead}}</ref><ref name=nano-oct-2008>{{Cite news| title =Transformation Optics May Usher in a Host of Radical Advances| newspaper =Azonano Nanotechnology (magazine)| location =online| pages =1 of 1| publisher =AZoM.com Pty.Ltd| date =October 17, 2008
  | url =http://www.azonano.com/news.asp?newsID=8164| access-date =2010-05-24}}</ref>

Transformation optics subscribes to the capability of bending [[Physics:Light|light]], or [[Physics:Electromagnetic waves|electromagnetic waves]] and [[Physics:Energy|energy]], in any preferred or desired fashion, for a desired application. [[Physics:Maxwell's equations|Maxwell's equations]] do not vary even though [[Coordinate system|coordinates]] transform. Instead it is the values of the chosen parameters of the materials which "transform", or alter,  during a certain time period. So, transformation optics developed from the capability to choose the parameters for a given material. Hence, since Maxwell's equations retain the same form, it is the successive values of the parameters, [[Physics:Permittivity|permittivity]] and [[Physics:Permeability (electromagnetism)|permeability]], which change over time.  Furthermore, permittivity and permeability are in a sense responses to the [[Physics:Electric field|electric]] and [[Physics:Magnetic field|magnetic field]]s of a radiated light source respectively, among other descriptions. The precise degree of  electric and magnetic response can be controlled in a metamaterial, point by point. Since so much control can be maintained over the responses of the material, this leads to an enhanced and highly flexible [[Physics:Gradient-index optics|gradient-index]] material. Conventionally predetermined [[Physics:Refractive index|refractive index]] of ordinary materials instead become independent spatial gradients in a metamaterial, which can be controlled at will. Therefore, transformation optics is a new method for creating novel and unique optical devices.<ref name=AAAS-322/><ref name=AAAS4/><ref name=nat-trans-opt>
{{Cite journal
  | last1 = Chen
  | first1 =Huanyang
  | author2=C. T. Chan, C.T. and Sheng, Ping
  | title =Transformation optics and metamaterials
  | journal =[[Physics:Nature Materials|Nature Materials]]
  | volume =9
  | issue =5
  | pages =387–396
  | date =April 23, 2010
  | pmid =20414221
  | quote = Underpinned by the advent of metamaterials, transformation optics offers great versatility for controlling electromagnetic waves to create materials with specially designed properties. Here we review the potential of transformation optics to create functionalities in which the optical properties can be designed almost at will. This approach can be used to engineer various optical illusion effects, such as the invisibility cloak.
  | doi =10.1038/nmat2743|bibcode = 2010NatMa...9..387C | s2cid =205404142
 }}</ref><ref name=AAAS5/><ref name=Pendry-imperial-C>{{cite web| last =Pendry| first =Sir John| title =Transformation Optics| publisher =Imperial College, London| year =2006| url =http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/TransOptics.html| format =online free access to description of Transformation Optics| access-date =2010-05-24| archive-url =https://web.archive.org/web/20090815085638/http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/TransOptics.html| archive-date =2009-08-15| url-status =dead}}</ref><ref name=Smith-Duke>

{{cite web| last1= Schurig| first1=David|author2=David Smith |author3=Steve Cummer| title =Transformation Optics and Cloaking| publisher =Center for Metamaterials & Integrated Plasmonics
  | year =2008| url =http://www.metamaterials.duke.edu/research/transformation-optics-and-cloaking| access-date =2010-05-24}}</ref>

==Science of cloaking devices==
The purpose of a ''cloaking'' device is to ''hide'' something, so that a defined region of space is [[Physics:Invisibility|invisibly]] isolated from passing electromagnetic fields (or sound waves), as with '''Metamaterial cloaking'''.<ref name=Eng-space>
{{Cite journal| last1= Kildishev| first1=A.V.|author2=Shalaev, V.M.| title =Engineering space for light via transformation optics| journal =[[Physics:Optics Letters|Optics Letters]]| volume =33 | issue =1 | pages =43–45| url=http://cobweb.ecn.purdue.edu/~shalaev/Publication_list_files/OL%2033%20(1)%20January%202007.pdf| doi =10.1364/OL.33.000043| pmid=18157252| access-date =2010-02-14|bibcode = 2008OptL...33...43K |arxiv = 0711.0183 | year=2007| s2cid=15407450}}</ref><ref>{{cite journal |title= Strange New Tricks With Light |journal=Science|page= 1622 |volume= 330 |date= 17 December 2010|bibcode= 2010Sci...330.1622S | doi=10.1126/science.330.6011.1622 |issue=6011 |pmid=21163994|last1=Service|first1=R. F.|last2=Cho|first2=A}}</ref>

Cloaking objects, or making them appear invisible with [[Physics:Metamaterial|metamaterial]]s, is roughly analogous to a magician's sleight of hand, or his tricks with mirrors. The object or subject doesn't really disappear; the vanishing is an illusion. With the same goal, researchers employ metamaterials to create directed blind spots by deflecting certain parts of the light spectrum (electromagnetic spectrum). It is the light spectrum, as the [[Physics:Transmission medium|transmission medium]], that determines what the human eye can see.<ref name=WSJ-03-12-2009/>

In other words, light is refracted or reflected determining the view, color, or illusion that is seen. The visible extent of light is seen in a [[Physics:Visible spectrum|chromatic spectrum]] such as the [[Earth:Rainbow|rainbow]]. However, visible light is only part of a broad spectrum, which extends beyond the sense of sight. For example, there are other parts of the light spectrum which are in common use today. The [[Physics:Microwave|microwave spectrum]] is employed by [[Engineering:Radar|radar]], cell phones, and [[Engineering:Wireless|wireless Internet]]. The infrared spectrum is used for thermal imaging technologies, which can detect a warm body amidst a cooler night time environment, and infrared illumination is combined with specialized [[Engineering:Charge-coupled device|digital cameras]] for [[Physics:Night vision#Active infrared|night vision]]. Astronomers employ the terahertz band for submillimeter observations to answer deep [[Astronomy:Astronomy|cosmological]] questions.

Furthermore, electromagnetic energy is light energy, but only a small part of it is [[Physics:Visible light|visible light]]. This energy travels in waves. Shorter wavelengths, such as visible light and [[Physics:Infrared|infrared]], carry more energy per [[Physics:Photon|photon]] than longer waves, such as [[Physics:Microwave|microwave]]s and radio waves. For the [[Science|science]]s, the light spectrum is known as the [[Physics:Electromagnetic spectrum|electromagnetic spectrum]].<ref name=WSJ-03-12-2009/><ref name=Discover-mag-2009-03-10/><ref name=NASA-words>
{{cite web| last =Diane Fisher, Nancy Leon, Alexander Novati|title =Space Place – Glossary
 |publisher =NASA| date =2008-06-17| url =http://spaceplace.nasa.gov/en/kids/spitzer/signs/sign_glossary.shtml#E
 |format =Public Domain – [[Organization:NASA|NASA]] web site| access-date =2010-03-08|display-authors=0}}</ref><ref>{{Cite book | title = Camera lenses: from box camera to digital | author = Gregory Hallock Smith | publisher = SPIE Press | year = 2006 | isbn = 978-0-8194-6093-6 | page = 4 | url = https://books.google.com/books?id=6mb0C0cFCEYC&pg=PA4 }}</ref>

===The properties of optics and light===
[[Physics:Prism (optics)|Prism]]s, [[Physics:Mirror|mirror]]s, and [[Physics:Lens (optics)|lens]]es have a long history of altering the diffracted visible light that surrounds all. However, the control exhibited by these ordinary materials is limited. Moreover, the one material which is common among these three types of directors of light is conventional [[Chemistry:Glass|glass]]. Hence, these familiar technologies are constrained by the fundamental, physical [[Physics:Optics|laws of optics]]. With metamaterials in general, and the cloaking technology in particular, it appears these barriers disintegrate with advancements in materials and technologies never before realized in the [[Physics:Physics|natural physical sciences]]. These unique materials became notable because electromagnetic radiation can be bent, reflected, or skewed in new ways. The radiated light could even be slowed or captured before transmission. In other words, new ways to focus and project light and other radiation are being developed. Furthermore, the expanded optical powers presented in the science of cloaking objects appear to be technologically beneficial across a wide spectrum of devices already in use. This means that every device with basic functions that rely on interaction with the radiated [[Physics:Electromagnetic spectrum|electromagnetic spectrum]] could technologically advance. With these beginning steps a whole new class of optics has been established.<ref name=Discover-mag-2009-03-10/><ref name=Duke-News-first-cloak/><ref name=comp>{{cite journal |doi=10.1103/PhysRevLett.84.4184 |title=Composite Medium with Simultaneously Negative Permeability and Permittivity |first5=S. |last5=Schultz |first4=S. |last4=Nemat-Nasser |first3=D. |last3=Vier |first2=Willie |year=2000 |last2=Padilla |last1=Smith |first1=D. R. |journal=[[Physics:Physical Review Letters|Physical Review Letters]] |volume=84 |issue=18 |pmid=10990641 |bibcode=2000PhRvL..84.4184S |pages=4184–7 |doi-access=free }}</ref><ref name=UCSD-press-release>

{{cite web|author=McDonald, Kim|title=UCSD Physicists Develop a New Class of Composite Material with 'Reverse' Physical Properties Never Before Seen |url=http://ucsdnews.ucsd.edu/newsrel/science/mccomposite.htm|publisher=UCSD Science and [[Engineering:Engineering|Engineering]]|date=2000-03-21|access-date=2010-12-17}}</ref><ref name=Vol-176-SciNews-cloak>

{{cite journal| last =Petit| first =Charles| title =Invisibility Uncloaked| journal =Science News
 |page = 18|volume=176|issue=11|date =2009-11-21| url =http://www.sciencenews.org/view/feature/id/49151/title/Invisibility_Uncloaked| access-date =2010-04-10| doi =10.1002/scin.5591761125}}</ref>

===Interest in the properties of optics and light===
Interest in the properties of optics, and light, date back to almost 2000 years to [[Biography:Ptolemy|Ptolemy]] (AD 85 – 165). In his work entitled ''Optics'', he writes about the properties of [[Physics:Light|light]], including [[Physics:Reflection|reflection]], [[Physics:Refraction|refraction]], and [[Color|color]]. He developed a simplified equation for refraction without [[Trigonometric functions|trigonometric functions]]. About 800 years later, in AD 984, [[Biography:Ibn Sahl (mathematician)|Ibn Sahl]] discovered a law of refraction mathematically equivalent to [[Physics:Snell's law|Snell's law]]. He was followed by the most notable Islamic scientist, Ibn Al-Haytham (c.965–1039), who is considered to be "one of the few most outstanding figures in optics in all times".<ref name=first-steps-optics/> He made significant advances in the science of [[Physics:Physics|physics]] in general, and [[Physics:Optics|optics]] in particular. He anticipated the universal laws of light articulated by seventeenth century scientists by hundreds of years.<ref name=Discover-mag-2009-03-10/><ref name=first-steps-optics/><ref name=Ptolemy-theory/><ref name=Hist-of-Science/>

In the seventeenth century both [[Biography:Willebrord Snellius|Willebrord Snellius]] and Descartes were credited with discovering the law of refraction. It was Snellius who noted that Ptolemy's equation for refraction was inexact. Consequently, these laws have been passed along, unchanged for about 400 years, like the laws of gravity.<ref name=Discover-mag-2009-03-10/><ref name=first-steps-optics>

{{Cite journal| last =Mourad| first =Zghal| title =The first steps for learning optics: Ibn Sahl's, Al-Haytham's and Young's works on refraction as typical examples| journal =OSA Technical Digest Series: ETOP(2007) ESB2| volume = Conference Paper| pages =01 (7 pages)| date =2007-06-03| url =http://spie.org/etop/2007/etop07fundamentalsII.pdf| format =Free PDF download. [http://www.opticsinfobase.org/abstract.cfm?URI=ETOP-2007-ESB2 Permanent citation link]| access-date =2010-04-27| display-authors =1| author2 =<Please add first missing authors to populate metadata.>| editor1-first =Marc| editor1-last =Nantel| bibcode =2007SPIE.9665E..09Z| doi =10.1117/12.2207465| series =Tenth International Topical Meeting on Education and Training in Optics and Photonics| s2cid =13875045| doi-access =free}}</ref><ref name=Ptolemy-theory>

{{cite book|last=Smith|first=A. Mark|year=1996
|url=https://books.google.com/books?id=mhLVHR5QAQkC&q=ptolemy+theory+of+visual+perception&pg=PP1
|title=Ptolemy's Theory of Visual Perception– An English translation of the Optics
|publisher=The American Philosophical Society|isbn=978-0-87169-862-9
|access-date=2009-06-27}}</ref><ref name=Hist-of-Science>

[https://books.google.com/books?id=SQXcpvjcJBUC&pg=PA69 Willebrord Snell] in ''Archimedes to Hawking: Laws of Science and the Great Minds Behind Them'' (Clifford A. Pickover, 2008).</ref>

===Perfect cloak and theory===
[[Physics:Electromagnetic radiation|Electromagnetic radiation]] and matter have a symbiotic relationship. Radiation does not simply act on a material, nor is it simply acted upon by a given material. Radiation interacts with [[Physics:Matter|matter]]. Cloaking applications which employ [[Physics:Metamaterial|metamaterial]]s alter how objects interact with the [[Physics:Electromagnetic spectrum|electromagnetic spectrum]]. The guiding vision for the metamaterial cloak is a device that directs the flow of light smoothly around an object, like water flowing past a rock in a stream, without [[Physics:Reflection|reflection]], rendering the object invisible. In reality, the simple cloaking devices of the present are imperfect, and have  limitations.<ref name=WSJ-03-12-2009>
{{Cite news| last = Hotz| first =Robert Lee| title =Behold the Appearance of the Invisibility Cloak| newspaper =Wall Street Journal| pages =Printed in The Wall Street Journal, page A7, Science Journal section| date =2010-03-07| url =https://www.wsj.com/articles/SB123689025626111191| access-date =2010-03-04}}</ref><ref name=Discover-mag-2009-03-10/><ref name=Smith-DR-DukeU>{{cite web| last1=Smith| first1=D.R.|author2=Research group of David R. Smith| title =Smith lab featured in Wall Street Journal| publisher =Duke University| date =2009-03-13| url =http://people.ee.duke.edu/~drsmith/news.html| format =Novel Electromagnetic Media, Meta Group, Duke U| access-date =2010-03-04}}</ref><ref name=Enc-Brit-03-05>
{{cite journal| author1 =Hirose, Akira| title =Wave Aspects of Light| date =2010-03-05| page =95| journal =Proc. SPIE |volume=3490| bibcode =1998SPIE.3490...95H| doi =10.1117/12.308894| series =Optics in Computing '98| s2cid =62568451| editor1-last =Chavel| editor1-first =Pierre H| editor2-last =Miller| editor2-first =David A. B| editor3-last =Thienpont| editor3-first =Hugo}}</ref><ref name="NYT">
{{cite news
 |author=Itzkoff, D. |work=Paper Cuts|publisher=New York Times|title=Why Don't We Invent It Tomorrow? |format= Popular accounting of the cloaking device in the New York Times.
 |url=http://papercuts.blogs.nytimes.com/2008/03/13/why-dont-we-invent-it-tomorrow/
 |access-date=2010-03-05|date=2008-03-13}}</ref><ref name=Chang-nyt-07/>
One challenge up to the present date has been the inability of metamaterials, and cloaking devices, to interact at frequencies, or [[Wavelength|wavelength]]s, within the visible light spectrum.<ref name=AAAS6/><ref name=Chang-nyt-07>
{{Cite news| last = Chang| first =Kenneth| title =Light Fantastic: Flirting With Invisibility| newspaper ={{wipe|New York Times}}| date =June 12, 2007| url =https://www.nytimes.com/2007/06/12/science/12invis.html?_r=1&pagewanted=print| access-date =2010-05-21}}</ref><ref name=BBCnews-first-cloak/>

===Challenges presented by the first cloaking device===
The principle of cloaking, with a cloaking device, was first proved (demonstrated) at frequencies in the [[Physics:Microwave|microwave radiation band]] on October 19, 2006. This demonstration used a small cloaking device. Its height was less than one half inch (< 13&nbsp;mm) and its diameter five inches (125&nbsp;mm), and it successfully diverted microwaves around itself. The object to be hidden from view, a small cylinder, was placed in the center of the device. The invisibility cloak deflected [[Physics:Microwave|microwave beams]] so they flowed around the cylinder inside with only minor distortion, making it appear ''almost'' as if nothing were there at all.

Such a device typically involves surrounding the object to be cloaked with a shell which affects the passage of [[Physics:Light|light]] near it. There was reduced reflection of electromagnetic waves (microwaves), from the object. Unlike a homogeneous natural material with its material properties the same everywhere, the cloak's material properties vary from point to point, with each point designed for specific electromagnetic interactions (inhomogeneity), and are different in different directions (anisotropy). This accomplishes a [[Physics:Gradient-index optics|gradient]] in the material properties. The associated report was published in the journal ''Science''.<ref name=AAAS6/><ref name=Duke-News-first-cloak>{{cite news|publisher=Office of News & Communications Duke University |title=First Demonstration of a Working Invisibility Cloak |url=http://www.dukenews.duke.edu/2006/10/cloakdemo.html |access-date=2009-05-05 |url-status=dead |archive-url=https://web.archive.org/web/20090719231753/http://www.dukenews.duke.edu/2006/10/cloakdemo.html |archive-date=2009-07-19 }}</ref><ref name=BBCnews-first-cloak>
{{cite news|title=Experts test cloaking technology|date=2006-10-19|work=BBC News|url=http://news.bbc.co.uk/1/hi/sci/tech/6064620.stm|access-date=2008-08-05|first=Paul|last=Rincon}}</ref><ref name=Scinews-Ornes>
{{cite web| last = Ornes| first = Stephen| title =The science of disappearing| publisher =ScienceNews the Magazine of the Society for Science & the Public| date =2010-02-15| url =http://www.sciencenews.org/view/generic/id/56357/title/FOR_KIDS_The_science_of_disappearing
 |format = This article is a brief overview of the first cloaking demonstration (2006) and recounted in February 2010.| access-date =2010-03-06}}</ref>

Although a successful demonstration, three notable limitations can be shown. First, since its effectiveness was only in the [[Physics:Microwave|microwave spectrum]] the small object is somewhat invisible only at microwave frequencies. This means invisibility had not been achieved for the [[Biology:Human eye|human eye]], which sees only within the [[Physics:Visible spectrum|visible spectrum]]. This is because the wavelengths of the visible spectrum are tangibly shorter than microwaves. However, this was considered the first step toward a cloaking device for visible light, although more advanced [[Engineering:Nanotechnology|nanotechnology-related]] techniques would be needed due to light's short wavelengths. Second, only small objects can be made to appear as the surrounding air. In the case of the 2006 proof of cloaking demonstration, the hidden from view object, a [[Chemistry:Copper|copper]] cylinder, would have to be less than five inches in diameter, and less than one half inch tall. Third, cloaking can only occur over a narrow frequency band, for any given demonstration. This means that a broad band cloak, which works across the [[Physics:Electromagnetic spectrum|electromagnetic spectrum]], from radio frequencies to microwave to the [[Physics:Visible spectrum|visible spectrum]], and to [[Physics:X-ray|x-ray]], is not available at this time. This is due to the [[Physics:Dispersion (optics)|dispersive nature]] of present-day metamaterials. The coordinate transformation ([[Physics:Transformation optics|transformation optics]]) requires extraordinary material parameters that are only approachable through the use of resonant elements, which are inherently [[Engineering:Narrowband|narrow band]], and [[Physics:Dispersion (optics)|dispersive]] at resonance.<ref name=AAAS-322/><ref name=AAAS6/><ref name=Duke2009/><ref name=Duke-News-first-cloak/><ref name=BBCnews-first-cloak/>

==Usage of metamaterials==
At the very beginning of the new millennium, metamaterials were established as an extraordinary new medium, which expanded control capabilities over [[Physics:Matter|matter]]. Hence, metamaterials are applied to cloaking applications for a few reasons. First, the parameter known as material response has broader range. Second, the material response can be controlled at will.<ref name=Discover-mag-2009-03-10/>

Third, optical components, such as lenses, respond within a certain defined range to [[Physics:Light|light]]. As stated earlier – the range of response has been known, and studied, going back to [[Biography:Ptolemy|Ptolemy]] – eighteen hundred years ago. The range of response could not be effectively exceeded, because natural materials proved incapable of doing so. In scientific studies and research, one way to communicate the range of response is the [[Physics:Refractive index|refractive index]] of a given optical material. Every [[Chemistry:Natural material|natural material]] so far only allows for a positive refractive index. Metamaterials, on the other hand, are an innovation that are able to achieve negative refractive index, zero refractive index, and fractional values in between zero and one. Hence, metamaterials extend the material response, among other capabilities.
However, negative refraction is not the effect that creates invisibility-cloaking. It is more accurate to say that gradations of refractive index, when combined, create invisibility-cloaking. Fourth, and finally, metamaterials demonstrate the capability to deliver chosen responses at will.<ref name=Discover-mag-2009-03-10>{{Cite news| last1 = Hapgood| first1 = Fred| last2 = Grant| first2 = Andrew| title = Metamaterial Revolution: The New Science of Making Anything Disappear| magazine = Discover| pages = 4 pages| date = 2009-03-10| url = http://discovermagazine.com/2009/apr/10-metamaterial-revolution-new-science-making-anything-disappear| access-date = 2015-04-12| archive-url = https://web.archive.org/web/20190331151639/http://discovermagazine.com/2009/apr/10-metamaterial-revolution-new-science-making-anything-disappear| archive-date = 2019-03-31| url-status = dead}}</ref>

== Device==
Before actually building the device, theoretical studies were conducted. The following is one of two studies accepted simultaneously by a scientific journal, as well being distinguished as one of the first published theoretical works for an invisibility cloak.

===Controlling electromagnetic fields===
[[File:Ondes cisaillement 2d 20 petit.gif|thumb|305px|Orthogonal coordinates — [[Cartesian coordinate system|Cartesian plane]] as it transforms from rectangular to curvilinear coordinates]]

The exploitation of "light", the [[Physics:Electromagnetic spectrum|electromagnetic spectrum]], is accomplished with common objects and materials which control and direct the [[Physics:Electromagnetic field|electromagnetic field]]s. For example, a glass [[Physics:Lens (optics)|lens]] in a camera is used to produce an image, a metal cage may be used to screen sensitive equipment, and radio antennas are designed to transmit and receive daily FM broadcasts. [[Physics:Homogeneity|Homogeneous]] materials, which manipulate or modulate [[Physics:Electromagnetic radiation|electromagnetic radiation]], such as glass lenses, are limited in the upper limit of refinements to correct for aberrations. Combinations of inhomogeneous lens materials are able to employ gradient refractive indices, but the ranges tend to be limited.<ref name=AAAS4/>

Metamaterials were introduced about a decade ago, and these expand control of parts of the [[Physics:Electromagnetic spectrum|electromagnetic spectrum]]; from [[Physics:Microwave|microwave]], to [[Physics:Terahertz radiation|terahertz]], to [[Physics:Infrared|infrared]]. Theoretically, metamaterials, as a [[Physics:Transmission medium|transmission medium]], will eventually expand control and direction of electromagnetic fields into the [[Physics:Visible spectrum|visible spectrum]]. Hence, a design strategy was introduced in 2006, to show that a metamaterial can be engineered with arbitrarily assigned positive or negative values of [[Physics:Permittivity|permittivity]] and permeability, which can also be independently varied at will. Then direct control of electromagnetic fields becomes possible, which is relevant to novel and unusual lens design, as well as a component of the [[Scientific theory|scientific theory]] for cloaking of objects from electromagnetic detection.<ref name=AAAS4/>

Each component responds independently to a radiated electromagnetic wave as it travels through the material, resulting in electromagnetic inhomogeneity for each component. Each component has its own response to the external [[Physics:Electromagnetic field|electric and magnetic fields]] of the radiated source. Since these components are smaller than the radiated [[Wavelength|wavelength]] it is understood that a [[Physics:Macroscopic|macroscopic]] view includes an effective value for both permittivity and permeability. These materials obey the laws of physics, but behave differently from normal materials. Metamaterials are artificial materials engineered to provide properties which "may not be readily available in nature". These materials usually gain their properties from structure rather than composition, using the inclusion of small inhomogeneities to enact effective macroscopic behavior.

The [[Periodic function|structural units]] of metamaterials can be tailored in shape and size. Their composition, and their form or structure, can be finely adjusted. Inclusions can be designed, and then placed at desired locations in order to vary the function of a given material. As the lattice is constant, the cells are smaller than the radiated light.<ref name=physicsengineering1>
{{cite book|last1= Engheta|first1=Nader |author-link = Nader Engheta |author2= Richard W. Ziolkowski|title = Metamaterials: physics and engineering explorations|publisher = Wiley & Sons

The design strategy has at its core inhomogeneous composite [[Physics:Metamaterial|metamaterial]]s which direct, at will, [[Physics:Conservation law|conserved quantities]] of [[Physics:Electromagnetism|electromagnetism]]. These quantities are specifically, the [[Physics:Electric displacement field|electric displacement field]] '''D''', the [[Physics:Magnetic field|magnetic field intensity]] '''B''', and the [[Poynting vector]] '''S'''. Theoretically, when regarding the conserved quantities, or fields, the metamaterial exhibits a twofold capability. First, the fields can be concentrated in a given direction. Second, they can be made to avoid or surround objects, returning without perturbation to their original path. These results are consistent with [[Physics:Maxwell's equations|Maxwell's equations]] and are more than only [[Physics:Ray (optics)|ray approximation]] found in [[Physics:Geometrical optics|geometrical optics]]. Accordingly, in principle, these effects can encompass all forms of electromagnetic radiation phenomena on all length scales.<ref name=AAAS4/><ref name=AAAS5/>
<ref name=Veselago1>

{{cite journal|last=Veselago|first=V. G.|title=The electrodynamics of substances with simultaneously negative values of [permittivity] and [permeability]|journal=Soviet Physics Uspekhi|year=1968|volume=10|issue=4|pages=509–514|doi=10.1070/PU1968v010n04ABEH003699|bibcode = 1968SvPhU..10..509V }}</ref>

The hypothesized design strategy begins with intentionally choosing a configuration of an [[Philosophy:Arbitrariness|arbitrary number]] of embedded sources. These sources become localized responses of [[Physics:Permittivity|permittivity]], ε, and magnetic permeability, μ. The sources are embedded in an [[Philosophy:Arbitrariness|arbitrarily]] selected [[Physics:Transmission medium|transmission medium]] with [[Physics:Dielectric|dielectric]] and [[Physics:Magnetic|magnetic]] characteristics. As an electromagnetic system the medium can then be schematically represented as a grid.<ref name=AAAS4/>

The first requirement might be to move a uniform [[Physics:Electric field|electric field]] through space, but in a definite direction, which avoids an object or obstacle. Next remove and embed the system in an elastic medium that can be warped, twisted, pulled or stretched as desired. The initial condition of the fields is recorded on a Cartesian mesh. As the elastic medium is distorted in one, or combination, of the described possibilities, the same pulling and stretching process is recorded by the Cartesian mesh. The same set of contortions can now be recorded, occurring as coordinate transformation''':'''

:::::<span style="font-size:125%;">''a'' (x,y,z), ''b'' (x,y,z), ''c'' (x,y,z), ''d'' (x,y,z) ....</span>

Hence, the permittivity, ε, and permeability, μ, is proportionally calibrated by a common factor. This implies that less precisely, the same occurs with the refractive index. Renormalized values of permittivity and permeability are applied in the ''new'' coordinate system. For the renormalization equations see ref. #.<ref name=AAAS4/>

====Application to cloaking devices====
Given the above parameters of operation, the system, a metamaterial, can now be shown to be able to conceal an object of arbitrary size. Its function is to manipulate incoming rays, which are about to strike the object. These incoming rays are instead electromagnetically steered around the object by the metamaterial, which then returns them to their original trajectory. As part of the design it can be assumed that no radiation leaves the concealed volume of space, and no radiation can enter the space. As illustrated by the function of the metamaterial, any radiation attempting to penetrate is steered around the space or the object within the space, returning to the initial direction. It appears to any observer that the concealed volume of space is empty, even with an object present there. An arbitrary object may be hidden because it remains untouched by external radiation.<ref name=AAAS4/>

A sphere with radius R<sub>1</sub> is chosen as the object to be hidden. The cloaking region is to be contained within the annulus R<sub>1</sub> < r < R<sub>2</sub>. A simple transformation that achieves the desired result can be found by taking all fields in the region r < R<sub>2</sub> and compressing them into the region R<sub>1</sub> < r < R<sub>2</sub>. The coordinate transformations do not alter Maxwell's equations. Only the values of ε{{prime}} and μ{{prime}} change over time.

====Cloaking hurdles====
There are issues to be dealt with to achieve invisibility cloaking. One issue, related to [[Physics:Ray tracing|ray tracing]], is the anisotropic effects of the material on the electromagnetic rays entering the "system". Parallel bundles of rays, (''see above image''), headed directly for the center are abruptly curved and, along with neighboring rays, are forced into tighter and tighter [[Arc (geometry)|arc]]s. This is due to rapid changes in the now shifting and transforming [[Physics:Permittivity|permittivity]] ε{{prime}} and [[Physics:Permeability (electromagnetism)|permeability]] μ{{prime}}. The second issue is that, while it has been discovered that the selected metamaterials are capable of working within the parameters of the anisotropic effects and the continual shifting of ε{{prime}} and μ{{prime}}, the values for ε{{prime}} and μ{{prime}} cannot be very large or very small. The third issue is that the selected metamaterials are currently unable to achieve broad, [[Physics:Dispersion (optics)|frequency spectrum]] capabilities. This is because the rays must curve around the "concealed" [[Sphere|sphere]], and therefore have longer trajectories than traversing [[Physics:Free space|free space]], or air. However, the rays must arrive around the other side of the sphere in [[Physics:Phase (waves)|phase]] with the beginning radiated [[Physics:Light|light]]. If this is happening then the [[Physics:Group velocity#Physical interpretation|phase velocity]] exceeds the velocity of light in a [[Physics:Vacuum|vacuum]], which is the speed limit of the universe. (Note, this does not violate the laws of physics). And, with a required absence of frequency dispersion, the [[Physics:Group velocity|group velocity]] will be identical with [[Physics:Phase velocity|phase velocity]]. In the context of this experiment, group velocity can never exceed the velocity of light, hence the analytical parameters are effective for only one [[Physics:Frequency|frequency]].<ref name=AAAS4/>

===Optical conformal mapping and ray tracing in transformation media===
The goal then is to create no discernible difference between a concealed volume of space and the propagation of electromagnetic waves through empty space. It would appear that achieving a perfectly concealed (100%) hole, where an object could be placed and hidden from view, is not probable. The problem is the following: in order to carry images, light propagates in a continuous range of directions. The [[Physics:Scattering|scattering]] data of electromagnetic waves, after bouncing off an object or hole, is unique compared to light propagating through empty space, and is therefore easily perceived. Light propagating through empty space is consistent only with empty space. This includes microwave frequencies.<ref name=AAAS5/>

Although mathematical reasoning shows that perfect concealment is not probable because of the wave nature of light, this problem does not apply to electromagnetic rays, i.e., the domain of [[Physics:Geometrical optics|geometrical optics]]. Imperfections can be made arbitrarily, and [[Exponential function|exponentially]] small for objects that are much larger than the wavelength of light.<ref name=AAAS5/>

Mathematically, this implies ''n'' < 1, because the rays follow the shortest path and hence in theory create a perfect concealment. In practice, a certain amount of acceptable visibility occurs, as noted above. The range of the refractive index of the dielectric (optical material) needs to be across a wide [[Spectrum|spectrum]] to achieve concealment, with the illusion created by wave propagation across empty space. These places where ''n'' < 1 would be the shortest path for the ray around the object without phase distortion. Artificial propagation of empty space could be reached in the microwave-to-[[Physics:Terahertz radiation|terahertz]] range.  In [[Engineering:Stealth technology|stealth technology]], impedance matching could result in absorption of beamed electromagnetic waves rather than reflection, hence, evasion of detection by [[Engineering:Radar|radar]]. These general principles can also be applied to sound waves, where the index ''n'' describes the ratio of the local phase velocity of the wave to the bulk value. Hence, it would be useful to protect a space from any sound sourced detection. This also implies protection from sonar. Furthermore, these general principles are applicable in diverse fields such as [[Physics:Electrostatics|electrostatics]], [[Physics:Fluid mechanics|fluid mechanics]], [[Physics:Classical mechanics|classical mechanics]], and [[Physics:Quantum chaos|quantum chaos]].<ref name=AAAS5/>

Mathematically, it can be shown that the [[Wave|wave]] propagation is indistinguishable from empty space where [[Physics:Ray (optics)|light rays]] propagate along straight lines. The medium performs an optical conformal mapping to empty space.<ref name=AAAS5/>

=== Microwave frequencies===
The next step, then, is to actually conceal an object by controlling electromagnetic fields.
Now, the demonstrated and theoretical ability for controlled electromagnetic fields has opened a new field, ''transformation optics''. This nomenclature is derived  from coordinate transformations used to create variable pathways for the propagation of light through a material.  This demonstration is based on previous theoretical prescriptions, along with the accomplishment of the prism experiment. One possible application of transformation optics and materials is electromagnetic cloaking for the purpose of rendering a volume or object undetectable to incident radiation, including radiated probing.<ref name=AAAS6>
{{cite journal
|last1=Schurig|first1=D.
|last2=Mock
|quote= A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was 'hidden' inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space.
|first2=J. J.
|last3=Justice
|first3=B. J.
|last4=Cummer
|first4=S. A.
|last5=Pendry
|first5=J. B.
|last6=Starr
|first6=A. F.
|last7=Smith
|first7=D. R.
|title=Metamaterial Electromagnetic Cloak at Microwave Frequencies
|journal=Science|year=2006|volume=314|issue=5801|pmid=17053110|pages=977–980
|doi=10.1126/science.1133628|bibcode = 2006Sci...314..977S
|s2cid=8387554
|display-authors=1 |doi-access=free
}}</ref><ref name=Davidsmith1>
{{cite web
|author=David R. Smith Duke U. Engineering
|title=Novel Electromagnetic Media — Research Group of David R. Smith
|url=http://people.ee.duke.edu/~drsmith/|publisher=Meta Group Duke University
|year=2009|access-date=2009-07-15}}</ref><ref name=Optexpress1>{{cite journal
 |last1        = Schurig
 |first1       = D.
 |author2      = Pendry JB, Smith DR
 |title        = Calculation of material properties and ray tracing in transformation media
 |journal      = Opt Express
 |date         = September 29, 2006
 |volume       = 14
 |format       = Free PDF download
 |url          = http://muri2.lci.kent.edu/References/NIM_Papers/Cloaking/2006_Smith_ray_trace.pdf
 |issue        = 21
 |pmid         = 19529371
 |pages        = 9794–9804
 |doi          = 10.1364/OE.14.009794
 |arxiv        = physics/0607205
 |bibcode      = 2006OExpr..14.9794S
 |s2cid        = 485494
 |access-date  = December 27, 2010
 |archive-date = June 26, 2010
 |archive-url  = https://web.archive.org/web/20100626091403/http://muri2.lci.kent.edu/References/NIM_Papers/Cloaking/2006_Smith_ray_trace.pdf
 |url-status   = dead
}}</ref>

This demonstration, for the first time, of actually concealing an object with electromagnetic fields, uses the method of purposely designed spatial variation.  This is an effect of embedding purposely designed electromagnetic sources in the metamaterial.<ref name=Optexpress2/>

As discussed earlier, the fields produced by the metamaterial are compressed into a shell (coordinate transformations) surrounding the now concealed volume. Earlier this was supported theory; this experiment demonstrated the effect actually occurs.  Maxwell's equations are scalar when applying transformational coordinates, only the permittivity tensor and permeability tensor are affected, which then become spatially variant, and directionally dependent along different axes. The researchers state''':'''
{{cquote|By implementing these complex material properties, the concealed volume plus the cloak appear to have the properties of free space when viewed externally. The cloak thus neither scatters waves nor imparts a shadow in the either of which would enable the cloak to be detected. Other approaches to invisibility either rely on the reduction of backscatter or make use of a resonance in which the properties of the cloaked object and the must be carefully matched.

...Advances in the development of [negative index metamaterials], especially with respect to gradient index lenses, have made the physical realization of the specified complex material properties feasible. We implemented a two-dimensional (2D) cloak because its fabrication and measurement requirements were simpler than those of a 3D cloak.<ref name=AAAS6/>}}

Before the actual demonstration, the experimental limits of the transformational fields were computationally determined, in addition to simulations, as both were used to determine the effectiveness of the cloak.<ref name=AAAS6/>

A month prior to this demonstration, the results of an experiment to spatially map the internal and external electromagnetic fields of negative refractive metamaterial was published in September 2006.<ref name=Optexpress2/> This was innovative because prior to this the microwave fields were measured only externally.<ref name=Optexpress2/> In this September experiment the permittivity and permeability of the microstructures (instead of external macrostructure) of the metamaterial samples were measured, as well as the scattering by the two-dimensional negative index metamaterials.<ref name=Optexpress2/> This gave an average effective refractive index, which results in assuming homogeneous metamaterial.<ref name=Optexpress2>{{cite journal
|last1=Justice|first1=BJ|author2=Mock JJ, Guo L, Degiron A, Schurig D, Smith DR.
|title=Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials|journal=Optics Express|year=2006|volume=14|issue=19
|pmid=19529250|pages=8694–8705|doi=10.1364/OE.14.008694|bibcode = 2006OExpr..14.8694J |s2cid=40725177|doi-access=free}}</ref>

Employing this technique for this experiment, spatial mapping of phases and amplitudes of the microwave radiations interacting with metamaterial samples was conducted. The performance of the cloak was confirmed by comparing the measured field maps to simulations.<ref name=AAAS6/>

For this demonstration, the concealed object was a conducting cylinder at the inner radius of the cloak. As the largest possible object designed for this volume of space, it has the most substantial scattering properties. The conducting cylinder was effectively concealed in two dimensions.<ref name=AAAS6/>

=== Infrared frequencies===
The definition optical frequency, in metamaterials literature, ranges from far infrared, to near infrared, through the visible spectrum, and includes at least a portion of ultra-violet. To date when literature refers optical frequencies these are almost always frequencies in the infrared, which is below the visible spectrum. In 2009 a group of researchers announced cloaking at optical frequencies. In this case the cloaking frequency was centered at 1500&nbsp;nm or 1.5 micrometers – the infrared.<ref name=optical-cloak>
{{cite journal
 |author1=Gabrielli
 |author2=Jaime Cardenas
 |author3=Poitras
 |author4=Michal Lipson
 |doi=10.1038/nphoton.2009.117
 |journal=Nature Photonics
 |volume=3
 |title=Silicon nanostructure cloak operating at optical frequencies
 |issue=8
 |pages=461–463
 |year=2009
 |arxiv=0904.3508
 |bibcode = 2009NaPho...3..461G
|s2cid=19395895
 }}</ref><ref>
{{cite arXiv
 |eprint=0807.4945
 |author1=Filiberto Bilotti
 |author2=Simone Tricarico
 |author3=Lucio Vegni
 |title=Plasmonic metamaterial cloaking at optical frequencies
 |class=physics.optics
 |year=2008
}}</ref>

=== Sonic frequencies===

A laboratory metamaterial device, applicable to ultra-sound waves was demonstrated in January 2011. It can be applied to [[Wavelength|sound wavelengths]] corresponding to frequencies from 40 to 80&nbsp;kHz.

The metamaterial acoustic cloak is designed to hide objects submerged in water. The metamaterial cloaking mechanism bends and twists sound waves by intentional design.

The cloaking mechanism consists of 16 concentric rings in a cylindrical configuration. Each ring has acoustic circuits. It is intentionally designed to guide sound waves in two dimensions.

Each ring has a different index of refraction. This causes sound waves to vary their speed from ring to ring. "The sound waves propagate around the outer ring, guided by the channels in the circuits, which bend the waves to wrap them around the outer layers of the cloak". It forms an array of cavities that slow the speed of the propagating sound waves. An experimental cylinder was submerged and then disappeared from sonar. Other objects of various shape and density were also hidden from the sonar. The acoustic cloak demonstrated effectiveness for frequencies of 40&nbsp;kHz to 80&nbsp;kHz.<ref name=watery-success>{{cite web|last=Laboratory News |title=Watery success for Acoustic cloak |publisher=Metropolis International Group Ltd |quote=Researchers from the University of Illinois – led by mechanical science and engineering professor, Nicholas Fang – have developed an acoustic cloak which renders submerged objects invisible. |url=http://www.labnews.co.uk/laboratory_article.php/6196/2/watery-success-for-acoustic-cloak- |format=Online article |access-date=February 12, 2011 |url-status=dead |archive-url=https://web.archive.org/web/20110724090224/http://www.labnews.co.uk/laboratory_article.php/6196/2/watery-success-for-acoustic-cloak- |archive-date=July 24, 2011 }}</ref><ref name=acousticcloak>{{Cite news|last=Nelson |first=Bryn |title=New metamaterial could render submarines invisible to sonar |newspaper=Defense Update |format=Online |date=January 19, 2011 |url=http://defense-update.com/wp/20110119_stealth_submarine.html |access-date=2011-01-31 |url-status=dead |archive-url=https://web.archive.org/web/20110122064849/http://defense-update.com/wp/20110119_stealth_submarine.html |archive-date=January 22, 2011 }}</ref><ref name=illinois>{{Cite news|title=Acoustic cloaking could hide objects from sonar |newspaper=Information for Mechanical Science and Engineering |format=Online |publisher=University of Illinois (Urbana-Champaign) |date=April 21, 2009 |url=http://mechse.illinois.edu/content/news/spotlight.php?id=177 |access-date=2011-02-01 |url-status=dead |archive-url=https://web.archive.org/web/20110217091323/http://mechse.illinois.edu/content/news/spotlight.php?id=177 |archive-date=February 17, 2011 }}</ref><ref>{{Cite news|title=Newly Developed Cloak Hides Underwater Objects From Sonar |newspaper=U.S. News – Science |format=Online |publisher=2011 U.S. News & World Report |date=January 7, 2011 |url=http://mechse.illinois.edu/content/news/spotlight.php?id=177 |access-date=2011-06-01 |url-status=dead |archive-url=https://web.archive.org/web/20110217091323/http://mechse.illinois.edu/content/news/spotlight.php?id=177 |archive-date=February 17, 2011 }}</ref>

In 2014 researchers created a 3D acoustic cloak from stacked plastic sheets dotted with repeating patterns of holes. The pyramidal geometry of the stack and the hole placement provide the effect.<ref>{{cite news |title=World's first 3D acoustic cloaking device created |first=Darren |last=Quick |date=March 11, 2014  |url=http://www.gizmag.com/3d-acoustic-cloak/31177/ |publisher=Gizmag }}</ref>

===Invisibility in diffusive light scattering media===

In 2014, scientists demonstrated good cloaking performance in murky water, demonstrating that an object shrouded in fog can disappear completely when appropriately coated with metamaterial.  This is due to the random scattering of light, such as that which occurs in clouds, fog, milk, frosted glass, etc., combined with the properties of the metatmaterial coating.  When light is diffused, a thin coat of metamaterial around an object can make it essentially invisible under a range of lighting conditions.<ref>{{cite journal|author=Smith, David R. |title= A cloaking coating for murky media |journal=Science|volume= 345 |issue= 6195 |pages= 384–5 |date= 25 July 2014 |doi=10.1126/science.1256753|bibcode = 2014Sci...345..384S |pmid=25061192|s2cid= 206559590 }}</ref><ref>{{cite journal|title= Invisibility cloaking in a diffuse light scattering medium |journal=Science|volume= 345 |issue= 6195 |pages=427–9|date= 25 July 2014 |doi=10.1126/science.1254524|pmid=24903561|bibcode = 2014Sci...345..427S |last1=Schittny|first1=R.|last2=Kadic|first2=M.|last3=Buckmann|first3=T.|last4=Wegener|first4=M.|s2cid=206557843|doi-access=free}}</ref>

==Cloaking attempts==

===Broadband ground-plane cloak===
If a transformation to quasi-[[Orthogonal coordinates|orthogonal coordinates]] is applied to [[Physics:Maxwell's equations|Maxwell's equations]] in order to conceal a perturbation on a flat [[Physics:Permittivity|conducting plane]] rather than a singular point, as in the first demonstration of a transformation optics-based cloak, then an object can be hidden underneath the perturbation.<ref name=AAASflatplane>
{{Cite journal| title =Broadband Ground-Plane Cloak| journal =Science| volume =323| issue =5912| pages =366–369| date =January 16, 2009|doi =10.1126/science.1166949| pmid=19150842|bibcode = 2009Sci...323..366L | last1 =Liu| first1 =R| last2 =Ji| first2 =C| last3 =Mock| first3 =J. J.| last4 =Chin| first4 =J. Y.| last5 =Cui| first5 =T. J.| last6 =Smith| first6 =D. R.| s2cid =206516809}}</ref> This is sometimes referred to as a "carpet" cloak.

As noted above, the original cloak demonstrated utilized resonant metamaterial elements to meet the effective material constraints. Utilizing a quasi-conformal transformation in this case, rather than the non-conformal original transformation, changed the required material properties. Unlike the original (singular expansion) cloak, the "carpet" cloak required less extreme material values. The quasi-conformal carpet cloak required anisotropic, inhomogeneous materials which only varied in [[Physics:Permittivity|permittivity]]. Moreover, the permittivity was always positive. This allowed the use of non-resonant metamaterial elements to create the cloak, significantly increasing the bandwidth.

An automated process, guided by a set of [[Algorithm|algorithm]]s, was used to construct a metamaterial consisting of thousands of elements, each with its own [[Geometry|geometry]]. Developing the algorithm allowed the manufacturing process to be automated, which resulted in fabrication of the metamaterial in nine days. The previous device used in 2006 was rudimentary in comparison, and the manufacturing process required four months in order to create the device.<ref name=Duke2009/> These differences are largely due to the different form of transformation: the original 2006 cloak transformed a singular point, while the ground-plane version transforms a plane, and the transformation in the carpet cloak was quasi-conformal, rather than non-conformal.

==Other theories of cloaking==
{{main|Physics:Theories of cloaking}}
Other theories of cloaking discuss various science and research based theories for producing an electromagnetic cloak of invisibility. Theories presented employ [[Physics:Transformation optics|transformation optics]], event cloaking, dipolar scattering cancellation, tunneling light transmittance, sensors and active sources, and acoustic cloaking.

==Institutional research==
The research in the field of metamaterials has diffused out into the American government science research departments, including the US Naval Air Systems Command, {{wipe|US Air Force}}, and US Army. Many scientific institutions are involved including:{{citation needed|date=January 2016}}
{{div col|colwidth=30em}}
*[[Organization:California Institute of Technology|California Institute of Technology]]
*[[Organization:Massachusetts Institute of Technology|Massachusetts Institute of Technology]]
*[[Organization:Colorado State University|Colorado State University]]
*[[Organization:Pennsylvania State University|Pennsylvania State University]]
*[[Organization:Duke University|Duke University]]
*[[Organization:Harvard University|Harvard University]]
*Aalto University
*[[Organization:Imperial College London|Imperial College London]]
*Max Planck Society
*[[Organization:MSU Faculty of Physics|MSU Faculty of Physics]]
*[[Organization:National Institute of Standards and Technology|National Institute of Standards and Technology]]
*Nederlandse Organisatie voor Wetenschappelijk Onderzoek
*[[Organization:University College London|University College London]]
*[[Organization:University of California, Berkeley|University of California, Berkeley]]
*[[Organization:University of California, Irvine|University of California, Irvine]]
*[[Organization:University of California, Los Angeles|University of California, Los Angeles]]
*[[Organization:University of California, San Diego|University of California, San Diego]]
*University of Colorado
*[[Organization:University of Delaware|University of Delaware]]
*[[Organization:University of Rochester|University of Rochester]]
{{div col end}}

Funding for research into this technology is provided by the following {{wipe|United States}} agencies:<ref name=Duke7>{{cite web|last1=Smith |first1=David R. |author2=NAVAIR, SensorMetrix, AFOSR, ARO, DARPA, NGA, MURI, and multiple universities |title=Programs Collaborators Funding |publisher=Duke University |year=2009 |url=http://people.ee.duke.edu/~drsmith/collaborators.htm |access-date=2009-07-04 |url-status=dead |archive-url=https://web.archive.org/web/20090819033958/http://people.ee.duke.edu/~drsmith/collaborators.htm |archive-date=August 19, 2009 }}</ref>
*Air Force Research Laboratory
*Defense Advanced Research Projects Agency
*Director of Central Intelligence
*[[Organization:National Geospatial-Intelligence Agency|National Geospatial-Intelligence Agency]]
*Naval Air Systems Command
*Office of Naval Research

Through this research, it has been realized that developing a method for controlling electromagnetic fields can be applied to escape detection by radiated probing, or sonar technology, and to improve communications in the [[Physics:Microwave|microwave]] range; that this method is relevant to [[Physics:Superlens|superlens]] design and to the cloaking of objects within and from electromagnetic fields.<ref name=AAAS5/>

==In the news==
On October 20, 2006, the day after Duke University achieved enveloping and "disappearing" an object in the microwave range, the story was reported by Associated Press.<ref name=Duke3>{{cite press release|title=Duke University in the News: Invisibility Could Become a Reality |url=http://news.duke.edu/2006/10/clips102006.html |year=2006 |access-date=2009-06-30 |url-status=dead |archive-url=https://web.archive.org/web/20090818041314/http://news.duke.edu/2006/10/clips102006.html |archive-date=August 18, 2009 }}</ref> Media outlets covering the story included USA Today, MSNBC's Countdown With Keith Olbermann: ''Sight Unseen'', The New York Times with ''Cloaking Copper, Scientists Take Step Toward Invisibility'', (London) The Times with ''Don't Look Now—Visible Gains in the Quest for Invisibility'', Christian Science Monitor with ''Disappear Into Thin Air? Scientists Take Step Toward Invisibility'', Australian Broadcasting, Reuters with ''Invisibility Cloak a Step Closer'', and the (Raleigh) News & Observer with '''Invisibility Cloak a Step Closer''.<ref name=Duke3/>

On November 6, 2006, the Duke University research and development team was selected as part of the Scientific American best 50 articles of 2006.<ref name=Duke4>{{cite press release|title=Invisibility Cloak Lands Duke Engineers on 'Scientific American 50' |url=http://news.duke.edu/2006/11/sciam50.html |year=2006 |access-date=2009-06-30 |url-status=dead |archive-url=https://web.archive.org/web/20100619113018/http://news.duke.edu/2006/11/sciam50.html |archive-date=June 19, 2010 }}</ref>

In the month of November 2009, "research into designing and building unique 'metamaterials' has received a £4.9 million funding boost. Metamaterials can be used for invisibility 'cloaking' devices, sensitive security sensors that can detect tiny quantities of dangerous substances, and flat lenses that can be used to image tiny objects much smaller than the wavelength of light."<ref name=UKfund2009>{{Cite news
  | last = Reeves
  | first = Danielle
  | format = news release
  | title =  £4.9 million to develop metamaterials for 'invisibility cloaks' and 'perfect lenses'
  | publisher =Imperial College London press office
  | date =November 12, 2009
  | url =http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/newssummary/news_12-11-2009-13-23-57
  | access-date =2010-12-30}}</ref>

In November 2010, scientists at the University of St Andrews in Scotland reported the creation of a flexible cloaking material they call "Metaflex", which may bring industrial applications significantly closer.<ref>[http://iopscience.iop.org/1367-2630/12/11/113006 Flexible metamaterials at visible wavelengths], Andrea Di Falco et al 2010 New J. Phys. 12 113006</ref>

In 2014, the world 's first 3D acoustic device was built by Duke engineers.<ref>{{cite web|url=http://www.pratt.duke.edu/news/acoustic-cloaking-device-hides-objects-sound|title=Acoustic Cloaking Device Hides Objects from Sound - Duke Pratt School of Engineering|website=www.pratt.duke.edu|date=11 March 2014}}</ref>

==See also==
{{div col|colwidth=22em}}
*[[Engineering:History of metamaterials|History of metamaterials]]
*Acoustic metamaterials
*[[Chirality]]
*[[Physics:Metamaterial|Metamaterial]]
*[[Engineering:Metamaterial absorber|Metamaterial absorber]]
*Metamaterial antennas
*Nonlinear metamaterials
*[[Physics:Photonic crystal|Photonic crystal]]
*Photonic metamaterials
*Plasmonic metamaterials
*Seismic metamaterials
*[[Physics:Split-ring resonator|Split-ring resonator]]
*[[Physics:Superlens|Superlens]]
*Terahertz metamaterials
*[[Physics:Theories of cloaking|Theories of cloaking]]
*[[Physics:Transformation optics|Transformation optics]]
*Tunable metamaterials
::::'''Academic journals'''
*''Metamaterials'' (journal)
::::'''Metamaterials books'''
*''[[Physics:Metamaterials Handbook|Metamaterials Handbook]]''
*''[[Engineering:Metamaterials: Physics and Engineering Explorations|Metamaterials]]''
{{div col end}}

==References==
{{reflist|30em}}

==Further reading==
*{{Cite journal
  | last1=Kundtz
  | first1= Nathan
  | author2=David R. Smith (advisor)
  | title =Advances in Complex Electromagnetic Media
  | journal =Duke Dissertations
  | page =185
  | date =December 18, 2009
  | url =http://dukespace.lib.duke.edu/dspace/handle/10161/1636
  | access-date =2011-02-23
  | bibcode =2009PhDT.......185K}} 148 pages. "''Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics in the Graduate School of Duke University 2009''"

==External links==
*[http://www.metamorphose-eu.org/index.php?id=9 Defining metamaterials]
*[http://online.itp.ucsb.edu/online/qo02/pendry/ Manipulating the Near Field with Metamaterials] Slide show, with audio available, by Dr. John Pendry, Imperial College, London
*[http://www.sciencenews.org/view/generic/id/47208/title/Metamaterials_mock_the_heavens Researchers propose mimicking the cosmos with metamaterials]

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[[Category:Electromagnetism]]
[[Category:Metamaterials]]

{{Sourceattribution|Metamaterial cloaking}}