Nagata–Biran conjecture: Difference between revisions

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A practical '''superlens''', '''super lens''' or '''perfect lens''', is a [[lens (optics)|lens]] which uses [[metamaterial]]s to go beyond the [[diffraction limit]]. The diffraction limit is an inherent limitation in conventional [[optical microscopy|optical devices]] or lenses.<ref name=perfect-lens-2000/>  As [[Ernst Abbe]] reported in 1873, the lens of a camera or microscope is incapable of capturing some very fine details of any given image. The super lens, on the other hand, is intended to capture these fine details. Consequently, conventional [[Lens (optics)|lens]] limitation has inhibited progress in certain areas of the [[biological science]]s. This is because a [[virus]] or [[DNA molecule]] is out of visual range with the highest powered microscopes. Also, this limitation inhibits seeing the minute processes  of [[cellular protein]]s moving alongside [[microtubules]] of a [[cell (biology)|living cell]] in their natural environments. Additionally, [[computer chip]]s and the interrelated [[microelectronics]] are manufactured to smaller and smaller scales. This requires specialized [[nanolithography|optical equipment]], which is also limited because these use the conventional lens.  Hence, the principles governing a super lens show that it has potential for imaging a DNA molecule and [[cellular protein]] processes, or aiding in the manufacture of even smaller computer chips and microelectronics.<ref name=overcome>
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{{cite journal
| last = Zhang 
| first = Xiang
| coauthors = and Liu,Zhaowei
| title = Superlenses to overcome the diffraction limit
| journal = Nature Materials
| volume = 7
| pages = 435–441
| publisher =
| format = Free PDF download
| year = 2008
| url = http://xlab.me.berkeley.edu/pdf/090.pdf
| doi = 10.1038/nmat2141
| accessdate =2013-06-03|bibcode = 2008NatMa...7..435Z }}</ref><ref name=Aguirre>
{{cite web
| last = Aguirre
| first = Edwin L.
| title = Creating a ‘Perfect’ Lens for Super-Resolution Imaging
| work =
| publisher = [[U-Mass Lowell]] News
| date = 2012-09-18
| url = http://www.uml.edu/News/stories/2011-12/Akyurtlu-research.aspx
| doi = 10.1117/1.3484153
| accessdate =2013-06-02}}</ref><ref name=100-nanometer/><ref name=half-wave-length/>
 
Furthermore, conventional lenses capture only the [[wave propagation|propagating]] light [[wave]]s. These are waves that travel from a light source or an object to a lens, or the human eye. This can alternatively be studied as the [[far field]]. In contrast, the superlens, or perfect lens, captures propagating [[visible light|light waves]] and waves that stay on top of the surface of an object, which, alternatively, can be studied as both the [[far field]] and the [[near and far field|near field]].<ref>Pendry, John. ''[http://www.cmth.ph.ic.ac.uk/photonics/pdf/OPNarticle.pdf Manipulating the Near Field]''. Volume 15. [http://www.osa-opn.org/home/articles/volume_15/issue_9/Optics & Photonics News September 2004].</ref><ref>
{{cite journal
| last = Anantha
| first = S. Ramakrishna
| coauthors = J.B. Pendry, M.C.K. Wiltshire and W.J. Stewart
| title = Imaging the Near Field
| journal = Journal of Modern Optics
| volume = 50
| issue = 09
| pages = 1419–1430
| publisher = Taylor & Francis
| location =
| year = 2003
| url = http://esperia.iesl.forth.gr/~ppm/DALHM/publications/papers/jmov50p1419.pdf
| doi = 10.1080/0950034021000020824
| accessdate = }}</ref>
 
In other words, a '''superlens''', '''super lens''' or '''perfect lens'''  is an optical lens with [[Image resolution|resolution]] capabilities that go substantially beyond ordinary [[microscope]]s. Such a device could significantly advance the field of [[optics]] and [[optical engineering]]. In 2000, a type of lens was proposed that consisted of a metamaterial that compensates for wave decay and [[Optical resolution|reconstructs images]] in the [[near and far field|near field]]. In addition, both [[Wave propagation|propagating]] and [[evanescent wave]]s contribute to the [[Optical resolution|resolution of the image]]. Theory and simulations show that the superlens and hyperlens can work, but engineering obstacles need to be overcome.<ref name=perfect-lens-2000/><ref name=thin-sliver/><ref name=ideal-focus>
{{Cite journal
| last =Brumfiel
| first =G
| year =2009
| title =Metamaterials: Ideal focus
| journal =[[Nature (journal)|Nature News]]
| volume =459 | issue =7246 | pages =504–5
| url= http://www.nature.com/news/2009/090527/full/459504a.html
| format = online web page
| doi =10.1038/459504a
| pmid =19478762}}</ref>
 
== Image formation ==
[[File:Loupe-binoculaire-p1030891.jpg|thumb|250px|The [[Binocular microscope]] is a conventional optical system. [[Spatial resolution]] is confined by a [[diffraction limit]] that is a little above 200 [[nanometer]]s.]]
[[Image:Commonly used metallic nanoprobes.jpg|thumb|250px|Schematic depictions and images of commonly used metallic nanoprobes that can be used to see a sample in nanometer resolution. Notice that the tips of the three nanoprobes are 100 nanometers.<ref name=100-nanometer/>]]
 
An image of an object can be defined as a tangible or visible representation  of the features of that object. A requirement for image formation is interaction with fields of  [[EM field|electromagnetic radiation]]. Furthermore, the level of feature detail, or image [[Image resolution|resolution]], is limited to a [[wavelength|length of a wave of radiation]]. For example, with [[optical microscopy]], image production and resolution depends on the length of a wave of [[visible light]]. However, with a superlens, this limitation may be removed, and a new class of image generated.<ref name=image=res>
{{cite journal
|last=Lauterbur |first=P.
|year=1973
|title=Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance
|url=http://www.nature.com/physics/looking-back/lauterbur/index.html
|journal=[[Nature (journal)|Nature]]
|volume=242 |issue=5394 |page=190
|doi=10.1038/242190a0
|bibcode=1973Natur.242..190L
}}</ref>
 
[[Electron beam lithography]] can overcome this [[diffraction limit|resolution limit]]. Optical microscopy, on the other hand cannot, being limited to some value just above  200 [[100 nanometers|nanometers]].<ref name=100-nanometer/> However, [[technology|new technologies]] combined with optical microscopy are beginning to allow for increased [[image resolution|feature resolution]] (see sections below).
 
One definition of being constrained by the [[diffraction limit|resolution barrier]], is a resolution cut off at half the [[light|wavelength of light]].  The [[visible spectrum]] has a range that extends from 390 nanometers to 750 nanometers. [[Green|Green light]], half way in between, is around 500 nanometers. Microscopy takes into account parameters such as [[lens aperture]], distance from the object to the lens, and the [[refractive index]] of the observed material. This combination defines the resolution cutoff, or Microscopy's [[Microscopy|optical limit]], which tabulates to 200 nanometers.  Therefore, [[conventional lens]]es, which literally construct an image of an object by using "ordinary" light waves, discard information that produce very fine, and minuscule details of the object that are contained in [[evanescent wave]]s. These dimensions are less than 200 nanometers. For this reason, conventional optical systems, such as [[microscope]]s, have been unable to accurately image very small, [[nanotechnology|nanometer-sized]] structures or nanometer-sized [[in vivo|organisms in vivo]], such as individual [[virus]]es, or [[DNA molecule]]s.<ref name=100-nanometer/><ref name=half-wave-length>
{{Cite journal
| last = Vinson | first =V
| last2= Chin |first2=G.
| year=2007
| title =Introduction to special issue – Lights, Camera, Action
| journal =[[Science (journal)|Science]]
| volume =316 | issue =5828 | page = 1143
| doi =10.1126/science.316.5828.1143
}}</ref>
 
The limitations of standard optical microscopy ([[bright field microscopy]]) lie in three areas:
 
* The technique can only image dark or strongly [[refractive index|refracting objects]] effectively.
* [[Diffraction]] limits the object, or [[cell (biology)|cell's]], resolution to approximately 200 [[nanometer]]s.
* Out of focus [[light]] from points outside the [[focal plane]] reduces image clarity.
 
Live biological [[cell (biology)|cells]] in particular generally lack sufficient contrast to be studied successfully, because the internal structures of the cell are colorless and transparent. The most common way to increase contrast is to [[staining (biology)|stain]] the different structures with selective [[dye]]s, but this involves killing and fixing the sample. Staining may also introduce [[artifact (microscopy)|artifacts]], apparent structural details that are caused by the processing of the specimen and are thus not a legitimate feature of the specimen.
 
=== Conventional lens ===
[[File:DVD.png|thumb|150px|'''DVD''' – A DVD is a large, fast compact digital disk that can hold video, audio, and/or [[computer data]]. A laser is employed for [[data transfer]].]]
 
The conventional [[conventional lens|glass lens]] is pervasive throughout our society and in the [[science]]s. It is one of the fundamental tools of [[optics]]. However,  the wavelength of [[light]] can be [[analogous]] to the width of a pencil used to draw the ordinary images.  The limit becomes noticeable, for example, when the [[laser]] used in a digital video system can only detect and deliver details from a [[DVD]] based on the [[visible light|wavelength of light]]. The image cannot be rendered any [[Airy disk|sharper]] beyond this limitation.<ref name=MIT-Pendry-lecture/>
 
When an object emits or reflects light there are two types of [[electromagnetic radiation]] associated with this [[phenomenon]]. These are the [[Evanescent wave|near field]] radiation and the [[Angular resolution|far field]] radiation. As implied by its description, the far field escapes beyond the object. It is then easily captured and manipulated by a conventional glass lens. However, useful (nanometer-sized) resolution details are not observed, because they are hidden in the near field. They remain localized, staying much closer to the light emitting object, unable to travel, and unable to be captured by the conventional lens. Controlling the near field radiation, for high resolution, can be accomplished with a new class of materials not found in nature. These are unlike familiar [[solid]]s, such as [[crystal structure|crystals]], which derive their properties from [[atom]]ic and [[molecular]] units. The new material class, termed '''[[metamaterials]]''',  obtains its properties from its artificially larger structure. This has resulted in novel properties, and novel responses, which allow for  [[Angular resolution|details of images]] that surpass the limitations imposed by the wavelength of light.<ref name=MIT-Pendry-lecture>
{{Cite web
| date =13 March 2007
| title = Prof. Sir John Pendry, Imperial College, London
| url =http://www.rle.mit.edu/60th/colloquiaseries.htm
| work=Colloquia Series
| publisher =[[Research Laboratory of Electronics at MIT|Research Laboratory of Electronics]]
| accessdate =2010-04-07}}</ref>
 
=== Subwavelength imaging ===
[[File:Electrocomposeur 1976.JPG|thumb|259px|The "Electrocomposeur" was an electron-beam lithography machine (Electron microscope) designed for mask writing. It was developed in the early 1970s and deployed in the mid 1970s]]
 
This has led to the desire to view [[cell (biology)|live biological cell]] interactions in a real time, [[natural environment]], and the need for ''subwavelength imaging''. Subwavelength imaging can be defined as [[optical microscopy]] with the ability to see details of an object or organism below the wavelength of visible light (see discussion in the above sections). In other words, to have the capability to observe, in real time, below 200 nanometers. Optical microscopy is a non-invasive technique and technology because everyday light is the [[transmission medium]]. Imaging below the optical limit in optical microscopy (subwavelength) can be engineered for the  [[cell (biology)|cellular level]], and [[Nanotechnology|nanometer level]] in principle.
 
For example, in 2007 a technique was demonstrated where a [[negative index metamaterial|metamaterials-based]] lens coupled with a conventional optical lens could manipulate visible light to see ([[nanoscale]]) patterns that were too small to be observed with an ordinary [[optical microscope]]. This has potential applications not only for observing a whole [[cell (biology)|living cell]], or for observing [[Cell (biology)#Functions|cellular processes]], such as how [[protein]]s and [[fat]]s move in and out of cells.  In the [[technology]] domain, it could be used to improve the first steps of [[photolithography]] and [[nanolithography]], essential for manufacturing ever smaller [[computer chip]]s.<ref name=100-nanometer/><ref name=Zhang-Science-2007>
{{cite web
| last = Yeager | first =A.
| date =28 March 2009
| title =Cornering The Terahertz Gap
| url = http://www.sciencenews.org/view/feature/id/41651/title/Cornering_the_Terahertz_Gap
| work=[[Science News]]
| accessdate =2010-03-02
}}</ref>
 
Focusing at [[subwavelength]] has become a unique [[Optical imaging|imaging]] technique which allows visualization of features on the viewed object which are smaller than the wavelength of the [[photons]] in use. A photon is  the minimum unit of light ([[Photon|see article]]). While previously thought to be physically impossible, subwavelength imaging has been made possible through the development of [[metamaterials]]. This is generally accomplished using a layer of metal such as [[gold]] or [[silver]] a few [[atoms]] thick, which acts as a superlens, or by means of 1D and 2D [[photonic crystals]].<ref>
{{Cite journal
|last =Savo | first=S.
|last2=Andreone |first2=A.
|last3=Di Gennaro |first3=E.
|year= 2009
|title =Superlensing properties of one-dimensional dielectric photonic crystals
|journal =[[Optics Express]]
|volume =17 |issue=22 | pages =19848–56
|doi =10.1364/OE.17.019848
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| bibcode = 2009OExpr..1719848S |arxiv = 0907.3821 }}</ref><ref>
{{Cite journal
|last =Parimi |first=P.
|year = 2003
|title = Imaging by Flat Lens using Negative Refraction
|journal= [[Nature (journal)|Nature]]
|volume=426 |issue =6965 | page=404
|doi =10.1038/426404a
|pmid=14647372
| bibcode = 2003Natur.426..404P
|display-authors =1
|last2 =Lu
|first2 =Wentao T.
|last3 =Vodo
|first3 =Plarenta
|last4 =Sridhar
|first4 =Srinivas }}</ref> There is a subtle interplay between propagating waves, evanescent waves, near field imaging and far field imaging discussed in the sections below.<ref name=100-nanometer>
{{Cite journal
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|last2=Inouye |first2=Y.
|last3=Verma |first3=P.
|year=2009
| title =Plasmonics for near-field nano-imaging and superlensing
| journal =[[Nature Photonics]]
| volume =3 | issue =  7 | pages =388–394
| doi =10.1038/nphoton.2009.111
| bibcode = 2009NaPho...3..388K }}</ref><ref name=MIT-magazine/>
 
=== Early subwavelength imaging ===
''Metamaterial lenses'' (Superlens) are able to compensate for the exponential [[evanescent wave]] decay via [[negative refractive index]], and in essence reconstruct the [[image]]. Prior to metamaterials, proposals were advanced in the 1970s to avoid this evanescent decay. For example, in 1974 proposals for two-[[dimensional]], fabrication techniques were presented. These proposals included [[contact lithography|contact imaging]] to create a pattern in relief, [[photolithography]], [[electron lithography]], [[X-ray lithography]], or [[ion]] bombardment, on an appropriate [[plane (geometry)|planar]] substrate.<ref name=contact-imaging-1>
{{Cite journal
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|year=1974
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|journal=[[Proceedings of the IEEE]]
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|doi =10.1109/PROC.1974.9627
}}</ref>
 
The shared technological goals of the metamaterial lens and the variety of [[lithography]] aim to [[optical resolution|optically resolve]] features having dimensions much smaller than that of the vacuum [[wavelength]] of the exposing [[light]].<ref name=surface-plasmon-Nanolithography/><ref name=contact-imaging-2/>
 
In 1981 two different techniques of contact imaging of planar (flat) sub[[microscopic]] metal patterns with [[visible spectrum|blue light]] (400 [[nanometre|nm]]) were demonstrated. One demonstration resulted in an [[image resolution]] of 100&nbsp;nm and the other a resolution of 50 to 70&nbsp;nm.<ref name=contact-imaging-2>
{{Cite journal
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|last2=Zingsheim |first2=H. P.
|year=1981
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|journal =[[Journal of Vacuum Science and Technology]]
| volume =19 | issue =4 | page =881
| doi =10.1116/1.571227
| bibcode = 1981JVST...19..881F }}</ref>
 
Since at least 1998 [[near and far field|near field]] [[optical lithography]] was designed to create nanometer-scale features. Research on this technology continued as the first experimentally demonstrated [[negative index metamaterial]] came into existence in 2000–2001. The effectiveness of [[electron-beam lithography]] was also being researched at the beginning of the new millennium for nanometer-scale applications. [[Nanoimprint lithography|Imprint lithography]] was shown to have desirable advantages for nanometer-scaled research and technology.<ref name=surface-plasmon-Nanolithography/><ref name=1998-Light-coupling-masks>
{{Cite journal
| last = Schmid | first=H.
| year =1998
| title =Light-coupling masks for lensless, sub-wavelength optical lithography
| journal =[[Applied Physics Letters]]
| volume =73 | issue = 19 | page = 237
|doi =10.1063/1.121362
| bibcode = 1998ApPhL..72.2379S
| display-authors = 1
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| first2 = Hans
| last3 = Michel
| first3 = Bruno
| last4 = Martin
| first4 = Olivier J. F. }}</ref>
 
Advanced deep [[photolithography|UV photolithography]] can now offer sub-100&nbsp;nm resolution, yet the minimum feature size and spacing between patterns are determined by the [[diffraction limit]] of light. Its derivative technologies such as evanescent [[near and far field|near-field]] lithography, near-field interference lithography, and phase-shifting mask lithography were developed to overcome the diffraction limit.<ref name=surface-plasmon-Nanolithography>
{{Cite journal
| last = Srituravanich |first =W.
| title =Plasmonic Nanolithography
| journal =[[Nano Letters]]
| volume =4 | issue =6 | pages =1085
| year =2004
| url = http://xlab.me.berkeley.edu/publications/pdfs/21.NanoLetters_2004_plasmonic-nanolith.pdf
| doi =10.1021/nl049573q
| bibcode = 2004NanoL...4.1085S
| display-authors = 1
| last2 = Fang
| first2 = Nicholas
| last3 = Sun
| first3 = Cheng
| last4 = Luo
| first4 = Qi
| last5 = Zhang
| first5 = Xiang }}</ref>
 
In the year 2000, [[John Pendry]] proposed using a metamaterial lens to achieve [[nanometer]]-scaled imaging for focusing below the [[wavelength]] of [[visible spectrum|light]].<ref name=perfect-lens-2000/><ref name=thin-sliver/>
 
==History==
The first superlens (2004) with a [[negative index metamaterial|negative refractive index]] provided resolution three times better than the diffraction limit and was demonstrated at [[microwave]] frequencies.<ref>
{{cite journal
|last=Grbic |first=A.
|last2=Eleftheriades |first2=G. V.
|year=2004
|title=Overcoming the Diffraction Limit with a Planar Left-handed Transmission-line Lens
|format=Free HTML copy of this article
|journal= [[Physical Review Letters]]
|volume=92 |issue=11 |page=117403
|doi=10.1103/PhysRevLett.92.117403
|pmid=15089166 |bibcode=2004PhRvL..92k7403G |url=http://scholar.googleusercontent.com/scholar?q=cache:u8pusPBFLW4J:scholar.google.com/&hl=en&as_sdt=0,22
}}</ref> In 2005, the first [[Near-field optics|near field]] superlens was demonstrated by N.Fang ''et al.'', but the lens did not rely on [[negative refraction]]. Instead, a thin silver film was used to enhance the [[evanescent wave|evanescent modes]] through [[surface plasmon]] coupling.<ref name=mielsen10>
{{cite journal
| doi=10.1007/s00340-010-4065-z
| url =http://cmip.pratt.duke.edu/tomuri2009/sites/cmip.pratt.duke.edu.tomuri2009/files/pubs_purdue/2010_APB_MDC_Superlensing.pdf
| title=Toward superlensing with metal–dielectric composites and multilayers
| year=2010
| last1=Nielsen
| first1=R. B.
| last2=Thoreson
| first2=M. D.
| last3=Chen
| first3=W.
| last4=Kristensen
| first4=A.
| last5=Hvam
| first5=J. M.
| last6=Shalaev
| first6=V. M.
| last7=Boltasseva
| first7=A.
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| journal=Applied Physics B
| volume=100
| pages=93|bibcode = 2010ApPhB.100...93N }}</ref><ref name=Fangetal05>
{{cite journal
| doi=10.1126/science.1108759
| pmid=15845849
| bibcode = 2005Sci...308..534F
| url=
| title=Sub-Diffraction-Limited Optical Imaging with a Silver Superlens
| year=2005
| last1=Fang
| first1=N.
| journal=Science
| volume=308
| issue=5721
| pages=534–7
| last2=Lee
| first2=H
| last3=Sun
| first3=C
| last4=Zhang
| first4=X}}</ref> Almost at the same time Melville and Blaikie succeeded with a near field superlens. Other groups followed.<ref>D.O.S. Melville, R.J. Blaikie, [[Optics Express]] 13, 2127 (2005)</ref><ref>C. Jeppesen, R.B. Nielsen, A. Boltasseva, S. Xiao, N.A. Mortensen, A. Kristensen, Optics Express 17, 22543 (2009)</ref> Two developments in superlens research were reported in 2008.<ref name=Valenitne-J.>
{{cite journal
|last=Valentine |first=J.
|year=2008
|title=Three-dimensional optical metamaterial with a negative refractive index
|journal=[[Nature (journal)|Nature]]
|volume=455 |issue=7211 |doi=10.1038/nature07247
|pmid=18690249
|bibcode = 2008Natur.455..376V
|display-authors=1
|last2=Zhang
|first2=Shuang
|last3=Zentgraf
|first3=Thomas
|last4=Ulin-Avila
|first4=Erick
|last5=Genov
|first5=Dentcho A.
|last6=Bartal
|first6=Guy
|last7=Zhang
|first7=Xiang
|pages=376–9 }}</ref> In the second case, a metamaterial was formed from silver nanowires which were electrochemically deposited in porous aluminium oxide. The material exhibited negative refraction.<ref>
{{cite journal
|last=Yao |first=J.
|year=2008
|title=Optical Negative Refraction in Bulk Metamaterials of Nanowires
|journal=[[Science (journal)|Science]]
|volume=321  |issue=5891 |page=930
|doi=10.1126/science.1157566
|pmid=18703734
| bibcode = 2008Sci...321..930Y
|display-authors=1
|last2=Liu
|first2=Z.
|last3=Liu
|first3=Y.
|last4=Wang
|first4=Y.
|last5=Sun
|first5=C.
|last6=Bartal
|first6=G.
|last7=Stacy
|first7=A. M.
|last8=Zhang
|first8=X. }}</ref>
 
The superlens has not yet been demonstrated at [[visible frequency|visible]] or near-[[infrared]] frequencies (Nielsen, R. B.; 2010). Furthermore as dispersive materials, these are limited to functioning at a single wavelength. Proposed solutions are metal–dielectric composites (MDCs) <ref>W. Cai, D.A. Genov, V.M. Shalaev, Phys. Rev. B 72, 193101 (2005)
 
* A.V. Kildishev,W. Cai, U.K. Chettiar, H.-K. Yuan, A.K. Sarychev, V.P. Drachev, V.M. Shalaev, J. Opt. Soc. Am. B 23, 423 (2006)
* L. Shi, L. Gao, S. He, B. Li, Phys. Rev. B 76, 045116 (2007)
* L. Shi, L. Gao, S. He, Proc. Int. Symp. Biophot. Nanophot. Metamat. (2006), pp. 463–466</ref> and multilayer lens structures.<ref>Z. Jacob, L.V. Alekseyev, E. Narimanov, Opt. Express 14, 8247 (2006)
* P.A. Belov, Y. Hao, Phys. Rev. B 73, 113110 (2006)
* P. Chaturvedi, N.X. Fang, Mater. Res. Soc. Symp. Proc. 919, 0919-J04-07 (2006)
* B. Wood, J.B. Pendry, D.P. Tsai, Phys. Rev. B 74, 115116 (2006)
* E. Shamonina, V.A. Kalinin, K.H. Ringhofer, L. Solymar, Electron. Lett. 37, 1243 (2001)</ref> The multi-layer superlens appears to have better subwavelength resolution than the single layer superlens. Losses are less of a concern with the multi-layer system, but so far it appears to be impractical because of [[Wave impedance|impedance]] mis-match.<ref name=mielsen10/>
 
== Perfect lens ==
 
When the world is observed through [[lens (optics)|conventional lenses]], the sharpness of the [[image]] is determined by and limited to the wavelength of [[light]]. Around the year 2000, a slab of [[negative index metamaterial]] was theorized to create a lens with capabilities beyond conventional ([[refractive index|positive index]]) lenses. Sir [[John Pendry]], a British [[physicist]],  proposed that a thin slab of [[Negative index metamaterial|negative refractive metamaterial]] might overcome known problems with common lenses to achieve a "perfect" lens that would focus the entire spectrum, both the [[wave propagation|propagating]] as well as the [[evanescent wave|evanescent]] spectra.<ref name=perfect-lens-2000/><ref name=further-research-p-lens/>
 
A slab of [[silver]] was proposed as the metamaterial. As light moves away (propagates) from the source, it acquires an arbitrary [[phase (waves)|phase]]. Through a conventional lens the phase remains consistent, but the evanescent waves [[exponential function|decay exponentially]]. In the flat [[Metamaterial#Double negative metamaterials|metamaterial DNG]] slab, normally decaying evanescent waves are contrarily [[amplifier|amplified]]. Furthermore, as the evanescent waves are now amplified, the phase is reversed.<ref name=perfect-lens-2000/>
 
Therefore, a type of lens was proposed, consisting of a metal film metamaterial. When illuminated near its [[plasma frequency]], the lens could be used for superresolution imaging that compensates for wave decay and [[Optical resolution|reconstructs images]] in the [[near and far field|near-field]]. In addition, both [[Wave propagation|propagating]] and evanescent waves contribute to the [[Optical resolution|resolution of the image]].<ref name=perfect-lens-2000/>
 
Pendry suggested that left-handed slabs allow "perfect imaging" if they are completely lossless, [[impedance matching|impedance matched]], and their [[refractive index]] is −1 relative to the surrounding medium. Theoretically, this would be a breakthrough in that the optical version resolves objects as minuscule as [[nanometer]]s across. Pendry predicted that Double negative metamaterials (DNG) with a refractive index of ''n = −1'', can act, at least in principle, as a "perfect lens" allowing imaging resolution which is limited not by the wavelength, but rather by material quality.<ref name=perfect-lens-2000>
{{Cite journal
| last =Pendry | first = J. B.
| year =2000
| title = Negative Refraction Makes a Perfect Lens
| url = http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/negref2.pdf
| journal =[[Physical Review Letters]]
| volume =85
| issue =18 | doi=10.1103/PhysRevLett.85.3966
| pmid=11041972
| bibcode=2000PhRvL..85.3966P
| pages =3966–9
}}</ref><ref name=far-field-microscope/><ref name=Superlens-breakthrough-2005>
{{cite web
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|date=21 April 2005
|title=Superlens breakthrough
|url=http://physicsworld.com/cws/article/news/22065
|work=[[Physics World]]
|accessdate=
}}</ref><ref>
{{cite web
|last=Pendry |first=J. B.
|date=18 February 2005
|title=Collection of photonics references
|url=http://www.cmth.ph.ic.ac.uk/photonics/references.html
}}</ref>
 
=== Other studies concerning the perfect lens ===
 
Further [[research]] demonstrated that Pendry's theory behind the perfect lens was not exactly correct. The analysis of the focusing of the [[evanescent wave|evanescent]] spectrum (equations 13–21 in reference <ref name=perfect-lens-2000/>) was flawed. In addition, this applies to only one (theoretical) instance, and that is one particular medium that is lossless, nondispersive and the constituent parameters are defined as:<ref name=further-research-p-lens/>
 
: ε(ω) / ε<sub>0</sub> = µ(ω) / µ<sub>0</sub> = −1, which in turn results in a negative refraction of n = −1
 
However, the final intuitive result of this theory that both the [[Wave propagation|propagating and evanescent]] waves are focused, resulting in a converging [[focus (optics)|focal point]] within the slab and another convergence (focal point) beyond the slab turned out to be correct.<ref name=further-research-p-lens/>
 
If the DNG [[transmission medium|metamaterial medium]] has a large negative index or becomes [[Absorption (electromagnetic radiation)|lossy]] or [[wikt:Special:Search/dispersive|dispersive]], Pendry's perfect lens effect cannot be realized. As a result, the perfect lens effect does not exist in general. According to [[FDTD|FDTD simulations]] at the time (2001), the DNG slab acts like a converter from a pulsed cylindrical wave to a pulsed beam. Furthermore, in reality (in practice), a DNG medium must be and is dispersive and lossy, which can have either desirable or undesirable effects, depending on the research or application. Consequently, Pendry's perfect lens effect is inaccessible with any metamaterial designed to be a DNG medium.<ref name=further-research-p-lens>
{{Cite journal
|last = Ziolkowski |first =R. W.
|last2=Heyman |first2=E.
|year =2001
|title =Wave propagation in media having negative permittivity and permeability
|url =http://mesoscopic.mines.edu/mediawiki/images/3/3d/Waveprop_DNG_media.pdf
|journal =[[Physical Review E]]
|volume =64 | issue = 5 | page =056625
|doi =10.1103/PhysRevE.64.056625
| bibcode = 2001PhRvE..64e6625Z }}</ref>
 
Another analysis, in 2002,<ref name=further-research-p-lens-2/> of the perfect lens [[concept]] showed it to be in error while using the lossless, dispersionless DNG as the subject. This analysis mathematically demonstrated that subtleties of evanescent waves, restriction to a [[Physics|finite]] slab and absorption had led to inconsistencies and divergencies that contradict the basic mathematical properties of scattered wave fields. For example, this analysis stated that [[absorption (electromagnetic radiation)|absorption]], which is linked to [[dispersion (optics)|dispersion]], is always present in practice, and absorption tends to transform amplified waves into decaying ones inside this medium (DNG).<ref name=further-research-p-lens-2>
{{Cite journal
|last = Garcia1 | first =N.
|last2=Nieto-Vesperinas |first2=M.
|year =2002
|title =Left-Handed Materials Do Not Make a Perfect Lens
|journal =[[Physical Review Letters]]
|volume =88 | issue =20 | pages =207403
|doi =10.1103/PhysRevLett.88.207403 | bibcode=2002PhRvL..88t7403G | pmid=12005605
}}</ref>
 
A third analysis of Pendry's perfect lens concept, published in 2003,<ref name=SNG-lens-Smith/> used the recent demonstration of [[negative refraction]] at [[microwave]] frequencies<ref name=AAAS2/> as confirming the [[wikt:viability|viability]] of the fundamental concept of the perfect lens. In addition, this demonstration was thought to be [[experimental]] [[evidence]] that a planar DNG metamaterial would refocus the [[far field]] radiation of a [[EM radiation|point source]]. However, the perfect lens would require significantly different values for [[permittivity]], [[permeability (electromagnetism)|permeability]], and [[split-ring resonator|spatial periodicity]] than the demonstrated negative refractive sample.<ref name=SNG-lens-Smith>
{{Cite journal
|last = Smith | first = D.R.
|year=2003
|title =Limitations on subdiffraction imaging with a negative refractive index slab
|url =http://people.engr.ncsu.edu/dschuri/Site/Publications_files/10.1063-1.1554779.pdf
|journal =[[Applied Physics Letters]]
|volume =82 | issue =10 | page =1506
|arxiv=cond-mat/0206568
|doi =10.1063/1.1554779
| bibcode = 2003ApPhL..82.1506S
|display-authors = 1
|last2 = Schurig
|first2 = David
|last3 = Rosenbluth
|first3 = Marshall
|last4 = Schultz
|first4 = Sheldon
|last5 = Ramakrishna
|first5 = S. Anantha
|last6 = Pendry
|first6 = John B. }}</ref><ref name=AAAS2>
{{Cite journal
|last=Shelby |first=R. A.
|last2=Smith |first2=D. R.
|last3=Schultz |first3=S.
|title=Experimental Verification of a Negative Index of Refraction
|year=2001
|journal=[[Science (journal)|Science]]
|volume=292 |issue=5514 |doi=10.1126/science.1058847
|pmid=11292865
| bibcode = 2001Sci...292...77S
|pages=77–9 }}</ref>
 
This study agrees that any deviation from conditions where ε = µ = −1 results in the normal, conventional, imperfect image that degrades exponentially i.e., the diffraction limit. The perfect lens solution in the absence of losses is again, not practical, and can lead to paradoxical interpretations.<ref name=further-research-p-lens-2/>
 
It was determined that although resonant [[surface plasmons]] are undesirable for imaging, these turn out to be essential for recovery of decaying evanescent waves. This analysis discovered that [[periodicity (metamaterials)|metamaterial periodicity]] has a significant effect on the recovery of types of evanescent components. In addition, achieving [[Photolithography|subwavelength resolution]] is possible with current technologies. [[Negative refractive indices]] have been demonstrated in structured metamaterials. Such materials can be engineered to have tunable material parameters, and so achieve the optimal conditions. Losses can be minimized in structures utilizing [[superconducting]] elements. Furthermore, consideration of alternate structures may lead to configurations of left-handed materials that can achieve subwavelength focusing. Such structures were being studied at the time.<ref name=further-research-p-lens-2/>
 
== Near-field imaging with magnetic wires ==
 
[[Image:Prism composed of high performance Swiss Rolls.jpg|thumb|330px| A prism composed of high performance [[Swiss roll (metamaterial)|Swiss roll]]s which behaves as a magnetic faceplate, transferring a magnetic field distribution faithfully from the input to the output face.<ref name=layered-DPG-DPS-lens/>]]
 
Pendry's theoretical lens was designed to focus both propagating [[wave]]s and the [[Near and far field|near-field]] evanescent waves. From [[permittivity]] "ε" and [[magnetic permeability]] "µ" an index of refraction "n" is derived. The index of refraction determines how light is bent on traversing from one material to another. In 2003, it was suggested that a metamaterial constructed with alternating, parallel, layers of ''n = −1'' materials and ''n = +1'' materials, would be a more effective design for a [[metamaterial lens]]. It is an effective medium made up of a multi-layer stack, which exhibits [[birefringence]], n<sub>2</sub> = ∞, n<sub>x</sub> = 0. The effective refractive indices are then [[perpendicular]] and [[parallel (geometry)|parallel]], respectively.<ref name=layered-DPG-DPS-lens/>
 
Like a conventional [[lens (optics)|lens]], the z-direction is along the [[Optical axis|axis]] of the roll. The resonant frequency (w<sub>0</sub>) – close to 21.3&nbsp;MHz – is determined by the construction of the roll. Damping is achieved by the inherent resistance of the layers and the lossy part of permittivity.<ref name=layered-DPG-DPS-lens/>
 
Simply put, as the field pattern is transferred from the input to the output face of a slab, so the image information is transported across each layer. This was experimentally demonstrated. To test the two-dimensional imaging performance of the material, an antenna was constructed from a pair of anti-parallel wires in the shape of the letter M. This generated a line of magnetic flux, so providing a characteristic field pattern for imaging. It was placed horizontally, and the material, consisting of 271 [[Swiss roll]]s tuned to 21.5&nbsp;MHz, was positioned on top of it. The material does indeed act as an image transfer device for the magnetic field. The shape of the antenna is faithfully reproduced in the output plane, both in the distribution of the peak intensity, and in the “valleys” that bound the M.<ref name=layered-DPG-DPS-lens/>
 
A consistent characteristic of the very near (evanescent) field is that the [[electric field|electric]] and [[magnetic field]]s are largely decoupled. This allows for nearly independent manipulation of the electric field with the [[permittivity]] and the magnetic field with the permeability.<ref name=layered-DPG-DPS-lens>
{{Cite journal
| last = Wiltshire | first = M. C. K.
| year =2003
| title =Metamaterial endoscope for magnetic field transfer: near field imaging with magnetic wires
| url=http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/Mike_OptexFinal.pdf
| journal =[[Optics Express]]
| volume =11 | issue =7 | pages =709–15
| doi = 10.1364/OE.11.000709
| pmid =19461782
| bibcode = 2003OExpr..11..709W
| display-authors = 1
| last2 = Hajnal
| first2 = J.
| last3 = Pendry
| first3 = J.
| last4 = Edwards
| first4 = D.
| last5 = Stevens
| first5 = C. }}</ref>
 
Furthermore, this is highly [[anisotropic|anisotropic system]]. Therefore, the transverse (perpendicular) components of the EM field which radiate the material, that is the wavevector components k<sub>x</sub> and k<sub>y</sub>, are decoupled from the longitudinal component k<sub>z</sub>. So, the field pattern should be transferred from the input to the output face of a slab of material without degradation of the image information.<ref name=layered-DPG-DPS-lens/>
 
== Optical super lens with silver metamaterial ==
 
{{Multiple image|direction=vertical|align=right|image1=|image2=|width=385|caption1=April, 2005. Optical super lens with silver metamaterial.
 
: (a)Lens stack with 35 nm silver layer (light blue).
: (b) control stack – [[Poly(methyl methacrylate)|PMMA]] layer replaced the silver layer.
: See the actual graphic results below:<ref name=thin-sliver/>|caption2=An arbitrary object, " NANO" was imaged with the 35 nm silver layer (2nd row left).<ref name=thin-sliver/>
: (Top center) The image of the object – focused ion beam image of the object "NANO" after fabrication on [[Chromium|Cr]] film.
: (Second row left) The object is then captured by the silver layer superlens.
: (Second row right) The imaged object with control layer (PMMA) replacing silver layer.
: (Third row left) A graph depicting resolution of silver layer. The line width is 90 nm across.
: (Third row right) A graph depicting resolution of control layer which resulted in a conventional diffraction limited image with line width of 360 nm, and is comparable to the exposure wavelength (365 nm).}}
 
In 2003, a group of researchers showed that optical evanescent waves would be enhanced as they passed through a [[silver]] metamaterial [[lens (optics)|lens]]. This was referred to as a diffraction-free lens. Although a [[coherence (physics)|coherent]], high-resolution, image was not intended, nor achieved, regeneration of the evanescent field was [[experiment]]ally demonstrated.<ref name=Superlens-breakthrough/><ref name=growth-of-evan-wve/>
 
By 2003 it was known for decades that evanescent waves could be enhanced by producing [[excited state]]s at the [[Interface (chemistry)|interface]] surfaces. However, the use of [[surface plasmon]]s to reconstruct evanescent components was not tried until Pendry's recent proposal (see "''Perfect lens''" above). By studying films of varying thickness it has been noted that a rapidly growing [[transmission coefficient]] occurs, under the appropriate conditions. This demonstration provided direct evidence that the foundation of superlensing is solid, and suggested the path that will enable the observation of superlensing at optical wavelengths.<ref name=growth-of-evan-wve>
{{Cite journal
| last = Liu | first =Z.
| year=2003
| title =Rapid growth of evanescent wave by a silver superlens
| url =http://xlab.me.berkeley.edu/publications/pdfs/17.AppPhysL_12.22.2003_evwave-superlens.pdf
| journal =[[Applied Physics Letters]]
| volume =83 | issue =25 | page =5184
| doi =10.1063/1.1636250
| bibcode = 2003ApPhL..83.5184L
| display-authors = 1
| last2 = Fang
| first2 = Nicholas
| last3 = Yen
| first3 = Ta-Jen
| last4 = Zhang
| first4 = Xiang }}</ref>
 
In 2005, a [[coherence (physics)|coherent]], high-resolution, [[Optical resolution|image]] was produced (based on the 2003 results). A thinner slab of [[silver]] (35&nbsp;nm) was better for [[Optical lithography|sub–diffraction-limited imaging]], which results in one-sixth of the illumination wavelength. This type of lens was used to compensate for wave decay and reconstruct images in the [[near and far field|near-field]]. Prior attempts to create a working superlens used a slab of silver that was too thick.<ref name=thin-sliver>
{{Cite journal
| last = Fang | first =N.
| year =2005
| title =Sub–Diffraction-Limited Optical Imaging with a Silver Superlens
| journal =[[Science (journal)|Science]]
| volume =308
| issue = 5721 | doi =10.1126/science.1108759
| pmid = 15845849
| bibcode = 2005Sci...308..534F
| display-authors = 1
| last2 = Lee
| first2 = H
| last3 = Sun
| first3 = C
| last4 = Zhang
| first4 = X
| pages = 534–7 }}</ref><ref name=far-field-microscope/>
 
Objects were imaged as small as 40&nbsp;nm across. In 2005 the imaging resolution limit for [[optical microscope]]s was at about one tenth the diameter of a [[red blood cell]]. With the silver superlens this results in a resolution of one hundredth of the diameter of a red blood cell.<ref name=Superlens-breakthrough/>
 
Conventional lenses, whether man-made or natural, create images by capturing the propagating light waves all objects emit and then bending them. The angle of the bend is determined by the index of refraction and has always been positive until the fabrication of artificial negative index materials. Objects also emit evanescent waves that carry details of the object, but are unobtainable with conventional optics. Such evanescent waves decay exponentially and thus never become part of the image resolution, an optics threshold known as the diffraction limit. Breaking this diffraction limit, and capturing evanescent waves are critical to the creation of a 100-percent perfect representation of an object.<ref name=thin-sliver/>
 
In addition, conventional [[Lens (optics)|optical materials]] suffer a diffraction limit because only the propagating components are transmitted (by the optical material) from a [[EM radiation|light source]].<ref name=thin-sliver/> The non-propagating components, the evanescent waves, are not transmitted.<ref name=further-research-p-lens-2/> Moreover, lenses that improve image resolution by increasing the [[index of refraction]] are limited by the availability of high-index materials, and point by point subwavelength imaging of [[electron microscopy]] also has limitations when compared to the potential of a working superlens. Scanning electron and atomic force microscopes are now used to capture detail down to a few nanometers. However, such microscopes create images by scanning objects point by point, which means they are typically limited to non-living samples, and image capture times can take up to several minutes.<ref name=thin-sliver/>
 
With current optical microscopes, scientists can only make out relatively large structures within a cell, such as its nucleus and mitochondria. With a superlens, optical microscopes could one day reveal the movements of individual proteins traveling along the microtubules that make up a cell's skeleton, the researchers said. Optical microscopes can capture an entire frame with a single snapshot in a fraction of a second. With superlenses this opens up nanoscale imaging to living materials, which can help biologists better understand cell structure and function in real time.<ref name=thin-sliver/>
 
Advances of [[magnetic coupling]] in the [[THz]] and [[infrared]] regime provided the realization of a possible metamaterial superlens. However, in the near field, the electric and magnetic responses of materials are decoupled. Therefore, for transverse magnetic (TM) waves, only the permittivity needed to be considered. Noble metals, then become natural selections for superlensing because negative permittivity is easily achieved.<ref name=thin-sliver/>
 
By designing the thin metal slab so that the surface current oscillations (the [[surface plasmons]]) match the evanescent waves from the object, the superlens is able to substantially enhance the amplitude of the field. Superlensing results from the enhancement of evanescent waves by surface plasmons.<ref name=thin-sliver/><ref name=Superlens-breakthrough>
{{cite web
| last =Dumé | first =B.
| title =Superlens breakthrough
| url =http://physicsworld.com/cws/article/news/22065
| work =[[Physics World]]
| date =4 April 2005
| accessdate =2009-11-10
}}</ref>
 
The key to the superlens is its ability to significantly enhance and recover the evanescent waves that carry information at very small scales. This enables imaging well below the diffraction limit. No lens is yet able to completely reconstitute all the evanescent waves emitted by an object, so the goal of a 100-percent perfect image will persist. However, many scientists believe that a true perfect lens is not possible because there will always be some energy absorption loss as the waves pass through any known material. In comparison the superlens image is substantially better than the one created without the silver superlens.<ref name=thin-sliver/>
 
== 50-nm flat silver layer ==
 
In February 2004, an [[electromagnetic radiation]] focusing system, based on a [[metamaterial|negative index metamaterial]] plate, accomplished [[subwavelength]] imaging in the [[microwave|microwave domain]]. This showed that obtaining separated [[image]]s at much less than the [[wavelength]] of [[light]] is possible.<ref name=2004-pancake-plate>
{{Cite journal
| last = Lagarkov
| first =A. N.
| coauthors =& V. N. Kissel
|title =Near-Perfect Imaging in a Focusing System Based on a Left-Handed-Material Plate
|journal =Phys. Rev. Lett.
| volume =92
| issue = 7
| pages =077401 (2004) [4 pages]
| date =2004-02-18
|doi =10.1103/PhysRevLett.92.077401
| bibcode=2004PhRvL..92g7401L}}</ref> Also, in 2004, a [[silver|silver layer]] was used for sub-[[micrometre]] near-field imaging. Super high resolution was not achieved, but this was intended. The silver layer was too thick to allow significant enhancements of evanescent field components.<ref name=silver-also/>
 
In early 2005, feature resolution was achieved with a different silver layer. Though this was not an actual image, it was intended. Dense feature resolution down to 250&nbsp;nm was produced in a 50&nbsp;nm thick [[photoresist]] using illumination from a [[mercury lamp]]. Using simulations ([[FDTD]]), the study noted that resolution improvements could be expected for imaging through silver lenses, rather than another method of near field imaging.<ref name=rough-dense-image>{{Cite journal
| last = Blaikie
| first =Richard J
| coauthors =David O. S. Melville
| title =Imaging through planar silver lenses in the optical near field
| journal =J. Opt. Soc. Am. A
|volume =7
| issue = 2
| pages = S176–S183
| date = 2005-01-20
| doi = 10.1088/1464-4258/7/2/023|bibcode = 2005JOptA...7S.176B }}</ref>
 
Building on this prior research, super resolution was achieved at [[Infrared|optical frequencies]] using a 50&nbsp;nm [[Plane (geometry)|flat]] silver layer. The capability of [[Optical resolution|resolving an image]] beyond the diffraction limit, for [[Fraunhofer diffraction|far-field imaging]], is defined here as superresolution.<ref name=silver-also/>
 
The image fidelity is much improved over earlier results of the previous experimental lens stack. Imaging of sub-micrometre features has been greatly improved by using thinner silver and spacer layers, and by reducing the surface roughness of the lens stack. The ability of the silver lenses to image the gratings has been used as the ultimate resolution test, as there is a concrete limit for the ability of a conventional (far field) lens to image a periodic object – in this case the image is a diffraction grating. For normal-incidence illumination the minimum spatial period that can be resolved with wavelength λ through a medium with refractive index n is λ/n. Zero contrast would therefore be expected in any (conventional) far-field image below this limit, no matter how good the imaging resist might be.<ref name=silver-also/>
 
The (super) lens stack here results in a computational result of a diffraction-limited resolution of 243&nbsp;nm. Gratings with periods from 500&nbsp;nm down to 170&nbsp;nm are imaged, with the depth of the modulation in the resist reducing as the grating period reduces. All of the gratings with periods above the diffraction limit (243&nbsp;nm) are well resolved.<ref name=silver-also/> The key results of this experiment are super-imaging of the sub-diffraction limit for 200&nbsp;nm and 170&nbsp;nm periods. In both cases the gratings are resolved, even though the contrast is diminished, but this gives experimental confirmation of Pendry's superlensing proposal.<ref name=silver-also>{{Cite journal
| last =Melville
| first =David
| coauthors = and Richard Blaikie
| title =Super-resolution imaging through a planar silver layer
| journal =Optics Express
| volume =13
|issue =6
|pages =2127–2134
|url=http://muri.lci.kent.edu/References/NIM_Papers/lens/2005_Blaikie_Ag_lens.pdf
| date =2005-03-21
|doi =10.1364/OPEX.13.002127
| accessdate =2009-10-23
| pmid =19495100|bibcode = 2005OExpr..13.2127M }}</ref>
 
::: For further information see [[Fresnel number]] and [[Fresnel diffraction]].
 
== Negative index GRIN lenses ==
 
Gradient Index (GRIN) – The larger range of material response available in metamaterials should lead to improved GRIN lens design. In particular, since the permittivity and permeability of a metamaterial can be adjusted independently, metamaterial GRIN lenses can presumably be better matched to free space. The GRIN lens is constructed by using a slab of NIM with a variable index of refraction in the y direction, perpendicular to the direction of propagation z.<ref name=GRIN-1>{{Cite journal
|last = Greegor
| first = R. B.
| title =Simulation and testing of a graded negative index of refraction lens
| journal =Applied Physics Letters
| volume =87
|issue = 9
| page =091114
|date =2005-08-25
| url =http://people.ee.duke.edu/~drsmith/pubs_smith_group/greegor_apl_2005.pdf
|doi = 10.1063/1.2037202
| accessdate =2009-11-01
|last2 = Parazzoli
|first2 = C. G.
|last3 = Nielsen
|first3 = J. A.
|last4 = Thompson
|first4 = M. A.
|last5 = Tanielian
|first5 = M. H.
|last6 = Smith
|first6 = D. R.|bibcode = 2005ApPhL..87i1114G
|author-separator = ,
|display-authors = 1 }}
</ref>
 
== Transmission properties of an optical far-field superlens ==
 
Also in 2005 a group proposed a theoretical way to overcome the near-field limitation using a new device termed a far-field superlens (FSL), which is a properly designed periodically corrugated metallic slab-based superlens.<ref name=corrugated-FSL>
{{Cite journal
| last = Durant
| first =Stéphane
|title =Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit
| journal =J. Opt. Soc. Am. B
|volume =23
|issue =11
|pages =2383–2392
|date =2005-12-02
|url =http://circuit.ucsd.edu/~zhaowei/Journals/JOSAB_Stephane.pdf
|doi =10.1364/JOSAB.23.002383
|accessdate =2009-10-26
| last2 = Liu
| first2 = Zhaowei
| last3 = Steele
| first3 = Jennifer M.
| last4 = Zhang
| first4 = Xiang|bibcode = 2006JOSAB..23.2383D
| display-authors = 1 }}</ref>
 
== Metamaterial crystal lens ==
 
An idea for a far-field scanless optical microscopy, with a resolution below diffraction limit, was investigated by exploiting the special dispersion characteristics of an anisotropic metamaterial crystal.<ref name=MM-crystal-lens>{{Cite journal
| last = Salandrino
| first =Alessandro
| coauthors =Nader Engheta
|title =Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations
| journal =Phys. Rev. B
| volume = 74
| issue = 7
| pages = 075103
| date =2006-08-16
| doi =10.1103/PhysRevB.74.075103|bibcode = 2006PhRvB..74g5103S }}</ref>
 
== Metamaterial lens goes from near field to far field ==
 
Imaging is experimentally demonstrated in the far field, taking the next step after near-field experiments. The key element is termed as a far-field superlens (FSL) which consists of a conventional superlens and a nanoscale coupler.<ref name=Far-field-nanocoupler>
{{Cite journal
| last =Liu
| first =Zhaowei
| title =Experimental studies of far-field superlens for sub-diffractional optical imaging
| journal =Optics Express
| volume =15
| issue =11
|pages =6947–6954
| date =2007-05-22
| url =http://xlab.me.berkeley.edu/publications/pdfs/58.OptExp2007_Zhaowei.pdf
| doi =10.1364/OE.15.006947
| accessdate =2009-10-26
| pmid =19547010
| last2 =Durant
| first2 =S
| last3 =Lee
| first3 =H
| last4 =Pikus
| first4 =Y
| last5 =Xiong
| first5 =Y
| last6 =Sun
| first6 =C
| last7 =Zhang
| first7 =X|bibcode = 2007OExpr..15.6947L
| display-authors =1 }}</ref>
 
=== Focusing beyond the diffraction limit with far-field time reversal ===
 
An approach is presented for subwavelength focusing of microwaves using both a time-reversal mirror placed in the far field and a random distribution of scatterers placed in the near field of the focusing point.<ref name=far-field-time-rev>
{{Cite journal
| last =Geoffroy
| first =Lerosey
| title =Focusing Beyond the Diffraction Limit with Far-Field Time Reversal
| journal =AAAS Science
| volume =315
| issue = 5815
| pages =1120–1122
| date =2007-02-27
| doi =10.1126/science.1134824
| pmid =17322059
| last2 =De Rosny
| first2 =J
| last3 =Tourin
| first3 =A
| last4 =Fink
| first4 =M|bibcode = 2007Sci...315.1120L
| display-authors =1 }}</ref>
 
=== Hyperlens ===
 
Once capability for near-field imaging was demonstrated, the next step was to project a near-field image into the far-field. This concept, including technique and materials, is dubbed "hyperlens".<ref name=MIT-magazine/><ref name=far-field-1/><ref name=far-field-2/>
 
The capability of a metamaterial-hyperlens for sub-diffraction-limited imaging is shown below.
 
==== Sub-diffraction imaging in the far field ====
 
With conventional [[lens (optics)|optical lenses]], the [[far field]] is a limit that is too distant for [[evanescent waves]] to arrive intact. When imaging an object, this limits the [[optical resolution]] of lenses to the order of the [[wavelength]] of light These non-propagating waves carry detailed information in the form of high [[spatial resolution]], and overcome limitations. Therefore, projecting image details, normally limited by [[diffraction]] into the far field does require recovery of the evanescent waves.<ref name=far-field-1/>
 
In essence steps leading up to this investigation and demonstration was the employment of an [[anisotropic]] metamaterial with a [[hyperbolic geometry|hyperbolic]] dispersion. The effect was such that ordinary evanescent waves propagate along the [[wikt:radial|radial]] direction of the layered metamaterial. On a [[microscopic]] level the large spatial frequency waves propagate through coupled surface plasmon excitations between the metallic layers.<ref name=far-field-1>{{Cite journal
| last =Liu
| first =Zhaowei
| title =Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects
| journal = AAAS Science
| volume =315
| page =1686
| date =2007-03-27
|url=http://xlab.me.berkeley.edu/publications/pdfs/54.%20Science.pdf
|doi =10.1126/science.1137368
| pmid =17379801
| last2 =Lee
| first2 =H
| last3 =Xiong
| first3 =Y
| last4 =Sun
| first4 =C
| last5 =Zhang
| first5 =X
| issue =5819|bibcode = 2007Sci...315.1686L
| display-authors =1 }}</ref>
 
In 2007, just such an [[anisotropic]] metamaterial was employed as a [[magnify]]ing optical hyperlens. The hyperlens consisted of a curved periodic stack of thin [[silver]] and [[alumina]] (at 35 nanometers thick) deposited on a half-cylindrical cavity, and fabricated on a quartz substrate. The radial and tangential [[permittivities]] have different signs.<ref name=far-field-1/>
 
Upon [[EM radiation|illumination]], the scattered [[evanescent field]] from the object enters the anisotropic medium and propagates along the radial direction. Combined with another effect of the metamaterial, a magnified image at the outer diffraction limit-boundary of the hyperlens occurs. Once the magnified feature is larger than (beyond) the diffraction limit, it can then be imaged with a conventional optical [[microscope]], thus demonstrating magnification and projection of a sub-diffraction-limited image into the far field.<ref name=far-field-1/>
 
The hyperlens magnifies the object by transforming the scattered evanescent waves into propagating waves in the [[anisotropic]] medium, projecting a spatial resolution high-resolution image into the far field. This type of metamaterials-based lens, paired with a conventional optical lens is therefore able to reveal patterns too small to be discerned with an ordinary optical microscope. In one experiment, the lens was able to distinguish two 35-nanometer lines etched 150 nanometers apart. Without the metamaterials, the microscope showed only one thick line.<ref name=MIT-magazine/>
 
In a control experiment, the line pair object was imaged without the hyperlens. The line pair could not be resolved because of the diffraction limit of the (optical) aperture was limited to 260&nbsp;nm. Because the hyperlens supports the propagation of a very broad spectrum of wave vectors, it can magnify arbitrary objects with sub-diffraction-limited resolution.<ref name=far-field-1/>
 
Although this work appears to be limited by being only a [[cylindrical]] hyperlens, the next step is to design a [[spherical]] lens. That lens will exhibit three-dimensional capability. Near-field optical microscopy uses a tip to scan an object. In contrast, this optical hyperlens magnifies an image that is sub-diffraction-limited. The magnified sub-diffraction image is then projected into the far field.<ref name=MIT-magazine/><ref name=far-field-1/>
 
The optical hyperlens shows a notable potential for applications, such as real-time biomolecular imaging and nanolithography. Such a lens could be used to watch cellular processes that have been impossible to see. Conversely, it could be used to project an image with extremely fine features onto a photoresist as a first step in photolithography, a process used to make computer chips. The hyperlens also has applications for DVD technology.<ref name=MIT-magazine>{{Cite news
| last = Bullis
| first =Kevin
| title =Superlenses and Smaller Computer Chips| newspaper =Technology Review magazine of [[Massachusetts Institute of Technology]]
| pages =2 pages
| date =2007-03-27
| url =http://www.technologyreview.com/computing/18428/?a=f
| accessdate =2010-01-13| postscript = <!-- None -->}}</ref><ref name=far-field-1/>
 
In 2010, spherical hyperlens for two dimensional imaging at visible frequencies is demonstrated experimentally. The spherical hyperlens based on silver and titanium oxide alternating layers has strong anisotropic hyperbolic dispersion allowing super-resolution with visible spectrum. The resolution is 160&nbsp;nm at visible spectrum. It will enable biological imaging such as cell and DNA with a strong benefit of magnifying sub-diffraction resolution into far-field.
<ref name=far-field-2>{{cite journal|last=Rho|first=Junsuk|coauthors=Ye, Ziliang; Xiong, Yi; Yin, Xiaobo; Liu, Zhaowei; Choi, Hyeunseok; Bartal, Guy; Zhang, Xiang|title=Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies|journal=Nature Communications|date=1 December 2010|volume=1|issue=9|pages=143 |url=http://xlab.me.berkeley.edu/publications/pdfs/147.NatComm_Jun.pdf|doi=10.1038/ncomms1148|bibcode = 2010NatCo...1E.143R }}</ref>
 
=== Plasmon-assisted microscopy ===
 
Plasmon assisted microscopy. (See [[Near-field scanning optical microscope]]).
 
=== Super-imaging in the visible frequency range ===
 
Also in 2007 researchers demonstrated super imaging using materials, which create [[negative refractive index]] and lensing is achieved in the visible range.<ref name=far-field-microscope/>
 
Continual improvements in [[optical microscopy]] are needed to keep up with the progress in [[nanotechnology]] and [[microbiology]]. Advancement in [[spatial resolution]] is key. Conventional optical microscopy is limited by a diffraction limit which is on the order of 200 [[nanometer]]s (wavelength). This means that [[virus]]es, [[protein]]s, [[DNA]] molecules and many other samples are hard to observe with a regular (optical) microscope. The lens previously demonstrated with [[negative refractive index material]], a thin [[plane (geometry)|planar]] superlens, does not provide [[magnification]] beyond the diffraction limit of conventional microscopes. Therefore, images smaller than the conventional diffraction limit will still be unavailable.<ref name=far-field-microscope>
{{Cite journal
| last = Smolyaninov
| first =Igor I.
| title =Magnifying Superlens in the Visible Frequency Range
| journal =Science
| volume =315
| issue =5819
|pages =1699–1701
| date =2007-03-27
| doi =10.1126/science.1138746
| pmid = 17379804
| first2 = YJ
| first3 = CC
| last2 = Hung
| last3 = Davis|arxiv = physics/0610230 |bibcode = 2007Sci...315.1699S }}</ref>
 
Another approach achieving super-resolution at visible wavelength is recently developed spherical hyperlens based on silver and titanium oxide alternating layers. It has strong anisotropic hyperbolic dispersion allowing super-resolution with converting evanescent waves into propagating waves. This method is non-fluorescence based super-resolution imaging, which results in real-time imaging without any reconstruction of images and information.<ref name=far-field-2/>
 
=== Super resolution far-field microscopy techniques ===
 
By 2008 the diffraction limit has been surpassed and lateral imaging resolutions of 20 to 50&nbsp;nm have been achieved by several "super-resolution" far-field microscopy techniques, including stimulated emission depletion (STED) and its related RESOLFT (reversible saturable optically linear fluorescent transitions) microscopy; saturated structured illumination microscopy (SSIM) ; stochastic optical reconstruction microscopy (STORM); photoactivated localization microscopy (PALM); and other methods using similar principles.<ref name=stochastic-optical>{{Cite journal
| last = Huang
| first =Bo
| title =Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy
| journal =Science
| volume =319
| issue =5864
| pages =810–813
| date =2008-02-08
| doi =10.1126/science.1153529
| first2 = W.
| first3 = M.
| first4 = X.
| last2 = Wang
| last3 = Bates
| last4 = Zhuang
| pmid = 18174397| pmc = 2633023|bibcode = 2008Sci...319..810H }}</ref>
 
== Cylindrical superlens via coordinate transformation ==
 
This began with a proposal by Sir John Pendry, in 2003. Magnifying the image required a new design concept in which the surface of the negatively refracting lens is curved. One cylinder touches another cylinder, resulting in a curved cylindrical lens which reproduced the contents of the smaller cylinder in magnified but undistorted form outside the larger cylinder. Coordinate transformations are required to curve the original perfect lens into the cylindrical, lens structure.<ref name=Pendry-cyl-lens>{{Cite journal
| last =Pendry
| first =John| authorlink = John Pendry
| title =Perfect cylindrical lenses
| journal =Optics express
| volume =11
| issue =7
| page =755
| date =2003-04-07
|url = http://esperia.iesl.forth.gr/~ppm/DALHM/publications/papers/oev11p755.pdf
|doi =10.1364/OE.11.000755
| accessdate =2009-11-04|bibcode = 2003OExpr..11..755P }}</ref>
 
This was followed by a 36 page conceptual and mathematical proof in 2005, that the cylindrical superlens works in the [[quasistatic process|quasistatic regime]]. The debate over the perfect lens is discussed first.<ref name=proof-cyl>{{Cite journal
| last = Milton
| first = Graeme W.
| title = A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance
| journal =Proceedings of the Royal Society A
| volume =461
| issue = 2064
| pages =3999 (36 pages)
| date =2005-12-08
| doi =10.1098/rspa.2005.1570
| last2 = Nicorovici
| first2 = Nicolae-Alexandru P.
| last3 = McPhedran
| first3 = Ross C.
| last4 = Podolskiy
| first4 = Viktor A.|bibcode = 2005RSPSA.461.3999M }}</ref>
 
In 2007, a superlens utilizing coordinate transformation was again the subject. However, in addition to image transfer other useful operations were discussed; translation, rotation, mirroring and inversion as well as the superlens effect. Furthermore,
elements that perform magnification are described, which are free from geometric aberrations, on both the input and output sides while utilizing free space sourcing (rather than waveguide). These magnifying elements also operate in the near and far field, transferring the image from near field to far field.<ref name=other-use-cyl>{{Cite journal
| last = Schurig
| first = D.
| coauthors =J. B. Pendry, and D. R. Smith
|title =Transformation-designed optical elements
| journal =Optics express
| volume =15
|issue =22
| pages =14772 (10 pages)
| date =2007-10-24
| doi =10.1364/OE.15.014772|bibcode = 2007OExpr..1514772S }}</ref>
 
The cylindrical magnifying superlens was experimentally demonstrated in 2007 by two groups, Liu et al.<ref name=far-field-1/> and Smolyaninov et al.<ref name=far-field-microscope/><ref>{{cite journal
|arxiv=0708.0262
|doi=10.1103/PhysRevB.77.035122
|title=Magnifying perfect lens and superlens design by coordinate transformation
|year=2008
|last1=Tsang
|first1=Mankei
|last2=Psaltis
|first2=Demetri
|journal=Physical Review B
|volume=77
|issue=3
|page=035122|bibcode = 2008PhRvB..77c5122T }}</ref>
 
== Nano-optics with metamaterials ==
 
=== Nanohole array subwavelength imaging ===
 
==== Nanohole array as a lens ====
 
<!-- Deleted image removed: [[File:Two arrays of nanoholes in a metal screen.gif|thumb|280px|Schematic diagrams. More than concentrating hot spots (left), as was accomplished previously; an image of the [[point source]] (right) is displayed a few tens of wavelengths from the array, on the other side of the array.<ref name=Nanohole-Array-Lens/>]] -->
 
A recent prior work (2007) demonstrated that a [[quasi-periodic]] array of [[Nanotechnology|nanoholes]], in a [[metal]] screen, were able to focus the [[infrared|optical energy]] of a [[plane wave]] to form [[subwavelength]] spots (hot spots). The distances for the spots was a few tens of [[wavelength]]s on the other side of the array, or, in other words, opposite the side of the [[Normal incidence|incident plane wave]]. The quasi-periodic array of nanoholes functioned as a [[light]] concentrator.<ref name=Nanohole-Array-Lens/>
 
In June 2008, this was followed by the demonstrated capability of an array of [[quasi-crystal]] nanoholes in a metal screen. More than concentrating hot spots, an image of the [[point source]] is displayed a few tens of wavelengths from the array, on the other side of the array (the image plane). Also this type of array exhibited a 1 to 1 linear displacement, – from the location of the point source to its respective, parallel, location on the image plane. In other words from x to x + δx. For example, other point sources were similarly displaced from x' to x' + δx', from x^ to x^ + δx^, and from x^^ to  x^^ + δx^^, and so on. Instead of functioning as a light concentrator, this performs the function of [[conventional lens]] imaging with a 1 to 1 correspondence, albeit with a point source.<ref name=Nanohole-Array-Lens/>
 
However, [[optical resolution|resolution]] of more complicated structures can be achieved as constructions of multiple point sources. The fine details, and brighter image, that are normally associated with the [[numerical apertures|high numerical aperture]]s of conventional lenses can be reliably produced. Notable applications for this [[technology]] arise when conventional optics is not suitable for the task at hand. For example, this technology is better suited for [[X-ray|X-ray imaging]], or [[photonic metamaterials|nano-optical]] circuits, and so forth.<ref name=Nanohole-Array-Lens>{{Cite journal
| last = Huang
| first =Fu Min
| title =Nanohole Array as a Lens
| journal = Nano Lett.
| volume =8
| pages =2469–2472
| publisher =American Chemical Society
| date =2008-06-24
| url =http://www.nanoscope.org.uk/publications/huang-2008-nal.pdf
| doi =10.1021/nl801476v
| accessdate =2009-12-21
| pmid = 18572971
| last2 = Kao
| first2 = TS
| last3 = Fedotov
| first3 = VA
| last4 = Chen
| first4 = Y
| last5 = Zheludev
| first5 = NI
| issue = 8|bibcode = 2008NanoL...8.2469H
| author-separator = ,
| display-authors = 1 }}</ref>
 
==== Nanolens ====
 
In 2010, a nano-wire array prototype, described as a three-dimensional (3D) [[metamaterial]]-nanolens, consisting of bulk nanowires deposited in a [[dielectric]] substrate was fabricated and tested.<ref name=nanotechwire-nanolens/><ref name=B-D-F-Casse/>
 
The metamaterial nanolens was constructed of millions of nanowires at 20&nbsp;nanometers in diameter. These were precisely aligned and a packaged configuration was applied. The lens is able to depict a clear, high-resolution [[image]] of nano-sized objects because it uses both normal propagating [[EM radiation]], and [[evanescent waves]] to construct the image. Super-resolution imaging was demonstrated over a distance of 6 times the [[wavelength]] (λ), in the far-field, with a resolution of at least λ/4. This is a significant improvement over previous research and demonstration of other near field and far field imaging, including nanohole arrays discussed below.<ref name=nanotechwire-nanolens>{{cite web
| title =Northeastern physicists develop 3D metamaterial nanolens that achieves super-resolution imaging
| work =prototype super-resolution metamaterial nanonlens
| publisher =Nanotechwire.com
| date =2010-01-18
| url =http://nanotechwire.com/news.asp?nid=9315
| accessdate =2010-01-20}}</ref><ref name=B-D-F-Casse>{{cite journal
| last1 =Casse
| first1 =B. D. F.
| last2 =Lu
| first2 =W. T.
| last3 =Huang
| first3 =Y. J.
| last4 =Gultepe
| first4 =E.
| last5 =Menon
| first5 =L.
| last6 =Sridhar
| first6 =S.
| title =Super-resolution imaging using a three-dimensional metamaterials nanolens
| journal =Applied Physics Letters
| volume =96
| issue =2
| pages =023114
| year =2010
| doi =10.1063/1.3291677|bibcode = 2010ApPhL..96b3114C }}</ref>
 
==== Light transmission properties of holey metal films ====
 
2009-12. The light transmission properties of holey metal films in the metamaterial limit, where the unit length of the periodic structures is much smaller than the operating wavelength, are analyzed theoretically.<ref name=EOT-Jung>
{{Cite journal
| last = Jung
| first =J. and
| coauthors =L. Martín-Moreno and F J García-Vidal
|title =Light transmission properties of holey metal films in the metamaterial limit: effective medium theory and subwavelength imaging
| journal =New Journal of Physics
| volume =11
| issue = 12
|pages =123013
| date =2009-12-09
| doi =10.1088/1367-2630/11/12/123013|bibcode = 2009NJPh...11l3013J }}</ref>
 
==== Transporting an Image through a subwavelength hole ====
 
Theoretically it appears possible to transport a complex electromagnetic image through a tiny subwavelength hole with diameter considerably smaller than the diameter of the image, without losing the subwavelength details.<ref name=Nanohole-Engheta>
{{Cite journal
| last = Silveirinha
| first =Mario G. |coauthors =Nader Engheta
| title =Transporting an Image through a Subwavelength Hole
| journal =Physical Review Letters
| volume =102
| issue = 10
| pages =103902
| date =2009-03-13
| pmid = 19392114
|doi =10.1103/PhysRevLett.102.103902
| last2 = Engheta
| first2 = Nader
| bibcode=2009PhRvL.102j3902S}}</ref>
 
=== Nanoparticle imaging – quantum dots ===
 
When observing the complex processes in a living cell, significant processes (changes) or details are easy to overlook. This can more easily occur when watching changes that take a long time to unfold and require high-spatial-resolution imaging. However, recent research offers a solution to scrutinize activities that occur over hours or even days inside cells, potentially solving many of the mysteries associated with molecular-scale events occurring in these tiny organisms.<ref name=q-dot-image/>
 
A joint research team, working at the National Institute of Standards and Technology (NIST) and the National Institute of Allergy and Infectious Diseases (NIAID), has discovered a method of using nanoparticles to illuminate the cellular interior to reveal these slow processes. Nanoparticles, thousands of times smaller than a cell, have a variety of applications. One type of nanoparticle called a quantum dot glows when exposed to light. These semiconductor particles can be coated with organic materials, which are tailored to be attracted to specific proteins within the part of a cell a scientist wishes to examine.<ref name=q-dot-image/>
 
Notably, quantum dots last longer than many organic dyes and fluorescent proteins that were previously used to illuminate the interiors of cells.  They also have the advantage of monitoring changes in cellular processes while most high-resolution techniques like electron microscopy only provide images of cellular processes frozen at one moment. Using quantum dots, cellular processes involving the dynamic motions of proteins, are observable (elucidated).<ref name=q-dot-image/>
 
The research focused primarily on characterizing quantum dot properties, contrasting them with other imaging techniques. In one example, quantum dots were designed to target a specific type of human red blood cell protein that forms part of a network structure in the cell's inner membrane. When these proteins cluster together in a healthy cell, the network provides mechanical flexibility to the cell so it can squeeze through narrow capillaries and other tight spaces. But when the cell gets infected with the malaria parasite, the structure of the network protein changes.<ref name=q-dot-image/>
 
Because the clustering mechanism is not well understood, it was decided to examine it with the quantum dots. If a technique could be developed to visualize the clustering, then the progress of a malaria infection could be understood, which has several distinct developmental stages.<ref name=q-dot-image/>
 
Research efforts revealed that as the membrane proteins bunch up, the quantum dots attached to them are induced to cluster themselves and glow more brightly, permitting real time observation as the clustering of proteins progresses. More broadly, the research discovered that when quantum dots attach themselves to other nanomaterials, the dots' optical properties change in unique ways in each case. Furthermore,  evidence was discovered that quantum dot optical properties are altered as the nanoscale environment changes, offering greater possibility of using quantum dots to sense the local biochemical environment inside cells.<ref name=q-dot-image/>
 
Some concerns remain over toxicity and other properties.  However, the overall findings indicate that quantum dots could be a valuable tool to investigate dynamic cellular processes.<ref name=q-dot-image>{{Cite journal
|last1 =Kang
|first1 =Hyeong-Gon
|last2 =Tokumasu
|first2 =Fuyuki
|last3 =Clarke
|first3 =Matthew
|last4 =Zhou
|first4 =Zhenping
|last5 =Tang
|first5 =Jianyong
|last6 =Nguyen
|first6 =Tinh
|last7 =Hwang
|first7 =Jeeseong
|title =Probing dynamic fluorescence properties of single and clustered quantum dots toward quantitative biomedical imaging of cells
|journal =Wiley Interdisciplinary Reviews: Nanomedicine and Nanobiotechnology
|volume =2
|pages =48–58
|year =2010
|doi =10.1002/wnan.62}}</ref>
 
The abstract from the related published research paper states (in part): Results are presented regarding the dynamic fluorescence properties of bioconjugated nanocrystals or quantum dots (QDs) in different chemical and physical environments. A variety of QD samples was prepared and compared: isolated individual QDs, QD aggregates, and QDs conjugated to other nanoscale materials...
 
{{NIST-PD}}
 
== A technical view of the original problem ==
 
The original deficiency related to the perfect lens is elucidated:
 
The general expansion of an EM field emanating from a source consists of both propagating waves and near-field or evanescent waves. An example of a 2-D line source with an electric field which has S-polarization will have plane waves consisting of propagating and evanescent components, which advance parallel to the interface.<ref name=further-research-p-lens-2/> As both the propagating and the smaller evanescent waves advance in a direction parallel to the medium interface, evanescent waves decay in the direction of propagation. Ordinary (positive index) optical elements can refocus the propagating components, but the exponentially decaying inhomogeneous components are always lost, leading to the diffraction limit for focusing to an image.<ref name=further-research-p-lens-2/>
 
A superlens is a lens which is capable of [[subwavelength imaging]], allowing for magnification of [[near and far field|near field rays]]. Conventional lenses have a [[Angular resolution|resolution]] on the order of one [[wavelength]] due to the so-called diffraction limit. This limit hinders imaging very small objects, such as individual atoms, which are much smaller than the wavelength of visible light. A superlens is able to beat the diffraction limit. A very well known superlens is the perfect lens described by John Pendry, which uses a slab of material with a negative index of refraction as a flat lens. In theory, Pendry's perfect lens is capable of perfect [[focus (optics)|focusing]] — meaning that it can perfectly reproduce the [[electromagnetic field]] of the source plane at the image plane.
 
=== Theory ===
 
==== The diffraction limit ====
 
The performance limitation of conventional lenses is due to the diffraction limit. Following Pendry (Pendry, 2000), the diffraction limit can be understood as follows. Consider an object and a lens placed along the z-axis so the rays from the object are traveling in the +z direction. The field emanating from the object can be written in terms of its [[angular spectrum method]], as a [[superposition principle|superposition]] of [[plane wave]]s:
 
: <math>E(x,y,z,t) = \sum_{k_x,k_y} A(k_x,k_y) e^{i\left(k_z z + k_y y + k_x x - \omega t\right)}</math>
 
where <math>k_z</math> is a function of <math>k_x, k_y</math> as:
 
: <math> k_z = \sqrt{\frac{\omega^2}{c^2}-\left(k_x^2 + k_y^2\right)} </math>
 
Only the positive square root is taken as the energy is going in the +z direction. All of the components of the angular spectrum of the image for which <math>k_z</math> is real are transmitted and re-focused by an ordinary lens. However, if
 
: <math> k_x^2+k_y^2 > \frac{\omega^2}{c^2} </math>
 
then <math>k_z</math> becomes imaginary, and the wave is an [[evanescent wave]] whose [[amplitude]] decays as the [[wave propagation|wave propagates]] along the z-axis. This results in the loss of the high [[angular frequency]] components of the wave, which contain information about the high frequency (small scale) features of the object being imaged. The highest resolution that can be obtained can be expressed in terms of the wavelength:
 
: <math> k_{max} \approx \frac{\omega}{c} = \frac{2 \pi}{\lambda} </math>
 
: <math>\Delta x_{min} \approx \lambda </math>
 
A superlens overcomes the limit. A Pendry-type superlens has an index of ''n = −1'' (ε = −1, µ = −1), and in such a material, transport of energy in the +z direction requires the z-component of the [[wave vector]] to have opposite sign:
 
: <math>k'_z = -\sqrt{\frac{\omega^2}{c^2}-\left(k_x^2 + k_y^2\right)}</math>
 
For large angular frequencies, the evanescent wave now ''grows'', so with proper lens thickness, all components of the angular spectrum can be transmitted through the lens undistorted. There are no problems with [[conservation of energy]], as evanescent waves carry none in the direction of growth: the [[Poynting vector]] is oriented perpendicularly to the direction of growth. For traveling waves inside a perfect lens, the Poynting vector points in direction opposite to the phase velocity.{{Citation needed
|date=May 2009}}
 
==== Negative index of refraction and Pendry's perfect lens ====
 
[[Image:Negative refraction index focusing.png|thumb|320px|a) When a wave strikes a positive refraction index material from a vacuum. b) When a wave strikes a negative refraction index material from a vacuum. c) When an object is placed in front of an object with n = −1, the waves are refracted so that they focus once inside the lens and once outside of the lens. Such refraction allows for subwavelength imaging.]]
 
Normally when a wave passes through the [[interface (chemistry)|interface]] of two materials, the wave appears on the opposite side of the [[Surface normal|normal]]. However, if the interface is between a material with a positive index of refraction and another material with a [[Refractive index#Negative refractive index|negative index of refraction]], the wave will appear on the same side of the normal. John Pendry's perfect lens is a flat material where n = −1. Such a lens allows for near field rays—which normally decay due to the diffraction limit—to focus once within the lens and once outside the lens, allowing for subwavelength imaging.<ref name="smith2004">"{{cite news
|title = Breaking the diffraction limit
|author = David R Smith
|url =  http://physicsworld.com/cws/article/print/19415 |agency = Institute of Physics
|date = May 10, 2004
|accessdate = May 31, 2009}}</ref>
 
== Superlens construction ==
 
Superlens was believed impossible until [[John Pendry]] showed in 2000 that a simple slab of [[left-handed material]] would do the job.<ref name="Pendry2000">{{cite journal
|last = Pendry
|first = J. B.
|year = 2000
|title = Negative refraction makes a perfect lens
|journal = Phys. Rev. Lett.
|volume = 85
|doi = 10.1103/PhysRevLett.85.3966
|pmid = 11041972
|issue = 18
| bibcode=2000PhRvL..85.3966P
|pages = 3966–9}}</ref> The experimental realization of such a lens took, however, some more time, because it is not that easy to fabricate metamaterials with both negative permittivity and [[permeability (electromagnetism)|permeability]]. Indeed, no such material exists naturally and construction of the required [[metamaterials]] is non-trivial. Furthermore, it was shown that the parameters of the material are extremely sensitive (the index must equal −1); small deviations make the subwavelength resolution unobservable.<ref name="Podolskiy2005">{{cite journal
|last = Podolskiy
|first = V.A.
|year = 2005
|title = Near-sighted superlens
|journal = Opt. Lett.
|volume = 30
|doi = 10.1364/OL.30.000075
|pmid = 15648643
|first2 = EE
|issue = 1
|last2 = Narimanov
| arxiv = physics/0403139 |bibcode = 2005OptL...30...75P
|pages = 75–7 }}</ref><ref name="Tasin2006">{{cite journal
|last = Tassin
|first = P.
|year = 2006
|title = Veselago's lens consisting of left-handed materials with arbitrary index of refraction
|journal = Opt. Commun.
|volume = 264
|page = 130
|doi = 10.1016/j.optcom.2006.02.013
|first2 = I
|first3 = G
|last2 = Veretennicoff
|last3 = Vandersande
| bibcode = 2006OptCo.264..130T }}</ref> Due to the resonant nature of metamaterials, on which many (proposed) implementations of superlenses depend, metamaterials are highly dispersive. The sensitive nature of the superlens to the material parameters causes superlenses based on metamaterials to have a limited usable frequency range.
 
However, Pendry also suggested that a lens having only one negative parameter would form an approximate superlens, provided that the distances involved are also very small and provided that the source polarization is appropriate. For visible light this is a useful substitute, since engineering metamaterials with a negative permeability at the frequency of visible light is difficult. Metals are then a good alternative as they have negative permittivity (but not negative permeability). Pendry suggested using [[silver]] due to its relatively low loss at the predicted wavelength of operation (356&nbsp;nm). In 2005, Pendry's suggestion was finally experimentally verified by two independent groups, both using thin layers of silver illuminated with UV light to produce "photographs" of objects smaller than the wavelength.<ref name="Melville-2005">{{cite journal
|last = Melville
|first = DOS
|year = 2005
|title = Super-resolution imaging through a planar silver layer
|journal = Optics Express
|volume = 13
|doi = 10.1364/OPEX.13.002127
|pmid = 19495100
|first2 = R
|issue = 6
|last2 = Blaikie
| bibcode = 2005OExpr..13.2127M
|pages = 2127–34 }}</ref><ref name="Fang-2005">{{cite journal
|last = Fang
|first = Nicholas
|year = 2005
|title = Sub–Diffraction-Limited Optical Imaging with a Silver Superlens
|journal = Science
|volume = 308
|doi = 10.1126/science.1108759
|pmid = 15845849
|first2 = H
|first3 = C
|first4 = X
|issue = 5721
|last2 = Lee
|last3 = Sun
|last4 = Zhang
| bibcode = 2005Sci...308..534F
|pages = 534–7 }}</ref> Negative refraction of visible light has been experimentally verified in an [[yttrium orthovanadate]] (YVO<sub>4</sub>) bicrystal in 2003.<ref>{{cite journal
|doi=10.1103/PhysRevLett.91.157404
|title=Total Negative Refraction in Real Crystals for Ballistic Electrons and Light
|year=2003
|last1=Zhang
|first1=Yong
|first2=B.
|first3=A.
|journal=Physical Review Letters
|volume=91
|page=157404
|pmid=14611495
|last2=Fluegel
|last3=Mascarenhas
|issue=15
| bibcode=2003PhRvL..91o7404Z}}</ref>
 
== See also ==
{{Multicol}}
 
* [[Acoustic metamaterials]]
* [[History of metamaterials]]
* [[Metamaterial]]
* [[Metamaterial absorber]]
* [[Metamaterial antennas]]
* [[Metamaterial cloaking]]
* [[Negative index metamaterials]]
* [[Nonlinear metamaterials]]
* [[Photonic crystal]]
* [[Photonic metamaterials]]
* [[Plasmonic metamaterials]]
* [[Seismic metamaterials]]
* [[Flat lens]]
 
{{Multicol-break}}
 
* [[Split-ring resonator]]
* [[Superresolution]]
* [[Terahertz metamaterials]]
* [[Theories of cloaking]]
* [[Transformation optics]]
* [[Tunable metamaterials]]
* [[Plasmonic lens]]
:::: '''Academic journals'''
* [[Metamaterials (journal)]]
:::: '''Metamaterials books'''
* [[Metamaterials Handbook]]
* [[Metamaterials: Physics and Engineering Explorations]]
 
{{Multicol-break}}
'''Metamaterials scientists'''
 
* [[Nader Engheta]]
* [[Ulf Leonhardt]]
* [[John Pendry]]
* [[Vladimir Shalaev]]
* [[David R. Smith]]
* [[Richard W. Ziolkowski]]
 
{{Multicol-end}}
 
== References ==
{{reflist|2}}
 
== External links ==
* [http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/sciam-pendry-4a.pdf The Quest for the Superlens] By [[John B. Pendry]] and [[David R. Smith]].  Scientific American. July 2006. Free PDF download from [[Imperial College]].
* [http://physicsweb.org/articles/news/9/4/12 Subwavelength imaging]
* [http://mitworld.mit.edu/video/455 ''Professor Sir John Pendry'' at MIT] – "''The Perfect Lens: Resolution Beyond the Limits of Wavelength''"
* [http://www.me.berkeley.edu/~lwlin/me118/papers/paper11.pdf Surface plasmon subwavelength optics] 2009-12-05
* [http://circuit.ucsd.edu/~zhaowei/Journals/Nature%20Material%20_%20superlenses.pdf Superlenses to overcome the diffraction limit]
* [http://physicsworld.com/cws/article/print/19415 Breaking the diffracion limit] Overview of superlens theory
* [http://www.emtalk.com/tut_4.htm Flat Superlens Simulation] EM Talk
* [http://physicsworld.com/cws/article/news/25892 Superlens microscope gets up close]
* [http://physicsworld.com/cws/article/news/22065 Superlens breakthrough]
* [http://physicsworld.com/cws/article/print/22746 Superlens breaks optical barrier]
* [http://www.physics.oregonstate.edu/~vpodolsk/NIM/index.html Materials with negative index of refraction by V.A. Podolskiy]
* [http://www.physics.oregonstate.edu/~vpodolsk/reprints.pdf/resolut.apl2005.pdf Optimizing the superlens: Manipulating geometry to enhance the resolution by V.A. Podolskiy and Nicholas A. Kuhta]
* [http://www.guardian.co.uk/science/story/0,,1766219,00.html Now you see it, now you don't: cloaking device is not just sci-fi]
* [http://www.nrel.gov/research_review/pdfs/2004/37011d.pdf Initial page describes first demonstration of negative refraction in a natural material]
* [http://physicsworld.com/cws/article/news/18434 Negative-index materials made easy]
* [http://technology.newscientist.com/channel/tech/dn13771-simple-superlens-sharpens-focusing-power.html?feedId=online-news_rss20 Simple 'superlens' sharpens focusing power] – A lens able to focus 10 times more intensely than any conventional design could significantly enhance wireless power transmission and photolithography (''New Scientist'', 24 April 2008)
* [http://www.fcm.in.cnr.it/lsbm/testi/tecnofisica/docs/TB08_micros_2.pdf Far-Field Optical Nanoscopy] by Stefan W.Hell. VOL 316. SCIENCE. 25 MAY 2007
 
[[Category:Electromagnetism]]
[[Category:Lenses]]
[[Category:Metamaterials]]
[[Category:Microscopy]]
[[Category:Nanomaterials]]
[[Category:2000 in science]]
[[Category:21st century in science]]

Latest revision as of 22:45, 4 May 2014

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