Superlens 3088223 223689142 2008-07-05T07:49:11Z 130.89.181.84 removed beamsplitter part, is not necessary in general case. Added minor additions A '''superlens''' is a [[Lens (optics)|lens]] which is capable of [[subwavelength imaging]]. Conventional lenses have a resolution on the order of one wavelength due to the so-called [[diffraction limit]]. This limit makes it impossible to image very small objects, such as individual atoms, which have sizes many times 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 [[metamaterial|material with a negative index of refraction]] as a flat lens. In theory, Pendry's perfect lens is capable of perfect focusing&mdash;meaning that it can perfectly reproduce the [[electromagnetic field]] of the source plane at the image plane. __TOC__ ==The diffraction limit== The performance limitation of conventional lenses is due to the diffraction limit. Following [[John Pendry|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 of plane waves: :<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 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 <math>n=-1</math> (<math>\epsilon=-1, \mu=-1</math>), and in such a material, transport of energy in the +z direction requires the z-component of the wavevector 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 ([[Poynting vector]] is 0 in the +z direction). ==Superlens construction== Before 2000, it was believed that it was impossible to construct a superlens. But in that year, [[John Pendry]] showed 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 | pages = 3966 | publisher = American Physical Society | doi = 10.1103/PhysRevLett.85.3966 }}</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 | pages = 75 | publisher = OSA | doi = 10.1364/OL.30.000075 }}</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 | pages = 130 | publisher = Elsevier | doi = 10.1016/j.optcom.2006.02.013 }}</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 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 | pages = 2127 | publisher = OSA | doi = 10.1364/OPEX.13.002127 }}</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 | pages = 534 | publisher = AAAS | doi = 10.1126/science.1108759 | pmid = 15845849 }}</ref> Negative refraction of visible light has been experimentally verified in a [[yttrium orthovanadate]] (YVO4) bicrystal by Yong Zhang et al at the [[National Renewable Energy Laboratory]] in Golden Colorado in 2003 (links are provided below). ==See also== * [[Metamaterial]] * [[Fresnel zone plate]] ==External links== * [http://physicsweb.org/articles/news/9/4/12/1 Superlens microscope gets up close] * [http://physicsweb.org/articles/news/9/4/12/1 Superlens breakthrough] * [http://physicsweb.org/articles/world/18/8/4 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://prola.aps.org/abstract/PRL/v91/i15/e157404 Link to research paper on negative refraction in visible light in YVO4 bicrystal] * [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) ==References== <references /> [[Category:Lenses]] [[fr:Superlentille]]