Superlens

A perfect lens, superlens or super lens is a metamaterial lens, which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens that was proposed, consisting of a metamaterial, which compensates for wave decay and reconstructs images in the near-field. In addition, both propagating and evanescent waves contribute to the resolution of the image.

Early subwavelength imaging attempts

Metamaterial lenses 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 imaging to create a pattern in relief, photolithography, electron lithography, X-ray lithography, or ion bombardment, on an appropriate planar substrate.

The shared technological goals of the metamaterial lens and and the variety of lithography is to achieve features having dimensions much smaller than that of the vacuum wavelength of the exposing light.

In 1981 two different techniques of contact imaging of planar (flat) submicroscopic metal patterns with blue light (400 nm) were demonstrated. One demonstration resulted in an image resolution of 100 nm and the other a resolution of 50 to 70 nm.

Since at least 1998 near field optical lithography was designed to create nanometer-scale features. Research on this technology continued as the first experimentally demonstrated LHM came into existence in 2000 / 2001. The effectiveness of electron-beam lithography was also being researched at the beginning of the new millenium for nanometer-scale applications. Imprint lithography was shown to have desirable advantages for nanometer-scaled research and technology.

Advanced deep UV photolithography can now offer sub-100 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 field lithography, near field interference lithography, and phaseshifting mask lithography were developed to overcome the diffraction limit.

In the year 2000, John Pendry proposed using a metamaterial lens to, achieve nanometer-scaled imaging for focusing below the wavelength of light.

Perfect lens

When the world is observed through 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 (positive index) lenses. A slab of silver is to be used. As light moves away (propagates) from the source, it acquires an arbitrary phase. Through a conventional lens the phase remains consistent, but the evanescent waves decay exponentially. In the flat metamaterial DNG slab, normally decaying evanescent waves are contrarily amplified. Furthermore, as the evanescent waves are now amplified, the phase is reversed.

Therefore, a type of lens that was proposed, consisting of a metamaterial, which compensates for wave decay and reconstructs images in the near-field. In addition, both propagating and evanescent waves contribute to the resolution of the image. | Theoretically, this is a breakthrough in that the optical version resolves objects as minuscule as nanometers across. Pendry predicted that DNGs with a refractive index of n < 0, 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.

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 spectrum (equations 13 thru 21 in reference ) was not correct. However, the final intuitive result of this theory that both the propagating and evanescent waves are focused, resulting in a converging focal point within the slab and another convergence (focal point) beyond the slab is correct. But, this applies to only one (theoretical) instance, and that is one particular medium that is lossless, nondispersive and the constituent parameters are defined as:

ε(ω) / ε₀ = µ(ω) / µ₀ = $-1,$ which in turn results in a negative refraction of n = $-1$

If the DNG metamaterial medium has a large negative index or becomes lossy or dispersive, Pendry's perfect lens effect cannot be realized. As a result, the perfect lens effect does not exist in general. According to 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.

Another analysis, in 2002, 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 subltlies of evanescent waves, restriction to a 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, which is linked to dispersion, is always present in practice, and absorption tends to transform amplified waves into a decaying ones inside this medium (DNG).

A third analysis of Pendry's perfect lens concept, published in 2003, used the recent demonstration of negative refraction at microwave frequencies as confirming the 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 point source. However, the perfect lens would require significantly different values for permitivity, permeability, and spatial periodicity than the demonstrated negative refractive sample.

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.

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 has a significant effect on the recovery of types of evanescent components. In addition, achieving 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. 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.

Near field imaging with magnetic wires

Pendry's theoretical lens was designed to focus both propogating waves and the near field evanescent waves. In 2003, a group of researhers wrote 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, n₂ = $\infty$, n_x = 0. The effective refractive indices are then perpendicular and parallel, respectively.

A consistent characteristic of the very near (evanescent) field is that the electric and magnetic fields are largely decoupled. This allows for nearly independent manipulation of the electric field with the permittivity and the magnetic field with the permeability.

Furthermore, this is highly anisotropic system. Therefore, the transverse (perpendicular) components of the EM field which radiate the material, wavevectors (k_x) and (k_y), are decoupled from the longitudinal component, (k_z). 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.

Like a conventional lens , the z-direction is along the axis of the roll. The resonant frequency (w₀) - close to 21.3MHz - is determined by the construction of the roll. Damping is achieved by the inherent resistance of the layers and the lossy part of permittivity. The details of construction are found in ref. below.

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 Rolls tuned to 21.5 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.

Optical super-imaging with silver

In 2005 researchers discovered that a thinner slab of silver was best for 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-field.

Conventional optical materials suffer a diffraction limit because only the propagating components are transmitted (by the optical material) from a light source. The evanescent waves are actually considered to be non-propaagating components. In addition, lenses that improve image resolution by increasing the index of refraction are limited by the availability of high-index materials, and point by point subwavelegnth imaging of electron microscopy also has limitations when compared to the potential of a working superlens. Prior attempts to create a working superlens used a slab of silver that was too thick.

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.

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.

50-nm planar silver layer

Also in 2005 another group achieved super-resolution imaging, by refining techniques with a 50-nm thick planar silver layer as a near-field lens at wavelengths around 365 nanometers (nm).

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.

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 corrugated metallic slab-based superlens.

Metamaterial crystal lens

Theoretically explore an idea for a far-field scanless optical microscopy with a subdiffraction resolution by exploiting the special dispersion characteristics of an anisotropic metamaterial crystal.

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.

Plasmon-assisted microscopy

Plasmon assisted microscopy.

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.

Sub-diffraction imaging in the far field

In 2007 researchers used an anisotropic medium experimentally demonstrate far field imaging. Magnification of the subwavelength object is achieved by transforming the scattered evanescent waves into waves which propagate through the medium and projects the image (high-resolution) at the far field. Possibilities in applications such as real-time biomolecular imaging and nanolithography.

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.

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 (wavelength). This means that viruses, proteins, 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 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.

However, a new lens is fabricated, which is capable of magnification beyond the diffraction limit of conventional (optical) microscopes, and its integration into a regular far-field optical microscope was demonstrated.

Super resolution far-field microscopy techniques

By 2008 the diffraction limit has been surpassed and lateral imaging resolutions of 20 to 50 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.

Cylindrical superlens via coordinate transformaion

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 orginal perfect lens into the cylindrical, lens structure.

This was followed by a 36 page conceptual and mathematical proof in 2005, that the cylindrical superlens works in the quasistatic regime. The debate over the perfect lens is discussed first.

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.

The cylindrical magnifying superlens was experimentally demonstrated in 2007 by two groups, Z. Liu et al. (Science 315, 1686 (2007)).; and I. I. Smolyaninov et al (Science 315, 1699 (2007)).

Imaging without negative refraction

Perfect imaging has been believed to rely on negative refraction, however an ordinary positively refracting optical medium may form perfect images as well. In principle, Maxwell’s fish eye has unlimited resolution.

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 electiric field which has S-polarization will have plane waves consisting of propagating and evanescent components, which advance parallel to the interface. 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.

A superlens is a lens which is capable of subwavelength imaging, allowing for magnification of near field rays. Conventional lenses have a 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 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 of plane waves:

$E(x,y,z,t)=\sum _{k_{x},k_{y}}A(k_{x},k_{y})e^{i\left(k_{z}z+k_{y}y+k_{x}x-\omega t\right)}$

where $k_{z}$ is a function of $k_{x},k_{y}$ as:

$k_{z}={\sqrt {{\frac {\omega ^{2}}{c^{2}}}-\left(k_{x}^{2}+k_{y}^{2}\right)}}$

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 $k_{z}$ is real are transmitted and re-focused by an ordinary lens. However, if

$k_{x}^{2}+k_{y}^{2}>{\frac {\omega ^{2}}{c^{2}}}$,

then $k_{z}$ 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:

$k_{max}\approx {\frac {\omega }{c}}={\frac {2\pi }{\lambda }}$

$\Delta x_{min}\approx \lambda$

A superlens overcomes the limit. A Pendry-type superlens has an index of $n=-1$ ($\epsilon =-1,\mu =-1$), and in such a material, transport of energy in the +z direction requires the z-component of the wave vector to have opposite sign:

$k'_{z}=-{\sqrt {{\frac {\omega ^{2}}{c^{2}}}-\left(k_{x}^{2}+k_{y}^{2}\right)}}$

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).

Negative index of refraction and Pendry's perfect lens

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 of two materials, the wave appears on the opposite side of the normal. However, if the interface is between a material with a positive index of refraction and another material with a 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.

Superlens construction

Superlens was believed impossible until John Pendry showed in 2000 that a simple slab of left-handed material would do the job. 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. 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. 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. Negative refraction of visible light has been experimentally verified in an yttrium orthovanadate (YVO₄) bicrystal in 2003.

See also

• Acoustic metamaterials
• Metamaterial
• Negative index metamaterials
• Metamaterial antennas
• Photonic metamaterials
• Photonic crystal
• Split-ring resonator
• Terahertz metamaterials
• Tunable metamaterials
• Fresnel zone plate
• Superprism
• Perfect mirror

Electromagnetic interactions

• Bloch wave
• Casimir effect
• EM radiation
• Electron mobility
• Impedance
• Permeability (electromagnetism)
• Permittivity
• Photo-Dember
• Wavenumber

External links

• Professor Sir John Pendry at MIT - "The Perfect Lens: Resolution Beyond the Limits of Wavelength"
• Breaking the diffracion limit Overview of superlens theory
• Flat Superlens Simulation EM Talk
• Superlens microscope gets up close
• Superlens breakthrough
• Superlens breaks optical barrier
• Materials with negative index of refraction by V.A. Podolskiy
• Optimizing the superlens: Manipulating geometry to enhance the resolution by V.A. Podolskiy and Nicholas A. Kuhta
• Now you see it, now you don't: cloaking device is not just sci-fi
• Initial page describes first demonstration of negative refraction in a natural material
• Negative-index materials made easy
• 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)