Superlens

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A superlens is a 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 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.

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For the argumentation, plane waves are used. A superlens begins with a beam splitter using frustrated total internal reflection. A superlens then adds a second layer of a material, which has a refractive index with the same absolute value, but the opposite sign of the first layer. If both layers are as thick, the beam splitter does not split anymore, but passes, for example, all energy and maybe the temporal evolution of a laser pulse. In this theory, the material with the high index of refraction can have a very high refractive index (absolute value), which means very small objects immersed into it are still resolved. This resolution is also sustained through the low refractive index material. The Kramers–Kronig relation states that this is only possible for a narrow range of frequencies (the material has to be tuned).

[edit] 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 kz is a function of kx,ky 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 kz 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 kz 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 (ε = − 1,μ = − 1), and in such a material, transport of energy in the +z direction requires the z-component of the wavevector 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).

[edit] 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.[1] 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.[2][3] 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. 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 and other convenient factors. 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.[4][5] 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).

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[edit] References

  1. ^ Pendry, J. B. (2000). "Negative refraction makes a perfect lens". Phys. Rev. Lett. 85: 3966. American Physical Society. doi:10.1103/PhysRevLett.85.3966. 
  2. ^ Podolskiy, V.A. (2005). "Near-sighted superlens". Opt. Lett. 30: 75. OSA. doi:10.1364/OL.30.000075. 
  3. ^ Tassin, P. (2006). "Veselago’s lens consisting of left-handed materials with arbitrary index of refraction". Opt. Commun. 264: 130. Elsevier. doi:10.1016/j.optcom.2006.02.013. 
  4. ^ Melville, DOS (2005). "Super-resolution imaging through a planar silver layer". Optics Express 13: 2127. OSA. doi:10.1364/OPEX.13.002127. 
  5. ^ Fang, Nicholas (2005). "Sub–Diffraction-Limited Optical Imaging with a Silver Superlens". Science 308: 534. AAAS. doi:10.1126/science.1108759. 
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