Do metamaterial perfect lenses violate Heisenberg's uncertainty principle?

"We also note that hyperbolic metamaterials behave as diffractionless “perfect lenses”.

Will Heisenberg's microscope gedanken experiment work for a diffractionless perfect lens?

I just pose the problem, just woke up to Art's message, having morning coffee, have not thought it through as yet.

Any opinions?

Heisenberg's argument

"Heisenberg's Microscope, with cone of light rays focusing on a particle with angle .
Heisenberg's argument can be found in (Heisenberg 1930), and is summarized as follows. Heisenberg begins by supposing that an electron is like a classical particle, moving in the x direction along a line below the microscope, as in the illustration to the right. Let the cone of light rays leaving the microscope lens and focusing on the electron makes an angle @ with the electron. Let λ be the wavelength of the light rays. Then, according to the laws of classical optics, the microscope can only resolve  he position of the electron up to an accuracy of" wavelength divided by sine of @.
http://en.wikipedia.org/wiki/Heisenberg's_microscope

The Abbe diffraction limit for a microscope

The observation of sub-wavelength structures with microscopes is difficult because of the Abbe diffraction limit. Ernst Abbe found in 1873 that light with wavelength λ, travelling in a medium with refractive index n and converging to a spot with angle φ will make a spot with radius

The denominator nsinφ is called the numerical aperture (NA) and can reach about 1.4 in modern optics, hence the Abbe limit is roughly d=λ/2. With green light around 500nm the Abbe limit is 250nm which is large compared to most nanostructures or biological cells which have sizes on the order of 1μm and internal organelles which are much smaller. To increase the resolution, shorter wavelengths can be used such as UV and X-ray microscopes. These techniques offer better resolution but are expensive, suffer from lack of contrast in biological samples and may damage the sample.
http://en.wikipedia.org/wiki/Diffraction-limited_system

Also besides n < 0 in metamaterial, what happens if in addition |n| >> 1

On Aug 11, 2011, at 9:15 AM, JACK SARFATTI wrote:

Thanks Art

arXiv.org Search Results
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The URL for this search is http://xxx.lanl.gov/find/physics/1/au:+Smolyaninov_I/0/1/0/all/0/1

Showing results 1 through 21 (of 21 total) for au:Smolyaninov_I

1. arXiv:1108.2203 [pdf]
Vacuum as a hyperbolic metamaterial
Igor I. Smolyaninov
Comments: 10 pages, 1 figure
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
2. arXiv:1107.4053 [pdf]
Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and the "end of time"
Igor I. Smolyaninov, Ehren Hwang, Evgenii Narimanov
Comments: 21 pages, 4 figures
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc)
3. arXiv:1104.0561 [pdf]
Modeling of Time with Metamaterials
Igor I. Smolyaninov, Yu-Ju Hung
Comments: 15 pages, 4 figures, this version is accepted for publication in JOSA B
Journal-ref: JOSA B, 28, 1591-1595 (2011)
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc)
4. arXiv:1101.4625 [pdf]
Virtual Black Holes in Hyperbolic Metamaterials
Igor I. Smolyaninov
Comments: 11 pages, 2 figures
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc)
5. arXiv:1101.3366 [pdf]
Fluorescence Enhancement in an Array of "Trapped Rainbows"
Vera N. Smolyaninova, Igor I. Smolyaninov
Comments: 8 pages, 2 figures
Subjects: Optics (physics.optics)
6. arXiv:1009.5663 [pdf]
Metamaterial-based model of the Alcubierre warp drive
Igor I. Smolyaninov
Comments: 10 pages, 1 figure
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc)
7. arXiv:1009.1180 [pdf]
Lattice models of non-trivial "optical spaces" based on metamaterial waveguides
Alexei I. Smolyaninov, Igor I. Smolyaninov
Comments: 3 pages, 4 figures, accepted for publication in Optics Letters
Journal-ref: Optics Letters, 36, 2420-2422 (2011)
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc)
8. arXiv:1007.1130 [pdf]
Metric Signature Transitions in Optical Metamaterials
Igor I. Smolyaninov, Evgenii E. Narimanov
Comments: 16 pages, 3 figures, accepted for publication in Physical Review Letters
Journal-ref: Phys.Rev.Lett.105:067402,2010
Subjects: Optics (physics.optics); Quantum Gases (cond-mat.quant-gas); General Relativity and Quantum Cosmology (gr-qc)
9. arXiv:1006.0914 [pdf]
Imaging Properties of Two-Dimensional Microlenses
Vera N. Smolyaninova, Igor I. Smolyaninov, Alexander V. Kildishev, Vladimir M. Shalaev
Comments: 15 pages, 7 figures
Journal-ref: Optics Letters 35, 3396-3398, (2010)
Subjects: Optics (physics.optics)
10. arXiv:1005.1002 [pdf]
Metamaterial "Multiverse"
Igor I. Smolyaninov
Comments: 13 pages, 2 figures, this version is accepted for publication in the Journal of Optics
Journal-ref: J.Optics 13:024004,2011
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc)
11. arXiv:0911.4464 [pdf]
Experimental observation of the trapped rainbow
V.N. Smolyaninova, I.I. Smolyaninov, A.V. Kildishev, V. M. Shalaev
Comments: 2 pages, 1 figure
Journal-ref: Appl.Phys.Letters 96, 211121 (2010)
Subjects: Optics (physics.optics)
12. arXiv:0910.3981 [pdf, other]
Broadband Purcell effect: Radiative decay engineering with metamaterials
Zubin Jacob, Igor Smolyaninov, Evgenii Narimanov
Subjects: Optics (physics.optics)
13. arXiv:0908.2407 [pdf, ps, other]
Optical models of the big bang and non-trivial space-time metrics based on metamaterials
Igor I. Smolyaninov
Comments: 3 pages
Journal-ref: Phys. Rev. Letters 105, 067402 (2010)
Subjects: Optics (physics.optics); General Relativity and Quantum Cosmology (gr-qc)
14. arXiv:0903.3437 [pdf]
Anisotropic Metamaterials Emulated by Tapered Waveguides: Application to Optical Cloaking
Igor I. Smolyaninov, Vera N. Smolyaninova, Alexander V. Kildishev, Vladimir M. Shalaev
Comments: 4 pages, 4 figures, corrected references
Journal-ref: Phys. Rev. Letters 103, 213901 (2009)
Subjects: Optics (physics.optics)
15. arXiv:0709.2862 [pdf]
Electromagnetic cloaking in the visible frequency range
I.I. Smolyaninov, Y.J.Hung, C.C. Davis
Comments: 3 pages, 1 figure
Journal-ref: Optics Letters 33, 1342-1344 (2008)
Subjects: Optics (physics.optics)
16. arXiv:physics/0610230 [pdf]
Magnifying superlens in the visible frequency range
I.I. Smolyaninov, Y.J.Hung, C.C. Davis
Comments: 3pages, 1 figure
Journal-ref: Science 315, 1699-1701 (2007)
Subjects: Optics (physics.optics)
17. arXiv:physics/0607144 [pdf, ps, other]
Hawking radiation in a waveguide is produced by self-phase modulation
Igor I. Smolyaninov
Comments: 2 pages, 1 figure
Subjects: Optics (physics.optics)
18. arXiv:physics/0606072 [pdf]
Unruh effect in a waveguide
Igor I. Smolyaninov
Comments: 12 pages, 2 figures, accepted for publication in Physics Letters A
Journal-ref: Physics Letters A 372, 5861-5864 (2008)
Subjects: Optics (physics.optics)

On Aug 11, 2011, at 7:53 AM, art wagner wrote:

http://xxx.lanl.gov/find/physics/1/au:+Smolyaninov_I/0/1/0/all/0/1