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"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

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