Superoscillation

Superoscillation is a phenomenon in which a signal which is globally band-limited can contain local segments that oscillate faster than its fastest Fourier components. The idea is originally attributed to Yakir Aharonov, and has been made more popularly known through the work of Michael Berry, who also notes that a similar result was known to Ingrid Daubechies.[1][2] A practical method for constructing superoscillations and a discussion of their potential for quantum field theory were given by Achim Kempf.[3] Chremmos and Fikioris have proposed a method for constructing superoscillations that approximate a desired polynomial with arbitrary accuracy within a given interval.[4] In 2013 experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams has been demonstrated.[5] Two years later, in 2015, it was shown experimentally that super-oscillations can generate features that are many-fold smaller than the diffraction limit. The experiment was done using visible light, demonstrating enhanced resolution of 35 nm.[6] Kempf and Ferreira proved[7] that superoscillations come at the expense of a dynamical range that has to increase exponentially with the number of superoscillations and polynomially with the frequency of the superoscillations.

Superoscillatory wave forms are being considered as a possible practical tool for engineering applications, such as optical superresolution, i.e., resolution beyond the diffraction limit.[8][9]

See also

References

  1. ↑ Berry, M V, 1994, 'Faster than Fourier', in 'Quantum Coherence and Reality; in celebration of the 60th Birthday of Yakir Aharonov' (J S Anandan and J L Safko, eds.) World Scientific, Singapore, pp 55-65.
  2. ↑ Berry, M V & Dennis, M R, 2009, 'Natural superoscillations in monochromatic waves in D dimension'
  3. ↑ A. Kempf, 'Black Holes, Bandwidths and Beethoven', J.Math.Phys. 41, pp. 2360-2374 (2000)
  4. ↑ I. Chremmos and G. Fikioris: 'Superoscillations with arbitrary polynomial shape' Journal of Physics A: Mathematical & Theoretical, vol. 48, 265204, 2015.
  5. ↑ Greenfield, Elad; Schley, Ran; Hurwitz, Ilan; Nemirovsky, Jonathan; Makris, Konstantinos G.; Segev, Mordechai (2013). "Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams". Optics Express. 21 (11): 13425–13435. Bibcode:2013OExpr..2113425G. doi:10.1364/oe.21.013425.
  6. ↑ David, Asaf; Gjonaj, Bergin; Blau, Yochai; Dolev, Shimon; Bartal, Guy (2015). "Nanoscale shaping and focusing of visible light in planar metal–oxide–silicon waveguides". Optica. 2 (12): 1045–1048. doi:10.1364/OPTICA.2.001045.
  7. ↑ P.J.S.G. Ferreira and A. Kempf. 'Superoscillations: Faster than the Nyquist Rate', in IEEE Transactions on Signal Processing, vol. 54, no. 10, pp. 3732-3740 (2006).
  8. ↑ Laura C Thomson, Yannick Boissel, Graeme Whyte, Eric Yao and Johannes Courtial. Simulation of superresolution holography for optical tweezers
  9. ↑ N.I. Zheludev, 'What diffraction limit?', Nature Materials 7, 420 - 422 (2008)

External links


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