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]

In 2007, Huang experimentally observed optical superoscillation phenomenon in the diffraction patterns of light transmitted through quasi-periodic nanohole arrays.[3] Optical foci much smaller than the diffraction limit were observed. The results matched simulations without evanescent waves.[4] In 2009, Huang et al further developed theoretical models to design superoscillation masks that can achieve extreme light concentration and imaging with arbitrary resolution.[5] A practical method for constructing superoscillations and a discussion of their potential for quantum field theory were given by Achim Kempf.[6] Chremmos and Fikioris have proposed a method for constructing superoscillations that approximate a desired polynomial with arbitrary accuracy within a given interval.[7] In 2013 experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams has been demonstrated.[8] 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.[9] Kempf and Ferreira proved[10] 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.[11][12]

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 Ddimensions". Journal of Physics A: Mathematical and Theoretical. 42 (2): 022003. doi:10.1088/1751-8113/42/2/022003. S2CID 120985111.
  3. ↑ Huang, Fu Min; Zheludev, Nikolay; Chen, Yifang; Javier Garcia De Abajo, F. (2007). "Focusing of light by a nanohole array". Applied Physics Letters. 90 (9): 091119. arXiv:physics/0611056. Bibcode:2007ApPhL..90i1119H. doi:10.1063/1.2710775. S2CID 10434523.
  4. ↑ Huang, Fu Min; Chen, Yifang; Garcia De Abajo, F Javier; Zheludev, Nikolay I. (2007). "Optical super-resolution through super-oscillations" (PDF). Journal of Optics A: Pure and Applied Optics. 9 (9): S285–S288. doi:10.1088/1464-4258/9/9/S01.
  5. ↑ Huang, Fu Min; Zheludev, Nikolay I. (2009). "Super-Resolution without Evanescent Waves". Nano Letters. 9 (3): 1249–1254. arXiv:0812.0508. Bibcode:2009NanoL...9.1249H. doi:10.1021/nl9002014. PMID 19182908. S2CID 14091064.
  6. ↑ Kempf, Achim (2000). "Black holes, bandwidths and Beethoven". Journal of Mathematical Physics. 41 (4): 2360–2374. arXiv:gr-qc/9907084. Bibcode:2000JMP....41.2360K. doi:10.1063/1.533244. S2CID 14858993.
  7. ↑ Chremmos, Ioannis; Fikioris, George (2015). "Superoscillations with arbitrary polynomial shape". Journal of Physics A: Mathematical and Theoretical. 48 (26): 265204. arXiv:1504.04822. Bibcode:2015JPhA...48z5204C. doi:10.1088/1751-8113/48/26/265204. S2CID 119137509.
  8. ↑ 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. PMID 23736595. S2CID 31157421.
  9. ↑ 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. Bibcode:2015Optic...2.1045D. doi:10.1364/OPTICA.2.001045.
  10. ↑ Ferreira, P.J.S.G.; Kempf, A. (2006). "Superoscillations: Faster Than the Nyquist Rate" (PDF). IEEE Transactions on Signal Processing. 54 (10): 3732–3740. Bibcode:2006ITSP...54.3732F. doi:10.1109/TSP.2006.877642. S2CID 17467946.
  11. ↑ Thomson, Laura C.; Boissel, Yannick; Whyte, Graeme; Yao, Eric; Courtial, Johannes (2008). "Simulation of superresolution holography for optical tweezers". New Journal of Physics. 10 (2): 023015. Bibcode:2008NJPh...10b3015T. doi:10.1088/1367-2630/10/2/023015.
  12. ↑ Zheludev, Nikolay I. (2008). "What diffraction limit?". Nature Materials. 7 (6): 420–422. Bibcode:2008NatMa...7..420Z. doi:10.1038/nmat2163. PMID 18497841. S2CID 30418364.


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