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Proceedings Paper

Natural superoscillation of random functions in one and more dimensions
Author(s): Mark R. Dennis; Jari Lindberg
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Paper Abstract

Superoscillations are regions of band-limited waves where the local wavenumber, defined as the local phase gradient, exceeds the global maximum wavenumber in the Fourier spectrum. In random functions, defined as superpositions of plane waves with random complex amplitudes and directions, considerable regions are naturally superoscillatory (M. R. Dennis, et al., Opt. Lett. 33, 2976-2978, 2008; M. V. Berry and M. R. Dennis, J. Phys. A: Math. Theor. 42, 022003, 2009). We discuss this result by deriving the joint probability density function for intensity and phase gradient of isotropic complex random wave in any dimension, with specific reference to the one-dimensional case.

Paper Details

Date Published: 2 September 2009
PDF: 9 pages
Proc. SPIE 7394, Plasmonics: Metallic Nanostructures and Their Optical Properties VII, 73940A (2 September 2009); doi: 10.1117/12.829750
Show Author Affiliations
Mark R. Dennis, Univ. of Bristol (United Kingdom)
Jari Lindberg, Univ. of Bristol (United Kingdom)

Published in SPIE Proceedings Vol. 7394:
Plasmonics: Metallic Nanostructures and Their Optical Properties VII
Mark I. Stockman, Editor(s)

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