Natural superoscillations in monochromatic waves in D dimensions

For monochromatic waves satisfying the Helmholtz equation with wavenumber k0, superoscillations correspond to local wavenumbers (magnitude of phase gradient) greater than k0. Large values of local wavenumber are associated with phase singularities. For isotropic random waves (superpositions of many...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 42; no. 2; pp. 022003 - 022003 (8)
Main Authors Berry, M V, Dennis, M R
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 16.01.2009
IOP
Subjects
Exact sciences and technology
Physics
Probability
Helmholtz equations
Singularity
Superoscillation
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Summary:For monochromatic waves satisfying the Helmholtz equation with wavenumber k0, superoscillations correspond to local wavenumbers (magnitude of phase gradient) greater than k0. Large values of local wavenumber are associated with phase singularities. For isotropic random waves (superpositions of many nonevanescent waves) in D dimensions, we show that the probability that a point in the field is superoscillatory increases from 0.293 to 0.394 as D increases from 1 to infinity. The peculiar case D = 1 is examined in detail.
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ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/2/022003