Natural superoscillations in monochromatic waves in D dimensions

MV Berry, MR Dennis

Research output: Contribution to journalArticle (Academic Journal)peer-review

101 Citations (Scopus)


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.
Translated title of the contributionNatural superoscillations in monochromatic waves in D dimension
Original languageEnglish
Article number022003
Number of pages8
JournalJournal of Physics A: Mathematical and Theoretical
Issue number2
Publication statusPublished - 16 Jan 2009


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