Natural superoscillation of random functions in one and more dimensions

Mark R. Dennis; Jari Lindberg

doi:10.1117/12.829750

2 September 2009 Natural superoscillation of random functions in one and more dimensions

Mark R. Dennis, Jari Lindberg

Proceedings Volume 7394, Plasmonics: Metallic Nanostructures and Their Optical Properties VII; 73940A (2009) https://doi.org/10.1117/12.829750
Event: SPIE NanoScience + Engineering, 2009, San Diego, California, United States

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.

Citation Download Citation

Mark R. Dennis and Jari Lindberg "Natural superoscillation of random functions in one and more dimensions", Proc. SPIE 7394, Plasmonics: Metallic Nanostructures and Their Optical Properties VII, 73940A (2 September 2009); https://doi.org/10.1117/12.829750

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