Superoscillations in Finite-Energy Airy Beams

Abstract

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Superoscillations naturally arise in optical fields with dense packing of nodal points of amplitude. Airy wave packets are highly oscillatory and rich of phase singularities. We study to the best of our knowledge, for the first time, the superoscillatory behavior in a band-limited Airy beam whose spectrum is sharply truncated. Our results show that not as expected, the superoscillations occur outside of the Airy-like region, but in regions above a defining line where the beam stops being Airy-like. The degree of superoscillation can be very high there.

Keywords

• airy beam
• superoscillation
• propagation
• paraxial wave equation
• diffraction-free