Abstract
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.
Highlights
The phenomenon that a band-limited signal can oscillate faster, locally somewhere in its domain, than its largest frequency is called superoscillation
Makris et al [6] constructed diffraction-less beams that can transport subwavelength features into the far field. These studies stimulate us to study the superoscillations embedded in optical Airy beams
To facilitate our current task, after briefly reviewing the theory of and the criterion for superoscillation in Section 2, we introduce in Section 3 the method of sharply truncating the Airy beam spectrum; in Section 4, we give the method to compute the local wave number through its relation to optical currents, and study the superoscillatory area in both a longisection and a transverse section; we give a conclusion of the study
Summary
The phenomenon that a band-limited signal can oscillate faster, locally somewhere in its domain, than its largest frequency is called superoscillation. The desired large local frequency, or local wave number in optical case, naturally occurs near phase singularities, where it diverges This connection leads to a recent method of achieving superoscillation using optical vortexed waves [5]. Makris et al [6] constructed diffraction-less beams that can transport subwavelength features into the far field These studies stimulate us to study the superoscillations embedded in optical Airy beams. To facilitate our current task, after briefly reviewing the theory of and the criterion for superoscillation, we introduce in Section 3 the method of sharply truncating the Airy beam spectrum; in Section 4, we give the method to compute the local wave number through its relation to optical currents, and study the superoscillatory area in both a longisection and a transverse section; we give a conclusion of the study To facilitate our current task, after briefly reviewing the theory of and the criterion for superoscillation in Section 2, we introduce in Section 3 the method of sharply truncating the Airy beam spectrum; in Section 4, we give the method to compute the local wave number through its relation to optical currents, and study the superoscillatory area in both a longisection and a transverse section; we give a conclusion of the study
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