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Fractional nonparaxial accelerating Talbot effect.

Yiqi Zhang, Hua Zhong, Milivoj R Belić

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    |July 16, 2016
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    We demonstrate the fractional Talbot effect for nonparaxial accelerating beams. This phenomenon arises from interfering solutions that accelerate along semicircular paths, forming Talbot images at specific angles.

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    Area of Science:

    • Optics and Photonics
    • Wave Phenomena
    • Beam Propagation

    Background:

    • The Talbot effect describes self-imaging of periodic structures under coherent illumination.
    • Nonparaxial beams exhibit complex propagation dynamics beyond the paraxial approximation.
    • Accelerating beams offer unique trajectory control in wave propagation.

    Purpose of the Study:

    • To theoretically and numerically demonstrate the fractional Talbot effect for nonparaxial accelerating beams.
    • To explore the origin of this effect from the interference of specific Helmholtz equation solutions.
    • To investigate the duality of single nonparaxial accelerating beams in relation to the Talbot effect.

    Main Methods:

    • Theoretical analysis based on the interference of nonparaxial accelerating solutions of the Helmholtz equation.
    • Numerical simulations to validate the theoretical predictions.
    • Superposition of solutions accelerating along concentric semicircular trajectories with varying radii.

    Main Results:

    • Demonstration of the fractional Talbot effect for nonparaxial accelerating beams.
    • Identification of Talbot images forming at specific central angles (Talbot angles).
    • Observation of beam duality, where a single beam can be viewed as a Talbot effect with infinite or zero Talbot angle.

    Conclusions:

    • The study enhances the understanding of nonparaxial accelerating beams and their associated Talbot effects.
    • The findings provide a new perspective on beam self-imaging phenomena.
    • The work offers insights into controlling and manipulating light fields with complex trajectories.