The Talbot effect is among the most fundamental wave propagation effect universal across the frequency spectrum and has been used extensively in both spatial and temporal domain for wide variety of applications. In this work, a generalized spatial Talbot effect is presented based on all-dielectric Huygens' metasurface, which when combined with the conventional Fractional Talbot effect, enables the scaling of aperture periodicities by any arbitrary real number. This is achieved by allowing and engineering the phase discontinuity distributions in space on the aperture using phase engineered all-dielectric reflectionless metasurfaces, in conjunction with free-space propagation. Specific implementations using Huygens' metasurfaces are proposed and their operation to achieve such non-integer scalings of the input aperture period is demonstrated using numerical results based on Fourier propagation method.

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Keywords Fourier optics and signal processing, Metasurfaces, Phase-only filters, Phase-space in wave optics, Talbot and self-imaging effects
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Journal Optics Communications
Gupta, S. (2017). Generalized spatial Talbot effect based on all-dielectric metasurfaces. Optics Communications, 384, 25–29. doi:10.1016/j.optcom.2016.10.011