Abstract Oscillations of a wavefield that are locally higher than the bandlimit of the field are known as superoscillations. Superoscillations have to date been studied primarily in coherent wavefields; here we look at superoscillations that appear in the phase of the correlation function in partially coherent Talbot carpets. Utilizing the Talbot effect, it is shown that superoscillations can be propagated into the far field, even under a decrease in spatial coherence. It is also shown that this decrease in spatial coherence can strengthen the superoscillatory behavior at the primary and secondary Talbot images.
We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam's initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.
We analyze and experimentally demonstrate a new (temporal) Talbot effect, where a pulsed phase grating is applied to a cloud of cold atoms (Bose-Einstein condensate). In contrast to the usual (spatial) Talbot effect, our atoms gain kinetic energy when diffracted by the pulsed grating. The energy gain and the matter-wave-dispersion relation result in an exact (no paraxial approximation) Talbot effect where the initial wave front is reconstructed at multiples of a ``Talbot time''
TT. We demonstrate the Talbot effect by applying a second pulsed phase grating after a variable delay. When this second grating is applied at even (odd) multiples of
TT/2, it doubles (cancels) the effect of the first pulsed grating.