Talbot self-imaging inPT-symmetric complex crystals

Abstract

The Talbot effect, i.e., the self-imaging property of a periodic wave in near-field diffraction, is a remarkable interference phenomenon in paraxial systems with continuous translational invariance. In crystals, i.e., systems with discrete translational invariance, self-imaging has been regarded so far as a rare effect, restricted to special sets of initial field distributions. Here it is shown that in a class of gapless $\mathcal{PT}$-symmetric complex crystals at the symmetry-breaking threshold Talbot revivals can arise for almost any initial periodic wave distribution which is commensurate with the lattice period. A possible experimental realization of commensurate Talbot self-imaging for light pulses in complex ``temporal'' crystals, realized in an optical dispersive fiber loop with amplitude and phase modulators, is briefly discussed.