Talbot self-imaging in $\mathcal{PT}$-symmetric complex crystals

TL;DR

This paper demonstrates that in certain gapless $ ext{PT}$-symmetric complex crystals, near-field self-imaging (Talbot effect) can occur for nearly any initial periodic wave, expanding the understanding of Talbot revivals beyond traditional systems.

Contribution

It reveals that Talbot self-imaging can occur in a broad class of $ ext{PT}$-symmetric complex crystals at the symmetry breaking threshold, for almost any initial periodic wave.

Findings

Talbot revivals occur in gapless $ ext{PT}$-symmetric complex crystals at threshold.

Self-imaging is possible for nearly any initial periodic wave distribution.

Potential experimental realization in optical fiber loops is discussed.

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 seldom 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.