Discrete Talbot effect in reciprocal and nonreciprocal dimer lattices

Abstract

We investigate the Talbot self-imaging in one-dimensional discrete dimer lattices, where the source of non-Hermiticity derives not from gain and loss but from anisotropic couplings. The conditions that guarantee the existence of the Talbot effect in discrete dimer lattices are defined. It is shown that the Talbot self-imaging effect is possible in both reciprocal (Hermitian) and nonreciprocal (non-Hermitian) dimer lattices when the period of the input pattern is chosen as a finite set of periodicities ( N = 1 , 2, 3, 4 for reciprocal lattice and N = 1 , 2 for nonreciprocal lattice). Unlike the Talbot effect in reciprocal lattices, where the self-imaging with conserved total energy of the central part of the model occurs during propagation, here the total energy of the field exhibits oscillatory behavior in the Talbot process for nonreciprocal dimer lattices. The Talbot distance can be controlled by adjusting the lattice coupling and anisotropic coupling coefficients. Our results can be extended to other photonic superlattices with an arbitrary number of sites in each unit cell.