$\mathcal{PT}$-symmetric optical lattices

$PT$ -symmetric optical lattices

Konstantinos G. Makris, Ramy El-Ganainy, Demetrios N. Christodoulides, and Z. H. Musslimani

Phys. Rev. A 81, 063807 – Published 4 June 2010

Abstract

The basic properties of Floquet-Bloch (FB) modes in parity-time ( $PT$ )-symmetric optical lattices are examined in detail. Due to the parity-time symmetry of such complex periodic potentials, the corresponding FB modes are skewed (nonorthogonal) and nonreciprocal. The conjugate pairs of these FB modes are obtained by reflecting both the spatial coordinate and the Bloch momentum number itself. The orthogonality conditions are analytically derived for a single cell, for both a finite and an infinite lattice. Some of the peculiarities associated with the diffraction dynamics in $PT$ lattices such as nonreciprocity, power oscillations, and phase dislocations, are also examined.