Bloch Oscillations in Complex Crystals withPTSymmetry

Abstract

Bloch oscillations in complex lattices with $\mathcal{P}\mathcal{T}$ symmetry are theoretically investigated with specific reference to optical Bloch oscillations in photonic lattices with gain or loss regions. Novel dynamical phenomena with no counterpart in ordinary lattices, such as nonreciprocal Bloch oscillations related to violation of the Friedel’s law of Bragg scattering in complex potentials, are highlighted.