Beam Dynamics inPTSymmetric Optical Lattices

The possibility of parity-time ($\mathcal{P}\mathcal{T}$) symmetric periodic potentials is investigated within the context of optics. Beam dynamics in this new type of optical structures is examined in detail for both one- and two-dimensional lattice geometries. It is shown that $\mathcal{P}\mathcal{T}$ periodic structures can exhibit unique characteristics stemming from the nonorthogonality of the associated Floquet-Bloch modes. Some of these features include double refraction, power oscillations, and eigenfunction unfolding as well as nonreciprocal diffraction patterns.