Locally Parity-Time Symmetric and globally Parity-Symmetric systems

We introduce a new class of systems holding Parity Time (PT)-symmetry locally whereas being globally Psymmetric. The potential is globally symmetric, U=U(|r|), and fulfills PT-symmetry with respect to periodically distributed points r0: U(|r0+r|)=U*(|r0-r|) being r0∫ 0. We show that such systems hold novel properties arising from the merging of the two different symmetries, leading to a strong field localization and enhancement at the double-symmetry center, r=0, when the coupling of outward to inward propagating waves is favored. We explore such general potentials in 1D and 2D, which could have actual realizations in different fields, in particular in optics, combining gain/loss and index modulations in nanophotonic structures. As a direct application, we show how to render a broad aperture VCSEL into a bright and narrow beam source.