Design of zero index metamaterials with PT symmetry using epsilon-near-zero media with defects

Inspired by the design of matched zero-index metamaterials (ZIMs) using defects in epsilon-near-zero (ENZ) media, we demonstrate in this letter that ZIMs with parity-time (PT) symmetry in a waveguide system can be achieved by introducing defects with loss/gain inside ENZ media. Such results are well verified from the phenomenon of unidirectional transparency, corresponding to the exceptional points in PT symmetric systems. Moreover, by changing the geometry configuration of ENZ, the effective loss/gain in the structure composed of ENZ and defects can be amplified immensely by virtue of the resonances of defects. Therefore, our work also provides a blueprint for obtaining amplified loss/gain in PT symmetric systems.