Parity-time symmetry from stacking purely dielectric and magnetic slabs

We show that parity-time symmetry in matching electric permittivity to magnetic permeability can be established by considering an effective parity operator involving both mirror symmetry and coupling between electric and magnetic fields. This approach extends the discussion of parity-time symmetry to the situation with more than one material potential. We show that the band structure of a one-dimensional photonic crystal with alternating purely dielectric and purely magnetic slabs can undergo a phase transition between propagation modes and evanescent modes when the balanced gain or loss parameter is varied. The cross matching between different material potentials also allows exceptional points of the constitutive matrix to appear in the long-wavelength limit where they can be used to construct ultrathin metamaterials with unidirectional reflection.