Non-Hermitian electromagnetic double-near-zero index medium in a two-dimensional photonic crystal

We report a general method to design a unique type of a non-Hermitian electromagnetic double-near-zero index medium by a two-dimensional photonic crystal. The synergy of a nonsymmorphic glide symmetry of the lattice, a period-doubling of the unit cell, and the non-Hermitian perturbation of the photonic crystal induces a phase transition in the eigenvalue spectrum. Near the Brillouin zone center, such a photonic crystal is effectively an anisotropic double-near-zero index medium. Along the direction of interest, the real parts of its effective permittivity and permeability are simultaneously near zero, while the imaginary parts of the effective parameters are nonzero values with opposite signs, leading to a real and positive effective refractive index. This medium enables many fascinating applications such as an angular sensor, a coherent perfect absorber, and a laser.