The effect of the centric graphene layer on the exceptional points of parity-time symmetric photonic crystals

Exceptional points are investigated in two different one-dimensional photonic crystals. Both periodic structures are parity-time-symmetric (PT) and have a three-layer unit-cell containing gain and loss medium in which a dielectric film is sandwiched between them. However, the unit-cell of one structure is not parity-time-symmetric solely, and the system has low symmetry. The introduction of a graphene layer leads to the appearance of new exceptional points, which their properties are strongly dependent on the chemical potential of graphene. Coherent perfect absorbing lasing (CPAL) points, their spectra, and Goos-Hänchen (GH) shifts are considered with the gain–loss factor and also with the chemical potential of graphene. In the low symmetry structure, to obtain maximum values of spectra, the small gain–loss factor is needed. Results of GH calculations show that both structures depict GH shifts at two different angles with small shift values. By increasing the chemical potential of graphene, GH shifts get high values, where, the angle dependency of GH shifts in the symmetric structures is considerable.