Exceptional-point restoration and fast-light edge states in photonic crystal waveguides with glide and time-reversal symmetries

Exceptional points (EPs) in propagation states induce intriguing properties as the group velocities. However, superluminal propagation near EPs is challenging due to the smoothing caused by symmetry breaking. In this study, we propose a photonic crystal waveguide design with glide and time-reversal symmetry and derive an effective Hamiltonian to realize fast-light edge states. We adopt a systematic method to generate EPs in edge states by introducing non-Hermitian perturbations to Dirac points guaranteed by glide symmetry, which ensures that EP modes are free from out-of-plane radiation losses. We identify the conditions for exact EP restoration and provide an analytical solution to offset the EP smoothing due to symmetry breaking, which significantly reduces the group velocity contrast. A glide symmetry of the photonic crystal waveguide allows us to derive the effective Hamiltonian in a simple form, and the EPs can be restored by adjusting the real part of the permittivity. Furthermore, we design a feasible photonic crystal slab waveguide incorporating graphene as the absorbing material, and numerically demonstrate a group velocity reaching ${v}_{g}=3.3c$ near the EP, which is up to 25 times that of the original structure. The proposed setup based on non-Hermitian photonics paves the way for the realization of superluminal devices in nanophotonics. In addition, the method for restoring EPs also addresses challenges in the phenomena arising from non-Hermitian properties.