Non-Hermitian physics of evanescent waves around band singularities

Band singularities in the momentum space, such as Weyl points, play an important role in topological physics. Their nontrivial topological properties provide a platform to investigate various intriguing phenomena associated with wave propagation inside or at the surfaces of the medium. Here we show that the evanescent waves near the band singularities can host a variety of non-Hermitian behaviors, in the absence of material gain or loss. Different from commonly investigated parity-time (𝑃𝑇)–symmetric systems, one can manipulate the 𝑃𝑇-symmetric phase of the evanescent waves via tuning the temporal growing/decaying behavior of the excitation rather than the gain/loss or coupling. Interestingly, the distribution of non-Hermitian Berry curvature for the evanescent waves around a Weyl point can be confined inside an exceptional cone in the momentum space, which leads to the transition of the winding of the reflection phase around the Weyl point. Our findings provide a different way of manipulating the 𝑃𝑇-symmetric photonic system and insight into the topological behavior of band singularities.