Unique band coalescence and exceptional points from two-dimensional photonic crystal waveguide

The exceptional points (EPs) in photonic crystals (PCs) with PT-symmetry involve the band coalescence at which the real bands are transformed into conjugate complex bands. The PC EPs are usually in the extended bands and cannot be excited in a guided form. To achieve some guided EPs, we design a two-dimensional photonic crystal waveguide with localized PT-symmetry. The waveguide edges are made of balanced gain and loss materials. With the increasing of material gain or loss coefficient, the coupled mode bands clearly undergo dynamical evolution. An interesting band attraction and coalescence behavior occurs, which leads to the formation of the first-order EP and the second-order EP. The second-order EP can be locally excited with multiple field distributions which is dependent on the line source position. In contrast to the other modes whose frequencies clearly change with material parameter, the EPs in this structure have unique frequency stability against the change of material parameters.