Defect states and exceptional point splitting in the band gaps of one-dimensional parity-time lattices

We investigated defect states in band gaps of one-dimensional photonic lattices with delicate modulations of gain and loss that respect parity-time-symmetry (PT-symmetry), viz. n(z) = n*(-z). For the sake of generality, we employ not only periodic structures but also quasiperiodic structures, e.g. Fibonacci sequences, to construct aperiodic PT lattices. Differed from lossless systems for which the defect state is related to only one exceptional point (EP) of the S-matrix, we observed the splitting of one EP into a pair after the introduction of judiciously designed gain and loss in those PT systems, where the defect state enters a non-threshold broken symmetry phase bounded by the EP pair. Some interesting properties associated with defect states and EP splitting are demonstrated, such as enhanced spectral localization, double optical phase abrupt change, and wavelength sensitive reversion of unidirectional transparency.