Recovering parity-time symmetry in highly dispersive coupled optical waveguides

Coupled photonic systems satisfying parity-time symmetry (PTS) provide exibility to engineer the ow of light including non-reciprocal propagation, perfect laser-absorbers, and ultra-fast switching. Achieving the required index pro le for an optical system with ideal PTS, i.e. n(x) =n(-x)*, has proven to be difficult due to the challenge of controlling gain, loss and material dispersion simultaneously. Consequently, most research has focused on dilute or low gain optical systems where material dispersion is minimal. In this paper, we study a model system of coupled inorganic semiconductor waveguides with potentially high gain (>1,500 cm-1) and dispersion. Our analysis makes use of coupled mode theory's parameters to quantify smooth transitions between PTS phases under imperfect conditions. We find that the detrimental influence of gain-induced dispersion is counteracted and the key features of parity-time symmetric optical systems are recovered by working with non-identical waveguides and bias pumping of the optical waveguides. Our coupled mode theory results show excellent agreement with numerical solutions, proving the robustness of coupled mode theory in describing various degrees of imperfection in systems with PTS