Temporal coupled-mode theory and topological charges for resonances in parity symmetric layered media with arbitrary loss and gain

The traditional temporal coupled-mode theory (TCMT) is used to explain the resonances in the resonators where material loss or gain is zero or small, such that the energy of the resonance is exactly or approximately conserved. However, with the development of non-Hermitian optical theories and experiments, a more widely applicable TCMT is required. In this work, we derive the TCMT suitable for parity symmetric layered structures with arbitrary degrees of non-Hermiticity, and obtain specific expressions for the transmissions and reflections of the original and its time-reversed cavities. The simulated results calculated by the scattering matrix method agree well with our theoretical predictions, proving the validity of our theory. Moreover, we find that in the space spanned by frequency and decay rate, there are poles where transmission and reflection tend to infinity simultaneously and zeros where reflection is zero in real frequency, their positions and topological properties can all be clearly explained by our theory. We believe that our research provides an important theoretical foundation for the applications of non-Hermitian media such as Fabry–Pérot cavity with arbitrary loss and gain.