Generalized temporal coupled-mode theory for perturbatively PT -symmetric optical resonators and its use to study resonance in a photonic heterostructure

Abstract

We have proposed the generalized temporal coupled-mode theory for a perturbatively parity-time ($\mathcal{PT}$) -symmetric optical resonator, and by utilizing this theory we have expounded successfully a resonance in a perturbatively $\mathcal{PT}$-symmetric photonic heterostructure. The introduction of perturbation changes the variation ranges of the amplitudes of all scattering coefficients. In particular, all amplitudes of scattering coefficients reach infinity simultaneously at the point of critical match. More than that, in the frequency-perturbation space, there is one vortex center for every scattering coefficient at the singular scattering point and one vortex center for each reflection at its minimum. The corresponding quantized topological charges, defined by the winding numbers of scattering coefficients, can also be predicted by our theory successfully. This work is a significant guide to study the resonance in a $\mathcal{PT}$-symmetric optical resonator of the real world.