Level attraction andPTsymmetry in indirectly coupled microresonators

Abstract

Benefiting from the tunability of their phase delay and gain, we show the possibility of realizing level attraction, parity-time ($\mathcal{PT}$)-, and anti-$\mathcal{PT}$-symmetric photonic structures with indirectly coupled active and passive microresonators mediated by drop-filter waveguides. We find that level attraction originates from two mechanisms, i.e., exceptional point and resonance, and it may emerge not only for dissipative coupling but also coherent coupling and hybrid coupling after considering the gain and loss of microresonators, which confirms the universality of level attraction in the coupled photonic system. On the other hand, the transition from $\mathcal{PT}$ to anti-$\mathcal{PT}$ symmetry or vice versa may be realizable by tuning their phase delay and gain; thus the indirectly coupled microresonators may provide an excellent platform for exhibiting the unique features of $\mathcal{PT}$ and anti-$\mathcal{PT}$ symmetry. Furthermore, we also reveal the intrinsic relationship of the line shape and phase behavior of the reflection spectrum with $\mathcal{PT}$ symmetry, anti-$\mathcal{PT}$ symmetry, and level attraction.