WITHDRAWN: The periodic evolution of the resonant mode in a lossy microfiber coil resonator with three turns

Abstract

The periodic evolution of the resonant mode in a lossy microfiber coil resonator with three turns is unraveled, and two types of loss conditions are assumed to investigate the characteristics of resonant mode with respect to the coupling state by means of numerical modeling. Under a given loss condition, the resonant mode exhibits periodic evolution between normal resonance, white-light cavity effect and resonance mode splitting as the change of the phase shift and coupling state. When the coupling state exceeds a certain threshold under a specific loss coefficient, the microfiber coil resonator predominantly exhibits normal resonance with characteristics akin to a single-ring resonator. Once the coupling state decreases to this threshold and matches the loss, white-light cavity effect will be activated. Moreover, as the coupling state falls below this threshold, the degeneracy of the resonance mode is raised and the resonant phase undergoes a bifurcation. The excitation conditions for each resonant mode have been derived, and the critical coupling conditions exist for both normal resonance and mode splitting in the case of relatively small losses. It’s found that there exists a threshold loss at which the critical coupling states of normal resonance and mode splitting coincide with the condition of white-light cavity effect. The characteristics of each mode have also been discussed.