Modeling of self-injection locking bandwidth of a whispering gallery mode microresonator

Whispering gallery mode microresonators are promising in applications where narrow linewidth laser and optical frequency comb are required. We analyze the influence of the parameters of a microresonator on the locking bandwidth of the self-injection locking effect. Both single-mode and multimode cases are discussed. In the single-mode state, we discuss the effects of the spatial gap between the coupler and the microresonator on the locking bandwidth. The variation of the locking bandwidth with respect to the gap is simulated under various parameters of both the microcavity and laser diode. The results show that the maximum locking bandwidth does not always occur at the critical coupling point. Consequently, the method of determining the intrinsic quality factor of the microresonator by measuring locking bandwidth can result in an underestimation of the value. In the case of the multimode state, the locking bandwidth may be affected by adjacent modes. Therefore, the multimode locking bandwidth is studied further. The result shows that when the initial phase case is zero, both the forward and backward scanning locking bandwidth will not exceed the frequency interval between the adjacent modes because of the overlapping of the locking ranges of the adjacent modes.