Nonlinear dynamics of Kerr optical microresonators with spatially fluctuating loss

Abstract

Dissipative soliton crystals (the so-called soliton combs) form in Kerr microresonators as a result of the competition between the group-velocity dispersion and the Kerr nonlinearity on one hand, and the balance of cavity loss by an external pump on the other hand. In some physical contexts, the loss can fluctuate within the microresonator cavity, inducing a saturable-absorption process which impacts the dynamics of the optical field. In this study, dissipative soliton crystals are investigated in a Kerr optical microresonator with spatially fluctuating loss. The underlying mathematical model consists of a modified Lugiato–Lefever equation with a space-dependent loss, coupled to a rate equation for the fluctuating loss. Adopting an ansatz that describes the optical-field envelope as a complex function of real amplitude and real phase with a characteristic modulation frequency, the mathematical model is reduced to a set of first-order nonlinear ordinary differential equations which are solved numerically. Simulations suggest that when the homogeneous cavity loss is small enough, the impact of loss fluctuation on the soliton-comb profile is rather moderate. The effect of loss fluctuations becomes noticeable when the homogeneous loss is sizable, with the recovery time of the induced saturable-absorption process being reasonably long to promote a slow saturable absorption. An analysis of the influence of the detuning on the amplitude and phase of the dissipative soliton crystal, as well as on the spatial variation of the loss for a fixed value of the characteristic frequency, is taken into consideration in the study.