Nonlinear-Fourier-Transform-Based Dynamic Analyses on the Multiple Cavity Solitons in Kerr Microresonators

The Kerr microresonators have aroused widespread interests for their ultrahigh integration, compatible fabrication and ultralow energy consumption. Similar to the traditional mode-locked fiber lasers, the microresontors can sustain the generation of dissipative solitons called cavity solitons relying on the double balance of gain and loss as well as nonlinearity and dispersion. The state of multiple solitons is common in the microresonator with anomalous dispersion. In particular, an ideal state named as soliton crystals is obtained when the multiple solitons have a equidistant arrangement. And recent experiments have successfullly observed soliton crystals in the Kerr microresonators. To intuitively reveal the formation and evolution dynamics of the multiple solitons and get insight into the underlying physical mechanisms of soliton crystals, we applied the nonlinear Fourier transform to project these states into nonlinear discrete spectrum. The discrete spectra of single soliton with different modulated background waves have been displayed, which can help distinguish different optical components. Then, the nonlinear spectrum evolution of normal multiple solitons state shows the typical nonlinear states of the intracavity field. And the equidistant solitons have the effects of power enhancement, whose spectral intensity is several times that of a single soliton state. Comparing with the discrete spectrum of the equidistant solitons, the solitons inside the soliton crystals interact with each other by the modulated background. Our results suggest that the nonlinear Fourier transform is a powerful technique to characterize soliton dynamics in the Kerr microresonator, which provides a new perspective to understand the interactions of cavity solitons.