Transform-limited dissipative Kerr solitons with an ultraflat spectrum in a Fabry-Pérot microresonator with a spectral filter

The interplay between the dispersion and spectral filtering effect in Kerr-ring resonators allows the formation of dispersion-less Kerr solitons, an alternative class of Kerr solitons featuring with ultrabroad spectrum and zero chirp. In contrast to a ring resonator, the nonlinear interactions between the counterpropagating light waves in a F-P resonator introduce an additional phase shift, which modifies the system-effective detuning, hence impacting the soliton existence range and its formation dynamics. In this article, we investigate numerically the formation of dissipative Kerr solitons (DKSs) in a 10-mm-long Fabry-P\'erot (FP) microresonator with a super-Gaussian spectral filter in the normal dispersion regime. Simulation results found that the spectral loss provided by the filter plays a significant role in the formation of DKS. Without the filter, the FP microresonator yields platicons featuring a flat-top pulse with oscillating tails on both sides. For a super-Gaussian spectral filter with an order of $n\ensuremath{\rightarrow}\ensuremath{\infty}$, the resonator approaches the transform-limited DKS regime with ultraflat spectrum. An intermediate state of chaotic states of multipulses was observed in the transition from the platicon to the transform-limited DKSs when using the detuning scan technology, the dependence of the appearance of the chaotic state on the spectral filtering effect. Finally, the energy-width scaling behavior and the enhancement of the performances of the transform-limited DKS are studied. Simulation results deepen our understanding of nonlinear dynamics of transform-limited DKS combs and point out a way for achieving a high-energy DKS comb with ultraflat spectrum in Kerr resonators.