Dissipative soliton interaction in Kerr resonators with high-order dispersion

We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized Lugiato-Lefever equation with fourth-order dispersion. We use an asymptotic approach to derive interaction equations governing the slow time evolution of the coordinates of two interacting dissipative solitons. We show that Cherenkov radiation induced by positive fourth-order dispersion leads to a strong increase of the interaction force between the solitons. As a consequence, a large number of equidistant soliton bound states in the phase space of the interaction equations can be stabilized. We show that the presence of even small spectral filtering not only dampens the Cherenkov radiation at the soliton tails and reduces the interaction strength, but can also affect the bound state stability.

Automated summary

This study investigates the interaction of dissipative solitons in an optical resonator with a photonic crystal fiber, using a generalized Lugiato-Lefever equation with fourth-order dispersion. The results show that positive fourth-order dispersion leads to increased interaction force between solitons and stabilizes multiple equidistant soliton bound states in the phase space. Additionally, spectral filtering, even at a small level, can reduce Cherenkov radiation at the soliton tails, weaken the interaction strength, and impact the stability of bound states.