Controlling the motion of localized structures in Kerr cavities with Raman and higher-order dispersion

We consider a microstructured, all-fiber optical resonator featuring higher-order dispersion and stimulated Raman scattering. We show that the combined influence of these effects enables effective control of the motion of both dark and bright localized structures, commonly known as dissipative solitons, including multi-peak and multi-dip bound states. Our focus is on the nascent optical bistability regime, where the dynamics is described by a Swift-Hohenberg equation with the stimulated Raman scattering. We first perform a linear stability analysis, which shows that the modulation instability region is greatly reduced in the presence of stimulated Raman scattering. Second, we show that a balance between the third-order dispersion and the Raman effect can minimize the temporal symmetry breaking induced by each effect individually, allowing the velocity of both periodic and localized structures to be reduced to nearly zero. Consequently, the frequency comb generated from these quasi-stationary structures exhibits a perfectly symmetric spectrum.