Dynamics of soliton microcombs in hybrid-nonlinear microresonators governed by higher-order dispersion and Raman effect

Integrated hybrid χ(2)-χ(3) microresonators provide a promising platform for realizing low-threshold broadband microcombs and on-chip self-referencing. However, under broadband operating conditions, higher-order dispersion, Raman self-frequency shift, and temporal walk-off significantly perturb soliton microcomb dynamics, and a systematic understanding of their coupled interaction mechanisms remains lacking. In this paper, we establish a generalized coupled Lugiato–Lefever equation incorporating higher-order dispersion, Raman response, and temporal walk-off. By employing the split-step Fourier method for numerical simulations, we systematically reveal how these higher-order effects modulate soliton spectral broadening, drift direction, and stability regimes. The results demonstrate that odd-order dispersion breaks spatiotemporal symmetry and dominates unidirectional soliton drift; the synergistic modulation of third- and fifth-order dispersion can suppress or even reverse this drift, creating a near-zero-drift operating regime. Even-order dispersion, conversely, restricts the spectral bandwidth, with sixth-order dispersion being more favorable than fourth-order for maintaining broadband operation. The Raman effect induces a shift in the spectral center wavelength and enables asymmetric control of flat-top combs, whereas temporal walk-off exerts only a weak modulatory effect. This work elucidates the physical mechanisms by which the coupling of higher-order dispersion and the Raman effect reshapes soliton dynamics in broadband hybrid microcavities. It resolves the critical limitation of traditional second-order approximation models in describing broadband asymmetric evolution, thereby providing a clear theoretical foundation and precise parameter guidelines for designing near-zero-drift, broadband-stable on-chip microcombs.