| Abstract: |
| Fluctuations of nonlinear coherent structures arise not only from direct stochastic forcing, but also from deterministic transfer among coupled collective coordinates. In this talk, I present a framework for resolving such noise pathways in a stable temporal cavity soliton governed by the generalized Lugiato-Lefever equation with Raman response. By projecting both the field dynamics and the vacuum noise onto four soliton coordinates: amplitude, frequency shift, temporal position, and global phase, we derive a reduced stochastic model whose linearization yields an analytic power-spectral-density matrix. This formulation separates direct noise injection from inter-coordinate transfer and thereby exposes the internal routing of fluctuations. It captures frequency-to-timing conversion associated with Gordon-Haus-type jitter, identifies amplitude-to-phase coupling as a major source of phase noise, and reveals Raman-enabled cascaded transfer pathways. It also explains the low-detuning enhancement of intensity and phase noise through an underdamped amplitude-phase relaxation mode that emerges before the onset of breathing. Comparisons with stochastic simulations of both the reduced model and the full equation show good agreement across most of the stable stationary regime. |
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