Raman-induced dynamics of ultrafast microresonator solitons

Soliton microcombs are evolving towards octave-spanning for $f$-$2f$ self-referencing and expanding applications in spectroscopy and timekeeping. As spectra broaden and pulses shorten, the Raman-induced soliton self-frequency shift (SSFS) becomes a principal limitation: it reduces pump-to-comb conversion efficiency, constrains achievable span, and can, in extremes, preclude stationary operation. We develop a complementary theory of SSFS in microresonators that remains valid when the soliton duration $\tau_s$ is shorter than the Raman response timescale. The theory predicts a reduced dependence of the SSFS on $\tau_s$ which also expands the soliton existence range. Such predictions are validated by numerical simulations and by experiments on Si$_3$N$_4$ microresonators. Our results provide practical guidelines for engineering efficient and broadband soliton microcombs.