  Temporal cavity solitons (CS) are optical pulses that can persist in passive
resonators, and they play a key role in the generation of coherent
microresonator frequency combs. In resonators made of amorphous materials, such
as fused silica, they can exhibit a spectral red-shift due to stimulated Raman
scattering. Here we show that this Raman-induced self-frequency-shift imposes a
fundamental limit on the duration and bandwidth of temporal CSs. Specifically,
we theoretically predict that stimulated Raman scattering introduces a
previously unidentified Hopf bifurcation that leads to destabilization of CSs
at large pump-cavity detunings, limiting the range of detunings over which they
can exist. We have confirmed our theoretical predictions by performing
extensive experiments in several different synchronously-driven fiber ring
resonators, obtaining results in excellent agreement with numerical
simulations. Our results could have significant implications for the future
design of Kerr frequency comb systems based on amorphous microresonators.
