Stimulated Raman Scattering Imposes Fundamental Limits to the Duration and Bandwidth of Temporal Cavity Solitons

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 redshift 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 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.

Figure 1

(a) Peak amplitude of the intracavity field, $|E{|}_{\max }$, as a function of cavity detuning $\mathrm{\Delta }$ for $X=130$. Black curves represent cw solutions, while red and blue curves show CS solutions with and without SRS, respectively. The dashed curves correspond to unstable solutions. (b) Temporal and (c) spectral CS profiles for $\mathrm{\Delta }=62$. The colors match those used in (a). The corresponding solutions are marked with crosses in (a). The green and red shaded areas in (a) indicate regions of monostability and bistability of the cw solutions, respectively.

Figure 2

(a) Cavity detunings ${\mathrm{\Delta }}_{\mathrm{H}2}$ and ${\mathrm{\Delta }}_{\max }$, where the CS solution loses its stability (blue markers) and ceases to exist (red markers), respectively, as a function of driving power $X$ and for a variety of ${\tau }_{\mathrm{s}}$. The squares correspond to simulated points, while the solid curves are a guide to the eye. Black curves indicate limits of CS existence in the absence of SRS. (b) Saturated limit detuning ${\mathrm{\Delta }}_{\mathrm{H}2\mathrm{S}}=\underset{X\gg 1}{\lim }{\mathrm{\Delta }}_{\mathrm{H}2}$ as a function of the normalization time scale ${\tau }_{\mathrm{s}}$. Dashed red curve shows a linear fit. The three values of ${\tau }_{\mathrm{s}}$ realized in our experiments are highlighted at the bottom of (b).

Figure 3

(a) Intracavity dynamics as the detuning is scanned from 0 to 110 (top $x$ axis) during about 7000 round trips (bottom $x$ axis) with $X\approx 130$. The cavity is 13 m long and has a normalization time scale ${\tau }_{\mathrm{S}1}=1.9\mathrm{ps}$. Dashed black and white vertical lines indicate zero detuning and the limit detuning ${\mathrm{\Delta }}_{\lim }$ at which CSs cease to exist, respectively. (b) Limit detuning ${\mathrm{\Delta }}_{\lim }$ at which CSs cease to exist as a function of driving power $X$ and for three different normalization time scales ${\tau }_{\mathrm{s}}$. The circle markers are extracted from experiments, while the dashed curves correspond to results from numerical simulations of the LLE. The solid black line shows the theoretical CS existence limit in the absence of SRS, i.e., ${\mathrm{\Delta }}_{\max }={\pi }^{2}X/8$.