Unified approach to cascaded stimulated Brillouin scattering and frequency-comb generation

We present a unified approach to cascaded stimulated Brillouin scattering and frequency-comb generation in which the multitude of interacting pump, Stokes, and anti-Stokes optical fields is described by a single forward wave and a single backward wave at a single carrier frequency. The envelopes of these two waves are modulated through coupling to a single acoustic oscillation and through four-wave mixing. Starting from a single pump field, we observe the emergence of a comb of frequencies as the intensity is increased. The set of three differential equations derived here is sufficient to describe the generation of any number of Brillouin sidebands in oscillator systems that would have required hundreds of coupled equations in the standard approach. We test this approach on some published experiments and find excellent agreement with the results.

Figure 1

(a,b) Spectra and temporal output for a 5-W cw pump in a 10-m silica fiber without facet reflections. (c,d) Spectra and temporal output for a 150-W cw pump in a 10-m silica fiber without facet reflections. Note the emergence of a second Stokes line. (e) Transmitted and reflected spectra from a fiber with a Fresnel reflecting input facet and a 5-W cw pump. Many Stokes and anti-Stokes lines are now visible due to four-wave mixing. (f) Reflected and transmitted spectra for fiber with Fresnel reflections but without four-wave mixing. Only pump, first-order, and second-order Stokes lines are seen.

Figure 2

(a) Output spectrum of a silica fiber ring cavity with feedback of $99\%$ of the backward Stokes. The odd-order Stokes and anti-Stokes lines are spaced by twice the Brillouin frequency. (b) Temporal output showing erratic pulsations.

Figure 3

Temporal output of 38-cm-long chalcogenide fiber Fabry-Perot cavity for a 500-ns pulse input and two different values of phase shift. (a) $\mathrm{\Delta }{\varphi }_0=1.8\pi$; (b) $\mathrm{\Delta }{\varphi }_0=0.62\pi$.