Stimulated Brillouin scattering (SBS)

Stimulated Brillouin scattering (SBS) is the nonlinear process in which a strong optical wave, its backscattered Stokes wave and an acoustic wave reinforce one another. The beat between pump and Stokes light compresses the glass through electrostriction, the resulting acoustic wave forms a moving Bragg grating, and that grating reflects more pump light into the Stokes wave. In standard single-mode fiber at 1550 nm the Stokes light travels backward, shifted down in frequency by about 11 GHz, within a gain band only about 20 MHz wide. For a narrow-linewidth continuous-wave laser the process sets in at a few milliwatts over a long span, which makes it the lowest-threshold nonlinear effect in silica fiber. The spontaneous process and its spectroscopy are covered under Brillouin scattering.

Frequency shift and gain

Because the acoustic grating must reflect the pump straight back, its period is half the optical wavelength in the glass, and the Stokes wave is Doppler-shifted by the grating's motion at the acoustic velocity $v_A$:

$$\nu_B = \frac{2 n v_A}{\lambda}$$

With $n = 1.45$ and $v_A = 5960$ m/s (the longitudinal sound velocity of fused silica), this gives 11.15 GHz at 1550 nm, 13.19 GHz at 1310 nm and 16.24 GHz at 1064 nm. The germanium-doped core of standard fiber has a slightly lower sound velocity, and measured shifts in such fiber are typically 10.8–10.9 GHz at 1550 nm.

The gain spectrum is Lorentzian, with a full width of roughly 20–30 MHz in silica fiber at 1550 nm, set by the damping of the acoustic phonon. A 20 MHz width corresponds to a phonon lifetime $1/(\pi\,\Delta\nu_B)$ of about 16 ns, so pulses shorter than roughly 10 ns see much less SBS than continuous light at the same peak power. The peak Brillouin gain coefficient of silica is about $g_B \approx 5 \times 10^{-11}$ m/W, several hundred times the Raman gain coefficient, which is why SBS reaches threshold far below stimulated Raman scattering for narrow-band light.

Threshold

Smith's criterion defines threshold as the input power at which the backward Stokes power grows to equal the transmitted pump:

$$P_\text{th} \approx 21\,\frac{A_\text{eff}}{g_B\,L_\text{eff}}$$ $$L_\text{eff} = \frac{1 - e^{-\alpha L}}{\alpha}$$

For standard fiber with an effective area of 80 µm², $g_B = 5 \times 10^{-11}$ m/W and an attenuation of 0.2 dB/km, a 20 km span has $L_\text{eff}$ = 13.1 km and a threshold of 2.6 mW. At 50 km $L_\text{eff}$ = 19.5 km, close to its limit of $1/\alpha$ = 21.7 km, and the threshold falls to 1.7 mW; a 1 km length needs about 34 mW. These values assume a pump linewidth well below the Brillouin bandwidth and matched polarization; with the random birefringence of ordinary fiber the effective gain is lower, by a factor of up to about 1.5.

How it is observed in the lab

The standard measurement launches a narrow-linewidth laser through an optical circulator into a fiber spool and records the backscattered power as the launch power is raised. Below threshold the reflected power is mostly Rayleigh backscatter and rises linearly; above it the reflection rises steeply and the transmitted power saturates. Heterodyning the backscattered light with the pump on a fast photodiode shows the Brillouin beat directly near 10.8 GHz, and an electrical spectrum analyzer resolves its 20 MHz width, which an optical spectrum analyzer with 0.02 nm (2.5 GHz) resolution cannot.

Where it matters

SBS limits the launch power of narrow-linewidth signals: analog CATV transmission, coherent links with a residual unmodulated carrier, and single-frequency fiber lasers and amplifiers, where it caps output at tens to hundreds of watts in large-mode-area fiber. The backward wave can also damage the seed laser. Common mitigations raise the threshold by spreading the pump power over more than the Brillouin bandwidth:

• phase dithering or broadening the source linewidth (spreading power evenly over 1 GHz raises the threshold by a factor $(1000 + 20)/20$ = 51, about 17 dB, for a 20 MHz gain width);
• a temperature or strain gradient along the fiber, or fibers with a nonuniform acoustic profile;
• shorter fiber, larger effective area, and acoustically antiguiding core designs.

SBS is also useful. Brillouin fiber lasers produce very narrow linewidths because the acoustic damping filters pump phase noise; and distributed fiber-optic sensors (BOTDA, BOTDR) map the shift along kilometres of fiber, since it changes by roughly 1 MHz/K and 0.05 MHz per microstrain in standard fiber. Brillouin analysis complements Rayleigh-based optical time-domain reflectometry, which locates loss but does not measure temperature or strain.

Common questions

Why does modulating the signal raise the threshold?

The Brillouin gain acts on the power spectral density inside a 20 MHz window. A 10 Gbaud modulated signal spreads its power over roughly 10 GHz, so only a small fraction falls within any one gain window, and the effective threshold rises by one to two orders of magnitude for phase-modulated formats. On-off keying leaves about half the power in a residual carrier, which keeps a low threshold, so the gain there is only a few decibels.

How is SBS different from stimulated Raman scattering?

Raman scattering involves optical phonons, with a shift near 13 THz and a gain band several terahertz wide that amplifies in both directions. Brillouin scattering involves acoustic phonons, with an 11 GHz shift, a 20 MHz band and backward gain. SBS dominates for narrow-band continuous light; SRS dominates for short pulses and broadband signals.

References: R. G. Smith, "Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering," Appl. Opt. 11, 2489 (1972); G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic Press, 2013), Ch. 9; R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008), Ch. 9.