Stimulated Raman scattering (SRS)

Stimulated Raman scattering is the high-intensity form of Raman scattering. Spontaneously scattered Stokes photons, shifted down in frequency by a molecular vibration, beat with the pump and drive that vibration coherently; the vibration in turn scatters more pump light into the Stokes wave, which grows exponentially with distance. In silica the gain spectrum is broad, extending over about 40 THz, with its peak at a shift of about 13.2 THz, or 440 cm⁻¹. A 1550 nm pump therefore generates Stokes light near 1664 nm, and a 1064 nm pump generates it near 1116 nm. The peak gain coefficient of fused silica is about $10^{-13}$ m/W for a pump near 1 µm and scales roughly as $1/\lambda_p$, giving about $6.5 \times 10^{-14}$ m/W at 1550 nm. Tight confinement over kilometres of fiber makes SRS observable at powers near a watt.

Stokes growth and threshold

For a weak Stokes wave in the presence of an undepleted pump of power $P_0$, the Stokes power grows as

$$P_S(L) = P_S(0)\,\exp\!\left( \frac{g_R P_0 L_\text{eff}}{A_\text{eff}} - \alpha L\right),$$

where $A_\text{eff}$ is the effective area and the effective length $L_\text{eff} = (1 - e^{-\alpha L})/\alpha$ accounts for pump attenuation. For a long fiber, $L_\text{eff} \to 1/\alpha$.

Without any injected Stokes light, the wave grows from spontaneous scattering. Smith (1972) defined the threshold as the pump power at which the output Stokes power equals the output pump power, and found for forward SRS

$$P_\text{th} \approx \frac{16\,A_\text{eff}}{g_R\, L_\text{eff}} .$$

For standard single-mode fiber at 1550 nm with $A_\text{eff}$ = 80 µm², an attenuation of 0.2 dB/km (so $L_\text{eff}$ ≈ 21.7 km for a long span), and $g_R$ = $6.5 \times 10^{-14}$ m/W, the threshold is about 0.9 W. For a 50 km span, $L_\text{eff}$ = 19.5 km and $P_\text{th}$ ≈ 1.0 W. In a 10 m ytterbium fiber laser at 1064 nm with $A_\text{eff}$ = 20 µm² and $g_R$ = $9.4 \times 10^{-14}$ m/W, the same formula gives about 340 W. These are continuous-wave or long-pulse estimates; the factor of 16 is itself approximate, and a fiber that scrambles polarization has an effective $g_R$ about half the co-polarized value, which roughly doubles the threshold.

Observing SRS in the lab

SRS appears on an optical spectrum analyzer as a Stokes peak about 13 THz below the pump, growing abruptly once the pump nears threshold, with the transmitted pump power saturating as energy moves to the Stokes band. At higher power the first Stokes wave pumps a second, producing a cascade of lines separated by 13.2 THz. The gain can be measured directly with a pump–probe arrangement: a weak tunable probe is launched with the pump, and its on-off gain versus frequency offset traces the Raman gain spectrum.

Where it matters

• Raman amplification: deliberately pumping transmission fiber about 13 THz above the signal gives distributed gain. This is covered in Raman amplifier, and compared with doped-fiber and semiconductor amplifiers in the article SOA vs EDFA vs Raman.
• Raman lasers: cascaded Raman fiber lasers use fiber Bragg gratings to reflect successive Stokes orders; six shifts of 13.2 THz from 1064 nm reach about 1480 nm, the pump band of erbium-doped amplifiers.
• WDM crosstalk: in wavelength-division multiplexing systems, channels at shorter wavelengths act as Raman pumps for longer-wavelength channels. The result is a power tilt across the band that grows with total launched power and bandwidth, and pattern-dependent crosstalk between channels. Wideband C+L systems apply pre-emphasis or dynamic gain equalization to compensate.
• High-power fiber lasers and amplifiers: SRS is, with transverse mode instability, one of the main limits on the power of narrow-core fiber sources. Large-mode-area fibers and short lengths raise the threshold.
• Ultrafast pulses: within a single short pulse the red edge is amplified at the expense of the blue edge. This intrapulse Raman scattering causes the soliton self-frequency shift and contributes to supercontinuum generation.

Pitfalls

The threshold formula assumes a continuous-wave pump. For pulses shorter than the walk-off time between pump and Stokes, which separate because of group-velocity mismatch, the effective interaction length is shorter and the threshold higher. In narrow-linewidth systems, stimulated Brillouin scattering usually reaches threshold first, at milliwatt levels, so SRS dominates only when the pump linewidth or pulse bandwidth is broad enough to suppress Brillouin gain. Quoted values of $g_R$ differ by polarization convention and reference wavelength; comparisons need both stated.

Common questions

What is the difference between spontaneous and stimulated Raman scattering?

Spontaneous Raman scattering grows linearly with pump power and is emitted in all directions, with each molecule scattering independently. Stimulated scattering occurs when the Stokes field is strong enough to drive the vibration coherently, so Stokes power grows exponentially with pump power and length and is emitted along the pump axis.

Does SRS occur in the backward direction?

Raman gain in silica is nearly the same for co- and counter-propagating Stokes waves, because optical phonons have little dispersion. Smith's estimate for backward SRS uses a factor of about 20 in place of 16, so forward SRS usually reaches threshold first in fiber.

References: R. G. Smith, Appl. Opt. 11, 2489 (1972); R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972); G. P. Agrawal, Nonlinear Fiber Optics, 6th ed. (Academic Press, 2019); R. W. Boyd, Nonlinear Optics, 4th ed. (Academic Press, 2020).