Nonlinear Fiber Optics - 4 ed. Agrawal

362 Chapter 9. Stimulated Brillouin Scattering
Figure 9.21: Evolution of Stokes (lower trace) and pump (upper trace) amplitudes over multiple
round trips in the self-pulsing regime: (left) initial build-up from noise; (right) fully formed pulse
train after 4800 round trips. (After Ref. [150]; c○1999 OSA.)
be designed to emit a soliton train, with a pulse width ∼10 ns and a repetition rate
(∼1 MHz) determined by the round-trip time of the ring cavity.
In a 2002 study, the origin of self-pulsing was attributed to the phenomenon of spectral
hole burning [151]. This phenomenon is well known for lasers and occurs when
the gain spectrum exhibits inhomogeneous broadening [152]. The SBS gain spectrum,
resulting from Eqs. (9.4.5)–(9.4.7) under steady-state conditions, is homogeneously
broadened and has a Lorentzian line shape with width Γ B , as shown in Eq. (9.1.3).
However, small variations in the Brillouin shift Ω B along the radial direction, resulting
from a finite numerical aperture of the fiber, can lead to inhomogeneous broadening of
the SBS gain spectrum [25]. This interpretation of self-pulsing phenomenon in Brillouin
lasers is debatable as the onset of spectral hole burning does not always require
inhomogeneous broadening [153].
The self-pulsing instability is also affected by the linear birefringence of the fiber
when the pump beam is not linearly polarized along one of the principal axes of a
polarization-maintaining fiber. In this case, the two orthogonally polarized components
of the pump generate their own Stokes waves, and Eqs. (9.4.5)–(9.4.7) should be
generalized to a set of five equations. The situation is even more complicated if the
fiber within the laser cavity is rotated so that its principal axes do not coincide at the
input and output ends. A detailed linear stability analysis has been performed for this
general situation, and it reveals the complicated dynamic behavior of such Brillouin
lasers [149]. Experimental results agree well with the theoretical predictions.
Problems
9.1 What is meant by Brillouin scattering? Explain its origin. What is the difference
between spontaneous and stimulated Brillouin scattering?
9.2 Use the phase-matching condition to derive an expression for the Brillouin shift.
Why does SBS occur only in the backward direction in single-mode fibers?
9.3 What are the main differences between SBS and SRS? What is the origin of these
differences and how do they manifest in practice?