Nonlinear Fiber Optics - 4 ed. Agrawal

360 Chapter 9. Stimulated Brillouin Scattering
generated with self-seeding provided by the amplified spontaneous emission of EDFA.
This pump then creates multiple Stokes lines through SBS gain. Such a laser produced
as many as 120 Stokes lines with nearly equal power levels that were separated by the
Brillouin shift of 11 GHz and occupied a 12-nm spectral window within the EDFA gain
bandwidth.
9.5.2 Pulsed Operation
Brillouin fiber lasers with long cavity lengths can be forced to emit a pulse train using
several different methods. The technique of active mode locking was used in a 1978 experiment
by placing an amplitude modulator inside the laser cavity [125]. Laser output
consisted of a train of pulses (width about 8 ns) at a repetition rate of 8 MHz, determined
by the cavity length. These pulses result from locking of multiple longitudinal
modes of the cavity.
Another type of mode locking can occur in Fabry–Perot cavities in which multiple
Stokes lines are generated through cascaded SBS. Relaxation oscillations can seed the
mode-locking process because their period is equal to the round-trip time in the cavity.
Indeed, partial mode-locking of such a Brillouin laser by itself was observed [125], but
the process was not very stable. The reason can be understood from Eq. (9.1.3) showing
that the Brillouin shift depends on pump wavelength. In cascaded SBS, different
Stokes waves act as pumps for the successive Stokes. As a result, multiple Stokes lines
are not spaced equally but differ in frequencies by a small amount ∼1 MHz. In a 1989
experiment, mode locking was achieved by using a multimode fiber [129]. As different
modes have a slightly different effective index (modal dispersion), equally spaced
Stokes lines can be generated by using different fiber modes.
An interesting technique for generating short Stokes pulses from a Brillouin laser
makes use of synchronous pumping using a mode-locked train of pump pulses [134].
The idea is quite simple. The length of a ring cavity is adjusted such that the round-trip
time exactly equals the spacing between pump pulses. Each pump wave is so short
that it is unable to excite the acoustic wave significantly. However, if the next pump
pulse arrives before the acoustic wave has decayed, the cumulative effect of multiple
pump pulses can build up the acoustic wave to a large amplitude. After the buildup
process is complete, a short Stokes pulse will be generated through transient SBS
with the passage of each pump pulse. This technique has produced Stokes pulses of
200-ps duration when 300-ps pulses from a mode-locked Nd:YAG laser were used for
pumping a Brillouin ring laser.
Brillouin ring lasers with long cavity lengths can produce pulse trains, even when
pumped continuously, through a nonlinear self-pulsing mechanism based on an inherent
instability of such lasers. The origin of this instability lies in the relaxation oscillations
discussed earlier in Section 9.4.4. Typically, pulses have widths in the range of
20 to 30 ns and are emitted with a repetition rate nearly equal to the longitudinal-mode
spacing Δν L ≡ 1/t r , where t r is the round-trip time.
Physics behind such lasers attracted considerable attention during the 1990s [147]–
[151]. Equations (9.4.5) through (9.4.7) describe the nonlinear dynamics in Brillouin