Nonlinear Fiber Optics - 4 ed. Agrawal

358 Chapter 9. Stimulated Brillouin Scattering
dex. For short fibers such that Δν L > Δν B , where Δν B is the Brillouin-gain bandwidth
(typically 20 MHz), the ring laser operates stably in a single longitudinal mode. Such
lasers can be designed to have low threshold [127] and to emit CW light with a narrow
spectrum [130]. In contrast, a Brillouin ring laser operates in multiple longitudinal
modes when Δν L ≪ Δν B , and the number of modes increases with fiber length. As
early as 1981, it was noted that such lasers required active intracavity stabilization to
operate continuously [126]. In fact, their output can become periodic, and even chaotic,
under some conditions. This issue is discussed in Section 9.5.2.
An important application of CW Brillouin lasers consists of using them as a sensitive
laser gyroscope [131]–[133]. Laser gyroscopes differ from fiber gyroscopes, both
conceptually and operationally. Whereas passive fiber gyroscopes use a fiber ring as an
interferometer, active laser gyroscopes use the fiber ring as a laser cavity. The rotation
rate is determined by measuring the frequency difference between the counterpropagating
laser beams. Similarly to the case of passive fiber gyroscopes, fiber nonlinearity
affects the performance of a Brillouin-laser fiber gyroscope through XPM-induced
nonreciprocity and constitutes a major source of error [132].
Considerable attention was paid during the 1990s to developing hybrid Brillouinerbium
fiber lasers capable of operating either at several wavelengths simultaneously or
in a single mode, whose wavelength is tunable over a wide range [136]–[146]. The basic
idea is to incorporate an erbium-doped fiber amplifier (EDFA) within the Brillouinlaser
cavity [137] that provides gain over its entire bandwidth of 40 nm or so. The
EDFA is pumped such that its gain is below the threshold gain of the cavity. The addition
of Brillouin gain allows the laser to reach the threshold over the narrow Brillouin
bandwidth (30 MHz or so) and to generate the first-order Stokes line. However, this
line acts as a pump to create the second-order Stokes line, and the process repeats again
and again, generating multiple wavelengths spaced apart exactly by the Brillouin shift
ν B of about 11 GHz. Since pump and its corresponding Stokes must propagate in the
opposite direction, even and odd order Stokes travel in opposite directions when a ring
cavity is used. As a result, output in any direction consists of laser modes spaced apart
by 2ν B . This problem can be solved if a Fabry–Perot cavity is employed because all
waves then propagate in both directions.
As early as 1998, the use of a fiber-loop Sagnac interferometer, acting as one of
the mirrors of a Fabry–Perot cavity, resulted in generation of up to 34 spectral lines
through cascaded SBS [139]. The other mirror was made 100% reflecting to ensure that
all laser modes exit through the Sagnac loop. This configuration has an added benefit.
Even though SBS generates only Stokes lines that are shifted toward the red side of
the injected pump, multiple anti-Stokes lines are also produced within the Sagnac loop
through four-wave mixing. As a result, the laser output has modes whose wavelengths
lie on both sides of the pump wavelength.
For some applications, tuning of the frequency comb generated inside a Brillouin
fiber laser is desirable. Several techniques can be used for this purpose. A Sagnac loop
made with 18 cm of polarization-maintaining fiber was used as an optical filter in a
2004 experiment for tuning the laser output [144]. Such a tunable filter selects different
spectral windows of the amplified spontaneous emission produced by the EDFA, while
SBS gain generates a frequency comb within this window. The laser produced its
output at 12 wavelengths that was tunable over 14.5 nm. A tuning range of up to