# Brief Review of Recent Developments in Fiber Lasers
## 5 Brillouin Fiber Lasers  
Brillouin scattering is the interaction of optical waves with acoustic waves in a medium. It was described by [PERSON] in 1922 [87], and independently by [PERSON] in 1926 [88]. In the 1960s, [PERSON], who introduced SRS in 1963, realized that parametric interactions could also occur between laser light and the acoustic branch of the phonon spectrum, that is, between laser light and acoustic oscillations (acoustic phonons), or sound waves. This process is known as stimulated Brillouin scattering (SBS). The first demonstration of SBS was reported in 1964 in quartz and sapphire crystals [89]. As a third-order nonlinear optical process, SBS requires intense radiation. Compared to typical Raman frequency shifts (50-1400 cm\({}^{-1}\)), the Brillouin frequency shift (0.1-2 cm\({}^{-1}\)) is extremely small. Brillouin scattering (both stimulated and spontaneous) manifests itself through the generation of backward or forward propagating waves shifted from the frequency of the incident pump wave by an amount determined by the frequency of the acoustic phonon. When the acoustic wave is moving away from the pump light beam, the Stokes shift takes place in the system (Figure 7a). When the acoustic wave is moving toward the pump light beam, the anti-Stokes shift takes place (Figure 7b).  
Figure 7: The energy level diagram of Brillouin scattering. (**a**) Brillouin Stokes scattering; (**b**) Brillouin anti-Stokes scattering. \(\omega_{P}\), \(\omega_{S}\), \(\omega_{aS}\), and \(\Omega_{ap}\) are the pump, Stokes, anti-Stokes, and acoustic phonon frequencies, respectively.  
The energy and momentum conservation requirements of Stokes and anti-Stokes Brillouin scattering have the forms  
\[\omega_{S}=\omega_{P}-\Omega_{ap}\quad\text{and}\quad\mathbf{k}_{S}=\mathbf{k}_{P}-\mathbf{K }_{ap} \tag{17}\]  
for Stokes scattering and  
\[\omega_{aS}=\omega_{P}+\Omega_{ap}\quad\text{and}\quad\mathbf{k}_{aS}=\mathbf{k}_{P}- \mathbf{K}_{ap} \tag{18}\]  
for anti-Stokes scattering. Here \(\omega_{P}\), \(\omega_{S}\), and \(\omega_{aS}\) are the pump, Stokes, and anti-Stokes photon frequencies, respectively. \(\Omega_{ap}\) is the acoustic wave frequency. \(\mathbf{k}_{P}\), \(\mathbf{k}_{S}\), \(\mathbf{k}_{aS}\), and \(\mathbf{K}_{ap}\) are the pump, Stokes, anti-Stokes, and acoustic phonon wave vectors, respectively. In the SBS process, \(\Omega_{ap}\ll\omega_{P},\ \omega_{S},\ \omega_{aS}\). As for Raman scattering, the Stokes scattering process is accompanied by phonon generation (heating); the anti-Stokes scattering process is accompanied by phonon absorption (cooling).  
SBS can be used for the development of Brillouin lasers. A typical Brillouin laser involves coupling a laser pump light source, whose spectral width is much less than the Brillouin gain bandwidth, to the optical fiber in order to produce SBS with the Stokes signal propagating in the backscattered path of the incident pump light. The first Brillouin fiber laser was presented in 1976 [90]. Since then, remarkable progress in the development of Brillouin fiber lasers has been made. Great effort went into the development of lasers with a relatively low pump threshold, high efficiency, small linewidth, and especially multiwavelength configurations.