trostriction. This phenomenon produces density fluc- tuations in the fiber medium, which in turn modulates the refractive index of the medium and results in an electrostrictive nonlinearity [25]. The modulated refractive index behaves as an index grating, which is pump-induced and the scattered light is frequency shifted (Brillouin shift) by the frequency of the sound wave. Quantum mechanically, the Brillouin shift originates from the coherent scattering between photon and local acoustic phonon, and the Brillouin shift is due to the Doppler displacement that is a consequence of the phonon momentum [26]. Brillouin scattering may be spontaneous or stimulated. In spontaneous Brillouin scat- tering, there is annihilation of a pump photon, which results in creation of Stokes photon and an acoustic phonon simultaneously. The conservation laws for energy and momen- tum must be followed in such scattering processes. For energy conservation, the Stokes shift WB must be equal to (@p ws), where Wp and WS are frequencies of pump and Stokes waves. The momentum conservation requires (4.48) where kp and ks are the pump photon and the phonon wave vectors j is an integer Klattice takes into account the pseudo-particle nature of the phonon and accounts for other Stokes orders after the fundamental In transmission systems, Brillouin effect has to be as small as possible; thus, only the first-order Stokes wave is to be taken into account, SO that Equation 4.48 can be simplified If VA is the acoustic velocity, then the dispersion relation Equation 4.48 can be written as (4.49) where I is the angle between the pump and Stokes momentum vectors and the modules of the pump and the Stokes wave vectors are assumed almost equal due to Equation 4.48 and to the fact that the light speed is much greater than the sound speed. From the aforemen- tioned expression, it is clear that the frequency shift depends on angle D. For D=0, the shift is zero, that is, there is no frequency shift in forward direction that means no Brillouin scattering. The o