Nonlinear Fiber Optics - 4 ed. Agrawal

9.1. Basic Concepts 331
Figure 9.1: Brillouin-gain spectra of three fibers for λ p = 1.525 μm: (a) silica-core fiber, (b)
depressed-cladding fiber, and (c) dispersion-shifted fiber. (After Ref. [17]; c○1986 IEE.)
phonon lifetime. As shown later in Section 9.4.1, when acoustic waves decay as
exp(−Γ B t), the Brillouin gain has a Lorentzian spectrum of the form [10]
g B (Ω)=
g p (Γ B /2) 2
(Ω − Ω B ) 2 +(Γ B /2) 2 , (9.1.4)
where the peak value of the Brillouin gain at Ω = Ω B is given by
g p ≡ g B (Ω B )=
8π 2 γ 2 e
n p λ 2 pρ 0 cv A Γ B
. (9.1.5)
Here, γ e ≈ 0.902 is the electrostrictive constant of silica and ρ 0 ≈ 2210 kg/m 3 is its
density [12]. The full width at half maximum (FWHM) of the gain spectrum is related
to Γ B as Δν B = Γ B /(2π). The phonon lifetime, T B = Γ −1
B
, is typically