# Optical Amplifiers for Access and Passive Optical Networks: A Tutorial
## 3 Optical Amplifiers in Telecommunications Networks
### Brillouin Amplification  
The last amplification technique discussed is based on SBS. SBS is similar to SRS but with notable exceptions: SBS occurs only in the backward direction, the scattered light is shifted by approximately 9-11 GHz (compared with 13 THz or 100 nm for SRS) and the gain spectrum is 100 MHz (for SRS, it is 30 THz). For SBS, energy absorbed by the fiberglass has the form of acoustic phonons (in contrast to an optical phonon in the case of SRS).  
Brillouin scattering is a \"photon-phonon\" interaction that occurs when annihilation of a pump photon simultaneously creates a Stokes photon and a phonon. The created phonon is the vibrational mode of atoms, which is also referred to as a propagation density wave or an acoustic phonon/wave. In a silica-based optical fiber, the Brillouin Stokes wave propagates dominantly backward, although very partially forward. The frequency (9-11 GHz) of a Stokes photon at a wavelength of 1550 nm differs considerably from that of Raman scattering (is smaller by three orders of magnitude and is dominantly downshifted due to the Doppler shift associated with the forward movement of created acoustic phonons [73].  
Depending on the frequency offset, the interference of the counterpropagating pump light with the signal light causes a moving density grating. The density grating coherently scatters pump photons into the signal beam, which is amplified. The characteristics of the SBR amplifier are the narrowband spectrum of approximately tens of MHz (based on an optical gain medium). Brillouin amplifiers have a built-in narrowband optical filter, which enables amplification of specific signals. In contrast to broadband amplifiers (EDFAs, SOAs, and Raman amplifiers), Brillouin amplifiers enable a maximum signal stage of 50 dB or higher [74].  
Brillouin amplifiers are not suitable for standard data communication due to their very narrow gain spectrum; however, new applications use different optical signals. We can provide examples of two new applications that have been extensively investigated: Accurate time transfer (that is, atomic clock comparison) and ultrastable frequency transfer. These signals are very slow (hundreds of MHz for accurate time, continuous wave (CW) for stable frequency), and therefore, their spectra are very narrow, which renders them suitable for Brillouin amplification, especially for ultrastable frequency transfer using very narrow laser sources. In this case, SBS can be used for very powerful amplification [75].  
Advantages of Brillouin amplifiers:  
* high gain and saturation power for narrowband signals,
* wavelength conversion,
* can enable amplification of a very small input signal (a few nanowatts) by more than 50 dB in a single gain step. Disadvantages of Brillouin amplifiers:
* limited range of use,  
\begin{table}
\begin{tabular}{c c c c} \hline
**Pump Power [mW]** & **Pump Wavelength [nm]** & **Amplified Wavelength [nm]** & **Amplified Saturation Power [dBm]** \\ \hline
10 & 1455.142 & 1552.062 & \(-\)10.803 \\ \hline
50 & 1455.162 & 1552.060 & \(-\)10.540 \\ \hline
100 & 1455.182 & 1552.066 & \(-\)10.148 \\ \hline
150 & 1455.188 & 1552.066 & \(-\)9.712 \\ \hline
200 & 1455.184 & 1552.064 & \(-\)9.276 \\ \hline
250 & 1455.202 & 1552.064 & \(-\)8.706 \\ \hline
300 & 1455.198 & 1552.064 & \(-\)8.280 \\ \hline \end{tabular}
\end{table}
Table 1: Pump power vs. saturation power of a Raman amplifier.  
* nonlinear phenomena.