Brillouin-enhanced four-wave mixing. In addition to SBS, light beams can interact in a Brillouin medium by means of the process known as Brillouinenhanced four-wave mixing (BEFWM), which is illustrated in the following figure.
In this process, the incoming signal wave A3 interferes with the backward-going pump wave A2 to generate an acoustic wave propagating in the forward direction. The forward-going pump wave scatters from the acoustic wave to generate the phase-conjugate wave A4. Since A4 is at the Stokes sideband of A1, it also undergoes amplification by the usual SBS process. Phase-conjugate reflectivities much larger than 100% have been observed in the BEFWM process. Using the general formalism outlined in Section 9.3, derive the form of the four coupled-amplitude equations that describe BEFWM under steady-state conditions. Solve these equations analytically in the constant-pump approximation