Brillouin-like amplification in rare-earth-doped optical fibers

We present a theoretical formalism to describe the amplification of two monochromatic waves counter-propagating in a rare-earth-doped optical fiber amplifier. Interaction of the waves through a dynamical population inversion grating inscribed in the active fiber by the waves during their amplification results in a strong power transfer from one wave to another providing a preferable amplification of one wave at the expense of another. In this sense, the effect is similar to stimulated Brillouin scattering and is expected to be observed with both pumped and unpumped rare-earth-doped fibers possessing a finite polarizability difference between the excited and ground states.