Brillouin amplification, the most prominent effect implemented with Brillouin dynamical gratings (BDG), enables exponential narrowband gain that is Stokes-shifted by some value in the GHz range. In this process, the interaction of the counterpropagating pump and Stokes waves through a BDG they produce causes an increase of the Stokes-shifted wave amplitude and decrease of the pump wave amplitude during their propagation through the fiber. Here, we report on a similar effect that could be implemented in rare-earth-doped fibers with the population inversion dynamical gratings. The effect is the most pronounced in a bidirectional rare-earth-doped optical fiber amplifier. Two monochromatic optical signal waves are introduced into the fiber from opposite ends and experience amplification (if the fiber is pumped) or attenuation (if the fiber is unpumped) as they propagate through the fiber. The signal waves are coherent on a sub-kHz level and slightly detuned. In terms commonly accepted in stimulated Brillouin scattering these counterpropagating signal waves correspond to what is referred to as "pump" and "Stokes" waves. However, in contrast to the Brillouin process, their interference inside the rare-earth-doped fiber creates not acoustic, but the population inversion dynamical gain grating. Then interaction between the signal waves and created population inversion dynamical gratings cause a strong power transfer from one signal wave to another.
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