This letter presents an analytical model which describes the dynamics
of the modulation instability in a nonlinear, dispersive, homogeneousl
y broadened and nonsaturable fiber amplifiers. The general case of arb
itrary detuning between the laser frequency and the resonance frequenc
y and arbitrary bandwidth of the amplifying transition is treated. The
model accounts both for the gain dispersion and for the gain-induced,
near resonant refractive index dispersion. Simple closed form express
ions for the combined gain coefficients of the Stokes and anti-Stokes
frequencies are obtained.