  We show that nonlinear phase shifts and third-order dispersion can compensate
each other in short-pulse fiber amplifiers. In particular, we consider
chirped-pulse fiber amplifiers at wavelengths for which the fiber dispersion is
normal. The nonlinear phase shift accumulated in the amplifier can be
compensated by the third-order dispersion of the combination of a fiber
stretcher and grating compressor. A numerical model is used to predict the
compensation, and initial experimental results that exhibit the main features
of the calculations are presented. In the presence of third-order dispersion,
an optimal nonlinear phase shift reduces the pulse duration, and enhances the
peak power and pulse contrast compared to the pulse produced in linear
propagation. Contrary to common belief, fiber stretchers can perform as well or
better than grating stretchers in fiber amplifiers, while offering the major
practical advantages of a waveguide medium. The relative benefits of a fiber
stretcher increase with increasing pulse energy, so the results presented here
will be relevant to fiber amplifiers designed for the highest pulse energies.
