  We demonstrate and analyse a novel approach to enhance the threshold power of
stimulated Brillouin scattering (SBS) in optical fibers, using a longitudinal
compressive strain gradient. We derive analytical expressions for the power
spectral density of the backscattered Stokes wave in the general case of
passive and amplifying optical fibers, by considering the strain and optical
power distributions. Our method provides an accurate prediction of the SBS gain
spectrum, that we illustrate with a quantitative comparison between
measurements and calculations of the SBS Stokes spectra, before and after
applying the compression gradient. Our experimental results demonstrate the
successful enhancement of the SBS threshold power by a factor of about 3 for
the passive fiber and 2 for the amplifying fiber. The enhancement that we
manage to calculate in the case of the passive fiber is in perfect agreement
with the experimental result.
