  We report the first direct observation of Brillouin-like propagation modes in
a dissipative periodic optical lattice. This has been done by observing, in
both theoretical and experimental work, a resonant behaviour of the spatial
diffusion coefficient in the direction corresponding to the propagation mode
with the phase velocity of the moving intensity modulation used to excite these
propagation modes. Furthermore, we show theoretically that the amplitude of the
Brillouin mode is a nonmonotonic function of the strength of the noise
corresponding to the optical pumping, and discuss this behaviour in terms of
nonconventional stochastic resonance.
