  In this paper we theoretically study the nonlinear dynamics of Wannier-Stark
states in the dissipative system consisting of interacting optical resonators,
whose resonant frequencies depend linearly on their number. It is shown that
the negative losses in some resonators can switch the system into a lasing
regime with Wannier-Stark states serving as working modes. It is shown by
extensive numerical simulations that there may be single-frequency stationary
regimes as well as multi-frequency regimes. In the latter case Bloch
oscillations can appear in the system. The possibility of selective excitation
of Wannier-Stark states by the appropriate choice of the dissipation profile is
investigated. A simple perturbation theory describing the quasi-linear regimes
is developed and compared against the numerical results.
