  Plasmonic distributed-feedback lasers based on a two-dimensional periodic
array of metallic nanostructures are the main candidate for nanoscale sources
of coherent electromagnetic field. Strong localization of the electromagnetic
field and the large radiation surface are good opportunities for achieving an
ultrashort response time to the external actions and creating beam
directionality. At the same time, the investigation of such a system is a
challenging problem. In this paper, we present an exhaustive study of the
operation of a two-dimensional plasmonic distributed-feedback laser. We show
that the complex structure of the modes of a periodic plasmonic array and the
nonlinear interaction between the modes through the active medium lead to a new
effect, namely, mode cooperation. Mode cooperation is manifested as the
generation of the modes in an allowed band with a high threshold instead of
modes localized near the band gap with a low threshold. Suppression of lasing
of the modes at the edge of the band gap results in widening of the radiation
pattern above the generation threshold. This paves the way for effective
control and manipulation of the radiation pattern of nanoscale systems, which
is of great importance for applications in spectroscopy and optoelectronics.
