  We consider excitons in a two-dimensional periodic potential and study the
linear response of the excitonic superfluid to an electromagnetic wave at low
and high densities. It turns out that the static structure factor for small
wavevectors is very sensitive to a change of density and temperature. It is a
consequence of the fact that thermal fluctuations play a crucial role at small
wavevectors, since exchanging the order of the two limits, zero temperature and
vanishing wavevector, leads to different results for the structure factor. This
effect could be used for high accuracy measurements in the superfluid exciton
phase, which might be realized by a gated electron-hole gas. The transition of
the exciton system from the superfluid state to a non-superfluid state and its
manifestation by light scattering are discussed.
