  We compute the dynamical polarization function for a graphene antidot lattice
in the random-phase approximation. The computed polarization functions display
a much more complicated structure than what is found for pristine graphene
(even when evaluated beyond the Dirac-cone approximation); this reflects the
miniband structure and the associated van Hove singularities of the antidot
lattice. The polarization functions depend on the azimuthal angle of the {\bf
q}-vector. We develop approximations to ease the numerical work, and critically
evaluate the performance of the various schemes. We also compute the plasmon
dispersion law, and find an approximate square-root dependence with a
suppressed plasmon frequency as compared to doped graphene. The plasmon
dispersion is nearly isotropic, and the developed approximation schemes agree
well with the full calculation.
