  The electronic properties of graphene may be changed from semimetallic to
semiconducting by introducing perforations (antidots) in a periodic pattern.
The properties of such graphene antidot lattices (GALs) have previously been
studied using atomistic models, which are very time consuming for large
structures. We present a continuum model that uses the Dirac equation (DE) to
describe the electronic and optical properties of GALs. The advantages of the
Dirac model are that the calculation time does not depend on the size of the
structures and that the results are scalable. In addition, an approximation of
the band gap using the DE is presented. The Dirac model is compared with
nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended
zigzag regions give rise to localized edge states, whereas armchair edges do
not. We find that the Dirac model is in quantitative agreement with TB for GALs
without edge states, but deviates for antidots with large zigzag regions.
