The report describes studies regarding how Finite Difference-Methods in the Time-Domain (FDTD) can be used to calculate the electromagnetic fields of plane periodic antenna arrays. The arrays are excited in such a way that a unit cell analysis can be applied. Two kinds of excitations, which render possible such a unit cell analysis are time shift excitation and argument shift excitation. A basic idea in the report is a definition of the concept unit cell, which is described as a torus space-time with two closed dimensions, and whose properties depend on the excitation of the antenna array. By creating such a spacetime, and putting an antenna element in it, we get an equivalent electromagnetic problem to the original case with an argument shift- or time shift-excited infinite structure. Considered in this way the problem of finding FDTD-methods for plane periodic antenna arrays, which are argument shift or time shift excited, is therefore equivalent to finding FDTD-methods for a torus space time (with an antenna element in it). Such methods are derived in the report, by first expressing the field equations in suitable coordinates of the torus space-time, and then discretizising these equations.