Exact demagnetisation field for periodic one-dimensional array of rectangular prisms

The magnetic field from a uniformly magnetised, rectangular prism is known exactly, which is the basis for a large number of micromagnetic simulations. Here we derive an analytical solution for the field from a periodically repeating infinite array of prisms aligned end-to-end, which becomes exact on the center axis in the limit of infinitesimally thin prisms. Using the same method we derive the on-axis field for a one-dimensional array of point dipoles. We validate the obtained results numerically and furthermore compare with the common macrogeometry approach and more recent uniform magnetisation method, demonstrating an excellent convergence rate for the novel method.