The finite difference modelling of infinite arrays in time domain

This paper presents an extended FDTD method that can treat phased shifted infinite 3D arrays with arbitrary pulsed excitation by modelling a single array element. The paper starts by considering the structure of fields on periodic media in the time domain. For the phased array (or a dichroic surface) under non-normal incidence, the scattered field appears to be periodic in a 4 dimensional basis. A coordinate transform in this 4 dimensional space is performed to reduce the problem to the normal incidence case in the new basis. It is shown that this coordinate transform links with the Lorentz transform of Maxwell's equations. Finally results are presented for the transmission through frequency selective surfaces (FSS).