Time domain Green´s function for an infinite phased periodic line array of dipoles

Periodic arrays of radiating or scattering elements play an important role in phased array antennas, frequency selective surfaces and related applications. We have begun a systematic investigation of the time domain (TD) behavior of Green´s functions which are relevant for the characterization of truncated planar periodic arrays, with emphasis on the TD Floquet waves (FW) in the propagating and evanescent parameter regimes. Such waves on semi-infinite and finite square arrays of dipoles have been and are being investigated in the frequency domain (FD). These prototypes furnish the models for the present studies in the time domain. Our principal aim is to understand the TD wave physics and phenomenologies on simple prototypes, invoking various methods that synthesize the solution from different perspectives. This paper deals with the first prototype, an infinite linearly phased periodic array of axial dipole radiators arranged along the z-axis of a rectangular or cylindrical coordinate system. This prototype is a basic building block for line arrays formed by a finite number of transversely phased line sources, and it also plays a direct role in the modeling of diffraction effects due to the transverse truncations. The prototype line array of dipoles is simple enough to admit closed form exact solutions which can be obtained via alternative routes. A route which includes inversion from the FD via the conventional Fourier transform is presented.