Periodicity-induced generalized Fourier transform pair

The field radiated by an infinite periodic structure can be expressed in terms of Floquet waves (FWs), both in the frequency domain (FD) and time domain (TD) (see Felsen, L.B. and Capolino, F., IEEE Trans. Antennas Propagat., vol.48, p.921-31, 2000). A new periodicity-induced generalized Fourier transform (FT) pair is derived relating FD-FWs to TD-FWs and vice versa, based on tabulated transforms and physical conditions at infinity. The new FTs are directly related to the simple canonical problem of a line array of sequentially excited dipoles that is a basic building block for more general phased periodic structures.