Parameterizing quasi-periodicity: generalized Poisson summation and its application to modified-Fibonacci antenna arrays

The fairly recent discovery of "quasi-crystals", whose X-ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity, has motivated studies of the wave-dynamical implications of "aperiodic order". Within the context of the radiation properties of antenna arrays, an instructive novel (canonical) example of wave interactions with quasi-periodic order is illustrated here for one-dimensional array configurations based on the "modified-Fibonacci" sequence, with utilization of a two-scale generalization of the standard Poisson summation formula for periodic arrays. This allows for a "quasi-Floquet" analytic parameterization of the radiated field, which provides instructive insights into some of the basic wave mechanisms associated with quasi-periodic order, highlighting similarities and differences with the periodic case. Examples are shown for quasi-periodic infinite and spatially-truncated arrays, with brief discussion of computational issues and potential applications.