A Generalized Approach to a Solution of Aperiodic Arrays and Modulated Surfaces

A generalized approach to a solution of the aperiodic phased-array problem, and derived periodically modulated surfaces, is possible by an extension, using linear superposition, of the solutions for the related periodic phased array. This approach can be applied to any aperiodic array of elements such as planar arrays of waveguides, or dipoles, or thick walled parallel-plate arrays. It also leads to the solution for the dispersion relation, in terms of the periodic phased-array solution, for the surface of short-circuited waveguide clements; the short circuit depth being periodically modulated along the surface.