Design of a passive element array

We introduce a procedure for designing an antenna system based on a single dipole element surrounded by an array of scattering elements. The goal is to achieve a desired pattern by astute placement of the elements in a fixed grid. This represents a departure from the traditional approach to directive arrays in which the current in each element is controlled. The problem is similar to the design of a reflector to achieve some arbitrary pattern. We describe the problem, propose a design approach, present simulations of the resultant system, and comment on the performance and optimality of such a system.