Design Methodology of a Single-Beam Passive Reflectarray for Controlling Arbitrary Illuminations

This paper proposes a general approach for designing a planar surface, which is able to focus incident waves within a particular direction. The array of factor is derived as a function of several parameters as the number of cells, the inter-element spacing, the intrinsic and structural excitation phase shifts, etc. Theoretical results compare well with simulations for the case in which there is no intrinsic excitation phase shift between the cells. In this case, it is seen that the reflected field is maximally focused in two complementary directions (θ₀ = θ_i, φ₀ = π + φ₁) and (θ₀ = π - θ₁, φ₀ = π + φ_i) within a permissible range of the inter-element spacing.