This question is about reflectarray antennas. In the paper below, it is mentioned that:
"A second useful property of aperiodic arrays is the possibility to reduce the number of elements in one assigned aperture without major impact on the beamwidth."
Viganó, M. C., Toso, G., Caille, G., Mangenot, C., & Lager, I. E. (2009). Sunflower Array Antenna with Adjustable Density Taper. International Journal of Antennas and Propagation, 2009, 1-10.
I understand that aperiodic lattices are able to reduce sidelobe levels by suppressing grating lobe formation. However, why does the periodicity of the lattice affect the beamwidth of the antenna? I am hoping to get an answer on this that includes a qualitative explanation in addition to any math that is required. Thank you!