Bandwidth Limitations of Linearly Polarized Infinite Planar Phased Arrays in Free Space

For elements of an infinite planar phased array in free space, fundamental bandwidth bounds are derived from the optical theorem for periodic scatterers. The bounds are based on Gustafsson's theory of fundamental bandwidth limits for electrically small antennas of arbitrary shape, but extended to periodic configurations. The element bandwidth bound is found to be a function of the strengths of the induced static dipole moments in constant background fields as well as the unit-cell dimensions and the scan angle. Explicit bandwidth bound expressions are found for narrowband and ultrawideband array cases. They are numerically tested using example free-space array designs.