On the asymptotic decay of coupling for infinite phased arrays

The asymptotic decay of coupling with distance from a single excited element it an infinite linear array has been analyzed for several special cases and is shown to behave according to exp (-jkr)/r
^3/2
where r is the distance from the excited element. This behavior is also characteristic of propagation over a lossy surface. By geometric extrapolation one would expect an asymptotic decay of coupling for planar arrays to behave according to exp (-jkr)/r
²
. This extension is carried out for an arbitrary infinite periodic planar current sheet with the expected result. In addition, this behavior is shown to be valid for an infinite parallel plate array immersed in a magnetized cold plasma. In all cases, the asymptotic behavior is shown to depend on the form of the singularity of the derivative of the reflection coefficient with scan angle. This singularity occurs at grazing incidence of the radiated beams.