Mutual coupling effects in semi-infinite arrays

An analysis of mutual coupling effects in linear and planar uniformly spaced semi-infinite arrays is presented. The currents under arbitrary excitations at the array ports are obtained by solving an infinite order difference equation with the aid of an extension of the Wiener-Hopf factorization procedure to finite Fourier transforms. The solution for mutual coupling coefficients as well as for the active reflection coefficients in a phased semi-infinite array is expressed explicitly in terms of the active impedance in a phased infinite array. The analytical results are directly applicable to the evaluation of "edge effects" in large phased arrays. Numerical results for active reflection coefficients and element patterns are presented for a semi-infinite array of slots in a perfectly conducting ground plane and for a linear dipole array.