The Active Element Patterns of a Finite Array-Space Wave and Leaky Wave Perspective

The active element patterns (AEPs) of a finite array of parallel-plate waveguides are studied. It is shown that an excited element in array environment produces a number of space and leaky wave modes (but no surface wave mode) that can be expressed in terms of branch-cut integrals and residues, respectively, in the complex wavenumber plane. The dominant space wave mode has a very sharp radiation pattern with large phase variation near its peak causing constructive and destructive interferences with the primary pattern of the excited element within a small angular region. As a result, the AEP exhibits sharp dips that are very close to the local peaks. The number and the extent of excited modes that cause interference depend on the location of the excited element in a finite array. Consequently, the shape of the AEP changes with the element location. It is found that an array generates forward and backward waves on its aperture, and for element spacing less than one wavelength, the backward wave dominates. As a result, the AEP for the left-edge element has a dip at the left-hand side of the boresight and the beam tilts toward the left. For large element spacing, multiple dips may occur on both sides. The present analysis explains several interesting characteristics of finite and infinite arrays and very closely agrees with the plane wave spectrum model.