Element pattern nulls in phased arrays and their relation to guided waves

In recent years, unusual dips or nulls have been observed in the element patterns of certain phased-array antennas at angles closer to broadside than that for which an endfire grating lobe exists. These nulls are known to bear a direct and simple relation to a total reflection condition which occurs when all elements of the array are excited. The purposes of this paper are to investigate the basic cause of these element pattern nulls, and to clarify the relationship between these nulls and possible guided waves which may be supported by the array face. It is shown herein that, for a certain class of arrays, these nulls (actually the total reflection condition) are caused by the forced resonance of a higher external mode in the vicinity of the array aperture. The nature of this resonance is demonstrated on a simple infinite array representative of a class of structures which permit external resonances. A detailed analysis of this array (of waveguide-fed slots covered by a dielectric layer) yields a simple equivalent network from which the existence, approximate angular location, and qualitative behavior of the element pattern null are determined by inspection. There are two types of guided waves which are of concern here, surface waves and leaky waves. It is shown that the actual array cannot support a true surface wave, and that the surface wave customarily associated with element pattern nulls is really a driven surface-wave-like field which appears on the array face only at precisely the total reflection condition, and which is indistinguishable in its properties from a true surface wave on a modified (corrugated) structure, not on the actual array. The leaky wave, whose role is explained here for the first time, is a true mode of the actual array and radiates at an angle close to that for the element pattern null. Its influence on the element pattern null is akin to the relation between free and forced resonances, and its attenuation constant yields the width of this null.