Shaping of flat-topped element patterns in a planar array of circular waveguides using a multilayered disk structure. I. Theory and numerical modeling

An infinite planar array of stepped circular waveguides radiating through a multilayered disk structure, which is arranged above the waveguide apertures in order to shape the flat-topped element patterns, is analyzed. The analysis is based on modal representations for the fields in the partial regions and for the currents on the disks with subsequent application of the mode-matching method and Galerkin´s method for determining the modal coefficients used in the calculation of the array characteristics. The application of the algorithm is demonstrated by an array design that provides flat-topped element patterns of ±20° width in the main planes within a 5.6% frequency band. Outside the indicated band, the disk structure can cause sharp dips in the element patterns at the broadside, and some features of this effect are discussed.