Rectangular slots are cut in the broad or narrow side walls of rectangular waveguides. The slots are arranged in a random-tilt fashion on a planar surface. Waveguides are excited by an arbitrary amplitude and phase combination wave in the dominant waveguide mode and are terminated by an arbitrary reflection coefficient. Scattering due to slots and mutual couplings between waveguides is accounted for by means of both internal and external Green's functions. A coupling system of Hallen-type integral equations for the slot fields excited in each of the array elements is formulated on the basis of the boundary condition for tangential magnetic fields in the slot aperture. The system of equations is solved numerically by the method of moments to determine the slot voltage distribution in each array element. Slot fields of a single-waveguide array are compared with those of a multi-waveguide array with equal magnitude and phase excitation.
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