Analysis of waveguide antenna arrays with protruding dielectricelements

The two-dimensional problem of radiation of TE and TM waves from a waveguide array with protruding smooth dielectric elements of arbitrary shape is considered, and solution algorithms are suggested. The algorithms are based on applying the method of auxiliary sources for the representation of electromagnetic fields outside and inside the protrusions in combination with the method of integral equations for the electric field at the waveguide aperture. The point matching of the field tangential components on the protrusion-to-free-space boundary and at the waveguide aperture is used to reduce the problem to a system of linear algebraic equations for the amplitudes of the auxiliary filamentary currents and of the waveguide aperture electric field, which is assumed to be piecewise constant. The amplitudes obtained from the solution of the system are used for computing the array reflection coefficient and element pattern, which are shown in some cases to be significantly dependent on the protrusion shape. Examples of arrays with flat-topped element patterns resulting from array geometry numerical optimization are also presented