A hybrid projection method for analysis of waveguide arrays with protruding dielectric elements: 2D problems

A method is proposed for the analysis of an array of parallel-plate waveguides with protruding longitudinally inhomogeneous dielectric elements. The method consists in expansion of the transverse electric ( for the case of E polarization) or magnetic ( for the case of H polarization) field in the domain containing the dielectric elements in terms of transverse functions of the Floquet channel. This expansion contains unknown variable coefficients. Projection of the Helmholtz equation for the aforementioned fields onto the transverse functions and application of a 1D finite- element method along the longitudinal coordinate in combination with projective matching of the fields in the waveguide apertures and at the boundary with free space reduces the problem to solution of a system of linear algebraic equations. The results of calculation of the reflection coefficient and the radiation pattern of an array element are presented. These results characterize both the efficiency of the proposed method and the possibility of formation of sector element patterns in the studied arrays.