Algorithm of the method of auxiliary sources for analysis of arrays of circular waveguides with protruding dielectric rods

A numerical algorithm based on the method of auxiliary sources combined with the mode-matching method for analysis of planar arrays of stepped circular waveguides with protruding dielectric elements is presented. The auxiliary sources used for representing the fields inside and outside the protrusions are chosen in the form of rings of azimuth electric and magnetic currents arranged, respectively, outside and inside the geometric region of protrusions. Satisfaction of the boundary conditions on the protrusion surface, as well as on the waveguide aperture, reduces the problem an algebraic system with respect to unknown current amplitudes and waveguide mode amplitudes. The effectiveness of the algorithm is enhanced by using a simple and efficient approach to calculation of the Green's function for periodic structures. Some examples of the calculated array characteristics are presented and discussed.