Variable permittivity dielectric material loaded stepped-horn antenna

14where * shows complex conjugate. In equation system (2.24), Vhh 7 Veh and Vee representthe TE to TE,TE to TM and TM to TM mode coupling coefficients, which are evaluatedrepectively, asAt each junction between two waveguide sections power is coupled between thedifferent modes on either side of the junction, including evanescent modes. This couplingis evaluated by integrating the fields over the surface. These coupling integrals have beenevaluated analytically in closed form to reduce the compuational burden. Furthermore, it isassumed that TE waves are coupled with the TM waves; TM waves are not coupled withTE waves (Vh e = 0). This effect is rigorously taken into account in (2.24). The equationsystem in (2.24) can be expressed in matrix form as