Variable permittivity dielectric material loaded stepped-horn antenna

10section asFrom (2.4), the transverse electromagnetic fields are represented in each waveguidewhere Aimn and Bimn 7, are the complex amplitudes of the incident and reflected waves for themn-th mode asSubindices h and e are used to differentiate T E and T M modes, respectively. Mode indicesin the summations are m = 1, 2..., M and n = 0, 1, 2, N. In the above equations ( dueto the closed nature of the model), in the i-th waveguide section, the integers M and Ntend to infinity, i.e., N —> oo and M —> oo . eihmn and hihmn are the transverse electric andmagnetic fields of the mn-th T E mode in the i-th waveguide section and eiemn and hie mn arenthe transverse electric and magnetic fields for the mn-th T M mode in the i-th waveguidesectionAt the overlapping aperture regions over the junction, the boundary conditions imposethe continuity of the tangential electric and magnetic fields and on non-overlapping regionover the larger cross-section, the tangential electric field is assumed to be equal to zero.