Variable permittivity dielectric material loaded stepped-horn antenna

18Figure 2.6 Generalized reflection matrix representation of an aperture.horn sizes the contributions of the outside wall currents to the input reflection coefficient arenegligibly small and can be ignored to avoid the complexity of formulation and numericalevaluations.The equivalence principle is used on the radiating aperture by dividing the originalproblem into two decoupled parts as waveguide region and half-space region, as shown inFigure 2.7. This is accomplished by closing the aperture with a perfect electric conductorand placing sheets of equivalent magnetic current density. By the equivalence principle,the electromagnetic fields in both regions remain unchanged if the aperture is closed by aconductor, a sheet of magnetic current If is placed on the inner side of the aperture and asheet of —M is placed on the outer region. Magnetic current density is given byIn (2.35), ft is the unit normal vector pointing into free space and EA is the unknownelectric field on the aperture plane of the original problem.Equivalent magnetic current sheet in waveguide is +M and that in half-space is —Mensures that the tangential component of electric field is continuous across the apertureof the original problem. The other boundary condition is the continuity of the tangentialcomponent of the magnetic field across the aperture which is