Greens function for an infinite slot printed between two homogeneous dielectrics-Part I: magnetic currents

This sequence of papers presents an analytical closed form for the Green's function of an infinite slot printed between two different homogeneous dielectrics. This first part is devoted to the derivation of the slot magnetic current and to the discussion of the relevant physical implications. The Fourier spectrum of the magnetic current is derived by solving in analytical form, under small width approximation, the integral equation (IE) representing the continuity of the magnetic field trough the slot axis. The accuracy of the result is validated trough a fine meshing Method of Moments. From the consequent spectral expression, a closed form approximation of the leaky-wave propagation and attenuation constants is derived. An asymptotic expression for the current is also obtained by steepest descent path evaluation of the pertinent spectral integral. Analytical expressions of the quasi static (reactive) contribution is given for both elementary dipole and delta gap excitations. The asymptotic, uniform closed form approximation for the field in every space point will be formulated and discussed in the second part of the paper.