Asymptotic Green´s function of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate

Published analyses of radiation modeling for slot structures on dielectric substrate are empirical or numerical. This paper proposes exact analytical asymptotic expressions of the far-field Green´s functions of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate of finite thickness. From these expressions, the radiation pattern of both the space wave and surface wave far away from an arbitrary shaped-slot antenna structure can be calculated, provided the source distribution across the slot is known. The potentials used in the analysis are defined and their boundary conditions are expressed. The Helmholtz equation is solved in the Laplace domain and the solutions are transformed into the space domain using the inverse Hankel transform and steepest descent method. The influences of the substrate thickness and dielectric constant are analyzed using the calculated expressions. The model is validated by comparison with surface wave and space wave measurements and with numerical results obtained from a commercial electromagnetic simulator