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Efficient Asymptotic Closed Form Approximation for Dyadic Green's Function for Anisotropic Substrates

Abstract : An efficient closed form asymptotic representation for a grounded double-layered anisotropic uniaxial geometry is developed. The large parameter of this asymptotic development is directly proportional to the lateral separation between the source and observation point. However the asymptotic solution remains accurate even for very small (a few tenths of a wavelength) lateral separation of the source and field points. the asymptotic closed form dyadic Green's function has been cast in such a form that the physical behavior of the electromagnetic fields due to anisotropy of the medium reveals itself through a simple mathematical parameters. Thus, the physical understanding of the interaction of the spatially confined source with an anisotropic (uniaxial) double-layered grounded slab is greatly enhanced through the newly developed asymptotic closed form representation of the dyadic Green's function. Also, this efficient representation is very useful in the moment method (MM) solution of the current excited on the microstrip antennas and arrays in a grounded double- layered uniaxial geometry, as well as the volumetric current excited within a dielectric scatterer buried in a grounded double layered anisotropic uniaxial slab. The MM analysis, especially for microstrip arrays and guided wave structures, requires a very large number of computations where the lateral distance between the source and the field points in the dyadic Green's function can range from extremely small to very large values.