Electrostatic Green's functions for planar multilayered anisotropic media

Abstract

This paper presents a concise 2 × 2 matrix formulation of the electrostatic Green's functions for planar multilayered anisotropic media. The media may consist of any number of layers bounded by optional Dirichlet, Neumann or mixed walls. Both potential and normal-displacement Green's functions for arbitrary field and source locations are determined simultaneously in the spectral domain. The optional boundary wall and open conditions are incorporated universally through the reflection coefficients which relate the upward-bounded and downward-bounded partial eigenfields. These coefficients avoid the indeterminate calculations that may occur for open structures or large spectral variables. The resultant Green's function expressions are written in illuminating and explicit form ready to be utilised. For illustration, the grounded three-layered dielectric structure is considered analytically, along with simple extension to biaxial and symmetric anisotropic media. Numerical results are also demonstrated for the capacitance of microstrip on anisotropic substrates, including lithium niobate characterised by sets of permittivity at constant strain and constant stress.