Field forms of the layered electromagnetic Green's functions by TE and TM potentials

A complete set of 3D layered electromagnetic Green's functions in the spatial domain is derived by way of transverse electric and transverse magnetic potentials, featuring a “direct” formulation for the field forms of the spectral Green's functions. The improper integrals underpinning the computation of the corresponding point-load solutions in the spatial domain are evaluated via the method of asymptotic decomposition, wherein the singular behaviors are entirely extracted and integrated analytically—so that the remaining residual components can be computed effectively and accurately via adaptive numerical quadrature over a suitable contour path. It is also found that, in the spectral domain, the decay of the (numerically-integrated) residual field forms is commensurate with that of their potential-form counterparts, which eliminates the perceived gap between the computation of the field forms and respective potential forms of the Green's functions in the spatial domain. The effectiveness and accuracy of the proposed methodology is evaluated via comparison with relevant examples in the literature.