  We discuss the application of Complex-Plane Gauss-Laguerre Quadrature (CGLQ)
to efficiently evaluate two-dimensional Fourier integrals arising as the
solution to electromagnetic fields radiated by elementary dipole antennas
embedded within planar-layered media with arbitrary material parameters. More
specifically, we apply CGLQ to the long-standing problem of rapidly and
efficiently evaluating the semi-infinite length "tails" of the Fourier integral
path while simultaneously and robustly guaranteeing absolute, exponential
convergence of the field solution despite diversity in the doubly anisotropic
layer parameters, source type (i.e., electric or equivalent magnetic dipole),
source orientation, observed field type (magnetic or electric), (non-zero)
frequency, and (non-zero) source-observer separation geometry. The proposed
algorithm exhibits robustness despite unique challenges arising for the fast
evaluation of such two-dimensional integrals. Herein, we develop the
mathematical treatment to rigorously evaluate the tail integrals using CGLQ and
discuss and address the specific issues posed to the CGLQ method when
anisotropic, layered media are present. To empirically demonstrate the CGLQ
algorithm's computational efficiency, versatility, and accuracy, we perform a
convergence analysis along with two case studies related to modeling of
electromagnetic resistivity tools employed in geophysical prospection of
layered, anisotropic Earth media and validating the ability of isoimpedance
substrates to enhance the radiation performance of planar antennas placed in
close proximity to metallic ground planes.
