Complex-valued levin transforms: A robust algorithm for field computation in anisotropic-layered media

Conventional techniques to compute Green´s functions using a spectral representation, based on real-axis integration of spectral integrals, often produce slow convergence in environments exhibiting stratified inhomogeneity. Here, we present a novel methodology to guarantee exponential-cum-algebraic convergence of the computed time-harmonic electromagnetic fields that are produced by either electric or (equivalently modeled) magnetic dipoles in such media. In particular, we address the more challenging case of dipole radiation in planar-stratified environments containing media of arbitrary anisotropy and loss, where a two-dimensional Fourier integral must be evaluated. Finally, convergence data and presented validation results confirm that such strong convergence robustly holds even in the (traditionally) prohibitive regime where the source and observer´s relative depth separation vanishes.