Robust computation of dipole electromagnetic fields in arbitrarily anisotropic, planar-stratified environments

Abstract

We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary and independent anisotropy in both its (complex) permittivity and permeability tensors. Among the salient features of our formulation are (i) computation of eigenmodes (characteristic plane waves) supported in arbitrarily anisotropic media in a numerically robust fashion, (ii) implementation of an hp-adaptive refinement for the numerical integration to evaluate the radiation and weakly evanescent spectra contributions, and (iii) development of an adaptive extension of an integral convergence acceleration technique to compute the strongly evanescent spectrum contribution. While other semianalytic techniques exist to solve this problem, none have full applicability to media exhibiting arbitrary double anisotropies in each layer, where one must account for the whole range of possible phenomena (e.g., mode coupling at interfaces and nonreciprocal mode propagation). Brute-force numerical methods can tackle this problem but only at a much higher computational cost. The present formulation provides an efficient and robust technique for field computation in arbitrary planar-stratified environments. We demonstrate the formulation for a number of problems related to geophysical exploration.

Pseudo-Analytical Modeling for Electromagnetic Well-Logging Tools in Complex Geophysical Formations

“…Recent studies have shown that this problem can be circumvented through suitable rescaling of various expressions involved in the computational chain [50,52], as well as expressing by the ratios of Bessel or Hankel functions [53]. The LWD tools modeled in this dissertation do not required high orders cylindrical functions, but for extreme conductivity media the techniques reported in [50,52,53] need to be used.…”

“…This problem comes from the complex large argument of the cylindrical functions. In that situations, we could consider approximated impedance boundary condition (as those proposed in Section 3.3.3.1) and also the rescaling of Bessel functions (recently proposed in [50,52,53]) to prevent this numerical problem.…”

“…In this case, the A-NMM becomes a more natural choice to be combined with the perturbation theory used to model bent waveguides presented in [51]. Regardless of the choice for the modal expansion, since the frequency of operation and physical parameters (in particular the resistivity of the mud fluid and the surrounding Earth formation) in typical well-logging problems can vary by several orders of magnitude, it is important to ensure that the method of analysis is sufficiently robust to yield accurate solutions under a wide range of input parameters [5,50,52,53]. In this chapter, we introduce a new axial mode-matching formulation to provide a flexible technique for analyzing directional well-logging tools in anisotropic formations.…”

Generation of light in spatially dispersive materials

“…The problem of dipole radiation in optically anisotropic layered media without spatial dispersion has been previously considered using the Green function formalism [19][20][21][22][23][24]. When using the formalism, the materials are described by single electric permittivity and magnetic permeability tensors.…”

“…However, they only determine the field in some specific types of materials, including homogeneous anisotropic materials [19][20][21][22][23][24], lossless photonic crystals with known Bloch modes [25], and one-dimensional nanomaterials, such as dielectric-metal stacks [26]. More complex media, especially spatially dispersive ones, are out of reach of these methods.…”