A Robust Method for the Computation of Green's Functions in Cylindrically Stratified Media

Abstract

Closed-form Green's functions for cylindrically stratified media are derived in terms of spherical waves and surface-wave contributions. The methodology is based on a two-level approximation of the spectral-domain Green's functions. In the first step, the large argument behavior of the zeroth-order Hankel functions is used for the extraction of the quasistatic images from the spectral-domain Green's functions with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated in terms of pole-residue expressions via the rational function fitting method. This robust, efficient, and fully numerical approach does not call for an analytical cumbersome extraction of the surface wave poles, prior to the spectrum fitting. Moreover, it can be applied in both the near-and far-field. Numerical results for the Green's functions of one-layer and two-layer structures are presented to verify the accuracy and efficiency of this approach.Index Terms-Closed-form Green's functions, cylindrically stratified media, discrete complex images method (DCIM), rational function fitting method (RFFM).

An Efficient Method for the Computation of Mixed Potential Green's Functions in Cylindrically Stratified Media

“…After the quasistatic-wave part is extracted in (16), the remaining dynamic part can be approximated by the RFFM method, which was proposed in [22]. Thus, the following expression is obtained…”

“…The DIP parameter T 2 should be chosen to ensure that k 0 1 + T 2 2 is greater than the wavenumbers of all layers, according to [22], and T 3 should be large enough, as discussed in [13]. The value of T 1 should be carefully chosen to meet the justification for shifting the path from the physical poles and branch point, according to [22].…”

“…Without the process of extracting all the surface-wave poles explicitly, this method was direct and convenient to implement. In [22], this approach was extended to the cylindrically stratified structure. The numerical results obtained for the spatial-domain field Green's functions showed good agreement with the direct numerical results.…”

“…The major contribution of this paper is to extend the RFFM method in [22] to the calculation of spatial-domain MPGFs of cylindrically stratified structure. For the sake of consistency, the spectral domain MPGFs for the e jωt time convention are derived, which have not yet been found from other published literature.…”

“…Since the infinite series involved converges slowly however, or even diverge, the series acceleration technique should be applied, according to [13]. After the quasistatic parts are completely extracted from the spectral-domain MPGFs, the RFFM method [22] can be applied for the approximation of the remaining parts. In Section 2, the details of the novel form spectral-domain MPGFs and the approximating RFFM method are presented, In Section 3, some numerical examples of the spatial domain MPGFs are presented for a cylindrically two-layered structure.…”