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

Abstract

Abstract-Closed-form mixed potential Green's functions (MPGFs) for cylindrically stratified media are derived in terms of quasistaticwave and surface-wave contributions. In order to avoid possible overflow/underflow problems in the numerical calculations of special cylindrical functions such as Bessel and Hankel functions, a novel form of the spectral-domain MPGFs is developed. Then, a twolevel methodology is used for the approximation of the spectraldomain MPGFs. In the first step, the qusistatic components are extracted from the spectral-domain MPGFs, and then transformed into the space domain with the use of the Sommerfeld identity and its derivatives. In the second step, the remaining parts of the spectral-domain MPGFs are approximated in terms of pole-residue expressions via the rational function fitting method (RFFM). The proposed method is efficient and fully automatic, which avoids an analytical cumbersome extraction of the surface wave poles (SWPs), prior to the spectrum fitting. In addition, this method can evaluate the spatial-domain MPGFs accurately and efficiently for both the nearand far-fields. Finally, numerical results for the spatial-domain MPGFs of a two-layer structure are presented and discussed.

Accurate Calculation of Mutual Coupling Between Apertures on a Large Coated Cylinder Using Mixed Potential Green's Functions

“…It can be seen that, by cooperation of the approaches in [19] and [20], the separate disadvantages are overcome and a robust approach is obtained. As a distinct advantage of our strategy, a uniform treatment is yielded for almost all source and field positions (except the case they are overlapped), and no special techniques or limitations on expansion functions are required along the axial line.…”

“…At this point, in the following, we will discuss the drawbacks of the approaches presented in [19] and [20], and the advances of the procedure described in this communication.…”

“…As a result, in [20] accurate results are obtained only in the near field. However, in the procedure presented in this communication, this drawback is overcome by using the RFFM, an effective tool to account for the contributions of the SWPs, as verified in [19] and [22]. Since is enforced during the RFFM implementation to ensure the causality and radiation conditions [19], [22], (16) decays exponentially when increases.…”

“…In [19], due to the use of the addition theorem of the zero-order Hankel function, the analytical form of the extracted envelope related to is represented as a function of . This expression is obviously singular at , leading to the so-called axial line problem.…”

“…Hence, it is of great interest to develop an accurate and efficient approach for the computation of the MPGF [16]- [20]. Recently, a novel procedure is outlined to generate accurate MPGF results both in the near and far field [19]. However, this procedure cannot deal with the axial line problem, rendering it not versatile in the MoM application.…”