An Efficient Method to Extract Surface-Wave Poles of Green's Functions near Branch Cut in Lossy Layered Media


Calculating the Green's functions in lossy layered media using the discrete complex image method (DCIM) is challenging, due to the difficulties in extracting the surface-wave poles that are very close to a branch cut. An efficient algorithm based on the contour method is proposed in this communication to locate these poles and calculate the residues. The proposed method is robust for both the lossless and lossy media. With the proposed approach, it is shown in numerical examples that some poles, very close to a branch cut, are successfully extracted in lossy media. The accurate calculation of the Green's functions in lossy layered media enables the accurate and efficient modeling of complex structures in lossy semiconductor substrates and new 3D IC structures including through-silicon vias (TSVs).


Electrical and Computer Engineering

Research Center/Lab(s)

Center for High Performance Computing Research

Second Research Center/Lab

Electromagnetic Compatibility (EMC) Laboratory

Keywords and Phrases

Algorithms; Electronics packaging; Green's function; Image processing; Integrated circuit interconnects; Poles; Semiconducting silicon; Surface waves; Discrete complex image method; Layered media; Pole extraction; Sommerfeld integrals; Spectral domains; Surface wave poles; Three dimensional integrated circuits; lossy layered media

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2015