A Novel Implementation of Discrete Complex Image Method for Layered Medium Green's Function

A novel implementation of discrete complex image method (DCIM) based on the Sommmerfeld branch cut is proposed to accurately capture the far-field behavior of the layered medium Green's function as a complement to the traditional DCIM. By contour deformation, the Green's function can be naturally decomposed into branch-cut integration (radiation modes) and pole contributions (guided modes). For branch-cut integration, matrix pencil method is applied, and the alternative Sommerfeld identity in terms of k(z) integration is utilized to get a closed-form solution. The guided modes are accounted for with a pole-searching algorithm. Both one-branch-cut and two-branch-cut cases are studied. Several numerical results are presented to validate this method.