Efficient computation of post-slot interactions in complex layered media with vertical interconnects

We present here the efficient computation of the integrals expressing the coupling between a cylindrical wave scattered by a vertical post in a layered structure and a slot etched on a metallic plane orthogonal to the post. This integral is required for the analysis of large layered structures with vertical interconnects. The twofold spatial integral is transformed into a single spectral integral. Its integration path is deformed in order to pass through the saddle point of the integrand, and obtain a Gaussian decay on the tail. A reduced number of quadrature points is required, and a significant speed up is achieved for complex structures composed of thousands of posts and slots.