Convergent expressions for periodic potentials in stratified media using asymptotic extractions

The efficient computation of periodic Green’s functions is discussed here for an arbitrarily directed array of point sources in layered media. These Green’s functions are necessary to formulate boundary integral equations for arrays of scatterers inside a general layered medium, solved with the method of moments in the spatial domain. For this reason, mixed-potential Green’s functions—having a mild spatial singularity—are selected. The case of horizontally oriented dipoles is rather simple and has been previously solved. On the other hand, the case of vertically oriented dipoles (i.e., aligned perpendicular to the layers) is more intricate, since the extracted terms cannot be transformed into well-known Green’s functions. Previous works dealt with arrays of line and point sources, but did not address the critical task of computing the curl of the dyadic potentials, required to treat slot arrays and dielectric inclusions, whose available Floquet series expressions do not converge if the source and observation points lie in the same transverse plane.