Enhanced Convergence of Periodic Potentials in Stratified Media Through Asymptotic Extractions

摘要

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 a method of moments approach 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 (i.e., orthogonal to the stratification direction) is rather simple and has been solved previously; asymptotic terms are extracted that correspond to free-space Green's functions of periodic arrays of dipoles. 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. A previous work dealt with arrays of line sources, while previous conference papers described the new approach for point sources, without providing analytical details. Applications to the dispersive analyses of leaky-wave antennas, not included here for the sake of brevity, will be presented at the conference.