Efficient Determination of the Poles and Residues of Spectral Domain Multilayered Green's Functions That are Relevant in Far-Field Calculations

In this work the total least squares algorithm (TLSA) is applied to the determination of the proper and improper poles of spectral domain multilayered Green's functions that are closer to the branch point, and to the determination of the residues at these poles. The introduction of an adequate transformation in the spectral domain permits that the TLSA provides accurate values of the poles and residues, regardless of the proximity of the poles to the branch point. It is shown that the poles and residues supplied by the TLSA can be used to write the far field of the spatial domain Green's functions in terms of closed-form expressions that are reliable in a wide variety of scenarios.