Planar layered media closed-form green's functions as a series of cylindrical waves

We have pointed out the advantages of writing the spatial domain Green's functions for a planar layered medium as a sum of cylindrical waves. Such a representation allows for multipole expansions with complexity O(kd) (with k the wavenumber and d the radius of the smallest sphere containing the domain), as opposed to the O((kd)²) dependence found for spherical waves. Two modalities of the Rational Function Fitting Method (TLS and VECTFIT) are explored, and the pros and cons of each of them are briefly summarized. In the first instance, TLS appears to be more convenient to have N_h small, although VECTFIT offers more flexibility if one wants to increase the larger distance at which this approximation is valid.