Layered Media Green´s Function Approximation in Terms of Spherical & Cylindrical Waves

A robust methodology is presented for the derivation of accurate, closed-from expressions for the Green´s functions in planar stratified media. The methodology is based on the separation of the spectrum into two parts; the quasi-static and the dynamic part. The quasi-static part is calculated analytically in closed form, both in the spectral and space domain, and translates to a finite sum of spherical waves. The spectrum of the dynamic part is fitted in terms of rational functions and results in a finite sum of cylindrical waves, in the space domain. High accuracy is achieved for both the near field and the far field region due to the fact that both spherical and cylindrical waves are included in the closed form expressions.