“Relay race” closed-form expressions of Green´s functions for planar layered media

In this paper, a "relay race" strategy is introduced in the derivation of closed-form expressions for spatial domain multilayered GF. First, far-field closed-form expressions are obtained which are proven to be accurate within 0.1% for distances between source and field points larger than one free-space wavelength. For the derivation of these far-field expressions, the spectral domain GF are approximated by means of a modified RFFM in terms of the spectral variable uq = (k2 - k^)1/2 [7], and uniform asymptotic expansions are determined for the Sommerfeld integrals of the resulting RFFM approximations. The spatial domain far-field expressions obtained consist of a combination of surface waves and residual waves. Second, near-field closed-form expressions are obtained which are accurate within 0.1% for distances between source and field points smaller than one free-space wavelength. For the derivation of the near-field expressions, the spectral Green\´s functions are approximated in two steps by means of both the DCIM and the standard RFFM in terms of the spectral variable kρ. The resulting spatial domain near-field expressions consist of a combination of quasi-static complex images and cylindrical surface waves.