Closed-Form Uniform Asymptotic Expansions of Green´s Functions in Layered Media

Far-field closed-form expressions are derived for spatial domain multilayered Green´s functions (GF). For the derivation of these far-field expressions, the spectral domain multilayered GF are approximated by means of the total least square algorithm (TLSA) in terms of the spectral variable u₀=(k_ρ²-k₀²)^1/2, and uniform asymptotic expansions are determined for the Sommerfeld integrals of the resulting TLSA approximations. Numerical results show that the far-field asymptotic expressions are accurate within 0.1% for distances between source and field points larger than one free-space wavelength. Also, it is shown that the hybrid use of the discrete complex image method and the TLSA in terms of the spectral variable k_ρ leads to near-field closed-form expressions of multilayered GF that are typically accurate within 0.1% for distances between source and field points smaller than one free-space wavelength. Therefore, the combination of the novel far-field asymptotic expressions and the well known near-field expressions makes it possible to compute multilayered GF with a great accuracy in the whole range of distances between source and field points, and in a wide range of frequencies.