Focusing of electric-dipole waves in the Debye and Kirchhoff approximations

We compare the Debye and Kirchhoff approximations for focusing of electromagnetic waves, with special emphasis on the focusing of converging electric-dipole waves. Numerical solutions for the spectral amplitude of the incident converging wave and for the focused field are provided in both approximations for a variety of Fresnel numbers and f-numbers. Comparisons of numerical solutions in Kirchhoff and Debye approximations show that for systems of Fresnel numbers larger than 20 and f-numbers less than 0.5, both approximations give indistinguishable results for focused electric-dipole waves; At low Fresnel numbers, the Kirchhoff approximation gives the best results irrespective of the f-number, as in the scalar case. The focal shift depends mainly on the Fresnel number, but at low Fresnel numbers, a reduction of the f-number gives an increase of the relative focal shift.