  The smallest possible focus is achieved when the focused wave front is the
time reversed copy of the light wave packet emitted from a point in space (S.
Quabis et al., Opt. Commun. 179 (2000) 1-7). The best physical implementation
of such a pointlike sub-wavelength emitter is a single atom performing an
electric dipole transition. In a former paper (N. Lindlein et al., Laser Phys.
17 (2007) 927-934) we showed how such a dipole-like radiant intensity
distribution can be produced with the help of a deep parabolic mirror and
appropriate shaping of the intensity of the radially polarized incident plane
wave. Such a dipole wave only mimics the far field of a linear dipole and not
the near field components. Therefore, in this paper, the electric energy
density in the focus of a parabolic mirror is calculated using the Debye
integral method. Additionally, a comparison with "conventional nearly 4pi"
illumination using two high numerical aperture objectives is performed. The
influence of aberrations due to a misalignment of the incident plane wave is
discussed.

Optics