  The self-assembled quantum dot with lens domain has rotational symmetry but
it is intrinsically asymmetric when the electron moves perpendicularly to its
circular base, {\it i. e.} along the rotational axis. To characterize this
asymmetry, an external electric field is applied along the positive or negative
direction of the rotational axis. We report the different Stark shifts
appearing in the spectra as a function of the field intensity for different
lens domains. It is shown that for a flat lens domain the asymmetry effects
decrease, but even for very flat lenses they can not be approximated by a
cylindrical domain. Finally, some optical properties such as the dielectric
constant and electroabsorption are studied. Signatures of the energy spectrum
reveal in these quantities. The importance of considering the proper lens
domain as long as the magnitude and direction field to tune a specific level
transition is stressed.
