  We study the effect of an electric-field on an electron-hole pair in an
asymmetric system of vertically coupled self-assembled quantum dots taking into
account their non-perfect alignment. We show that the non-perfect alignment
does not qualitatively influence the exciton Stark effect for the electric
field applied in the growth direction, but can be detected by application of a
perpendicular electric field. We demonstrate that the direction of the shift
between the axes of non-aligned dots can be detected by rotation of a weak
electric field within the plane of confinement. Already for a nearly perfect
alignment the two-lowest energy bright exciton states possess antilocked
extrema as function of the orientation angle of the horizontal field which
appear when the field is parallel to the direction of the shift between the dot
centers.
