  Using an exact diagonalization approach we show that one- and two-electron
InAs quantum dots exhibit avoided crossing in the energy spectra that are
induced by the spin-orbit coupling in the presence of an in-plane external
magnetic field. The width of the avoided crossings depends strongly on the
orientation of the magnetic field which reveals the intrinsic anisotropy of the
spin-orbit coupling interactions. We find that for specific orientations of the
magnetic field avoided crossings vanish. Value of this orientation can be used
to extract the ratio of the strength of Rashba and Dresselhaus interactions.
The spin-orbit anisotropy effects for various geometries and orientations of
the confinement potential are discussed. Our analysis explains the physics
behind the recent measurements performed on a gated self-assembled quantum dot
[S. Takahashi et al. Phys. Rev. Lett. 104, 246801 (2010)].
