  We perform a systematic exact diagonalization study of spin-orbit coupling
effects for stationary few-electron states confined in quasi two-dimensional
double quantum dots. We describe the spin-orbit-interaction induced coupling
between bonding and antibonding orbitals and its consequences for
magneto-optical absorption spectrum. The spin-orbit coupling for odd electron
numbers (one, three) %only weakly perturbs the ground-state wave functions.
%Nevertheless, %the spin-orbit interaction opens avoided crossings between low
energy excited levels of opposite spin orientation and opposite spatial parity.
For two-electrons the spin-orbit coupling allows for low-energy optical
transitions that are otherwise forbidden by spin and parity selection rules. We
demonstrate that the energies of optical transitions can be significantly
increased by an in-plane electric field but only for odd electron numbers.
Occupation of single-electron orbitals and effects of spin-orbit coupling on
electron distribution between the dots are also discussed.
