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Using a three-dimensional quasiclassical technique we explore moleculardouble ionization by a linearly polarized, infrared (800~nm) 27~fs laser pulse.For intensities ranging from the tunneling to the over-the-barrier regime, weidentify the double ionization pathways in a unified way as a function of totalelectron energy. For the tunneling regime, we discuss the differences in theinterplay of double ionization (DI) pathways between strongly driven He andstrongly driven $N_{2}$. For intermediate intensities in the over-the-barrierregime, we find that both the correlated momenta and the double ionizationprobability distribution as a function of total energy probe the tunnelingphase of the re-colliding electron. This allows for a direct verification ofthe re-colliding electron tunneling at a large phase of the laser field in theover-the-barrier regime in contrast to a small tunneling phase in the tunnelingregime.

Strongly driven molecules: probing the tunneling phase in the over-the-barrier regime and prevalence of different double ionization pathways