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We study the out-of-equilibrium current through a multilevel quantum dotcontacted to two superconducting leads and in the presence of Rashba andDresselhaus spin-orbit couplings, in the regime of strong dot-lead coupling.The multiple Andreev reflection (MAR) subgap peaks in the current voltagecharacteristics are found to be modified (but not suppressed) by the spin-orbitinteraction, in a way that strongly depends on the shape of the dot confiningpotential. In a perfectly isotropic dot the MAR peaks are enhanced when thestrength $\alpha_R$ and $\alpha_D$ of Rashba and Dresselhaus terms are equal.When the anisotropy of the dot confining potential increases the dependence ofthe subgap structure on the spin-orbit angle$\theta=\arctan(\alpha_D/\alpha_R)$ decreases. Furthermore, when an in-planemagnetic field is applied to a strongly anisotropic dot, the peaks of thenon-linear conductance oscillate as a function of the magnetic field angle, andthe location of the maxima and minima allows for a straightforward read-out ofthe spin-orbit angle $\theta$.

Multiple Andreev reflections in a quantum dot coupled to superconductors: Effects of spin-orbit coupling