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Summary form only given.The quantum-confined Stark effect (QCSE) in one-dimensional (1D) structures is expected to display enhanced transfer of oscillator strength and enhanced Stark shifts compared with two-dimensional (2D) systems. 1D quantum wires (QWRs) are, however, characterized by a 2D confinement potential that may have important consequences: the QCSE thus becomes two dimensional (2D-QCSE). Here we report an experimental and theoretical investigation of the 2D-QCSE in V-groove QWRs. We observe the 2D-QCSE and find striking effects due to electron or hole wave-function splitting. Furthermore, interplay of electric field, geometry and valence band mixing gives rise to new tunable features in polarization anisotropy.