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Spatially structured light fields applied to semiconductor quantum dots yieldfundamentally different absorption spectra than homogeneous beams. In thispaper, we theoretically discuss the resulting spectra for different light beamsusing a cylindrical multipole expansion. For the description of the quantumdots we employ a model based on the effective mass approximation includingCoulomb and valence band mixing. The combination of a single spatiallystructured light beam and state mixing allows all exciton states in the quantumdot to become optically addressable. Furthermore, we demonstrate that the beamscan be tailored such that single states are selectively excited, without theneed of spectral separation. Using this selectivity, we propose a method tomeasure the exciton wave function of the quantum dot eigenstate. Themeasurement goes beyond electron density measurements by revealing the spatialphase information of the exciton wave function. Thereby polarization sensitivemeasurements are generalized by including the infinitely large spatial degreeof freedom.

physical review. b./physical review. b

Selection rules for the excitation of quantum dots by spatially  structured light beams -- Application to the reconstruction of higher excited  exciton wave functions