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The electronic properties of a structure with columnar quantum dots obtained by close stacking of InAs submonolayers have been investigated by contactless electroreflectance (CER) and photoluminescence. These dots have an almost ideally rectangular cross section and uniform composition, which is promising for polarization independent gain. After energy level calculations in the effective mass approximation using composition profiles obtained from cross-sectional transmission electron microscopy the part of the CER spectrum related to the two-dimensional surrounding layer has been explained and single heavy-hole-like and light-hole-like transitions related to the columnar dots identified, due to a single electron state confined in a shallow in-plane potential.