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We report a theoretical study on the magnetooptical properties of recently synthesized concentric quantum double rings, as a function of the inner-outer ring coupling. The transition from a single to a double ring, as it is reflected in the the changes of the Aharonov-Bohm oscillation periods of the energy levels, is shown. It is found that, even when the system can be described as a single quantum ring with a small cleft, the electron energy levels show two different Aharonov-Bohm oscillation periods, which indicate that the carriers are localized in either the inner or the outer ring. For most distances between the rings, the electron and hole energy levels show almost identical Aharonov-Bohm oscillation periods. However, there is a short distances range in which they do not localize in the same ring, showing very different periods. In this region, the exciton ground state becomes dark. [ABSTRACT FROM AUTHOR]