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We investigate the excitonic optical properties in thin quantum boxes in the intermediate regime between the two-dimensional (2D) and zero-dimensional (0D) with a theoretical analysis that rigorously treats excitonic confinement effects. It is found that the exciton binding energy is substantially enhanced and that the oscillator strength concentrates to the lowest excitonic transition, even in a thin box whose lateral width is considerably (about five times) larger than the Bohr radius. Novel optical properties experimentally observed in semiconductor quantum disks, which are the intense photoluminescence spectrum and ultranarrow photoluminescence excitation spectrum, are explained well by the theoretical results. We also calculate exciton absorption in a thin box in which an electric field is applied in the lateral direction. The present theory can simulate how the electroabsorption evolves from the quantum confined Stark effect in the 0D to the quantum confined Franz–Keldysh effect in the 2D with an increase in the lateral size of the box. In the intermediate regime between 2D and 0D, a strong excitonic electric-field effect, distinct from the well-known electroabsorption effects at 0D and 2D, is found. These theoretical results demonstrate that even though the lateral confinement is weak, it considerably enhances the electron–hole Coulomb interaction and alters excitonic optical features markedly in the thin quantum box. © 1997 American Institute of Physics.