Dependence on dimensionality of excitonic optical nonlinearity in quantum confined structures

The dependence on dimensionality of the excitonic optical nonlinearity and the figures of merit in quantum confined structures is clarified for the resonant third-order optical nonlinearity. An important parameter which determines the dimensionality dependence of the figures of merit is found to be the ratio of the homogeneous linewidth to the exciton binding energy or the ratio of the exciton coherence length to the exciton Bohr radius. It is predicted that for the III-V compound semiconductors the exciton confinement in low-dimensional structures (d=1,2 d:dimensionality) is favorable for enhancing the figures of merit, whereas for the I-VII compound semiconductors the exciton confinement does not always improve the figures of merit.