Analytical model for the refractive index in quantum wells derived from the complex dielectric constant of Wannier excitons in noninteger dimensions

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Abstract
Absorption spectra of low-dimensional structures such as quantum wells or wires have been strikingly well reproduced by expressions based on solutions of the Schrödinger equation for the Coulomb potential in noninteger dimensions, which require much less computational effort than more elaborate calculations. The compact and analytical complex dielectric constant of Wannier excitons in d dimensions is given, and included in a simple model of the refractive index in quantum well structures in the vicinity of the absorption threshold.