Exciton and polariton dispersion curves ofInxGa1−xAs∕GaAs(001)superlattice quantum wells: Model calculation

Abstract

Wannier exciton dispersion curves of ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}∕\mathrm{Ga}\mathrm{As}(001)$ quantum well superlattice are obtained by computing exciton energies, for different $\mathbit{K}$ points in the corresponding Brillouin zone, using a variational exciton envelope function model. The effective mass and the spatial dispersion of the exciton show strong variations depending on energy bands and $\mathbit{K}$ points. Polariton dispersion curves are computed in the semiclassical framework by using a nonlocal exciton susceptibility and solving self-consistently the Schr\odinger-Maxell equations. Photon dispersion curves of the one-dimensional photonic crystal, resulting from the periodicity of the dielectric constant in the superlattice, are also computed and reported in comparison with exciton and polariton bands. In order to mimic mesoscopic uniaxial photonic crystals, the versatility of ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}∕\mathrm{Ga}\mathrm{As}(001)$ superlattice is highlighted by selected numerical examples.