Optical constants of GaAs-AlxGa1−xAs superlattices and multiple quantum wells

The optical properties of GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As superlattices are calculated as a function of the frequency and superlattice structure. The computations are performed using a partition method which combines the k⋅p method with the pseudopotential technique. The influence of the superstructure on the electronic properties of the system is accounted for by appropriate quantization conditions. We show that the anisotropy and structure dependence of the dielectric constant result mainly from the contribution of the Γ region, while the contributions of the other regions of the Brillouin zone are rather insensitive to the superlattice structure. The superlattice index of refraction values are shown to attain maxima at the various quantized transition energies, where for certain structures, the difference between the refractive indices of the superlattice and its corresponding ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As alloy can be as large as 2%. In general, our results are in good agreement with the experimental data.