Index of refraction of GaAs-Al(x)Ga(1-x)As superlattices and multiple quantum wells

A theoretical study of the index of refraction of superlattices and its variation as a function of frequency and the superlattice parameters, i.e., layer width and AlAs composition, is presented. Gamma-region exciton and valence-band mixing effects are included in the model. It is found that these two effects have an important influence on the value of the index of refraction and that superstructure effects rapidly decrease for energies greater than the superlattice potential barriers. Because of the quasi-two-dimensional character of the Gamma-region excitons, the results indicate that the superlattice index of refraction can vary by about two percent at the quantized, bound-exciton, transition energies. Overall, the theoretical results are in good agreement with the experimental data.