From band structures to linear and nonlinear optical spectra in semiconductors

The theory of the relation between optical properties and electronic band s tructures is reviewed. In the first part, we describe various approaches to go beyond the long-wavelength limit perturbation theoretical approach in t he independent particle approximation for linear optical response functions . In the latter, electron-electron interaction effects are only included in as far as they are implicit in the underlying band structure (typically wi thin the local density functional approximation). We discuss the inclusion of quasiparticle corrections to the band structures, local-field and electr on-hole interaction effects. A case study of GaN is used to illustrate the discrepancies between theory and experiment that arise from neglect of thes e effects. On the other hand, the paper also illustrates that in the proces s of extracting the band structure information from optical spectra, the in dependent particle model still plays a central role. In the case of nonline ar optical response, even the independent particle model was only recently fully developed. Recent progress in this area and their implementation with in the context of first-principles band structure methods is presented next . Some examples are used to illustrate the potentially richer information c ontained in NLO spectra in relation to the underlying band structures. Seco ndly, progress in understanding the trends in NLO coefficients in some clas ses of materials is illustrated with a study of chalcopyrites.