Empirical relationships for predicting nonlinear refractive index changes in optical solids

The development of high-power glass lasers has stimulated interest in materials with low index nonlinearity. A number of authors have proposed empirical relations between the nonlinear index and linear dispersion parameters. We review these expressions and relate them to both classical and quantum theoretic derivations of the index nonlinearity. We show that the major differences arise in the treatment of local field corrections. We further show that the good agreement obtained between experiment and theory may be fortuitous, due to the fairly large experimental uncertainty and the fact that all the materials investigated to date are really quite similar, being essentially oxide or fluoride materials.