Frequency Dependence of Miller's Rule for Nonlinear Susceptibilities

The frequency dependence of Miller's phenomenological relation is examined. Recent measurements of harmonic generation in semiconductors suggest that Miller's coefficient $\delta$ may be more nearly frequency independent than had been expected, and therefore the anharmonic oscillator, a model for which $\delta$ is known to be independent of frequency, is considered. It is shown that if the anharmonic potential is identified with the average antisymmetric potential of Phillips's theory of covalent bonding, values for the nonlinear susceptibilities of semiconductors at low frequencies are obtained which are in excellent agreement with experiment. When more realistic models of the dispersion of the nonlinearity are examined, it is found that for these models $\delta$ is nonsingular despite singularities in both the linear and nonlinear susceptibilities.