Miller's Rule


In optics, Miller’s rule is an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient.

More formally, it states that the coefficient of the second order electric susceptibility response is proportional to the product of the first-order susceptibilities at the three frequencies which is dependent upon. The proportionality coefficient is known as Miller’s coefficient.

Related formulas


χ1(ω)first order electric susceptibility, as a function of ω (dimensionless)
Nnumber density of oscillating charge carriers (electrons) (dimensionless)
qfundamental charge (1.602176565e-19 Coulomb) (dimensionless)
mmass of the oscillating charges, the electron mass (dimensionless)
ϵ0electric constant (8.854187817e-12 F m^-1) (dimensionless)
ω0frequency of oscillation of the electric field in free space (Hz) (dimensionless)
ωfrequency of oscillation of the electric field (Hz) (dimensionless)
iImaginary unit
τfree carrier relaxation time (s) (dimensionless)