# Miller's Rule

## Description

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## Variables

χ1(ω) | first order electric susceptibility, as a function of ω (dimensionless) |

N | number density of oscillating charge carriers (electrons) (dimensionless) |

q | fundamental charge (1.602176565e-19 Coulomb) (dimensionless) |

m | mass of the oscillating charges, the electron mass (dimensionless) |

ϵ_{0} | electric constant (8.854187817e-12 F m^-1) (dimensionless) |

ω_{0} | frequency of oscillation of the electric field in free space (Hz) (dimensionless) |

ω | frequency of oscillation of the electric field (Hz) (dimensionless) |

i | Imaginary unit |

τ | free carrier relaxation time (s) (dimensionless) |