Miller's rule (optics)


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.

Definition

The first order susceptibility response is given by:
where:
For simplicity, we can define, and hence rewrite :
The second order susceptibility response is given by:
where is the first anharmonicity coefficient.
It is easy to show that we can thus express in terms of a product of
The constant of proportionality between and the product of at three different frequencies is Miller's coefficient: