Generalized Miller Formulae

TL;DR

This paper generalizes the Miller formula to any order of non-linearity, providing a spectral dependence of non-linear susceptibility based solely on linear dispersion, applicable to frequency-degenerate cases for arbitrary non-linear indices.

Contribution

It introduces a generalized Miller formula that relates non-linear susceptibilities to linear dispersion for all orders, extending previous models.

Findings

Spectral dependence of non-linear susceptibility derived

Generalized Miller formula applicable to any non-linearity order

Spectral dependence of non-linear refractive indices obtained

Abstract

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.