  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.
