Nonlinear dispersion and absorption effects

Nonlinear dispersion effects arise in the vincinity of absorption lines, i.e. where the Rayleigh equation for the group refractive index

$$N_{Gr}=N-\lambda \frac{dN}{d\lambda}$$ (15)

is no longer valid and higher order terms have to be included. Another effect related to this topic is the partial absorption of the laser pulse changing the pulse shape while propagation through the absorbing medium. A detailed description of these effects can be found in [Galkin et.al.(1999)]. GALKIN [Galkin (2000)] did a calculation including both effects for selected laser wavelengths. The resulting corrections for $850nm$ a water vapour partial pressure of $13.33$ mbar at a temeperature of $23$ C is about $0.4\times 10^{-7}$ in terms of the group refractivity.