Nonlinear resonant change in refractive index of a doped saturable medium at short-pulse excitation

A novel method is reported for calculating the nonlinear resonant change in refractive index of a doped saturable medium at the short-pulse excitation. The derived system of equations for energy density and phase of a short pulse propagating in the doped medium allows one to address a rather general case of the resonant index non-linearity caused by the dope's population perturbation (bleaching) effect. As an example, the energy-dependent changes in the refractive index and transmission coefficient of a Cr⁴⁺:YAG crystal under the ns-range (wavelength 1.06 μm) excitation are modeled.