The theory of pump-probe experiments is examined using the nonlinear optical susceptibility ${\ensuremath{\chi}}^{(3)}$. The results of this calculation are shown to differ from those based on a commonly employed heuristic model of pump-probe experiments which assumes that the pump beam "prepares" the system which the probe beam subsequently monitors. This model consequently accounts only for processes where the interactions with the pump field come first in time. The correct expression for the probe absorption line shape as predicted by $\mathrm{Im}{\ensuremath{\chi}}^{(3)}$ contains a sum over all the possible time orderings of the various radiative interactions. The interference terms missing from the simplified treatment are shown to account for the spectral hole in homogeneously broadened lines observed recently [L. W. Hillman et al., Opt. Commun. 45, 416 (1983)]. In addition we derive a generalized expression for ${\ensuremath{\chi}}^{(3)}$ that is valid away from the impact limit and contains a realistic population relaxation ( ${T}_{1}$ ) matrix.The theory of pump-probe experiments is examined using the nonlinear optical susceptibility ${\ensuremath{\chi}}^{(3)}$. The results of this calculation are shown to differ from those based on a commonly employed heuristic model of pump-probe experiments which assumes that the pump beam "prepares" the system which the probe beam subsequently monitors. This model consequently accounts only for processes where the interactions with the pump field come first in time. The correct expression for the probe absorption line shape as predicted by $\mathrm{Im}{\ensuremath{\chi}}^{(3)}$ contains a sum over all the possible time orderings of the various radiative interactions. The interference terms missing from the simplified treatment are shown to account for the spectral hole in homogeneously broadened lines observed recently [L. W. Hillman et al., Opt. Commun. 45, 416 (1983)]. In addition we derive a generalized expression for ${\ensuremath{\chi}}^{(3)}$ that is valid away from the impact limit and contains a realistic population relaxation (${T}_{1}$) matrix.

Physical Review AApr 1, 1984102 citations

Generalized line broadening and saturation behavior

Albert T. Rosenberger

One characteristic normally used to distinguish inhomogeneous broadening from homogeneous broadening is the saturation behavior occurring when irradiation takes place at line center. The usual behavior found is that the absorption coefficient decreases as a negative power of 1 + I/Isat; a power of −1 indicates homogeneous broadening and a power of −½ denotes inhomogeneous broadening. It is shown here that, in the rate equation limit, this behavior is followed in most cases even though the homogeneous and inhomogeneous absorption profiles can have any line shape. The homogeneous line shape, in particular, need not be Lorentzian; its line center saturation behavior will be the same as that of a Lorentzian, however. If the inhomogeneous broadening is due to a distribution of atomic center frequencies, in the inhomogeneous limit the usual line center saturation behavior will be found no matter what the combination of homogeneous and inhomogeneous line shapes. However, if the broadening is inhomogeneous because of a distribution, among the individual atoms, in any property of the absorption profile other than center frequency (for example, the homogeneous linewidth), the saturation properties are not as simple, and in fact the inhomogeneous limit may not even exist.One characteristic normally used to distinguish inhomogeneous broadening from homogeneous broadening is the saturation behavior occurring when irradiation takes place at line center. The usual behavior found is that the absorption coefficient decreases as a negative power of 1 + I/Isat; a power of −1 indicates homogeneous broadening and a power of −½ denotes inhomogeneous broadening. It is shown here that, in the rate equation limit, this behavior is followed in most cases even though the homogeneous and inhomogeneous absorption profiles can have any line shape. The homogeneous line shape, in particular, need not be Lorentzian; its line center saturation behavior will be the same as that of a Lorentzian, however. If the inhomogeneous broadening is due to a distribution of atomic center frequencies, in the inhomogeneous limit the usual line center saturation behavior will be found no matter what the combination of homogeneous and inhomogeneous line shapes. However, if the broadening is inhomogeneous because of a distribution, among the individual atoms, in any property of the absorption profile other than center frequency (for example, the homogeneous linewidth), the saturation properties are not as simple, and in fact the inhomogeneous limit may not even exist.

Annual Meeting Optical Society of AmericaJan 1, 19890 citations

A Method for Calculating the Inhomogeneously Broadened Resonance Line Shape

E. I. Neimark, Inna Nikolayevna Nurutdinova, A. B. Roǐtsin

physica status solidi (b)Mar 1, 19901 citation

{T}_{1}

) matrix.