Homogeneously broadened transitions

Traditionally the two-pulse photon-echo of a two-level system is described in terms of dynamics where there is a separation of the frequency fluctuations into two widely separated time scales, one of which is much faster and the other much slower than the time that characterizes the inhomogeneous distribution of frequencies. This gives rise to a hxed distribution of homogeneously broadened transitions for each spectral transition of the solute. The echo electric held generated from two very short pulses interacting with a molecule but separated by an interval x is, apart from constant factors, given by... 

In Vol. 1, Sect. 3.6 we saw that the saturation of homogeneously broadened transitions with Lorentzian line profiles results again in a Lorentzian profile with the... 

In the case of T2, the results for incoherent light are entirely the same as those for short pulse except that the T2 decay characteristic in the correlation trace appears symmetrically with respect to x for homogeneously broadened transition. In the case of Tj = T2, however, the appearance of T -dependent background and the modification of relaxation decay due to the Ti effect occur for incoherent light, while the results are independent of for short pulse input. These features complicate the interpretation of the results for incoherent light. But they still serve for the determination of T2, because the decay characteristics are dominantly governed by T2. All these behaviors can well be explained physically by... 

If both levels a) and b) decay with the relaxation constants ya and y, respectively, the line profile of the homogeneously broadened transition a)... 

There is essential difference between homogeneous and inhomogeneous laser transitions. For homogeneously broadened transitions, the whole area under the gain profile of Fig.5.14 above the threshold line can be converted into induced emission at a single frequency w. The induced emission power is according to (2.67)... 

We now proceed to consider gain saturation in detail for the case of a homogeneously-broadened transition. Although experimentally this is not the most common situation the analysis required is somewhat less involved than that necessary in the case of the inhomogeneously-broadened lines. 

Energy transfer in solution occurs through a dipole-dipole interaction of the emission dipole of an excited molecule (donor) and the absorptive moment of a unexcited molecule (acceptor). Forster<40) treated the interaction quantum mechanically and derived and expression for the rate of transfer between isolated stationary, homogeneously broadened donors and acceptors. Dexter(41) formulated the transfer rate using the Fermi golden rule and extended it to include quadrupole and higher transition moments in either the donor or the acceptor. Following the scheme of Dexter, the transfer rate for a specific transition is... 

The resonant susceptibility associated with a homogeneously broadened Raman transition, j, is,... 

Equations (6) and (7) predict a transition whose width will be small if the NC sample is monodisperse (i.e., all particles have the same a value). However, even samples with a narrow size distribution show transition line widths of —30 nm FWHM (full width half maximum), which is significantly broader than expected. This line broadening is due to both homogeneous broadening related to phonon excitations in the NC and inhomogeneous broadening due to interactions with the surrounding environment. ... 

Figure 4 Schematic showing both correlated and uncorrelated transitions in an inhomogeneously broadened electronic spectrum. Each single site spectrum shows relatively narrow, homogeneously broadened features. Correlated features track with the energy of a narrow electronic origin. Noncorrelated sidelines appear at any energy within its full, inhomogeneously broadened band...

The s-p absorption band of the solvated electron can be thought of as three overlapping, homogeneously broadened s-p transitions. 

In Eq.(l), the distribution of initial states and the distribution of transition moments from each initial state to the group of dissociative states give rise to inhomogeneous broadening. Levels included in the sum may be as completely specified as desired. For our analyses, the sums have explicitly included terms for individual J, M rotational sublevels. For Ne C2H and Ar C2H the sums were expanded to include internal rotation levels. Homogeneous broadening for an individual transition is... 

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