Inhomogeneous absorption lines

However a quantitative analysis of the absorption bands requires the formalism of the stochastic theory, outlined in Section 10.2, which is able to connect the measured solvent shifts and inhomogeneous bandwidths to two microscopic parameters of the system, namely the respective number densities p of matrix units aroimd a dye molecule and the depths e of the dye-matrix interaction potentials. While for polymer matrices the stochastic theory was to be used to determine geometric parameters [4], they are already known for our rare gas model systems from independent investigations. This enabled us to reduce the number of fit factors and calculate the p and values as listed in Tab. 10.3. 

The widely used continuum approximation turned out to lead to the unreasonable result that p exceeds the number densities measured in bulk rare gas crystals The physical reason for this discrepancy is that the continuum approximation does not prevent matrix units from occupying identical positions, since their mutual steric exclusion has been neglected Therefore the calculation is based upon too many matrix units - reflected in the unrealistically large number density - giving insufficient weight to the individual matrix unit [20], Taking matrix correlations into account, as sketched in Section 10.2, the depth of the dye-matrix interaction potential e is increased and the number density p reduced to appropriate values (Table 10.3). 

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If, by absorption of monochromatic light, i.e. a laser beam, a molecule can be so modified in its structure or in its interaction with the local environment that a laser pulse of the same wavelength cannot - even at a later time - again be absorbed (bleaching), then this molecule is excluded from the ensemble of molecules which contribute to the broad, inhomogeneous absorption line. In the broad absorption band, a hole then appears at the position of the individual absorption of the bleached molecule. This forms the basis of the method of hole-burning (cf Fig. 12.17). 

Loring RA (1990) Statistical mechanical calculation of inhomogeneously broadened absorption line shapes in solution. J Phys Chem 94 513-515... 

To apply the Forster equation, the emission and absorption line shapes must be identical for all donors and acceptors, respectively. However, in many types of condensed-phase media (e.g., glasses, crystals, proteins, surfaces), each of the donors and acceptors lie in a different local environment, which leads to a distribution of static offsets of the excitation energies relative to the average, which persists longer than the time scale for EET. When such inhomogeneous contributions to the line broadening become significant, Forster theory cannot be used in an unmodified form [16, 63]. 

Therefore, the absorption line is massively inhomogeneously broadened at low temperature. An inhomogeneous lineshape can be used to determine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical information whatsoever [94, 95]. As T is increased to 300 K, the absorption linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inhomogeneous environments, a well known phenomenon termed motional narrowing [95]. 

Fig. 2. (a) Disordered lattice doped with guest molecules, (b) Absorption line shape of guest molecules in a disordered lattice, where F is the inhomogeneous width. 

Fig. 12.17 Photochemical hole-burning within an inhomogeneously-broadened spectral line, narrow-band laser light is applied. A hole is then burned into the broad absorption line, with the spectral width of the laser light or with the homogeneous linewidth The absorption line of the...

Especially in glasses and in solid matrices with strongly inhomogeneously-broadened absorption lines of the molecules within them, one can obtain sharp molecular absorption lines and sharp holes by applying this principle with narrow-band laser light. If the quantum energy of the laser light is varied by small steps, many holes can be burned adjacent to one another in the broad absorption line. 

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