Transitions emission

As seen from (12) and Fig. 6, the peaks in the excitation anisotropy spectrum indicate a small angle between the absorption and emission transition dipoles suggesting allowed 1PA transitions while valleys indicate large angles between these two dipoles, suggesting a forbidden 1PA transition. Due to selection rules for symmetrical cyanine-like dyes, the valleys in the anisotropy spectrum could indicate an allowed 2PA transition as demonstrated in Fig. 6. Thus, an excitation anisotropy spectrum can serve as a useful guide to suggest the positions of the final states in the 2PA spectra. 

Most chromophores absorb light along a preferred direction1 (see Chapter 2 for the definition of absorption transition moment, and for examples of transition moments of some fluorophores, see Figure 2.3), depending on the electronic state. In contrast, the emission transition moment is the same whatever the excited state reached by the molecule upon excitation, because of internal conversion towards the first singlet state (Figure 5.2). 

Fig. 5.5. System of coordinates for characterizing the orientation of the emission transition moments.

Let us consider a population of N molecules randomly oriented and excited at time 0 by an infinitely short pulse of light polarized along Oz. At time t, the emission transition moments ME of the excited molecules have a certain angular distribution. The orientation of these transition moments is characterized by 0E, the angle with respect to the Oz axis, and by (azimuth), the angle with respect to the Oz axis (Figure 5.5). The final expression of emission anisotropy should be independent of

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For a particular molecule i, the components of the emission transition moments along the three axes Ox, Oy, Oz are MEa,(t), MEfit(t) and Mg>, ( ), where a,(t), / ,(t) and yt(t) are the cosines of the angles formed by the emission transition moment with the three axes (such that afpfyf = 1) and Me is the modulus of the vector transition moment. 

Finally, because y = cos dE, the relation between the emission anisotropy and the angular distribution of the emission transition moments can be written as... 

When the absorption and emission transition moments are parallel, 6a = 6e, the common value being denoted 6 hence cos2 6a = cos2 0E = cos2 6. Before excitation, the number of molecules whose transition moment is oriented within angles 6 and 8 + dd, and and 0 I delementary surface on a sphere whose radius is unity, i.e. 2n sin dddd< > (Figure 5.6). 

Fig. 5.6. The fraction of molecules whose absorption and emission transition moments are parallel and oriented in a direction within the elementary solid angle. This direction is defined by angles 8 and .

This situation occurs when excitation brings the fluorophores to an excited state other than the first singlet state from which fluorescence is emitted. Let a be the angle between the absorption and emission transition moments. The aim is to calculate cos dE and then to deduce r by means of Eq. (5.20). 

Fig. 5.7. Definition of angles and yr when the absorption and emission transition moments are not parallel.

The Brownian rotation of the emission transition moment is characterized by the angle co(t ) through which the molecule rotates between time zero (b-pulsc excitation) and time t, as shown in Figure 5.11. 

Fig. 5.9. Rotational motions inducing depolarization of fluorescence. The absorption and emission transition moments are assumed to be parallel.

We have considered spherical molecules so far, but it should be noted that isotropic rotations can also be observed in the case of molecules with cylindrical symmetry and whose absorption and emission transition moments are parallel and oriented along the symmetry axis. In fact, any rotation around this axis has no effect on the fluorescence polarization. Only rotations perpendicular to this axis have an effect. A typical example is diphenylhexatriene whose transition moment is very close to the molecular axis (see Chapter 8). 

In most cases, fluorescent molecules undergo anisotropic rotations because of their asymmetry. A totally asymmetric rotor has three different rotational diffusion coefficients, and in cases where the absorption and emission transition moments are not directed along one of the principal diffusion axes, the decay of r(t) is a sum of five exponentials (see Box 5.3). 

The fluorophore should be well characterized in terms of absorption and emission transition moments, quantum yield, polarization bands of interest, and behavior at different temperatures. The quantum yield should be high enough so that the level of probe needed for acceptably low signal noise would not be great enough to cause significant perturbation effects. 

EXAMPLE 1.2 An allowed emission transition for a given optical ion in a solid has a lifetime of 10 ns. Estimate its natural broadening. Then estimate the... 

Figure 1.9 The energy-level and transition schemes and possible luminescence spectra of a three-level ideal phosphor (a) the absorption spectrum (b, c) emission spectra under excitation with light of photon energies hvi and /iV2, respectively (d, e) Excitation spectra monitoring emission energies at /i( V2 — vi) and at /i vi, respectively. Arrows mark the absorption/emission transitions involved in each spectrum. Eixed indicates that the excitation or emission monochromator is fixed at the energy (wavelength) corresponding to this transition.

Table 5.1 The relative intensities and wavenumbers of the different 0 1, 2, 3, 4, 5 (absorption and emission) transitions for the spectroscopic parameters given in Example 5.5.

With this information, we can calculate the different radiative rates Ay j by using Equation (6.8) (remembering that it is given in MKS units). The calculated values of Sj j and Aj j are listed for the different emission transitions in Table 6.3. 

The branching ratio for a given emission transition, Ji Jf, is defined by... 

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