Linearly polarized fluorescence

Let us follow in time the intensity /p (t) of fluorescence linearly polarized at an angle linearly polarized excitation and with the geometry... 

Let us consider tire case of a donor-acceptor pair where tire acceptor, after capturing excitation from tire donor, can emit a photon of fluorescence. If tire excitation light is linearly polarized, tire acceptor emission generally has a different polarization. Common quantitative expressions of tliis effect are tire anisotropy of fluorescence, r, or tire degree of polarization,... 

A depolarization measurement consists of exciting a fluorescent sample with linearly polarized light and measuring the polarization of emitted light at right angles to the plane of excitation. The polarization of the emitted light is defined as... 

Steady-State Fluorescence Depolarization Spectroscopy. For steady state depolarization measurements, the sample is excited with linearly polarized lig t of constant intensity. Observed values of P depend on the angle between the absorption and emission dipole moment vectors. In equation 2 (9), Po is the limiting value of polarization for a dilute solution of fluorophores randomly oriented in a rigid medium that permits no rotation and no energy transfer to other fluorophores ... 

The fluorescence depolarization technique excites a fluorescent dye by linearly polarized light and measures the polarization anisotropy of the fluorescence emission. The fluorescence anisotropy, r, is defined as... 

Figure 4.6 shows an apparatus for the fluorescence depolarization measurement. The linearly polarized excitation pulse from a mode-locked Ti-Sapphire laser illuminated a polymer brush sample through a microscope objective. The fluorescence from a specimen was collected by the same objective and input to a polarizing beam splitter to detect 7 and I by photomultipliers (PMTs). The photon signal from the PMT was fed to a time-correlated single photon counting electronics to obtain the time profiles of 7 and I simultaneously. The experimental data of the fluorescence anisotropy was fitted to a double exponential function. 

Like Raman scattering, fluorescence spectroscopy involves a two-photon process so that it can be used to determine the second and the fourth rank order parameters. In this technique, a chromophore, either covalently linked to the polymer chain or a probe incorporated at small concentrations, absorbs incident light and emits fluorescence. If the incident electric field is linearly polarized in the e direction and the fluorescent light is collected through an analyzer in the es direction, the fluorescence intensity is given by... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

Fig. 4.9. Schematic of time-resolved fluorescence anisotropy sample is excited with linearly polarized light and time-resolved fluorescence images are acquired with polarization analyzed parallel and perpendicular to excitation polarization. Assuming a spherical fluorophore, the temporal decay of the fluorescence anisotropy, r(t), can be fitted to an exponential decay model from which the rotational correlation time, 6, can be calculated.

The concept of transition moment is of major importance for all experiments carried out with polarized light (in particular for fluorescence polarization experiments, see Chapter 5). In most cases, the transition moment can be drawn as a vector in the coordinate system defined by the location of the nuclei of the atoms4 therefore, the molecules whose absorption transition moments are parallel to the electric vector of a linearly polarized incident light are preferentially excited. The probability of excitation is proportional to the square of the scalar product of the transition moment and the electric vector. This probability is thus maximum when the two vectors are parallel and zero when they are perpendicular. 

Thus, when a population of fluorophores is illuminated by a linearly polarized incident light, those whose transition moments are oriented in a direction close to that of the electric vector of the incident beam are preferentially excited. This is called photoselection. Because the distribution of excited fluorophores is anisotropic, the emitted fluorescence is also anisotropic. Any change in direction of the transition moment during the lifetime of the excited state will cause this anisotropy to decrease, i.e. will induce a partial (or total) depolarization of fluorescence. 

Optical fluorescence microscopy is a powerful and sensitive method for obtaining information about the orientation of luminescent dye molecules in small crystals. In Figure 1.10, we show unpolarized and linearly polarized fluorescence of two perpendicularly lying zeolite L crystals loaded with DSC. 

Figure 1.10. Fluorescence microscopy pictures of two 1500-nm long zeolite L crystals containing DSC. Excitation with unpolarized light at 480 nm. Left Unpolarized observation. Middle and right Linearly polarized observation. The arrows indicate the polarization direction. (See insert for color representation.)...

One can employ linearly polarized light to excite selectively those fluorophores that are in a particular orientation. The difference between excitation and emitted light polarization changes whenever fluorophores rotate during the period of time between excitation and emission. The magnitude of depolarization can be measured, and one can therefore deduce the fluorophore s rotational relaxation kinetics. Extrinsic fluorescence probes are especially useful here, because the proper choice of their fluorescence lifetime will greatly improve the measurement of rotational relaxation rates. One can also determine the freedom of motion of the probe relative to the rotational diffusion properties of the macromolecule to which it is attached. When held rigidly by the macromolecule, the depolarization of a probe s fluorescence is dominated by the the motion of the macromolecule. 

It should be pointed out, however, that the details of the vibronic structure of the Lb band are significantly different in some of the spectra which have appeared in the literature and which have been mentioned above. For example, while Jones et al. [44] and Dick et al. [46] have reported only one relatively strong peak in the range 600-625 nm, Mikami et al. [45] observed two peaks. There are also differences in the relative intensities of the Lb transition and the transition to the gerade state around 450 nm. In [44,45], the spectra were obtained in the same solvent (cyclohexane) and for similar concentrations (0.05 M in one case, 0.1 M in the other), while in [46] the solvent used was ethanol. In all three cases the experiments utilized linearly polarized light and detected the 2P-induced fluorescence. The observed differences are probably ascribable to some other experimental condition or a source of error that was not accounted for. This is another example of the repro-... 

The decomposition of linearly polarized wave is the reverse of compounding of two plane polarized waves of the same phase angle (8 = 0). Depending on the slope tan-1 (b/a), the amplitudes a and b of the two waves, will differ and can be computed. For fluorescence depolarization studies, these amplitudes will correspond to Ij. and Ig components of the emitted radiation. 

The first measurements of Na nd fine structure intervals using quantum beats were the measurements of Haroche et al41 in which they detected the polarized time resolved nd-3p fluorescence subsequent to polarized laser excitation for n=9 and 10. Specifically, they excited Na atoms in a glass cell with two counterpropa-gating dye laser beams tuned to the 3s1/2—> 3p3/2 and 3p3/2— ndj transitions. The two laser beams had orthogonal linear polarization vectors et and e2 as shown in Fig. 16.9. 

Figure 17 Fluorescence photocounts of individual fluorescent spots versus the number of occurrences of each fluorescent spot for (A) 10-7-, (B) 10-6-, (C) 10-5-, and (D) 10 7-M submonolayers. Bin width is 20 counts. The histogram of 10 4-M submonolayers was not obtained because of difficulty in identifying fluorescent spots due to an increase in photocounts of background regions without fluorescent spots. The observation in (D) was obtained under the different experimental conditions from those used for the observation in (A), (B), and (C) excitation using linearly-polarized light (se the text in subsection B), the use of 532-nm light, and the reduced excitation power density ( 1.2 W/cm2) to balance the unitary photocounts (MOO counts) in (A), (B), and (C) with the unitary photocounts in (D). (From Ref. 16.)...

It is rather likely that understanding of the anisotropic distribution of the angular momenta of atoms was enhanced by Hanle s [184] discovery in 1924. Hanle observed the effect of the disappearance of linear polarization in fluorescence in a weak magnetic field directed at right angles to the E-... 

Fig. 2.5. The geometry adopted in calculating the degree of polarization V and the anisotropy of polarization of fluorescence 77 at excitation by linear polarized light beam directed along the a -axis with E z.

Fig. 5.4. Calculated fluorescence circularity rate under linear polarized excitation as dependent on squared electric field 2 for different absorption and fluorescence branches.

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