Excitation linearly polarized

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. 

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.

This effect, which is in a loose sense the nonlinear analog of linear optical rotation, is based on using linearly polarized fundamental light and measuring the direction of the major axis of the ellipse that describes the state of polarization of the second-harmonic light. For a simple description of the effect, we assume that the expansion coefficients are real, as would be the case for nonresonant excitation within the electric dipole approximation.22 In this case, the second-harmonic light will also be linearly polarized in a direction characterized by the angle... 

FIGURE 5.5 Polarized PL from a gel-processed, uniaxially drawn film of EHO-OPPE (cf. Figure 5.4) in UHMW-PE. Twisted tapes (drawn to a draw ratio A = 80) are shown under excitation with UV light (365 nm) and the pictures were taken through a linear polarizer with its polarization axis oriented horizontally (a) and vertically (b). (After Weder, C., Sarwa, C., Bastiaansen, C., and Smith, P., Adv. 

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. 

If the incident light is linearly polarized, the probability of excitation of a chro-mophore is proportional to the square of the scalar product MA.E, i.e. cos2 0A, 8 being the angle between the electric vector E of the incident light and the absorption transition moment MA (Figure 5.2). This probability is maximum when E is parallel to MA of the molecule it is zero when the electric vector is 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. 

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. 

Fig. 5 Bottom 2PA spectrum for linearly polarized light (intensity in arbitrary units) and (top) polarization ratio of naphthalene in ethanol. 0-0 is the origin of the band (I), the La band (II) is not visible, and the numbers III-VI identify transitions to higher electronic states. The abscissa, representing the total excitation energy, is in units of cm". Reproduced with permission from [46]. 1981, Elsevier...

Femtosecond pulse trains offer another control knob to rotational excitation of molecules, namely, the control of its directionality. By applying a series of laser pulses, linearly polarized at an angle with respect to one another, either clockwise or counterclockwise rotation can be initiated in a molecular ensemble [27]. The effect has been experimentally demonstrated with a sequence of only two pulses [28], and longer pulse trains [29, 30]. The latter were dubbed chiral because of the directional rotation of light polarization from pulse to pulse shown in Figure 10.3a. Chiral pulse trains enable control of the sense of molecular rotation... 

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