Angle Polarizer Conditions

It is widely brown that the total intensity is given by A 4 2fx, but the origin of this lesnlt is less widely understood. This relationship is the result of the transmission properties of polarizers, in pstticular, the dependence of the intensity on cos a, when a is the angle between the transition moment and the transmitting direction of the polarizer. 

Consider a collection of fluotophotes, eatdi enrittiirg an intensity h. The total intensity is given by 

When the intensity is observed through a polarizer (4) oriented along an axis p, the intensity is given by 

F re 10.11. nuompbofe at m aibitrary orienlAtlQn in the Catiedm oooedimaB syalem. 

The effects of rotational difhision and energy transfer ate easily sqiarated fey juifidous choice of the experimental conditions. For example, Brownian rotations cause negligible depolarization when the rotational rate is much slower than the rate of fluorescence emisaon. In contrast, RET occurs only in concentrated solution where the average distance between the fluorophore molecules is comparable to a characteristic distance Rg, which is typically near 40 A. One may readily calculate that millimolar concentrations are required to obtain this average distance (Chapter 13). Hence, since the usual concentradons requited for fluotesoence measurements ate about l0r U, RET is easily avdded by the use of dilute solutions. 

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A. Time-Resolved Fluorescence Measurements Performed Under Magic Angle Polarization Condition... 

It is known that in polar chloroform, 1 remains in the molecularly dissolved state, but that in n-alkanes self-assembled chiral organized structures are formed [2], Our experiments include the measurement of fluorescence transients under magic angle and polarization conditions. The... 

Sample preparation was given elsewhere [2]. Femtosecond fluorescence upconversion and picosecond time-correlated single-photon-counting set-ups were employed for the measurement of the fluorescence transients. The system response (FWHM) of the femtosecond fluorescence up-conversion and time-correlated single-photon-counting setups are 280 fs and 16 ps, respectively [3] The measured transients were fitted to multiexponential functions convoluted with the system response function. After deconvolution the time resolution was 100 fs. In the upconversion experiments, excitation was at 350 nm, the transients were measured from 420 nm upto 680 nm. Experiments were performed under magic angle conditions (to remove the fluorescence intensity effects of rotational motions of the probed molecules), as well as under polarization conditions in order to obtain the time evolution of the fluorescence anisotropy. 

Figure 7. Depolarized small-angle light scattering patterns (under cross-polarIzatIon condition) from perfluorinate carboxylic and sulfuric acid membranes showing the effect of swelling In water and ethanol. Reproduced from Ref. 30. Copyright 1982 American Chemical Society.

Figure 9.16 Polarization states and interference effects under large-angle imaging condition. (Courtesy of B.W. Smith.)...

Fig. 5. Polarized IR spectra for natural beiyl under different polarized conditions at RT. (a) From E//c-axis to E c-axis in the (lOO)-section (the sample thickness of 20 [im). The angle of the c-axis (i.e., the direction of the channels) respective to E is shown on the left of each spectrum (b) Under E c-axis in the (OOl)-section (the sample thickness of 120 gm).

The different values of AM correspond to different angular distributions of the radiation and to different polarization conditions. For AM = 0 only the z component of p = -er contributes and the radiation can be compared to that of a classical dipole oscillating along the direction of the field (quantization axis). The radiation then has an intensity which is proportional to sin, e being the angle between the field and the direction of... 

S. V. Dvinskikh and V. I. Chizhik, Cross-Polarization with Radio-Frequency Field Phase and Amplitude Modulation under Magic-Angle Spinning Conditions, J. Exp. Theor. Phys. 102 91-101 (2006). 

Figure Cl.5.14. Fluorescence images of tliree different single molecules observed under the imaging conditions of figure Cl.5.13. The observed dipole emission patterns (left column) are indicative of the 3D orientation of each molecule. The right-hand column shows the calculated fit to each observed intensity pattern. Molecules 1, 2 and 3 are found to have polar angles of (0,( ))=(4.5°,-24.6°), (-5.3°,51.6°) and (85.4°,-3.9°), respectively. Reprinted with pennission from Bartko and Dickson [148]. Copyright 1999 American Chemical Society.

This equation also limits the set of observable LEED spots by the condition that the expression inside the brackets must be greater than zero. With increasing electron energy the number of LEED spots increases while the polar emission angle relative to the surface normal, 6 = arctan(k /kz), decreases for each spot except for the specular spot (0,0) which does not change. Eig. 2.47 shows examples of common surface unit cells and the corresponding LEED patterns. 

Each unit of structure in the oriented polymer will also be considered to possess transverse isotropy. Its orientation can therefore be defined by polar and azimuthal angles (0, tp), but the condition of transverse isotropy for the whole sample means that the observed second moment will depend only on functions of 0 (in fact, P200 and P400) the functions involving (p taking fixed average values. 

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