Vertical polarization

Figure 10,5 Definition of the variables used to describe the electric field produced by the oscillation of the charge q under the influence of vertically polarized light. (Reprinted from Ref. 2, p. 164.)...

The sin 0 factor shows that the field produced by the oscillator is maximum in the xy plane, zero along the z axis, and symmetrical with respect to the z axis. This geometry is consistent with the vertical polarization of the field which is driving the dipole and producing the field described by Eq. (10.19). 

The subscript v is attached to both of these intensities as a reminder that the foregoing analysis is based on the assumption of vertical polarization for the incident light beam. The ratio of these intensities gives the fraction of light scattered per molecule by vertically polarized light ... 

Since the vertically polarized light postulated in the derivation of Eq. (10.25) involves both the z component of the electric field and the angle 0, it is... 

The intensity of the vertically polarized scattered light is proportional to sin 0 which, in polar coordinates, is described by a figure 8-shaped curve centered at the origin and having maximum values of 1 at 0 = 90°, Because 0 is symmetrical with respect to the z axis, this component of scattered light is described in three dimensions by a doughnut-shaped surface in which the hole has shrunk to a point - centered symmetrically in the xy plane. 

Along the y axis, sin 0y contributes nothing but sin 0 = 1, so the net scattered light is vertically polarized. 

Along the x axis, both sin 0y and sin 0 equal unity. The light consists of equal amounts of horizontally and vertically polarized components, that is, it is unpolarized, and has twice the intensity observed in the perpendicular directions. 

These are plotted in Fig. 10.6, which shows the net intensity envelope in the xy plane as a solid line and represents the horizontally and vertically polarized contributions to the resultant by the broken lines. Since 0 is symmetrical with respect to the x axis, the three-dimensional scattering pattern is generated by rotating the solid contour around the x axis. 

The slope-intercept ratios have units of cubic centimeters per gram, and the intercepts are c/R where the subscript v indicates vertically polarized light. In this case Ky = 47t (n "/dc2The following values of n and dn/dc2 can be used to evaluate Ky ... 

Mw = 2.1 x 106g/mol) in water, which is denoted Cw(t) in the original work [44]. The subscript indicates that both the incoming beam and the scattered light are vertically polarized. The correlation function was recorded for a solution with a concentration of c = 0.005 g/L at a scattering vector of q = 8.31 x 106m-1. The inset shows the distribution function of the relaxation times determined by an inverse Laplace transformation. 

Synchrotron light is, in general, polarized in horizontal direction ([10], p. 9-13). Nevertheless, the polarization of the beam is never perfect. In order to be able to carry out a quantitative polarization correction, the quality of polarization should be monitored by means of a polarization monitor [11] that is positioned in the primary beam. The polarization monitor is registering the horizontally polarized component, 4, and the vertically polarized component, 4- From these two intensities the quality... 

Fig. 19. Hypothetical orientation of the SO - SI transition dipoles (blue band) of the bluelight photoreceptor in the Phycomyces sporangiophore as concluded from polarized light experiments96). Horizontally polarized light is about 20% more effective than vertically polarized light, as sketched...

Vibration Diagram Method. In actuality the last cases above are not described accurately by this dipole array model because actual phases of the electric fields are significantly altered from those of linear waves. (A more realistic, but complex model is to consider amplitude and phase characteristics of the oscillating vertically polarized component of electric field resulting from rotation of a line of transverse dipoles of equal magnitude but rotated relative to each other along the line such that their vertical components at some reference time are depicted by Figure 2.) For this reason and to handle details of focused laser beams one must resort to a more mathematically based description. Fortunately, numerical... 

Figure 9.2 Quantitative description of optical rotation. A vertically polarized electric field Em is incident on chiral system and induces vertically directed dipole moment i and magnetic moment m. Both act as sources of radiation, p, giving rise to vertically polarized field, m giving rise to horizontally polarized field. Sum of both fields is a new field E0ut with polarization rotated over angle 0.

When the incident light is vertically polarized, the vertical axis Oz is an axis of symmetry for the emission of fluorescence according to the Curie principle, i.e. Ix = Iy. The fluorescence observed in the direction of this axis is thus unpolarized. 

The components of the fluorescence intensity that are parallel and perpendicular to the electric vector of the incident beam are usually denoted as i and ij, respectively. For vertically polarized incident light, Iz = I) and Ix = Iy = I . 

It is easy to show that rn = r/2. Therefore, the emission anisotropy observed upon excitation by natural light is half that upon excitation by vertically polarized light. In view of the difficulty of producing perfectly natural light (i.e. totally unpolarized), vertically polarized light is always used in practice. Consequently, only excitation by polarized light will be considered in the rest of this chapter. 

Let us recall the definition of the emission anisotropy r (see Chapter 5) in a configuration where the exciting light is vertically polarized and the emitted fluorescence is observed at right angles in a horizontal plane (Figure 6.4) ... 

Now, for a given angle 9, excitation can be considered as the superimposition of two beams, one vertically polarized with a weight of cos2 9, and the other horizontally polarized with a weight of sin2 9. Therefore, the intensity components are... 

Equation (3) is valid when the dimensions of the particle are less than the wavelength of the light and the concentration is sufficiently small. These limits are given in Eq. (3 ). Eurthermore the light of the primary beam has to be vertically polarized. The scattered light that enters the detector is the sum of the two contributions and Yy which corresponds to the scattered light with an analyzer vertically oriented to the scattering plane (i.e., parallel to the polarization direction of the primary beam) and horizontally oriented, respectively. Eor branched structures the Yy contribution is very small and can be... 

Photon correlation light scattering was carried out by methods described elsewhere (6) to give the (unnormalized) correlation function G( )(q,T). Data were obtained with vertically polarized incident light for G 5)(q,T) and Gjj5)(q,T) obtained, respectively, with the vertical and horizontal components of the scattered light. 

A lj is a constant expressed for the vertically polarized incident light as... 

Fig. 4.70. Laser-induced steady-state luminescence spectra of thorite (a) and monazite (b-d) natural and heated demonstrating uranyl, Eu ", Sm and Nd " centers. Straight line-vertical polarization, dashed Zi e-horizontal polarization...

Experiment II. Horizontal and Vertical Polarizers. (1) Let P be a horizontal polarizer the amplitude of the transmitted wave is E and the irradiance 1 recorded by the detector is E E. (2) Let P be a vertical polarizer the amplitude of the transmitted wave is E and the irradiance I recorded by the detector is E E. The difference between these two measured irradiances is... 

Describe the experiment and apparatus, including the following information (a) sample identification (b) conditioning of the sample, if any (c) solvent, temperature, and instrument used (d) filtration technique (e) basic data such as wavelength, dn/dc, n, vertically polarized or unpolarized light, nature of reference, and calibration constant and (f) correction factors and any basic data (absorbance, depolarization) used in deriving them. 

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