Polarization vector, fluctuating

In this expression, a is a factor proportional to the scattered light intensity, Sij q) is the amplitude of the Fourier component with wavevector q of the dielectric tensor fluctuation, while vectors f and i are polarizations of, respectively, reflected and incident light waves. In the context of Bragg reflection from the cholesteric helix, we know already from the expression (2.25) that there is just one Fourier component with wavevector 2q. Its amplitude is complex because the second term in the expression (2.25) can be written as... 

B) FRET efficiency as a function of Mg2+ ion concentration for the SB and BC vectors. The data have been fitted to a two-state ion binding model. Fluorescence emission spectra were recorded at 4 °C using an SLM-Aminco 8100 fluorimeter with modernized Phoenix electronics (ISS Inc., Champaign, IL, USA). Spectra were corrected for xenon lamp fluctuations and instrumental variations, and polarization artifacts were avoided by crossing excitation and emission polarizers at 54.7°. 

The consequence of dispersion in wavelength is that the polarization properties of the electric vector will fluctuate randomly in time. The parametric mapping of the electric vector shown in Figure 1.2 will produce blurred contours and the light will be partially polarized. If the light shows no preference towards a particular polarization state, it is referred to as unpolarized, or natural light. The Stokes vector for this case is... 

If we subtract this zeroth order solution, fourier transform the x coordinates, convert the time coordinate to conformal time, r), defined by dr) = dt/a, and ignore vector and tensor perturbations (discussed in the lectures by J. Bartlett on polarization at this school), the Liouville operator becomes a first-order partial differential operator for /( (k, p, rj), depending also on the general-relativistic potentials, (I> and T. We further define the temperature fluctuation at a point, 0(jfc, p) = f( lj i lodf 0 1 /<9To) 1 where To is the average temperature and )i = cos 6 in the polar coordinates for wavevector k. 

Fluctuations in the dielectric properties near the interface lead to scattering of the EW as well as changes in the intensity of the internally reflected wave. Changes in optical absorption can be detected in the internally reflected beam and lead to the well-known technique of attenuated total reflectance spectroscopy (ATR). Changes in the real part of the dielectric function lead to scattering, which is the main topic of this review. Polarization of the incident beam is important. For s polarization (electric field vector perpendicular to the plane defined by the incident and reflected beams or parallel to the interface), there is no electric held component normal to the interface, and the electric field is continuous across the interface. For p polarization (electric field vector parallel to the plane defined by the incident and reflected beams), there is a finite electric field component normal to the interface. In macroscopic electrodynamics this normal component is discontinuous across the interface, and the discontinuity is related to the induced surface charge at the interface. Such discontinuity is unphysical on the molecular scale [4], and the macroscopic formalism may have to be re-examined if it is applied to molecules within a few A of the interface. 

Here the index I is used to denote a particular charge distribution (i.e. a particular electronic state of the system). The displacement field P/(r) represents a charge distribution p/(r) according to the Poisson equation V T>i = npi. In (16.79) D(r ) and the associated p(r) represent a fluctuation in the nuclear polarization, defined by the equilibrium relationship between the nuclear polarization and the displacement vector (cf. Eqs (16.14) and (16.15))... 

In a QELS experiment, the autocorrelation function of the polarized scattered field is measured with K as the scattering vector. The scattered field is proportional to the amplitude of the fluctuations of the local polymer concentration in the gel. These concentration fluctuations are related to the local deformation in the gel. 

Fig. 11.11 Geometry of quasi-elastic scattering in general (a) and scattering on the director fluctuations with director nllz, and vectors of incident (f) and scattered (s) light polarizations...

One of the cross-polarization pulse sequences used to measure is shown in Figure 6.9. During the evolution time, At, of this pulse sequence, the magnetization is spin-locked along Any reorientation of the internuclear vectors induces fluctuations of the dipolar local fields, and the COcomponent of these fluctuating fields participates in the relaxation of the spins. This is a spin-lattice relaxation mechanism which is related... 

For unpolarized light the phases fluctuates statistically. For linearly polarized light with its electric vector in x-direction = 0. When E points into a direction a against the X axis, (j)x = (j)y and tana = A )y/A )x. For circular polarization Aqx = Oy (j) = (py nl2. The different states of polarization can be characterized by their Jones vectors, which are defined as follows ... 

The parameters of the Hamiltonian (3), i.e. the frequencies and the number of oscillators (more specifically, the strength of oscillators) are determined by the imaginary part of a complex dielectric function a(k, co) which characterizes the dielectric losses for polarization fluctuations in a medium. This model is, strictly speaking, applicable to homogeneous isotropic media in which the spatial correlations of polarization fluctuations SP r)dP r ), which determine the dependence of s k, co) on the wave vector k, depend on the difference of coordinates r—r only. 

BDS measure the time fluctuation of the polarization. Polymers can have dipole moments parallel to the chain backbone, leading to a net "end-to-end" vector. The part of the polarization related with these dipole moments is proportional to the time fluctuation of the end-to-end vector (p t) = [1 (f) (0)] [Pg.12]

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