Plane polarization

Let us consider the scheme showed in Fig. I to calculate the field scattered by a rough cylindrical surface (i.e. a wire). The wire is illuminated by a monochromatic, linearly polarized plane wave at an angle of incidence a with its axis of symmetry. The surface is described, in a system fixed to the wire, by p = h (cylindrical coordinates. We shall denote the incident wave vector lying on the x-z plane as kj and the emergent wave vector simply as k. 

For graphic purposes, the polar plane is usually drawn as a series of concentric circles with the center at the origin and radii 1, 2, 3.Rays from... 

Thus, the process of PAN transformation under the effect of IR radiation proceeds with considerable self-acceleration. The irradiation of uniaxially oriented PAN films gives a polymer with a distinct anisotropy of optical properties, dichroism in the visible spectral region in particular. Figure 8 presents dichroism curves [D =/(X)] at various angles (ip) between the polarization plane and the orientation axis. The same figure shows the dependence D =f(uniaxially oriented film. 

Fig. 8. Dichroism of electronic absorption spectra of oriented and nonoriented PAN films after IR irradiation, (a) Dependence of optical density ( >) on the wavelength for various values of (angle between film orientation axis and light polarization plane).

Z n + DJ (where D and DL stand for optical density when tp = 0° and

high orientation degrees. The fact that the absorption of plane-polarized light is maximal only if the polarization plane... 

Pulsed method. Using a pulsed or modulated excitation light source instead of constant illumination allows investigation of the time dependence of emission polarization. In the case of pulsed excitation, the measured quantity is the time decay of fluorescent emission polarized parallel and perpendicular to the excitation plane of polarization. Emitted light polarized parallel to the excitation plane decays faster than the excited state lifetime because the molecule is rotating its emission dipole away from the polarization plane of measurement. Emitted light polarized perpendicular to the excitation plane decays more slowly because the emission dipole moment is rotating towards the plane of measurement. 

Acid-base reactivity is an important property of oxide catalysts, and its control is of interest in surface chemistry as well as being of importance in industrial applications. The exposed cations and anions on oxide surfaces have long been described as acid-base pairs. The polar planes of ZnO showed dissociative adsorption and subsequent decomposition of methanol and formic acid related with their surface acid-base properties[3]. Further examples related to the topic of acid-base properties have been accumulated to date[ 1,4-6]. 

Enantiomers have structures of exactly the same kind and yet are different. Their structures correspond to mirror images. In their physical properties they differ only with respect to phenomena that are polar, i.e. that have some kind of a preferred direction. This especially includes polarized light, the polarization plane of which experiences a rotation when it passes through a solution of the substance. For this reason enantiomers have also been called optical isomers. In their chemical properties enantiomers differ only when they react with a compound that is an enantiomer itself. 

The principal axis of the cone represents the component of the dipole under the influence of the thermal agitation. The component of the dipole in the cone results from the field that oscillates in its polarization plane. In this way, in the absence of Brownian motion the dipole follows a conical orbit. In fact the direction of the cone changes continuously (because of the Brownian movement) faster than the oscillation of the electric field this leads to chaotic motion. Hence the structuring effect of electric field is always negligible, because of the value of the electric field strength, and even more so for lossy media. 

Figure 8.6 Three-dimensional slice of C2 symmetrical SmC phase, showing tilt cone, polar axis (congruent with twofold symmetry axis), smectic layer planes, tilt plane, and polar plane.

The layer stacking is synclinic in the tilt plane and antiferroelectric in the polar plane. The phase composed of an infinite number of SmCP layers stacked in this way is termed SmCsP, where the subscripts S and A each refer a structural feature of the layer interfaces between adjacent pairs of layers. If two adjacent layers are tilted in the same direction, the interface is synclinic (subscript S) in the tilt plane. If two adjacent layers have antiparallel orientation of their polar axes, then the layer interface is said to be antiferroelectric (A) in the polar plane. 

Note 2 The radial droplet texture shows four dark brushes located in the regions where the director is in the polarization plane of either the polarizer or the analyser. 

Polymer capable of rotating the polarization plane of a transmitted beam of linear-polarized light. 

Optics Refractometry, interferometry, timhidimetry, polarimetry Refraction index, interference, turbidity, rotation of polarization plane... 

The dipole moment p = emaE0e, 0 tex of an ideal dipole, located at z = 0 and illuminated by an x-polarized plane wave is0exp(/ kz — iut)ex, oscillates with the frequency of the applied field therefore, the dipole radiates (i.e., scatters) an electric field E, (Stratton, 1941, p. 453)... 

At the beginning of this section we stated, without proof, that only circularly polarized plane waves can propagate in media described by the constitutive relations (8.5). It is now a relatively easy matter to show that this is so. Let us consider plane homogeneous waves exp(/k x) propagating in the e direction, where k = ke. From (8.11) we have X Q = Q, and the transver-sality condition (8.12) implies that e Q = 0. Therefore, we can write Q = ( H ,l + Q ex, where e X e = n and X = -e , which yields... 

Rotation of the polarization plane (or the axes of the dichroic ellipse) by a small angle a occurs when the phases for the two circular components become different, which requires a difference in the refractive index n (Pearlman and Nguyen 1991). This effect is called circular birefringence. The change of optical rotation with wavelength is called optical rotary dispersion (ORD). 

Fig. 8. Principle of the magnetooptical read-out of domain patterns by the polar Kerr effect. The polarization plane of the incoming laser beam is rotated clock- or counterclockwise according to the orientation (up or down) of the magnetic moments.

The Rhodonines, when in the liquid crystalline state, are complete chromophores. They need not be associated with any other material to accomplish the absorption process. When still suspended in a liquid medium, they will not, as a large group, display any unique polarization properties. If they are brought to an ever higher level of concentration in a liquid, they will form a gel which will exhibit preferred polarization planes. They can also be precipitated onto a surface after which they will exhibit preferred planes of polarization. They can be precipitated onto glass as well as a protein substrate. They must, of course, be associated with some type of nervous tissue in order to generate the necessary nerve signals. This is clearly not a role for opsin, defined as a protein, to play. 

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