Polarized light phase angle

In the 1920s, Lyot [36] discovered that the polarization plane of the reflected light from the Moon and different terrestrial materials rotates by 90 at a phase angle called the inversion angle A branch of negative polarization at phase angles smaller than was also observed. Later it was discovered that this phase dependence is typical of all atmosphereless solar... 

The lamellar liquid crystalline phase consists of several bilayers of surfactant molecules and shows a mosaic-type texture (with Maltese crosses) when viewed under polarizing light. Low-angle X-ray diffraction shows spacing characteristic of a lamellar structure and the repeat unit is the back-to-back bilayer of the surfactant molecules with their alkyl groups in contact. The phase is built up from these flexible bilayers which are arranged parallel to each other [25]. The surfactant bilayer... 

In ellipsometry monochromatic light such as from a He-Ne laser, is passed through a polarizer, rotated by passing through a compensator before it impinges on the interface to be studied [142]. The reflected beam will be elliptically polarized and is measured by a polarization analyzer. In null ellipsometry, the polarizer, compensator, and analyzer are rotated to produce maximum extinction. The phase shift between the parallel and perpendicular components A and the ratio of the amplitudes of these components, tan are related to the polarizer and analyzer angles p and a, respectively. The changes in A and when a film is present can be related in an implicit form to the complex index of refraction and thickness of the film. 

As discussed above, the reflection of linearly polarized light from a surface generally produces elliptically polarized light, because the parallel and perpendicular components are reflected with different efficiencies and different phase shifts. These changes in intensity and phase angle can be analyzed to characterize the reflecting system. This approach is called ellipsometry. 

While s-polarized radiation approaches a phase change near 180° on reflection, the change in phase of the p-polarized light depends strongly on the angle of incidence [20]. Therefore, near the metal surface (in the order of the wavelength of IR) the s-polarized radiation is greatly diminished in intensity and the p-polarized is not [9]. This surface selection rule of metal surfaces results in an IR activity of adsorbed species only if Sfi/Sq 0 (/i = dipole moment, q = normal coordinate) for the vibrational mode perpendicular to the surface. 

If polarized light passes through a medium that exhibits optical rotation, the motion along one of the circular vectors is slower than that of the other. The resultant vector is thus displaced from the original vector by some angle, . Figure 16.5 shows the vector model in which the phase difference is [Pg.588]

In ellipsometric spectroscopy, an elliptically polarized light is allowed to reflect on the interface and the change in ellipticity and phase angle are determined from complex reflectivity. 

Fig. 10. A SPR Detection realized in a BIAcore system. A fan of polarized light passes a prism and is focused at the interface to an aqueous phase under conditions of total reflection. An evanescent wave enters the solvent phase. If the prism is coated with a thin gold layer at the interface the free electrons in the metal absorb energy from the evanescent wave for a distinct angle, depending on the refractive index of the solvent near the interface. B The gold layer can be modified with, e.g., a carboxydextrane matrix, where catcher molecules can be immobilized by standard chemistry. If a ligand is applied with the aqueous phase it may interact with the catcher and accumulate in the matrix, causing a shift in the resonance angle. If no specific binding occurs the refractive index in proximity of the sensor is less affected...

Figure 9.9 Simulated normalized line shapes of -polarized (a-c) and p-polarized (if-/) second-harmonic signals for quarter waveplate measurements (a) and (if) hypothetical achiral surface (hs = 0.5 fp = 0.75, gp = —0.5), (b) and (if) hypothetical chiral surface with in-phase chiral coefficient (fs = 0.75, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25), (c) and (/) hypothetical chiral surface with out-of-phase chiral coefficient ( fs = 0.75 0.25i, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25z). Upper (solid line) and lower (dashed line) sign in expansion coefficients correspond to two enantiomers. Rotation angles of 45° and 225° (135° and 315°) correspond to right-hand (left-hand) circularly polarized light and are indicated for one of enantiomers with open and filled circles, respectively.

Fig. 32 Dependence of cosine of A and tangent of where A and are ellipsometric angles related to the change of amplitude and phase shift of the incident polarized light, on the wavelength of the incident polarized light collected from PDMAEMA- -PAA brushes immersed in solutions of a constant ionic strength 0.001 M) and pH ranging from 3.52 to 9.50. The data in figures a and b (c and d) have been collected at the position 1 (4). For clarity the data for cos(A) and tan(V ) collected at pH > 3.53 were shifted vertically by - 0.2 relative to each previous set...

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