Polarization of incident radiation

Around the selective-reflection band the plane of polarization of incident radiation is strongly rotated, the spectral dependence of this optical rotation resembles a dispersion curve as outlined below, position and shape give indication of both structure parameters. 

The quality of the right or left circular polarization depends on the relative amphtudes of the two phases and is readily adjusted by controlling the linear polarization of incident radiation (-45° with respect to the polarizer in the circnlar polarizer reflector) and the aforementioned phase shift in the reflective circular polarizer. 

The frequency dependence of A(ty) = d J(02((iS) x oS) for untwinned Y123 and Y124 crystals with polarizations of incident radiation along a- and b-axes is shown in fig, 17. In the limit of zero frequency, A(m) extrapolates to the penetration depth of a... 

Fig. 6. Reflectance of Tl2Ba2Cu04. > measured with S c and S ab polarizations of incident radiation. The c-axis reflectance is nearly insulating in the normal state but at T < 80 K is dominated by the Josephson-like...

For films on non-metallic substrates (semiconductors, dielectrics) the situation is much more complex. In contrast with metallic surfaces both parallel and perpendicular vibrational components of the adsorbate can be detected. The sign and intensity of RAIRS-bands depend heavily on the angle of incidence, on the polarization of the radiation, and on the orientation of vibrational transition moments [4.267]. 

Adaptations to Habitats. Because of Eaith s geom-etiyf and the position of its axis, the equator receives more solar energy per unit area than the polar regions. Because Earth s axis is tilted relative to the plane of Earth s orbit around the Sun, this angle of incident radiation varies seasonally. These factors, combined with Earth s rotation, establish the major patterns of temperature, air circulation, and precipitation. 

Figure 4.7-3 Polarized infrared spectra of salmon sperm DNA films. Top 98% RH. B form bottom 58% RH, A form. Electric field of incident radiation directed perpendicularly (full line) or parallelly (dotted line) to the preferential orientation of the sample.

The RTE is a simplified form of the complete Maxwell equations describing the propagation of an electromagnetic wave in an attenuating medium. The simplified RTE does not include the effects of polarization of the radiation or the influence of nearby particles on the radiation scattered or absorbed by other particles (dependent scattering or absorption). For example, if polarization effects are present (as they are when reflections occur at off-normal incidence from polished surfaces or in reflections from embedded interfaces), then the analyst should revert to complete solution of the Maxwell equations, which is a formidable task in complex geometries Delineating the bounds of applicability of the radiative transfer equation is an area of active research. 

The PEM is made of a piezoelectric transducer that is glued to a ZnSe crystal. The piezoelement converts a periodic voltage to a periodic mechanical (acoustic) wave, which compresses or expands the crystal. This movement changes the refractive index in the x direction and imposes a periodic retardation (or acceleration) of the fix component of the incident linearly polarized wave. The fiy component remains unchanged. The PEM is operated at its resonant frequency (50 kHz). If the optical element is at rest, the polarization of the radiation remains unchanged. If the optical element undergoes compression or expansion, the component fix has a positive (retardation) or negative (acceleration) phase shift relative to the phase component of the component fiy. 

The depth of penetration of the electrical field from the surface of the metal substrate into the adsorbed sample is between 5 and 500 nm. This enables investigation of submonolayers. IRRA spectra differ from conventional transmission spectra of bulk compounds, because only vibrations with transition dipole moments perpendicular to the surface wiU be excited. Since the evanescent field decays rapidly, vibrating groups closer to the surface yield larger absorption bands. Moreover, the polarization status of incident radiation is crucial, only p-polarized light will interact. 

Fig. 3.28. Plane polarization of infrared radiation by several plates. If I is the incident parallel beam of radiation striking at the angle of the incidence, i, the reflected beam R is polarized. The incident plane is the plane of the paper, therefore beam R is vibrating normal to the paper. This reflection-polarization process occurs at each face of the stack of plates. After a sufficient number of reflections the transmitted beam T has been depleted of vibrations normal to the plane of incidence and consists almost completely of vibrations in this plane. Thus, two beams of polarized light are produced. (Coltbup et ai, 1964.)...

Infrared Imaging and Mapping for Biosensors, Fig. 3 (a) Principle of IR synchrotron mapping ellipsometry. Due to reflection at the sample, the polarization of the radiation is changed. For example, the incident linearly polarized radiation becomes elliptically polarized. The sample Is moved by a two-dimensional mapping table, and a spectrum Is taken for every probed spot. The elllpsometiic parameters defined by the quantity p, which is the ratio of the complex reflection coefficients Tp and r, are measured for every spot. A is the phase shift... 

Figure 3.70. Calculated absorbances forp-polarized radiation In IRRAS spectra of hypothetical absorbate vibration at 3000 cnr on silicon (ns = 3.42) as function of angle of incidence for different cone angles k of incident radiation. Film parameters dz = 1 nm, nz = 1.5, /cz = 0.1. Reprinted, by permission, from FI. Brunner, U. Mayer, and FI. Floffmann, Appl. Spectrosc. 51, 209 (1997), p. 215, Fig. 7. Copyright 1997 Society for Applied Spectroscopy.

This model does not take into account certain secondary effects such as the dependence of Ip on the angle of incidence, the plane of polarization of the radiation, and the effect of different crystal faces of the electrode. It cannot be used to interpret anodic photocurrent at metals in its present form. 

If the molecules and their direction of polarization are not distributed statistically in the sample (anisotropy), a preferred spatial direction for the fluorescence exists. If polarized light is used for excitation [199], only those molecules whose axis of polarization is parallel to the axis of polarization of incident light are excited substantially. This results in a preferred direction of polarization for the fluorescence radiation. However, if molecules... 

Similarly, for backscattering, the same intensity if obtained by summing Eqs. (24) and (25). Here, for unpolarized light collection, the scattered intensity is independent of the polarization state incident radiation ... 

As explained, the polarization plane of linearly polarized radiation can be tilted when it passes through a crystal that has any anisotropy or a medium in which molecules are oriented. In general, the rotation of the plane of polarization is a function of the thickness of the crystal or medium and the difference between the refractive indices along the two orthogonal axes perpendicular to the direction of incident radiation. CD spectroscopy detects differences in the absorption of a chiral molecule for left- and right-circularly polarized radiation. 

The averaged Poynting vector determines the cross-section for scattering of radiation into a unit solid angle about the direction specified by the Euler angles associated with the scattering of incident radiation of a given polarization into radiation with prescribed polarization. It can be written as... 

The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

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