Polarized radiation,

Like the real refractive index, the imaginary refractive index is also a dimensionless quantity. For pure materials, is given by 

If a beam of unpolarized electromagnetic radiation is transmitted in the z direction, the amplitudes of the components of the sinusoidally varying electric field in the x and y planes are identical. When the beam is passed through a polarizer, the component of the electric field in one plane is transmitted, as described in more detail in Chapter 12. For unoriented samples such as all gases and liquids and isotropic solids, the absorbance of all bands in the spectrum is independent of the orientation of the polarizer. If the molecules in a certain sample are preferentially oriented in a given direction, however, the component of the dynamic dipole moment derivative of each vibrational mode, d i./dQ, in the direction that the radiation is polarized will change as the polarizer is rotated. 

Since the largest intensity of each band is observed when the beam is polarized in the direction for which the change in dipole moment for that vibrational mode is greatest, important information on the orientation of samples can be derived by installing a polarizer in the beam. For example, one of the more important applications of the use of polarized light is the measurement of the orientation of the chains in drawn or extmded polymers. A more esoteric application is the estimation of the angle at which surfactants are adsorbed on the surface of water. 

Several different types of reflection spectroscopy yield more information when the radiation is polarized. For example, very thin films of molecules adsorbed on the surface of metals only absorb radiation polarized parallel to the plane of incidence. The reflection of light from bulk samples depends on the polarization of the light with respect to the plane of the sample. The effective depth into a sample that can be sensed by internal reflection spectroscopy is also different for radiation polarized perpendicular and parallel to the surface. Polarized radiation may even be used to eliminate interference fringes from the spectra of thin polymer films. 

It is hoped that these few examples will give the less experienced reader an indication as to why FT-IR spectroscopy is even more popular today than when it was used primarily as a tool for structural elucidation. 

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Figure 9.29 Two-photon fluorescence excitation spectrum of 1,4-difluorobenzene. The upper and lower traces are obtained with plane and circularly polarized radiation, respectively, but the differences are not considered here. (Reproduced, with permission, Ifom Robey, M. J. and Schlag, E. W., Chem. Phys., 30, 9, 1978)...

With p-polarized radiation and incident angles near grazing incidence an increase in sensitivity of approximately a factor of 25 can be achieved in comparison with transmission experiments [4.265]. This advantage is reduced to a factor of 17 for a more realistic experimental situation in which the spread of incident angles is ca. 5° at approximately 85°. 

Fig. 4.54. IR reflection spectra from an ODS monolayer on silicon for s- and p-polarized radiation at different incident angles ft Symmetric (s), asym-...

For perpendicular polarized radiation, the reflection (Fresnel) coefficients are given by the expressions ... 

A role is also played by the temperature and frequency dependence of the photocurrent, the variable surface sensitivity at various parts of the cathode and the vector effect of polarized radiation [40]. All the detectors discussed below are electronic components whose electrical properties vary on irradiation. The effects depend on external (photocells, photomultipliers) or internal photo effects (photoelements, photodiodes). 

Figure 2 Theoretical spin-resolved VB-XPS spectra of Coo.6Pto.4 for left (LCP) and right (RCP) circularly polarized radiation and photon energy hu 1253.6 eV.

Despite the first prediction [34] of a measurable PECD effect being a few decades old, it is only in the last few years that experimental investigations have commenced. Practical experiments have needed to await advances in experimental technology, and improvements in suitable sources of circularly polarized radiation in the vacuum ultraviolet (VUV) and soft X-ray (SXR) regions needed for single-photon ionization have been been key here. In the meantime, developments in other areas, principally detectors, also contribute to what can now be accomplished. 

Figure 15. Circular dichroism of the C=0 C li peak (BE = 292.7 eV) in fenchone at three different photon energies, indicated, (a) Photoelectron spectrum of the carbonyl peak of the (1S,4R) enantiomer, recorded with right (solid line) and left (broken line) circularly polarized radiation at the magic angle, 54.7° to the beam direction, (b) The circular dichroism signal for fenchone for (1R,4A)-fenchone (x) and the (lS,41 )-fenchone (+) plotted as the raw difference / p — /rep of the 54.7° spectra, for example, as in the row above, (c) The asymmetry factor, F, obtained by normalizing the raw difference. In the lower rows, error bars are included, but are often comparable to size of plotting symbol (l/ ,4S)-fenchone (x), (lS,4R)-fenchone (+). Data are taken from Ref. [38],...

FIG. 4 FT-IRRAS spectrum in midfrequency region for gold substrate treated with 5 -TsTsTsTsTsTCTCATACATG-3. The i-polarized radiation was introduced on the sample at 85° off the surface normal and data were collected at a spectral resolution of 4 cm with 256 scans. 

Integral intensities were obtained after dead-time corrections, background subtraction and normalization to averaged monitor counts. The Lp correction was applied in the usual way. Since the polarization ratio was not measured at BW5 so far, 90% linear horizontally polarized radiation was assumed for all scans. Calculations show that even a change in the beam polarization of 10% would effect the intensities of the highest order reflections of less than 1.5%. 

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. 

The problem of solvent absorption can be overcome by measuring the change in reflectivity of the electrode either by (a) modulating the state of light polarization between p-polarized and s-polarized radiation, or (b) using p-polarized radiation and taking spectra at two different electrode potentials. 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

Relation (3.1.25) for the integral intensity of the /th spectral line for s- and p-polarized radiation is conveniently expressed in terms of polarization vectors (3.3.3) ... 

Ho, W.C.G., Lai, D. (2003), Transfer of polarized radiation in strongly magnetized plasmas and thermal emission from magnetars effect of vacuum polarization , MNRAS 338, 233. 

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