Polarization parallel incident

For specimens where gradients in the ms etic moment are of interest, similar arguments apply. Here, however, two separate reflectivity experiments are performed in which the incident neutrons are polarized parallel and perpendicular to the surfiice of the specimen. Combining reflectivity measurements under these two polarization conditions in a manner similar to that for the unpolarized case permits the determination of the variation in the magnetic moments of components parallel and perpendicular to the film surface. This is discussed in detail by Felcher et al. and the interested reader is referred to the literature. 

In order to understand RAIR spectroscopy, it is convenient to model the experiment (see Fig. 4). Consider a thin film with refractive index n =n ik and thickness d supported by a reflecting substrate with refractive index ni = ri2 — iki- The refractive index of the ambient atmosphere is o- Infrared radiation impinges on the film at an angle of incidence of 6 . The incident radiation can be polarized parallel to or perpendicular to the plane of incidence. 

Normal incidence transmission IRLD measurements are used to study thin films (typically 100 pm thickness and less, depending on the molar extinction coefficient of the bands) with in-plane uniaxial orientation. Two spectra are recorded sequentially with the radiation polarized parallel (p) and perpendicular (s) to the principal (machine) direction of the sample. The order parameter of the transition moment of the studied vibration is calculated from either the dichroic ratio (R — Ap/As) or the dichroic difference (AA = Ap—As) as ... 

Fields polarized parallel (p) or perpendicular fr) to the plane of incidence are given by... 

The scattering functions S, and S2 are particularly useful for interpreting experimental data. For incident light polarized parallel to the scattering plane, typically chosen to be the horizontal plane for which = 90°, the ratio of the scattered irradiance to the incident irradiance is given by... 

If the incident light is 100% polarized parallel to a particular scattering plane (it makes no difference which scattering plane), the Stokes parameters of the scattered light are... 

Incident light polarized parallel to the scattering plane. 

The angular distribution of the scattered light (normalized to the forward direction) for incident light polarized parallel and perpendicular to the scattering plane and unpolarized is shown in Fig. 5.1 both linear and polar plots are given. 

Let us now consider an infinite right circular cylinder of radius a, which is illuminated by a plane homogeneous wave E, = E0e ke, x propagating in the direction e, = - sin ex — cos fez, where is the angle between the incident wave and the cylinder axis (Fig. 8.3). There are two possible orthogonal polarization states of the incident wave electric field polarized parallel to the xz plane and electric field polarized perpendicular to the xz plane. We shall consider each of these polarizations in turn. 

Figure 8.7 Scattering cross section per unit particle volume for normally incident light polarized parallel (---) and perpendicular (...) to the axis of an infinite cylinder in air.

We list in Table 13.1 all the possible measured irradiances (for unit incident irradiance) with a polarizer before the scattering medium and an analyzer before the detector. The light transmitted by an ideal polarizer Ps is polarized in state s R and L denote right-circular and left-circular polarization and L denote light polarized parallel and perpendicular to the scattering plane + and — denote light polarized obliquely to the scattering plane at +45° and — 45°. U denotes the absence of a polarizer or analyzer if U is indicated as... 

We consider the case when oj3 = 3a>i. In (3.1) E = Ea a, a = 1, 3 with Ea the magnitude and ea the polarization of the incident field. Let k3 = 3ki, corresponding to parallel incident fields. Given the initial state of the molecule, the probability of forming a product molecule in exit channel q with energy E is... 

BREWSTER ANGLE. The Brewster angle, or polarizing angle, of a dielectric is that angle of incidence for which a wave polarized parallel to the plane of incidence is wholly transmitted (no reflection). An unpolarized wave incident at this angle is therefore resolved into a transmitted partly-polarized component and a reflected perpendicularly-polarized component. See Fig. I. 

Figure 13.5 Potential modulated reflectance spectrum of p-aminonitrobenzene (PANB) on platinum (solution phase 0.5 mM Na2S04 + 0.05 mM PANB). Applied dc 0.44 V vs. SHE. Modulation amplitude 50 mV. Modulation frequency 33 Hz. Incidence angle 65°. 11 signifies incident polarization parallel to incident plane and perpendicular to electrode surface. J signifies incident polarization perpendicular to incident plane (hence parallel to electrode surface). [From Ref. 50.]...

Figure B3.6.12 Depolarization of fluorescence indicates rotation of the chromophore. Monochromatic radiation from the source (S) has all but the vertically polarized electric vector removed by the polarizer (P). This is absorbed only by those molecules (see Fig. B3.6.5) in which the transition dipole of the chromophore is aligned vertically. In the case where these molecules do not rotate appreciably before they fluoresce ( no rotation"), the same molecules will fluoresce (indicated by shading) and their emitted radiation will be polarized parallel to the incident radiation. The intensity of radiation falling on the detector (D) will be zero when the analyzer (A) is oriented perpendicular to the polarizer. In the case where the molecules rotate significantly before fluorescence takes place, some of the excited chromophores will emit radiation with a horizontal polarization ( rotation ) and some with a vertical polarization. Finite intensities will be measured with both parallel and perpendicular orientations of the analyzer. The fluorescence from the remainder of the excited molecules will not be detected. The heavy arrows on the left of the diagram illustrate the case where there is rotation.

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