Polarization, of scattered light

In addition to irradiance and frequency, a monochromatic (i.e., time-harmonic) electromagnetic wave has a property called its state of polarization, a property that was briefly touched on in Section 2.7, where it was shown that the reflectance of obliquely incident light depends on the polarization of the electric field. In fact, polarization would be an uninteresting property were it not for the fact that two waves with identical frequency and irradiance, but different polarization, can behave quite differently. Before we leave the subject of plane waves it is desirable to present polarization in a systematic way, which will prove to be useful when we discuss the polarization of scattered light. 

Thus, the degree of polarization of scattered light, given unpolarized incident... 

Fig. 2.30. Schematic diagram of a Raman spectrometer with 90° scattering. P, and P are half-wave and polarizing plates, respectively, to study the state of polarization of scattered light (after Griffith, 1975 reproduced with the publisher s permission).

The intensity of the vertically polarized scattered light is proportional to sin 0 which, in polar coordinates, is described by a figure 8-shaped curve centered at the origin and having maximum values of 1 at 0 = 90°, Because 0 is symmetrical with respect to the z axis, this component of scattered light is described in three dimensions by a doughnut-shaped surface in which the hole has shrunk to a point - centered symmetrically in the xy plane. 

The arrangement illustrated in Figure 1 is commonly used for angular characterization of scattered light. The light source is usually a laser. The incident beam may be unpolarized, or it can be linearly polarized with provisions for rotating the plane of polarization. Typically the plane of polarization is perpendicular to the plane of... 

Fig. 3—Measurement of surface by HDI surface reflectance analyzer. In electromagnetic radiation (light), the polarization direction is defined as the direction of the electric field vector. The incident polarization of the light can be controlled. The instrument uses a variety of detectors to analyze the reflected polarization state of the light. (U.S. Patent 6,134,011). (a) Plane of the disk The SRA uses a fixed 60 degree (from the surface normal) angle of incidence. The plane of incidence is the same as the paper plane (b) Pit on a surface detected by reflected light channels of HDI instrument (c) Scratches on disk surface measured by HDI surface reflectance analyzer (d) Particles on the surface of disk detected by reflected light (black spot) and by scattered light (white spot) [8].

Each of the resonances appearing in the spectra are identified and characterized by the type (TE or TM), mode number n, and mode order 5 (i.e., TE J. Allowances were made in the fit for a small amount of scattered light polarized perpendicular to the scattering plane (due to imperfect alignment of the polarizer) and a small change in the particle radius due to evaporation during the experiment. Once the resonances are identified there are no adjustable parameters in the simulation of an excitation spectrum of a... 

Equation (3) is valid when the dimensions of the particle are less than the wavelength of the light and the concentration is sufficiently small. These limits are given in Eq. (3 ). Eurthermore the light of the primary beam has to be vertically polarized. The scattered light that enters the detector is the sum of the two contributions and Yy which corresponds to the scattered light with an analyzer vertically oriented to the scattering plane (i.e., parallel to the polarization direction of the primary beam) and horizontally oriented, respectively. Eor branched structures the Yy contribution is very small and can be... 

The variation of scattered light intensity with 0 as typified by Fig. 9.19 clearly becomes more complex as the particle size increases, with sharp oscillations seen at a 10. However, recall that this is for a spherical homogeneous particle of a fixed size and for monochromatic light (e.g., a laser) when the particle is irregular in shape, these oscillations are far less prominent. This is also true for a group of particles of various sizes, that is, a polydisperse aerosol, where the overall scattering observed is the sum of many different contributions from particles of various sizes. Finally, nonmonochro-matic light and fluctuations in polarization also help to smooth out the oscillations. 

If the incident light is 100% polarized, the scattered light will be similarly polarized. However, because light of two different polarization states is scattered differently, the scattered light will be partially polarized if the incident light is unpolarized. From (4.78) we have... 

The heart of the polarization-modulated nephelometer is a photoelastic modulator, developed by Kemp (1969) and by Jasperson and Schnatterly (1969). The latter used their instrument for ellipsometry of light reflected by solid surfaces (the application described here could be considered as ellipsometry of scattered light). Kemp first used the modulation technique in laboratory studies but soon found a fertile field of application in astrophysics the modulator, coupled with a telescope, allowed circular polarization from astronomical objects to be detected at much lower levels than previously possible. 

Noctilucent cloud particles are now generally believed to be ice, although more by default—no serious competitor is still in the running—than because of direct evidence. The degree of linear polarization of visible light scattered by Rayleigh ellipsoids of ice is nearly independent of shape. This follows from (5.52) and (5.54) if the refractive index is 1.305, then P(90°) is 1.0 for spheres, 0.97 for prolate spheroids, and 0.94 for oblate spheroids. 

Here, a. and a L are the polarizabilities of the diatom parallel and perpendicular to the internuclear separation, R12. The electrostatic theory accounts for the distortions of the local field by the proximity of a point dipole (the polarized collisional partner) and suggests that the anisotropy is given by ft Rn) 6intermolecular interactions). This is the so-called dipole-induced dipole (DID) model, which approximates the induced anisotropy of such diatoms often fairly well. It gives rise to pressure-induced depolarization of scattered light, and to depolarized, collision-induced Raman spectra in general. 

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