Linear polarized 7-rays

Birefringence (or double refraction) is an optical property of structurally anisotropic crystals. Such materials transform an incident light beam into two perpendicularly linearly polarized rays, the ordinary and extraordinary (e) rays, which propagate at different velocities in the medium. Unless the direction of incidence coincides with that of the optical axis of the (uniaxial) crystal, the e ray emerging from the crystal is displaced parallel to the o ray in the plane of the particular principal section of the crystal (see, for example. Ref 2). The well-known double images that appear when an object is viewed through a polished calcite crystal are a manifestation of the phenomenon. 

Work on the structure of crystals and fibers was not the only way in which Mark made use of x-rays. With several collaborators, he reported the results of a number of significant investigations of the physics of x-rays in 1926 and 1927. With Ehrenberg he reported studies of the index of refraction of x-rays, and with Leo Szilard studies verifying the linear polarization of x-rays scattered from electrons at 90. An investigation of the width of x-ray lines was carried out by Mark and Ehrenberg, and Mark and Kallmann reported work on the properties of Compton-scattered x-radiation and on the theory of the dispersion and scattering of x-rays. 

Information concerning the orientation of the molecule can be inferred from the polarization dependence. NEXAFS is sensitive to bond angles, whereas EXAFS is sensitive to the interatomic distances. Linearly polarized X-rays are best suited for molecules possessing directional bonds. This is best exemplified for flat 7T-conjugated molecules lying flat on surfaces. When the electric field vector E is aligned along the surface normal, features due to the out-of-plane tt orbitals... 

The plane of vibration of a linearly polarized beam emerging from a quarter-wave plate depends on the phase difference 8 between the interfering ray and is measured by the angle a between the optical axes of the quarter-wave plate and the analyzer ... 

The calculation of the x-ray emission spectra are now not a difficult target for the DV-Xa method. The development of experimental method using the synchrotron radiation now provides circularly and linearly polarized x-ray spectra, spin-selective x-ray spectra, and resonance x-ray spectra. These x-ray spectra will be calculated by the present DV-Xa method without any revision of the FORTRAN code. When the agreement between the experiment and the calculation is not satisfactory in the x-ray spectra, the only thing we must do is to check the experiment or to check the cluster model we used in the calculation. 

Uniaxial (birefrigerent) crystals have an index of refraction that depends on the projection of the oscillating electric field of linearly polarized radiation on the unique axis (the optic axis) of the crystal. Consider the plane defined by the optic axis of the uniaxial crystal, c, and the propagation direction of the oq beam, which is described by the unit vector, k = k uji)/ k(ui ). Light polarized perpendicular to the c,k plane is called the ordinary ray and propagates according to the ordinary index of refraction,... 

If some other angle of polarization with respect to the plane of incidence is employed, such as 45°, then one usually resolves the electric field vector into the parallel and perpendicular components. Thus, any linearly polarized beam incident on a surface can be regarded as a combination of separate beams with parallel and perpendicular polarization. Each ray in the parallel-polarized beam has a partner in the beam with perpendicular polarization, and they are locked in phase so that the orientation of the resultant electric field vector is always at the constant angle of polarization of the beam as a whole. 

If a linearly polarized beam is reflected from a surface, one usually finds that the parallel and perpendicular components undergo different changes in amplitude and phase. Thus individual pairs of rays in the two beams are in phase upon incidence, but are out of phase upon reflection. This effect has interesting consequences, as shown in Figure... 

The total cross section cre of an electron for x-ray scattering, given in Equation (1.38), was calculated for an unpolarized incident x-ray. Calculate the total scattering cross section for a linearly polarized incident beam. 

Polarization. The emitted synchrotron radiation is also highly polarized. For those x-rays emitted in the plane of the electron orbit, that is, in the direction = 0, the radiation is completely linearly polarized, with the electric vector of the radiation parallel to the electron orbit. For the x-rays emerging in the direction not exactly on the orbital plane, that is, j/ 0, the radiation is elliptically polarized, with a small vertically polarized component present. The polarization factor given in Equation (1.35) for the scattering of x-rays from an electron is valid only for unpolarized incident x-rays and has to be suitably modified for measurements with synchrotron radiation. 

Polarization is also very important for X-ray fluorescence experiments because of its effect on the scattered X-ray background. In the case of 100% linear polarization there can be no elastic or inelastic scatter at 90° in the plane of polarization. By placing the fluorescence detector at 90° in the polarization (horizontal) plane, the scattered background is greatly reduced, compared to an unpolarized laboratory source, or to a detector placed in a non-optimal position. 

The polarization factor, Pol, takes into account the variation in scattering intensity caused by the beam polarization, as can be anticipated because elastic scattering is forbidden along the polarization direction of the incident beam. Synchrotron sources typically produce X-ray beams that are linearly polarized in the horizontal plane. Most synchrotron-based scattering measurements are performed with the scattering angle measured in the vertical plane, so that P= 1. For horizontal scattering spectrometers with a horizontally-polarized beam, the polarization factor is P = cos(2 ). A number of spectrometers scan the detector in both the vertical and horizontal planes. 

Recently Mishchenko et al. [10] predicted that at small phase angles near opposition, asteroids produce a sharp narrow spike of the measurable linear polarization due to coherent backscattering of reciprocal rays (named Opposition Effect). This mechanism operates in planets, asteroids and comets. The polarimetric observations made recently by Rosenbush et al. [11] with 125cm telescope at the Crimean Astrophysical Observatory confirm this prediction. 

Another, linearly polarized, radio source in the Crab nebula, where a supernova explosion was observed in the year 1054, leaving behind a pulsating neutron star, could be of similar origin as the radiation in the Milky Way. The likelihood that the pulsar drives the acceleration of both relativistic electrons and of cosmic rays could imply that most cosmic rays in the Galaxy are also... 

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