Polarized Beam Experiments

In a single crystal experiment weaker reflections may be measured more easily and the form factor for Ni2+ in NiO was one of the first ionic form factors to be accurately determined (27). 

Significant problems often remain however, both in measuring very weak magnetic reflections and in separating magnetic from nuclear intensities. More accurate 

When the spins are all parallel or anti-parallel to a given direction, the cross section is (7) 

The first two terms are the nuclear coherent (3.15) and incoherent scattering (3.9) and the last term is the purely magnetic scattering (3.26). The third term is an interference term between nuclear and magnetic scattering and is zero if ij x, if the scattering is purely nuclear or purely magnetic, and if P = 0. P describes the polarization of the incident beam (0 P 1). 

For ferromagnets, nuclear and magnetic reflections occur at the same t, and fj may be established by an applied magnetic field. In particular, for if perpendicular to X 

---

The conventional polarized beam experiment is useful only for systems with polarization dependent cross sections. More information can often be gained if the polarization of the scattered neutrons is measured relative to the incident polarization (polarization analysis). This may be done in a triple-axis mode with a polarization sensitive analyzing crystal (Fig. 11). The technique was introduced experimentally by Moon et al. (59). In their apparatus the magnetic field at the sample may be rotated about a horizontal axis. With the sample field vertical the neutron polarization remains vertical, but with the sample field horizontal the neutron polarization at the sample becomes horizontal (a reverse rotation occurs after the sample so that the polarization at the analyzing crystal is again vertical). Thus P can be either parallel or perpendicular to the scattering vector n. 

In a reflectance or ellipsometry experiment, measurements are always referred to the physical plane of incidence, as defined in Fig. 27.24. If the polarization is parallel to this plane of incidence, the parameters related to it are denoted by the subscript p. For polarization perpendicnlar to the plane, the subscript s is used. When a linearly polarized beam is reflected, one often finds that the parallel and perpendicular components nndergo changes in amplitude and phase. Thus, two beams that are in... 

Various reactions in which the reactants are in particular vibrational and rotational states have been investigated and state-to-state kinetics have been studied. Two procedures have been used in these investigations. Brooks and coworkers first employed the molecular beam method for studying the state-to-state kinetics. The reactants molecules are put into desired vibrational and rotational states by laser excitation and identified the states by their fluorescence. In molecular beam experiments, it is possible to control the translational energy and mutual orientation of the reactants and to determine the degree of polarization of the rotational angular momentum of the product. 

For a description of the electron-counting procedure as applied to metal clusters, see Ref 37.) The paramagnetism of the nickel cluster, in principle, could be detected directly by neutron diffraction with a polarized beam and an external magnetic field. However, such measurements were not undertaken, and the effects of paramagnetism on the observed diffraction intensities, that are small in the present experiment, were ignored. 

One of the main goals of the crossed-beam experiment is to measure the internal energy AEvlh rol transferred to the molecule. In principle, this is possible in either of two ways. First, the scattered molecules could be detected and their product-state population analyzed. Infrared emission or absorption techniques may be considered, similar to those used in cell experiments.13 21 Although such studies would lead to the most detailed results (at least for polar molecules), under crossed-beam conditions they are impossible for intensity reasons, even if the possibility of measuring differential cross sections is renounced and the molecules in the scattering volume itself are detected. Detection via electronic molecular transitions may be invisaged. Unfortunately, the availability of tunable lasers limits this possibility to some exotic molecules such as alkali dimers. The future development of UV lasers could improve the situation. Hyper-Raman... 

The actual situation in a dielectric waveguide is somewhat more complicated because when a beam is totally internally reflected, the optical field actually penetrates a finite distance into the lower index material, and the reflected beam experiences a phase shift that depends on both angle and polarization. These effects complicate calculations of the mode characteristics, and split each mode into two modes with orthogonal polarizations, but the simple zigzag picture is adequate for most qualitative considerations (13). 

The purpose of such a device consists in changing the orientation of the polarization plane of a beam by 90°. That means the initial Stokes vector 1,1,0,0 of a horizontally polarized beam becomes 1,-1,0,0 after passing through the retarder. Retarders are most often birefringent crystals of definite thickness. If the fast and slow axes of such a crystal orthogonal to each other are crossed at 45° with respect to the polarization plane, the retarder rotates the latter by 90°. The Stokes-Mueller transformation corresponding to this experiment should be ... 

A light beam falling normally on the entrance face of the polarizer is split into ordinary and extraordinary beams that propagate together until they reach the oblique face where the ordinary beam experiences total reflection. The extraordinary beam polarized perpendicularly to the optical axis of the crystal enters the second triangle prism and emerges from it with unchanged polarization. The symmetric construction of the polarizers ensures that both sides can be used as a beam entrance. 

The advantage of using polarized neutrons to determine weak magnetic reflections is clearly apparent. For example, if T =0.01 then the magnetic contribution to the intensity in an unpolarized beam experiment is 0.01 percent, but R Ri 1.04, i.e., there is a 4 percent effect on changing the incident neutron polarization. It is necessary to know the nuclear scattering amplitude accurately if an accurate magnetic amplitude is to be obtained and extinction corrections in particular must be accurately performed. 

The spin density in the unit cell is determined from (3.49)i ). The majority of such experiments have been concerned with ferromagnetic metals and compounds. For these, and for paramagnetic materials the polarized beam technique gives F(t) for t/ 0 and the form factor can be normalized by a determination of the bulk magnetization [giving F(0)]. 

Two routes have been followed in reaction stereodynamics. One is to orient a molecular reactant in space and see how the reaction cross-section varies with the molecular orientation. This direction has been pioneered in molecular beam experiments using focusing of an electric hexapole field to control the molecular orientation [221-223a]. Numerous studies have applied this technique to electron-transfer reactions of alkaline-earth atoms [223b]. This technique is now complemented by the so-called brute force technique, where polar molecules are oriented in extremely strong electric fields [83]. 

All azocopolymer was employed by Hattori et to produce SRGs with pulsed lasers as well as with a cw laser. In the first experiment, s-polarized beams of a 532 nm line of the mode-locked Nd YAG laser were made to impinge on the polymer surface. The average beam power was 0.4W, with a pulse duration of 100 ps and repetition rate of 82 MHz. In the second experiment, an SRG with 25 nm modulation amplitude was formed by exposing the film to an interference pattern of two s-polarized lights with 2.8 W/ern intensity, for 40 minutes. Infrared (IR) absorption spectroscopy indicated... 

Figure 6. Schematic drawing of the spectral and polarization imaging experiment using one of the two-transducer AOTFs with three cameras to image the two diffracted and one of the undiffracted beams. The two cameras on the side, image orthogonally polarized spectral images from the two diffracted beams and the middle camera with a linear polarization filter in front, acquires a broadband image from one of the zero order...

---