Polarizer spatial

PKS. 14.3 Typical experimental setup for prodtrdng SBGs on an azobenzene-containing film. A laser beam, usually from an Art- (4S8 nm or 514 nm) laser, is polarized, spatially filtered, and collimated. 

We shall pass now to the consideration of the results of experimental study of spatial distribution of pyroelectric coefficient IT and light refraction index n. The assumption that IT is inversely proportional to the polarization and n is its square, permits to relate the profiles of latter quantities to that of polarization. This means that the experimental investigations of pyroelectric coefficient IT and light refraction index n profiles can be the source of information about polarization spatial distribution. 

Because micellar systems do not have a net quantum mechanical angular momentum, a paramagnetic probe must be inserted into the sample. The use of spin probes is a useful technique for studying micellar systems provided that (1) the probe does not perturb the micelles and aggregates of the surfactant being studied, (2) the probe is stable at least for the duration of the ESR measurement, and (3) the probe is sensitive to the polarity, spatial restriction, and viscosity of its environment. The choice of the spin label is a critical step in the ESR study, as the... 

The polarization P is given in tenns of E by the constitutive relation of the material. For the present discussion, we assume that the polarization P r) depends only on the field E evaluated at the same position r. This is the so-called dipole approximation. In later discussions, however, we will consider, in some specific cases, the contribution of a polarization that has a non-local spatial dependence on the optical field. Once we have augmented the system of equation B 1.5.16. equation B 1.5.17. equation B 1.5.18. equation B 1.5.19 and equation B 1.5.20 with the constitutive relation for the dependence of Pon E, we may solve for the radiation fields. This relation is generally characterized tlirough the use of linear and nonlinear susceptibility tensors, the subject to which we now turn. 

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... 

The anisotropy of the product rotational state distribution, or the polarization of the rotational angular momentum, is most conveniently parametrized tluough multipole moments of the distribution [45]. Odd multipoles, such as the dipole, describe the orientation of the angidar momentum /, i.e. which way the tips of the / vectors preferentially point. Even multipoles, such as the quadnipole, describe the aligmnent of /, i.e. the spatial distribution of the / vectors, regarded as a collection of double-headed arrows. Orr-Ewing and Zare [47] have discussed in detail the measurement of orientation and aligmnent in products of chemical reactions and what can be learned about the reaction dynamics from these measurements. 

Figure Cl.4.3. Schematic diagram of the Tin-periD-lin configuration showing spatial dependence of the polarization in the standing-wave field (after 1171).

Figure Cl.4.4. Schematic diagram showing how the two 2 levels of the ground state couple to the spatially varying polarization of the Tin-periD-iin standing wave light field (after 1171).

Figure C 1.4.7. Spatial variation of the polarization from tire field resulting from two counteriDropagating, circularly polarized fields witli equal amplitude but polarized in opposite senses. Note tliat tire polarization remains linear but tliat tire axis rotates in tire x-y plane witli a helical pitch along tire z axis of lengtli X.

One consequence of the spin-polarized nature of the effective potential in F is that the optimal Isa and IsP spin-orbitals, which are themselves solutions of F ( )i = 8i d >i, do not have identical orbital energies (i.e., 8isa lsP) and are not spatially identical to one another (i.e., (l)isa and (l)isp do not have identical LCAO-MO expansion coefficients). This resultant spin polarization of the orbitals in P gives rise to spin impurities in P. That is, the determinant Isa 1 s P 2sa is not a pure doublet spin eigenfunction although it is an eigenfunction with Ms = 1/2 it contains both S = 1/2 and S = 3/2 components. If the Isa and Is P spin-orbitals were spatially identical, then Isa Is P 2sa would be a pure spin eigenfunction with S = 1/2. 

A UHF wave function may also be a necessary description when the effects of spin polarization are required. As discussed in Differences Between INDO and UNDO, a Restricted Hartree-Fock description will not properly describe a situation such as the methyl radical. The unpaired electron in this molecule occupies a p-orbital with a node in the plane of the molecule. When an RHF description is used (all the s orbitals have paired electrons), then no spin density exists anywhere in the s system. With a UHF description, however, the spin-up electron in the p-orbital interacts differently with spin-up and spin-down electrons in the s system and the s-orbitals become spatially separate for spin-up and spin-down electrons with resultant spin density in the s system. 

If, however, it is assumed from Eq. (2-40) that the protection current density corresponds to the cathodic partial current density for the oxygen reduction reaction, where oxygen diffusion and polarization current have the same spatial distribution, it follows from Eq. (2-47) with = A0/7 ... 

In the first case, that is with dipoles integral with the main chain, in the absence of an electric field the dipoles will be randomly disposed but will be fixed by the disposition of the main chain atoms. On application of an electric field complete dipole orientation is not possible because of spatial requirements imposed by the chain structure. Furthermore in the polymeric system the different molecules are coiled in different ways and the time for orientation will be dependent on the particular disposition. Thus whereas simple polar molecules have a sharply defined power loss maxima the power loss-frequency curve of polar polymers is broad, due to the dispersion of orientation times. 

Let us first consider the case where a molecule has no net charge, but the spatial distribution of the positive and negative charges is such that a permanent dipole moment exists. Highly polar molecules such as water, HCI, HF, and NH are examples of such molecules. 

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