Magnetic field, plane-polarized

Such an anisotropic sample becomes birefringent for the incident linearly polarized probe beam. Its plane of polarization is slightly rotated after having passed the anisotropic sample. This effect is quite analogous to the Faraday effect, where the nonisotropic orientation of J is caused by an external magnetic field. For polarization spectroscopy no magnetic field is needed. Contrary to the Faraday effect where all molecules are oriented, here only those molecules that interact with the monochromatic pump wave show this nonisotropic orientation. As has already been discussed in Sect. 2.2, this is the subgroup of molecules with the velocity components... 

The effective index represents the dimensionless in-plane component of the propagation vector of the mode (the propagation vectors are in units of A being the vacuum wavelength). The optical modes can be characterized as transversal electric (TE the electric field is polarized in-plane) and transversal magnetic (TM the magnetic field is polarized in-plane). For unsymmetric slab waveguides, a minimum thickness (cutoff) exists for each mode to appear [48]. 

Thus the modal and ray transit times are equal only when tj - 1. This condition is satisfied only by those rays belonging to modes well above cutoff, i.e. when Vp U, or, equivalently, when 0 < 0c- Hence is inaccurate for arbitrary values of 9. This inaccuracy arises because the ray transit time ignores diffraction effects, which were discussed in Chapter 10. The step-profile planar waveguide is a special case, however, because all diffraction effects can be accounted for exactly by including the lateral shift at each reflection, together with recognizing the preferred ray directions. TWs was carried out in Section 10-6, and for rays, or local plane waves, whose electric field is polarized in the y-direction in Fig. 10-2, leads to the modified ray transit time of Eq. (10-13). If we use Table 36-1 to express 0, and 0(.in terms of U, Vand Wand substitute rj for TE modes from Table 12-2, we find that Eqs. (10-13) and (12-8) are identical since 0 = 0. It is readily verified that the same conclusion holds for TM modes and local plane waves whose magnetic field is polarized in the y-direction of Fig. 10-2. 

Plane-polarized electromagnetic radiation showing the electric field, the magnetic field, and the direction of propagation. 

Iodine vapor is characterized by the familiar violet color and by its unusually high specific gravity, approximately nine times that of air. The vapor is made up of diatomic molecules at low temperatures at moderately elevated temperatures, dissociation becomes appreciable. The concentration of monoatomic molecules, for example, is 1.4% at 600°C and 101.3 kPa (1 atm) total pressure. Iodine is fluorescent at low pressures and rotates the plane of polarized light when placed in a magnetic field. It is also thermoluminescent, emitting visible light when heated at 500°C or higher. 

For an oriented polymer, the magnitude of the observed second moment static magnetic field H0, which can be conveniently defined by the polar and azimuthal angles A, transverse isotropy, to which the following discussion is limited, the observed second moment will depend only on the angle A, there being no preferred orientation in the plane normal to the 3 direction. The treatment follows that originally presented by McBrierty and Ward 9>. 

When ordinary light is passed through a polarizer, the polarizer interacts with the electric field so that the electric field of the light emerges from the polarizer (and the magnetic field perpendicular to it) is oscillating only in one plane. 

Figure 6.4 shows the magnetic field vector B in the molecular Cartesian axes system xyz whose orientation is defined by the polar angles 0 (between B and z) and < ) (between the projection of B on the x-y plane and x). The third dimension of the... 

FIGURE 6.4 Vectors to describe a walk on the unit sphere. The orientation of a vector b of unit length along the dipolar magnetic field vector B in a Cartesian molecular axes system xyz is defined by the two polar angles 9 between b and the z-axis, and cp between the projection of b on the x-y plane and the x-axis. 

If the foregoing created the impression that the electric and magnetic vectors of a propagating electromagnetic field are confined to vibrate in fixed planes, that was unintentional. A field like that would be plane polarized and to create that requires a special device known as a polarizer. Ordinary unpolarized light consists of an array of plane waves that are randomly oriented with respect to a plane perpendicular to the directions of propagation. 

In paramagnetic resonance experiments, the sample is usually placed in a large constant magnetic field H0, whose direction is taken as that of the z axis. This field determines the quantum levels of the individual spins and polarizes them according to Curie s law. In a typical nuclear resonance experiment, a radiofrequency field H1( perpendicular to H0 and rotating in the x,y plane is applied to the sample. The response of the system is, under stationary conditions, described by the radiofrequency susceptibility %(co). The rotating field is given by... 

The factor 1(0) in Eq. (7.2) is a function of 8 and the polarization of the incident light these features are discussed shortly. However, we first examine the remarkable amplitude, polarization, and phase behaviors of the electric fields [from which 1(0) is derived] and the magnetic fields of the TIR evanescent wave. The field components are listed below, with incident electric field amplitudes Aps and phase factors relative to those of the incident E field s phase at z = 0. (The coordinate system is chosen such that the x-z plane is the plane of incidence. Incident polarizations p and s are parallel and perpendicular to the plane of incidence, respectively.)... 

FIGURE 3.10 The instantaneous electric (Ev) and magnetic (H. ) field strength vectors of a plane-polarized light wave as a function of position along the axis of propagation (jc) (from Calvert and Pitts, 1966). 

Suppose that a plane jc-polarized wave is incident on a homogeneous, isotropic sphere of radius a (Fig. 4.1). As we showed in the preceding section, the incident electric field may be expanded in an infinite series of vector spherical harmonics. The corresponding incident magnetic field is obtained from the curl of (4.37) ... 

Extinction calculations for obliquely incident light, also taken from Asano (1979), are shown in Fig. 11.16. The symmetry axis is parallel to the z axis and the direction of the incident beam, which makes an angle with the symmetry axis, lies in the xz plane, the plane of incidence. The incident light is polarized cither with its electric field or its magnetic field perpendicular to the plane of incidence these two polarization states are denoted by TE (transverse electric) and TM (transverse magnetic). 

The magnetic field is oriented perpendicular to the plane inscribed by a completely polarized electron-positron pair [17]. The virtual electron-positron... 

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