Plane-polarized wave

Any plane polarized wave may be represented by a vector whose amplitude is given by... 

If the plane of polarization is defined as xz, the electric vector can be represented in terms of the unit vector i in the direction of x as E = E0i cos 0. This plane polarized wave may be decomposed into two circularly polarized components propagating in the same direction. A simple description of these waves are given by... 

Last but not least, it must be further investigated whether light manifests itself differently under different conditions. One of these manifestations is represented by an axisymmetric solution of the present theory, which has the nonzero angular momentum of a boson particle. Another is represented by a plane-polarized wave having zero angular momentum. 

Let the coordinate system be such as that given in Figure 4. IS. The electric vectors of a plane polarized radiation vibrate along OZ in the ZX plane and OX is the direction of propagation of the plane polarized wave. When a solution of anisotropic molecules is exposed to this plane polarized radiation, the electric vector will find the solute molecules in random orientation. Only those molecules absorb with maximum probability which have their transition moment oriented parallel to OZ (photoselection). Those molecules which are oriented by an angle 6 to this direction will have their absorption probability reduced by a factor cos 6, and the intensity of absorption by cos2 6. Finally, the molecules oriented perpendicular to the electric vector will not absorb at all. These statements are direct consequences of directional nature of light absorption... 

The decomposition of linearly polarized wave is the reverse of compounding of two plane polarized waves of the same phase angle (8 = 0). Depending on the slope tan-1 (b/a), the amplitudes a and b of the two waves, will differ and can be computed. For fluorescence depolarization studies, these amplitudes will correspond to Ij. and Ig components of the emitted radiation. 

Pi orbitals, 68, 310, 317 Pi-star orbital, 309, 310 Planarity, 224-225 Planck, M., 122 Plane of symmetry, 53 Plane-polarized wave, 114 Plane polar normal coordinates, 272 Point groups, 53-56,388-389 character tables of, 458-462 see also Group theory... 

The various forms of polarization can be understood by considering a plane-polarized wave travelling in the z direction. It can be resolved into two... 

Because the wave velocities u+ and u of the two components differ, a phase difference angular rotation 6/L of the plane of polarization per unit path length can be estimated as follows. Suppose that the plane-polarized wave travels a distance L through a medium of relative permittivity er and relative permeabilities /r. and /r. If the average velocity is v, then the fast and slow components travel distances of (L/u)u+ and (L/u)u respectively, where u+ and u are the fast and slow speeds. The path difference is... 

PROBLEM 2.7.7. For the plane polarized wave propagating along x, as described in Problem 2.7.6, find the magnetic field. 

Figure 24-1 Wave nature of a beam of single-frequency electromagnetic radiation. In (a), a plane-polarized wave is shown propagating along the y-axis. The electric field oscillates in a plane perpendicular to the magnetic field. If the radiation were unpolarized, a component of the electric field would be seen in all planes. In (b), only the electric field oscillations are shown. The amplitude of the wave is the length of the electric field vector at the wave maximum, while the wavelength is the distance between successive maxima.

In the plane-polarized wave considered, from a maximum in the +y direction thro(i direction and back again, at any particular instant of time, say r == 0, E varies in the s... 

An important example is known as Faraday rotation, which involves the rotation of the plane of polarization of a plane wave as it travels through the waveguide. A plane-polarized wave is equivalent to two circularly polarized waves, polarized in opposite senses (i.e., a right-polarized and a left-polarized component). Each component interacts very differently with the precessing spins and encounters different permeabilities, which affect the velocities of the two waves. The left component is retarded relative to the right, causing a clockwise rotation of the plane of polarization. 

The most direct application of Faraday rotation is to use waveguides in the same way that polarizers and analyzers are used in light optics to accept or reject plane polarized waves. 

A further polarization phenomenon is depicted in the bottom part of Figure 2.8, namely that of circular polarization. A circular-polarized wave can be thought of as the sum of two plane-polarized waves of equal ampUtude and at right angles to each other, which differ in phase by 90°. 

The electric and magnetic fields are at right angles to each other, and to the direction of propagation, and move with the velocity c. We are thus dealing with a plane-polarized wave with a well-defined frequency. Using the expression for V of Equation 12.9 in Equation 7.29, we obtain... 

Figure 4.59. (a) The depiction of a plane-polarized wave moving in the x direction, the points 1 through 5 are drawn to represent the vectors shown in the pictnres of part (b) (b) a depiction of how the harmonic motion of (a) can be the resnlt of two oppositely directed circular motions. 

Any state of polarization can be considered as a combination of (or can be decomposed into) two perpendicularly plane polarized waves with different amplitudes and a specific phase difference. Conversely, adding two such waves can produce any polarization state. If the sum is to be constant over time the two waves must be coherent, so that the phase relation between them remains the same. A state of polarization can also be considered as a combination of a right and left circularly polarized wave. If two such waves have the same amplitude they add up to produce a plane polarized wave. The direction of the plane of polarization is controlled by the phase difference of the two circularly polarized waves. 

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