Polarized waves circularly

C2.15.2 a right circularly polarized wave is illustrated. As tire wave propagates, Eq sweeps out a circle in tire x-y plane. It is clear tliat, given a well characterized light source, tliere are many attributes we can attempt to control (wavelengtli, polarization, etc.) tire question is how to generate well-characterized light ... 

These basis vectors represent right-circularly and left-circularly polarized waves and are orthonormal in the sense that... 

We have shown that only circularly polarized waves may propagate in optically active media without change in their state of polarization. However, the... 

We have written the field A as a superposition of plane waves. However, it will be more convenient to write it as a superposition of circularly polarized waves, in the same way as in quantum electrodynamics [58]. With this aim, we define the components right (R) and left (L) as... 

A linearly vibrating vector can be considered as made up of two equal vectors that rotate at the same rate in opposite sense, as shown schematically in Figure 6.3. The resultant electric vector for two circularly polarized waves with 9r = 6t is of the form E = E0 cos 9. More generally, in complex... 

For high-symmetry media like gases, liquids, cubic crystals, or uniaxial crystals with their optical axis parallel to B, and with the propagation direction of the light parallel to B, the optical eigenmodes are right- and left-handed circularly polarized waves, denoted by + and —. For such media, Eq. (1) can be simplified to [8,9]... 

A compound is considered optically active if it rotates the plane of plane-polaxized light, as described in Chapter 5. An explanation for optical activity is that, upon entering a crystal, plane-polarized light is split into two circularly polarized waves, one right-handed and the other left-handed. Since the crystal has a right-handed or left-handed character, the two circularly polarized waves travel through it with different velo-... 

The amplitude of the new wave is V2 times larger than that of either of the original waves, and its direction of polarization forms an angle of 4S° with the polarization directions of either of the two waves. If the phases of wave I and wave 2 differ by -ir/2, which according to Equation (1.2) is equivalent to a difference in optical path lengths of x = A/4, the superposition of the two waves results in a circularly polarized wave... 

The absorption of unpolarized light by a chiral medium with a dielectric constant as given by Eq. (2) is most readily calculated by considering linearly polarized light, which can be decomposed into two circularly polarized waves of the same amplitude and opposite handedness. If e + e" , Q, yS5, yi 5 and neglecting reflection, the transmission coefficient T for linearly polarized light of such a medium with thickness L is found to be... 

OL-nj, the "circular birefringence", which is proportional to the angle of rotation a. When the wavelength dependence of a is measured in the range of an absorption band, the left and right circularly polarized wave will not only propagate with different speeds, but will also be absorbed to different extents. The difference, Ae = El-Er/ is the "circular dichroism" (CD). 

In electromagnetic theory the Faraday effect can be explained as follows. When the medium magnetization has non-zero projection on the wave vector ko of the incident radiation, two independent fundamental Maxwell equations solutions are circular polarized waves with different refractive indexes n+M n, respectively. At the output of the magnetic medium these waves gain phase shift and when added give Unearly polarized wave with rotated polarization plane. That is why Faraday effect is also called magnetic circular birefringence [26, 27]. 

We can then write the difference equations in a simple manner because, as stated earlier, circularly polarized waves travel practically without change of form, so that the interference of the multiply reflected waves with one another and with the primary wave can be evaluated directly. 

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. 

A polarizer is a device that transforms a linear polarized wave into a circular polarized wave, or vice versa. The common principle is simply to decompose the incident field into two components where the phase of one is advanced and the other is delayed such that their difference is 90° while their amplitudes are the same. It appears that Pakan [128] was the first to utilize this principle. Later improvements were introduced by Lemer [129]. These devices were not of the meander-line type, as will be discussed here. These seem to appear first in a paper by Young et al. [130] and were subsequently unproved by Epis [131]. Later, a paper by Terret et al. [132] discussed how to calculate the susceptance of a meander line. All of these contributions were primarily focused on normal angle of incidence while Chu and Lee [133] extended the calculation to include oblique angle of incidence. A recent contribution was supplied by Marino [134], It was apparent that meander-line polarizers gradually deteriorate for higher angles of incidence. The present appendix will demonstrate that introduction of a dielectric profile can greatly improve this calamity. 

Figure 2.8 Schematics ofpolarized lightwaves, with view in direction toward the source on the right. From top to bottom horizontal linear-polarized wave (oscillation in Y-Z plane) vertical linear polarized wave (oscillation in X-Z plane) left-hand circular-polarized wave and right-hand circular-polarized wave...

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°. 

Note that, by convention, a linear polarized hght wave is often termed n-polarization, and right-hand and left-hand circular-polarized waves are termed and O -polarization respectively. These are of great importance when considering photon transition probabihties and selection rules in atoms and molecules. 

Depending on the polarization of the two counterpropagating laser beams the linJ lin configuration can be used with two orthogonal linear polarizations or the configuration with a circularly polarized wave, superim-... 

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