Elliptically-polarized wave

Fig. 7.57. Perspective view of the x and y components of an elliptically polarized wave. The ellipse results as a resolute of the two components. (Reprinted from R. A. Serway, C. J. Moses, and C. A. Moyer, Modem Physics, Saunders College Publishing, 1997, p. 208.)...

Behind the exit window the superposition of the a and or components of the linearly polarized probe wave traveling into the z-direction yields the elliptically polarized wave... 

In order to interpret these remarkable effects one has to consider the optical torque exerted by an elliptically polarized beam. Note that because Fop is a quadratic function of the field strength this torque is not the sum of the torques exerted separately by the two orthogonal components of the electric field vector. As shown in R18 and R22 the optical torque of an elliptically polarized wave has a component along the wave vector. It can be given as... 

This is an elliptically polarized wave in the system. It would be misleading to call m the refractive index, though it plays this role in (10). It has very uncommon properties, since (10) describes the wave motion in a screwed system. By substituting (10) in (9) one obtains tw m A... 

Eq and Bq are constant complex amplitudes, and e- and 2 shall be constant unit vectors. As a consequence the electric field vector always points in the direction of Cy and such an electromagnetic wave is said to be linearly polarized. By superpositions of two such linearly polarized waves with different phases and amplitudes so-called elliptically polarized waves may be constructed. However, we do not need to further discuss this possibility here. 

If both components are again superimposed at z = L after having passed through the sample cell, an elliptically polarized wave comes out with a major axis which is slightly rotated against the x axis. The y component of this elliptical wave is... 

Fig. 1.4.1 Electric vector in an elliptically polarized wave propagating in the x-direction. The magnetic vector is orthogonal to the electric vector.

Equation (2.78) describes an ellipse, the vibration ellipse (Fig. 2.11). If A = 0 (or B = 0), the vibration ellipse is just a straight line, and the wave is said to be linearly polarized , the vector B then specifies the direction of vibration. (The term plane polarized is also used, but it has become less fashionable in recent years.)If A = B and A B = 0, the vibration ellipse is a circle, and the wave is said to be circularly polarized. In general, a monochromatic wave of the form (2.77) is elliptically polarized. 

Figure 4.11 Two optical retarders. F fast axis, S slow axis. In both cases the incident beam is polarized under 45°. Left a quarter wave plate retards the slow component of the polarization by 7t/2 and elliptical polarization is achieved. Right a half-wave plate rotates the plane of polarization from 45° to -45°.

A typical experimental ellipsometer is illustrated in Figure 3.7. Monochromatic light, typically from a continuous wave laser, e.g. a He-Ne laser, is plane polarized (the angle of polarization is given by p) and impinges on a surface. A compensator is then used to convert the elliptically polarized reflected beam to a plane polarized beam (with a being the angle of polarization). The analyzer then determines the... 

Circular polarization of electromagnetic radiation is a polarization such that the tip of E, at a fixed point in space, describes a circle as time progresses. E, at one point in time, describes a helix along the direction of wave propagation k. The magnitude of the electric field vector is constant as it rotates. Circular polarization is a limiting case of elliptical polarization. The other special case is the easier-to-understand linear polarization. Circular (and elliptical) polarization is possible because the propagating E and El fields... 

Hence, the components of E parallel and perpendicular to the plane of incidence undergo phase retardations 5 and 5x, respectively, although the amplitudes are unaltered by reflection. If the incident wave is plane-polarized, the incident components are in phase, while those of the reflected wave are not, so that elliptical polarization is produced. The magnitude of the phase shift for 9i > 6 is... 

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