Retardation angle

In an electrooptic material the phase retardation angle is controlled by altering birefringence, which is in turn controlled by the potential of an apphed electric field. An electrooptic device thus acts as a variable phase optical retardation plate, and can be used to modulate the wavelength or intensity of an incident beam. 

Applications of visible light such as the use of polarized light, birefringence, retardation, angles of extinction, dispersion staining, and phase contrast will be explained, discussed and related primarily to asbestos with some discussion of quartz. 

As the three angles u, a and y increase the current waveform moves to the right of the phase voltage waveform. The centre of the current waveform is approximately the position of the peak value of the fundamental current component. Consequently as the current increases the power factor of the fundamental current decreases. Table 15.1 shows values of the harmonic components of current and the power factor as the retardation angle u is increased from zero to 60°. The fundamental component is taken as unity reference at each value of u. 

Defining the total twist angle = lnhlP and total retardation angle Y = lnt nhlX, then... 

The light beam to be studied is incident on a combination of a quarter-wave plate and a polarizer as shown in Figure 3.5. The slow optical axis of the wave plate is along the x axis and the retardation angle is = 90°. The transmission axis of the polarizer is at the angle a. 

For a retarder with retardation angle F = InAnh/X and the slow axis along x axis... 

We consider how the three-component Stokes vector S evolves on the Poincare sphere under the action of retardation films. The Mueller matrix of a uniform uniaxial retarder with the retardation angle F and the slow axis making the angle (p with the x axis is given by (from Equations (3.77) and (3.78))... 

For a uniform retardation film with the retardation angle F, even if its thiekness is not small, the Stokes vector of the outgoing light can be derived from Equation (3.93) and is... 

We now consider the Mueller matrix of a uniformly twisted nematic (or cholesteric) liquid crystal. The problem can be simplified if we consider the Stokes vector and the Mueller matrix in the local frame x y, in which the liquid crystal director lies along the x axis. Divide the liquid crystal film into N thin slabs. The thickness of each slab is dz = h/N, where h is the thickness of the liquid crystal film. The angle between the liquid crystal director of two neighboring slabs is dxff = qdz, where q is the twisting rate. The retardation angle of a slab is liT = k Andz. If the... 

The reflectance is maximized when phase retardation angle = 2m+1)ti. The... 

Fig. 60. Ferrierite crystal. Phase retardation angle (proportional to birefringence) as function of temperature for domains (1) and (2) [lOLl].

The PEM introduces a wavenumber- and time-dependent phase retardation angle, a(v, f), on the beam. The magnitude of the intensity variation generated by the PEM depends on the sine of a(v, t), given by... 

The optimum value of S which corresponds to the maximum of /j [ (Vi)] is a function of retardation angle and w 0.57 when v, is equal to a quarter wavelength of the PEM. However, because the PEM is designed to satisfy this condition for a fixed wavenumber of the incident radiation, the phase difference deviates from the optimum value for the other wavenumbers. In addition to the 5, thebirefringent plate adds a time-independent phase difference of = 2%VjdAn, where d is the thickness of the birefringent plate and An is the difference between refractive indices. As a result, the electric-field vector at the exit of the analyzer is given as... 

A = absorbance g = ground electronic state vibrational sublevel I = intensity = first-order Bessel function V = Fourier frequency = retardation angle d = mirror position 6 = phase function V = wavenumber frequency r = time constant of lock-in amplifier. 

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