Phase retarder plates

In practice, phases of the beams are adjustable by tilt angle, q>, of phase retarder plates (glass plates) inserted into the beamlets. The tilt defines the the optical path Ax = nd/cos((p) typically cover-glass shdes with refractive index of n = 1.5 and thickness of d = 180 p.m suffice as variable phase-retarders. 

A homogeneous cell is useful as a tunable phase retardation plate. Figure 8.35 plots the voltage-dependent transmittance curve of a homogeneous LC cell at X = 633 nm. The polarizers are crossed and the angle between the front polarizer and the LC rubbing direction is 45°. 

Fast switching with a high contrast was obtained recently in the S-cell (Fig. 4.1(a)) combined with a phase retardation plate. The operation took place at the last transmission circle (Fig. 4.7) [276]. Optimal liquid crystals for this fast switching mode were proposed [277]. 

To improve the viewing angle dependence and contrast ratio of the twist cell, phase retardation plates are used [116]. Sometimes a second twist cell is placed after the first one with a 90° twist in the opposite sense. The two cells optically compensate for each other when place so that their directors are perpendicular on the facing surfaces. Thus the double-layered twisted device appears black between crossed polars for all wavelengths and has better viewing characteristics at oblique incidence [117]. 

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. 

Pelander et al. [81] developed a computer program for optimization of the mobile phase composition in TLC. They used the desirability function technique combined with the PRISMA model to enhance the quahty of TLC separation. They apphed the statistical models for prediction of retardation and band broadening at different mobile phase compositions they obtained using the PRISMA method the optimum mobile phase mixtures and a good separation for cyanobacterial hepatotoxins on a normal phase TLC plate and for phenolic compound on reversed-phase layers. 

The microscope should be equipped for rapidly switching modes between phase contrast and phase contrast with retardation plates and crossed polars. 

Fig. 17 SPR interferometric sensor 1 light beam, (2,4) polarizer, (3,10) beam-splitting cubes, (5) phase-retarding glass plate, (6) mirror, (7) SPR prism, ) gold film, (9) patterned coating, (11) analyzer, (12,13) imaging lenses, (14) CCD camera. Reprinted from [49], copyright 2000, with permission from Elsevier...

The Mueller-Jones matrix provides a complete description of the anisotropy properties of an object [9,10]. However, the information in the matrix is in implicit form. The history of the problem of analysis of the Jones and Mueller-Jones matrix goes back to the derivation of three equivalence theorems by Hurwitz and Jones [17]. According to the first theorem, an optical system (object) composed of any number of retardation plates (that is an object with linear phase anisotropy) and rotators (circular phase anisotropy) is optically equivalent to a system containing only two elements a retardation plate, and a rotator. The second theorem is analogous to the first and but is concerned with partial polarizers (linear amplitude anisotropy) and rotators. The third theorem claims that an optical system composed of any number of partial polarizers, retardation plates, and rotators is optically equivalent to a system containing only four elements two retardation plates, a partial polarizer, and rotator. 

Fig. 5.24 Molecular structure and optical textures of the Colhex phase (cooling from isotropic state) of compound 86/8 a at T = 40 °C with X-retarder plate, b the molecular star conformation. Reproduced from Ref [136] by permission of The Royal Society of Chemistry...

The phase-matching peaks of 3-5 should appear at the same temperature. With the incoming beam circularly polarized and without the retardation plate in position, only 3 was excited. The observed phase matching peak shown in Fig. 13 appeared at the predicted temperature. Also as predicted, the third harmonic was generated only in the backward direction and had a 10 1 polarization ratio between the right and left circular components. With the retardation plate inserted, 5 was excited and the same phase-matching peak was observed with a smaller amplitude. The third-harmonic output was nearly left circularly polarized as predicted. For reasons mentioned earlier, the peak due to 4 was not observed. 

A half wave plate is a special example of the generalized retarder. In this case, the thickness of the plate has been chosen to give a phase retardation of exactly r=jt. Hence the Jones matrix for a half wave plate at an angle y will be... 

The behavior of the output beam depends on the amplitude of the PZTs, since this amplitude determines the change in refractive index along the stress axis. At a certain amplitude, the maximum phase retardation for a particular wavenumber (vo) is 90° and the beam emerging from the ZnSe plate becomes circularly polarized. The handedness of the circularly polarized radiation switches sinusoidally from left to right with a frequency equal to the frequency at which the ZnSe plate is being extended and compressed. (It is this property that is used for the measurement of VCD spectra.) For most other wavenumbers in the spectrum, the radiation is elliptically polarized, with the ellipticity increasing with the difference between... 

When the amplitude of the motion of the PZTs is doubled relative to the case discussed above, the phase retardation is 180° and the plane of polarization of the output beam from the PEM at A,q changes by 90° at the extreme of the modulation cycle. When there is no tension on the ZnSe plate, the plane of polarization of the output beam is the same as that of the input beam. At the extremes of the extension and compression cycles, the plane of polarization is rotated by 90°. At this amplitude, therefore, the plane of polarization is modulated between s and p at a frequency of... 

To test the basic feature of Eq. (10-22), namely, the competition between the instantaneous and memory contributions to the total torque, one can trace the director dynamics by measuring the optical phase retardation of the cell filled with MLC2048. The dielectric torque is maximized by choosing a high value of the angle between the director and the normal to the bounding plates, 9q 45° [11, 12], The cell thickness was 10 xm. 

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