Phase plate with optical retardation

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...

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. 

In frequency regions where absorption is small the two indices of refraction , and n2 give rise to the phenomenon of double refraction. One of the most common uses for this property is in making wave retarders such as quarter-wave plates incident light linearly polarized with equal x and y field components is phase shifted upon transmission because of the two different phase velocities c/w, and c/n2. An entire field, usually referred to as crystal optics, arises out of this and further applications of crystal anisotropy. 

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]. 

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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