Optical retarder plates

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. 

Optical retarder plates, of appropriate thicknesses, made of birefrin-gent material, normally crystalline quartz or mica, can be used to rotate the plane of polarization for linearly polarized light or to produce circularly polarized light. To rotate linearly polarized light by an arbitrary angle, a double Fresnel rhomb is very useful (Fig.6.46). 

Figure 3. Images of a cross-section of carbon fibers after propylene pyrolysis. 3a Scanning Electron Microscopy of a piece of the carbon cloth. 3b optical microscopy (crossed polarizers with a wave retarding plate).

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. 

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 rotary polarization modulator simply consists of an optical element that rotates uniformly at a frequency Q about the transmission axis of light. In practice, retardation plates and polarizers are used. In either case, the Mueller matrix of such a device is found by simply replacing the angle 6 by Q.t in the equations listed in Appendix I. Typical PSGs based on rotary modulators and the associated Stokes vectors, Sp G, that are produced are listed in table 8.2. 

If the birefringence is low as in asbestos minerals, or if the particle is thin, the color seen will be a low order white or gray. A retardation plate or compensator added to the optical path can add or subtract retardation. Whether retardation is added or subtracted depends upon whether the slow ray of the com-... 

The most important applications are as follows retardation plates, cholesteric reflectors and filters, storage materials for optical informations, agents for preventing unauthorized copying of documents, and pigments for iridescent and polarizing coatings. 

Retardation plates or foils are widely used as optical elements. Mostly used applications are A/4 or i/2 plates. Their purpose is to convert linear polarized light to circular polarized light or circular to linear polarized light. As a special application retardation plates with high damage resistance are requested for high energy lasers. For this purpose a nematic LC silicone material was studied [17]. 

A more sophisticated retardation plate is a film consisting of the perpendicular arranged combination of two optical uniaxial materials, e g., uniaxially stretched polycarbonate foil with a homeotropic oriented LC siloxane layer [18]. The purpose of such a foil is the improvement of the optical properties of LC displays, especially the viewing angle dependence of the contrast. 

IR or UV reflecting cholesterics are colorless in the visible region of the spectrum. Therefore, retardation plates can be realized for STN displays using a long pitch material. Also UV reflecting LC siloxanes are of interest for retardation plates because they exhibit behavior like an optical negative uniaxial material. 

The optical system used to assess flow-induced birefringence consisted of a 2-mW polarized He-Ne laser focused by a condenser lens on the center of the flow field. The birefringence patterns are observed between crossed polars by using a quarter wave (X/4) retardation plate as a Senarmont compensator. The polarized laser has an extinction ratio of 100 1 the polarizer and analyzer are Carl Zeiss components with extinction ratios of approximately 10... 

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 number of compensator methods are numerous and will not be discussed in detail here. The interested reader is referred to Refs. 6-8. Basically what is involved is that a known retardation is used to nullify or compensate the retardation induced by the sample. This amounts to putting some birefringent (anisotropic) material into the light path, e.g. a wedge or plate of quartz or calcite. By changing the thickness of such a material the degree of optical retardation can be controlled— recall eqn. (3). 

Fig. 5.a) Experimental scheme EOM, electrooptic modulator B, static tranverse magnetic field X/4, retardation plate inserted with one of its main axes parallel to the polarization of the probe field , polarization analyzer PD, photodetector, b) Modulated excitation process of Zeeman coherence for the Zeeman-split J=1-J =0 transition of Sm. c) Detection process showing the induced Raman sidebands, d) Schematic of the Doppler distribution indicating the velocity selectivity of the optical excitation and detection of sublevel coherence. 

FIGURE 3.17 Schematic representations of the different orientation of the columns for a unidirectional planar alignment onto a teflon coating and the corresponding optical pictures observed by polarizing microscopy after the insertion of full wave retardation plate into the optical path in the case of pyrene 15 (a) and benzoperylene 18 (b) derivatives, respectively. Reprinted with permission from Reference 125. Copyright 2008 American Physical Society. 

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]. 

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