Retardation Plates

Retardation plates are frequently used in polarimetry instruments. Quarter-wave and half wave plates are most often used and may be fabricated in either wavelength-dependent or achromatic forms. 

Crystalline materials with precisely known birefringences are normally used for this purpose, with mica being commonly used. It is difficult, however, to machine most bi-refringent crystals so that a retardation of precisely rc/2 is produced. This is because the thicknesses of the crystal calculated using equaiton (9.1) may be too thin to be practical. Instead, multiple ordered quarter-wave plates can be fabricated with retardation, 8 = 2nj + n/2, where j = 1,2,3. If a single-order quarter-wave retardation is required, this can be achieved by combining two multiple-order quarter-wave plates of retardation 8 = 2nj + k/2 and 8 = 2nj + jt + n/2, at a relative orientation of 90°. 

Half wave plates are used to rotate the principal axis of the polarization ellipse (see section 2.4.2). Half wave plates for applications involving single wavelengths can be fabricated in precisely the same manner as quarter wave plates, but with thicknesses that are twice those specified by equation (9.1). 

10 are possible with wire grid polarizers but it must be emphasized that these devices only 

Here 8 is the retardation of the laminate, v is the central frequency, and 8 is the desired retardation (normally Jt/2 or n). In other words, the end result should be a retardation plate with the correct retardation in the center of the spectral region of interest, and its properties should be slowly changing with frequency or wavelength. The latter requirement is achieved by forcing the derivative of the retardation with frequency to be zero at  

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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. 

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 9.6 Experimental setup for measuring the angular distribution of the scattered light at different temperatures and externally applied electric fields. L is a He-Ne-laser, A/2 a half-wave retarder plate, P a Glan-Thomson prism, BS a beam splitter, PDl and PD2 are photodiodes and HV the high voltage amplifier. The sbn sample with 0.66 mol% Cerium is placed on a stack of Peltier-elements to control the temperature.

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. 

The Jones matrix of the laminate, JL, has the form of a true retardation plate. 

Figure 9.5 Composite laminate of three retardation plates to form a single, achromatic...

We consider here the case of a laminate consisting of three retardation plates with retardations 8, , 8 2, and 8 J, and orientation angles 0 j, 02, and 03. Multiplying the... 

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

These are organic fibers, usually plant fibers. Occasionally, plant fibers show a single color with a retardation plate which changes in color in a manner similar to asbestos. If morphology suggests the possibility of plant fibers, do a dispersion staining test. 

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]. 

If crosslinkable materials are used, patterned retardation plates can be realized using the temperature dependence of A . Starting from high An values at low temperature the An for higher temperature can be fixed by photopolymerization up to An = 0 above T. ... 

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. 

Retardation plates structured by light using the rotation diffusion mechanism are based on non-crosslinkable cholesteric cyclic siloxanes [34,35], The following samples demonstrate light-induced variation of A . 

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. 

The system described here is based on the principles of ellipsometry (47). Figure 8 gives a block diagram of our experimental setup. The Psi-meter consists of a 2 mW helium-neon polarized laser source, a quarter wave retardation plate to generate circularly polarized light, a synchronously rotating polarizer to... 

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