Anisotropic Retarders Birefringence

This type of material was the subject of the example calculation in section 1.2.1. The refractive index tensor is anisotropic with principal values ( , n. n ), defined in 

Two special retardation devices find wide application in the design of optical po-larimeters. These are the quarter-wave plate with 8 = jc/2 and the half wave plate with 8 = re. The utility of a quarter-wave plate can be demonstrated by observing its effect on 

The electric vector, A t, of the light generated by the quarter-wave plate is 

Half-wave plates are used to rotate the electric vector of light. Incident light with its polarization vector oriented at an angle 0 relative to the principal axes of n has an elec-T 

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Circular birefringence will induce a differential retardation in the phase of the orthogonal states of circularly polarized light. Circular dichroism, on the other hand, results in anisotropic attenuation of left- and right-circularly polarized light. The Jones matrix of circularly dichroic materials is normally written as ... 

Birefringent retarders are made of anisotropic uniaxial crystals such as calcite, a-quartz, sapphire, zinc sulphide, cadmium selenide and others. As Eq. (3.2-14) shows, the produced retardation is exact for a definite wavenumber or for its multiples. Between them all remaining possible polarization states are passed through. 

Orthoscopic examination with crossed polars is carried out first of all to determine the isotropism or the anisotropism of a sample. The polarization colors, the defects and variation in molecular orientation, and the orientation pattern or texture of liquid crystals are observed in this examination. With a heating stage the temperature of phase transition is also determined. In addition, with use of a compensator, the determination of vibration directions of the ordinary and extraordinary rays, the determination of relative retardation and birefringence are possible. In this section, the optical basics for orthoscopic observations are briefly outlined. The description of textures frequently observed for polymeric liquid crystals is given in Section 4.1.4. 

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). 

In white light, anisotropic structures may appear brightly colored when viewed in crossed (or parallel) polars. These polarization or interference colors depend on the retardation (Section 3.3). An estimate of sample retardation can be made from the standard sequence of colors, published as the Michel-Levy chart in many texts [4, 7, 9, 17, 18]. Color can also be used to find the sign of birefringence when a first order red plate is inserted as a compensator in white light. 

Here n (n denotes the fast and slow indices (for anisotropic materials with rod-shaped molecules n = n and = nj, d is the thickness of the birefringent film, and A is the wavelength of the light. The component that feels larger refractive index will be slower, i.e., retarded with respect to the other polarization directions. 

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