Isotropic absorber oscillator

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

Since polarisability is a tensor quantity, the resulting optical properties may also be directionally dependent unless this tensor is isotropic. A simple example is illustrated by Fig. 1 where one can envisage that the interaction of the bond electrons will be greater for the imposed field that is oscillating in a plane parallel to the direction of the bond than for a field oscillating in a plane perpendicular to the bond, i.e. where the polarisability is highest. This interaction leads to a decrease in the velocity of the incident wave by an amount defined by the refractive index, n. For a non-absorbing system, the polarisability is related to the refractive index by the Lorenz-Lorentz equation ... 

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