Optics of anisotropic materials

Light is an electromagnetic wave, and its propagation can be derived from the well-known Maxwell equations, which in their differential form read as  

Here j = aE is the current density, and p is the free charge density. 

The electric displacement D and electric field E are connected through the dielectric tensor as  

The magnetic induction B and magnetic field H are related through the magnetic permeability tensor as  

First we assume that there are no free charges (p = 0), and the material is insulating (DC conductivity Opc = 0). Assuming also that the material is nonmagnetic p = 1), and taking the time derivative of (5.1) and using the relation (5.3), we get  

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In tire following we split our description of the optics of anisotropic materials to two parts. First we investigate the optical properties of achiral and nonhelical systems then we will see how these results will be modified in chiral and helical systems, which are especially important in biological materials. 

Although Taylor (5) discussed the development of optical properties of anisotropic material formed during carbonization in 1961, and together with Brooks (6) reviewed the concept of liquid crystals as an intermediate to coke formation in 1968, it was not until well into the 1970 s that the potential of this knowledge was realised. 

Therefore it is suggested that modifiers giving special magnetic, electrical or optical properties, differing in solution and dispersion, can be used for an in situ generation of anisotropic materials. 

The refractive indices of anisotropic materials are conveniently represented in terms of the optical indicatrix, the surface of which maps the refractive indices of propagating waves as a function of angle. Solution of Maxwell s equations for an anisotropic medium leads to the result that for a particular wave-normal, two waves may propagate with orthogonal plane-polarisations and different refractive indices. An ellipsoid having as semi-axes the three principal refractive indices defines the optical indicatrix. In general for any wave-normal, the section of the indicatrix perpendicular to the wave-normal direction will be an ellipse, and the semi-axes of this ellipse are the refractive indices of the two propagating waves. 

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

Scattering problems in which the particle is composed of an anisotropic material are generally intractable. One of the few exceptions to this generalization is a normally illuminated cylinder composed of a uniaxial material, where the cylinder axis coincides with the optic axis. That is, if the constitutive relation connecting D and E is... 

TABLE 1. Physical Properties of Selected Liquid-Crystal Derivatives Derived Using Optical Anisotropic Materials"... 

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