The Anisotropic Oscillator Model

Common liquids are optically isotropic, and the solids that physicists seem to like most are cubic and therefore isotropic. As a consequence, treatments of optical properties, particularly from a microscopic point of view, usually favor isotropic matter. Among the host of naturally occurring sohds, however, most are not isotropic. This somewhat complicates both theory and experiment for example, measurements of optical constants must be made with oriented crystals and polarized light. But because of the prevalence of optically anisotropic solids, we are compelled to extend the classical models to embrace this added complexity. 

In the preceding sections the optical response of matter has been described by a scalar dielectric function e, which relates the electric field E to the displacement D. More generally, D and E are connected by the tensor constitutive relation (5.46), which we write compactly as D = e0e E. The dielectric tensor is often symmetric, so that a coordinate system can be found in which it is diagonal  

To give physical meaning to the principal dielectric functions, we consider propagation of plane waves E0exp(/k x — ioot) in an anisotropic medium that is, we ask What kind of plane waves can propagate in such a medium without change of polarization If we follow the same reasoning as in Section 2.6, we obtain from the Maxwell equations 

If c3 = 0, then E0z = 0 the wave is transverse. There are two solutions to these equations  

plane waves can propagate along the z axis without change of polarization provided that they are either x-polarized or j-polarized. The complex refractive indices for these two types of waves, however, are different  

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