Dielectric constant tensor

The practical method to compute "backward"—that is, to calculate the dielectric constant tensor values, or the complex index of refraction—from a set of the observed polarizer and analyzer angles is not presented here. Instead, for a biaxial crystal, the technique indicated below is as follows ... 

The electrical permittivity (dielectric constant) tensor e can be defined by... 

It can be seen that, D and E, in the general case, are connected by a second-rank tensor. This tensor can be either the permittivity tensor or the dielectric constant tensor, depending on how the individual components are expressed. In the above equation, the tensor is a permittivity tensor. To convert it to a dielectric constant tensor, each element, Stj is divided by the permittivity of free space, sq. 

It is well-known that the simplest approach to the study of the optical properties of condensed media is the macroscopic electrodynamics approach, making use of the concept of the dielectric constant tensor f..tJ (oj, k) where w and k are the frequency and the wavevector of the light wave. Calculation of this tensor for a specific medium is, however, a problem of microscopic theory. For instance, the procedures for calculating the tensor k) for the excitation region of the... 

We can use the local field method to find the dielectric constant tensor for systems of this type. This method goes back to Lorentz who used it to derive the well-known formula for the optical refractive index in isotropic media (the Lorenz-Lorentz formula). Let us recall the derivation of this formula. 

Furthermore, since the dielectric constant tensor of the given medium is found from the relationship ... 

In this approximation (the additive refraction or mean polarizability approximation) eqn (5.42) with the addition of eqn (5.37) fully determines the dependence of the dielectric constant tensor on the impurity concentration c. The optical properties of mixed crystals with large impurity concentrations are discussed in Section 5.6. As we did above for crystals with one molecule per unit cell, we shall discuss here the case of small values of c when we can ignore terms of the order of c2, c3, etc. in the expansion of the tensor (5.42) in powers of c. Then we obtain ... 

In order to rewrite this relationship in a more explicit form let us turn back to the dielectric constant tensor (5.32) for the pure crystal. Using eqns (5.24) and (5.31) we can rewrite eqn (5.51) in the form ... 

Now we shall discuss some features of the electromagnetic wave spectrum in mixed crystalline solutions using the equations for the dielectric constant tensor of the solution derived in the mean polarizability approximation. We know that the effects of concentration broadening of absorption spectra are lost in this approximation. However, Onodera and Toyozawa (16), Dubovsky and Konobeev (17), Hoschen and Jortner (18), and Hong and Robinson (19), who have actually studied the corrections to the mean polarizability approximation, have shown that... 

The treatment of anisotropic crystalline solutions can also be carried out very simply. For such solutions consisting of two types of isotopic molecules and having two molecules per unit cell the dielectric constant tensor has been derived above in the additive refraction approximation (see eqn 5.42). This equation shows... 

We will start the discussion of the problem of surface excitons in disordered media considering macroscopic states. It is necessary to know the dielectric constant tensor to determine these states.We will use here the mean polarizability method, which we discussed in Chapter5 and which we apply for a cubic molecular crystal whose molecules differ only in the isotopic composition of the nuclei. 

For simplicity we consider at the outset a medium with a local dielectric constant tensor... 

In the uniaxially oriented case, the system is transversely isotropic and the dielectric constant tensor reduces to... 

In general, for a uniaxial birefringent medium such as a liquid crystal, the dielectric constant tensor may be written as... 

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