Introduction the local field method

This chapter presents a consistent description of the local field method and some of its results. First, we should make a brief note. 

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 

Numerous theoretical and experimental studies have been carried out in this field so that a whole branch of molecular optics - the optics of molecular crystals and molecular liquids - has been established. Even before Frenkel put forward his exciton concept, workers in this branch of optics had developed a variety of exact and approximate methods for the theoretical description of optical phenomena many of these methods were also substantiated in experimental studies. However, after the discovery of excitons the use of these methods became increasingly rare and many of the results obtained with them have not been sufficiently understood in the framework of exciton theory. Therefore, further development and generalization of these methods were impeded. On the other hand, since the results of pre-excitonic molecular optics were underestimated, the optical properties of crystals were treated in terms of only exciton theory even in those cases when this could be done much more easily by using the earlier, simpler 

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. 

According to Lorentz, the electric field E acting on a molecule in the isotropic medium (local field) and causing its polarization is not equal to the mean (macroscopic) field E which satisfies the phenomenological Maxwell s equations, but is determined by 

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