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We know that a crystal containing N atoms constitutes a mechanical oscillator with 3N degrees of freedom, which give the 3N frequencies of the normal mode vibrations. These frequencies are excited by thermal agitation. Under the action of infrared monochromatic radiation one forced oscillation can be excited in a crystal. Such a vibration has a large amplitude when the frequency of the radiation resonates with one eigen frequency of the oscillator. Knowing the deformation of the crystal lattice under the action of infrared radiation, its polarization P can be predicted. Now the relative dielectric constant εR can be determined from the polarization. In the case of an isotropic medium, the relation is particularly simple: P0R– l)E. Thus the dielectric constant can be obtained and so also the complex index of refraction n = n – jk of the crystal, where n is the index of refraction, and k the index of absorption. They respectively give the phase velocity v = cjn for the radiation of angular frequency ω, and the absorption coefficient K = 2kw/c, related to Beer's law which gives the transmission T for a plate of thickness x: T = e−Kx. The aim of this chapter is to show how to calculate the optical constants of the crystal from data concerning both its structure and its dynamics.

Let us consider a chain (Fig. 3.1) formed by a regular array of two ions of masses M and m respectively at a

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