Dielectric tensor of cubic crystals

As was shown by Born and Huang (4) in cubic crystals with one molecule per unit cell the tensor Q f is reduced to the scalar QtJ = (An/ yv)dlJ where v is the volume of the unit cell, if we ignore spatial dispersion. Moreover, a - = aSij so that eqn (5.3) yields the tensor Ai3 = Adij where A = [1 — (47ra/3v). Substituting this expression into eqn (5.6) we obtain c,3 = eSl3 where 

Let us now consider the dispersion of e taking into account only one of the resonances of a(w). In this approximation we obtain  

Equation (5.10) shows that if we take into account the internal field correction, that is, the fact that A 1, the oscillator strength for the transition is not changed and only the resonance frequency is shifted - the e(w) resonance is shifted by Au C towards lower frequencies from the frequency of the transition in the isolated molecule  

Decay is taken into account by adding the imaginary terms —i 5 to the denominator of eqn (5.10). Since e = (n + ik)2 where n and re are the refractive and absorption indexes, for S — 0 we obtain, 

---