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# Dielectric function

The dielectric function of a material ε(ω) describes its optical properties at all energies $\hbar\omega$.

The optical dielectric function is given by the fundamental expression $\epsilon(\omega)=1+\frac{8\pi^2e^2}{m^2}\sum_{c,v}\int_{}^{} W_{cv}(E) \left[\phi(\hbar\omega-E)-\phi(\hbar\omega+E) \right ] \, dx$. In this expression, Wcv(E) represents the product of the Brillouin-zone-average transition probability at the energy E and the JDS, Jcv(E); φ is the broadening function. In general, the broadening is intermediate between Lorentzian and Gaussian; for an alloy it is somewhat closer to Lorentzian because of strong scattering from statistical fluctuations in the local composition on a nanometer scale.