Optical Absorption and the Use of Crystal Program

When an electromagnetic wave, described by an electric field, E, impinges on a material, the absorption of the electromagnetic wave as a function of z behaves as E - exp /2, so the intensity falls off as / - exp . The immediate goal is to relate this classical absorption coefficient, a, which is the quantity of experimental interest, to the theory, wherein the quantum-mechanical mechanism responsible for absorbing a photon of a given frequency is found. To do this, a is defined as [18] 

The real and imaginary parts of Eq. (3) are related by the Kramers-Kronig relationship [19]  

In optics, the complex refractive index is defined as N = n + ik = ( r(co))l/1, where the real index of refraction, n, and extinction coefficient, k, are related to the real and imaginary parts of the complex dielectric constant by  

A plane wave propagating in the z-direction would therefore have an electric field given by  

Because the magnetic vector potential, A, is more naturally suited for including in the quantum-mechanical Hamiltonian [20, vll, pg 15-8], the incident light is represented mathematically by the magnetic vector potential  

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