Resonant Absorption in the Presence of Faraday Rotation

A general treatment of electro- and magneto-optical phenomena in the presence of resonant absorption is given. The resulting expressions in terms of the real and imaginary parts of a matrix index of refraction are easily utilized in calculations. We consider in detail the effects of these phenomena in M\"ossbauer experiments with polarized γ rays, presenting expressions for absorption as a function of polarization as well as for the polarization of the transmitted beam, which are valid for arbitrarily thick absorbers. Comparisons with experimental data are presented.