Optical lineshapes of impurities in crystals: a lattice model of inhomogeneous broadening by point defects

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Abstract
Previous theories of inhomogeneous broadening by point defects of impurity transitions in crystals have invoked a continuum approximation for the defect positions. The authors generalize these theories by treating the crystal as a discrete lattice. At low defect densities they recover the results of the continuum theory, finding a Lorentzian lineshape. At high defect densities the lineshape is approximately Gaussian. At intermediate densities, the lineshape displays satellite structure due to different configurations of nearby defects. For all densities they derive approximate analytic expressions for the lineshape that are in good agreement with exact numerical results.