OPTICAL LINESHAPES OF IMPURITIES IN CRYSTALS - A LATTICE MODEL OF INHOMOGENEOUS BROADENING BY POINT-DEFECTS

Previous theories of inhomogeneous broadening by point defects of impurity transitions in crystals have invoked a continuum approximation for the defect positions. We generalize these theories by treating the crystal as a discrete lattice. At low defect densities we 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 we derive approximate analytic expressions for the lineshape that are in good agreement with exact numerical results.