Lattice Anharmonicity and Optical Absorption in Polar Crystals: I. The Linear Chain

A calculation of the optical absorption spectrum of an anharmonic one-dimensional lattice of alternating positively and negatively charged particles of different masses is carried out using two different approaches: the recent theory of Born and Huang, and ordinary second-order time-dependent perturbation theory. Closed-form expressions for the absorption spectrum are obtained for both low and high temperatures. It is found that subsidiary absorption peaks may be expected at frequencies other than the dispersion frequency ${\omega }_d$. At high temperatures the absorption at ${\omega }_d$ varies as $T^{-2\mathrm{}}$ or $T^{-3\mathrm{}}$ depending on how certain thermal averages are carried out. Predictions based on these results are made regarding which features of the present spectra can be expected to persist for three-dimensional lattices.