Frequency and temperature dependence of the refractive index of sapphire

Because the index of refraction is temperature dependent, a temperature gradient across a window causes image blur and bore sight error. Prior to this paper, there have been no direct temperature-dependent measurements reported on the mid-infrared refractive index for sapphire, a popular infrared window material of high durability. Measurements of dn/dT are reported on the ordinary ray of sapphire in the 4 μm region for the first time. Accurate temperature and frequency dependent refractive index models can now be constructed from visible measurements of the refractive index, far-infrared reflectance measurements, thermo-optic coefficient measurements, and infrared measurements of the absorption coefficient. Visible measurements determine the contribution to the refractive index from electronic transitions. Far-infrared measurements determine the contributions from fundamental lattice vibrations (phonons). Infrared absorption data are used to determine parameters in a multiphonon sum band model. By applying the Hilbert transform to this multiphonon absorption model, a model for the multiphonon refractivity is obtained. Two- and three-phonon contributions to the refractive index are important for an accurate model that includes temperature dependence. Results for the ordinary- and extraordinary-rays are obtained.