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.

[1]  W. Ho.  High-Temperature Dielectric Properties of Polycrystalline Ceramics , 1988 .

[2]  Michael E. Thomas,et al.  A Computer Code For Modeling Optical Properties Of Window Materials , 1989, Defense, Security, and Sensing.

[3]  M. Grimsditch,et al.  Refractive index and elastic properties of single‐crystal corundum (α‐Al2O3) up to 2100 K , 1991 .

[4]  Alexei A. Maradudin,et al.  Temperature Dependence of the Width of the Fundamental Lattice-Vibration Absorption Peak in Ionic Crystals. II. Approximate Numerical Results , 1967 .

[5]  Paul C. Nordine,et al.  Refractive Index of Liquid Aluminum Oxide at 0.6328 μm , 1991 .

[6]  Y. S. Touloukian.  Thermal Expansion: Nonmetallic Solids , 1977 .

[7]  W J Tropf,et al.  Infrared transmission properties of sapphire, spinel, yttria, and ALON as a function of temperature and frequency. , 1988, Applied optics.

[8]  A. Maradudin,et al.  Use of Morphic Effects for the Study of Vibrational and Optical Properties of Impurity Atoms in Crystals , 1967 .

[9]  Michael E. Thomas,et al.  A Comprehensive Model For The Intrinsic Transmission Properties Of Optical Windows , 1988, Defense, Security, and Sensing.

[10]  A. A. Maradudin,et al.  Lattice Anharmonicity and Optical Absorption in Polar Crystals. III. Quantum Mechanical Treatment in the Linear Approximation , 1962 .

[11]  R. French.  Electronic Band Structure of {Al2O3}, with Comparison to Alon and {AIN} , 1990 .

[12]  Irving H. Malitson,et al.  Refraction and Dispersion of Synthetic Sapphire , 1962 .

[13]  F. Gervais,et al.  Anharmonicity in several-polar-mode crystals: adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit infrared reflectivity , 1974 .

[14]  S. S. Mitra,et al.  Temperature Dependence of Infrared Dispersion in Ionic Crystals LiF and MgO , 1966 .

[15]  D. Smith,et al.  Optical constants of far infrared materials. 2: crystalline solids. , 1973, Applied optics.

[16]  J. Tapping,et al.  Index of refraction of sapphire between 24 and 1060°C for wavelengths of 633 and 799 nm , 1986 .

[17]  A. S. Barker.  Infrared Lattice Vibrations and Dielectric Dispersion in Corundum , 1963 .

[18]  M. Thomas.  Temperature Dependence of the Complex Index of Refraction , 1997 .

[19]  Albert Feldman,et al.  Optical materials characterization final technical report february 1, 1978-september 30, 1978. Technical note , 1979 .

[20]  R. K. Kirby,et al.  Numerical Data on Thermal Linear Expansion of Nonmetallic Solids , 1977 .