OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS

1 P d A d R d T d 4. OPTICAL AND PHYSICAL . PROPERTIES OF. MATERIALS . CHAPTER 33. PROPERTIES OF. CRYSTALS AND GLASSES. William J. Tropf, Michael E. Thomas, and Terry J. Harris Applied Physics Laboratory Johns Hopkins Uniy ersity Laurel , Maryland GLOSSARY. Ai , B , C , D , E , G constants a, b, c crystal axes B inverse dielectric constant B bulk modulus C heat capacity c speed of light c elastic stiffness D electric displacement d piezoelectric coefficient d (2). ij nonlinear OPTICAL coefficient E Young's modulus E energy E electric field e strain G shear modulus g degeneracy Hi Hilbert transform h heat flow k extinction coefficient kB Boltzmann constant , phonon mean free path MW molecular weight m integer N( ) occupation density OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS .

2 N refractive index n complex refractive index 5 n 1 ik P electric polarization Px ,y relative partial dispersion p elasto-optic tensor p elasto-optic compliance p pyroelectric constant q piezo-optic tensor r electro-optic coefficient r amplitude reflection coefficient rij electro-optic coefficient S( ) line strength s elastic compliance T temperature t amplitude transmission coefficient U enthalpy u atomic mass unit V volume v velocity of sound x displacement x variable of integration Z formulas per unit a linear expansion coefficient a intensity absorption a thermal expansion am macroscopic polarizability a, b, g crystal angles b power absorption coefficient g( ) line width g Gruneisen parameter e dielectric constant, permittivity e emittance D Debye temperature k thermal conductivity L( ) complex function m permeability wave number (v / 2 c ).

3 R density r intensity reflectivity s stress intensity transmission power transmittance PROPERTIES OF CRYSTALS AND GLASSES susceptibility (2). second-order susceptibility solid angle v radian frequency Subscripts ABS absorptance bb blackbody c nm d nm EXT extinctance F nm i integers 0 vacuum, T 5 0 , or constant terms P constant pressure p, s polarization component r relative SCA scatterance V constant volume INTRODUCTION. Nearly every nonmetallic crystalline and glassy material has a potential use in optics. If a nonmetal is sufficiently dense and homogeneous, it will have good OPTICAL PROPERTIES . Generally, a combination of desirable OPTICAL PROPERTIES , good thermal and mechanical PROPERTIES , and cost and ease of manufacture dictate the number of readily available MATERIALS for any application.

4 In practice, glasses dominate the available OPTICAL MATERIALS for several important reasons. Glasses are easily made of inexpensive MATERIALS , and glass manufacturing technology is mature and well-established. The resultant glass products can have very high OPTICAL quality and meet most OPTICAL needs. Crystalline solids are used for a wide variety of specialized applications. Common glasses are composed of low-atomic-weight oxides and therefore will not transmit beyond about mm. Some crystalline MATERIALS transmit at wavelengths longer ( , heavy-metal halides and chalcogenides) or shorter ( , fluorides) than common glasses. Crystalline MATERIALS may also be used for situations that require the material to have very low scatter, high thermal conductivity, or high hardness and strength, especially at high temperature.

5 Other applications of crystalline OPTICAL MATERIALS make use of their directional PROPERTIES , particularly those of noncubic ( , uni- or biaxial) crystals. Phasematching ( , in wave mixing) and polarization ( , in wave plates) are example applications. This chapter gives the PHYSICAL , mechanical, thermal, and OPTICAL PROPERTIES of selected crystalline and glassy MATERIALS . Crystals are chosen based on availability of property data and usefulness of the material. Unfortunately, for many MATERIALS , property data are imprecise, incomplete, or not applicable to OPTICAL -quality material. Glasses are more accurately and uniformly characterized, but their OPTICAL property data are usually limited to wavelengths below mm.

6 Owing to the preponderance of glasses, only a representative OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS . small fraction of available glasses are included below. SI derived units, as commonly applied in material characterization, are used. Property data are accompanied with brief explanations and useful functional relation- ships. We have extracted property data from past compilations1 11 as well as recent literature. Unfortunately, property data are somewhat sparse. For example, index data may be available for only a portion of the transparent region or the temperature dependence of the index may not be known. Strength of many MATERIALS is poorly characterized.

7 Thermal conductivity is frequently unavailable and other thermal PROPERTIES are usually sketchy. OPTICAL MATERIALS . Crystalline and amorphous (including glass) MATERIALS are differentiated by their structural (crystallographic) order. The distinguishing structural characteristic of amorphous sub- stances is the absence of long-range order; the distinguishing characteristics of crystals are the presence of long-range order. This order, in the form of a periodic structure, can cause directional-dependent (anisotropic) PROPERTIES that require a more complex description than needed for isotropic, amorphous MATERIALS . The periodic features of crystals are used to classify them into six crystal systems,* and further arrange them into 14 (Bravais) space lattices, 32 point groups, and 230 space groups based on the characteristic symmetries found in a crystal.

8 Glass is by far the most widely used OPTICAL material, accounting for more than 90. percent of all OPTICAL elements manufactured. Traditionally, glass has been the material of choice for OPTICAL systems designers, owing to its high transmittance in the visible- wavelength region, high degree of homogeneity, ease of molding, shaping, and machining, relatively low cost, and the wide variety of index and dispersion characteristics available. Under the proper conditions, glass can be formed from many different inorganic mixtures. Hundreds of different OPTICAL glasses are available commercially. Primary glass-forming compounds include oxides, halides, and chalcogenides with the most common mixtures being the oxides of silicon, boron, and phosphorous used for glasses transmitting in the visible spectrum.

9 By varying the chemical composition of glasses (glasses are not fixed stoichiometrically), the PROPERTIES of the glass can be varied. Most notably for OPTICAL applications, glass compositions are altered to vary the refractive index, dispersion, and thermo-optic coefficient. Early glass technologists found that adding BaO offered a high-refractive-index glass with lower than normal dispersion, B2O3 offered low index and very low dispersion, and by replacing oxides with fluorides, glasses could be obtained with very low index and very low dispersion. Later, others developed very high index glasses with relatively low dispersions by introducing rare-earth elements, especially lanthanum, to glass compositions.

10 Other compounds are added to silica-based glass mixtures to help with chemical stabilization, typically the alkaline earth oxides and in particular Al2O3 to improve the resistance of glasses to attack by water. To extend the transmission range of glasses into the ultraviolet, a number of fluoride and fluorophosphate glasses have been developed. Nonoxide glasses are used for infrared applications requiring transmission beyond the transmission limit of typical OPTICAL glasses ( to mm for an absorption coefficient of 1 cm21). These MATERIALS include chalcogen- ides such as As2S3 glass and heavy-metal fluorides such as ZrF4-based glasses. Crystalline MATERIALS include naturally occurring minerals and manufactured crystals.