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[( )572( for many materials)]TJ 9.9 0 0 9.9 414.4 183 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 416.8 183 Tm 0 Tc 0.323 Tw [( )572( property data are)]TJ -31.2 -1.111 TD -0.248 Tw [( imprecise)]TJ 9.9 0 0 9.9 173.4 173 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 175.8 173 Tm 0 Tc -0.248 Tw [( )-561(incomplete)]TJ 9.9 0 0 9.9 224.3 173 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 226.7 173 Tm 0 Tc 0.313 Tw [( )562( or not applicable to optical-quality material)]TJ 9.9 0 0 9.9 415.6 173 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 418 173 Tm 0 Tc 0.313 Tw [( )562( Glasses are more)]TJ -31.333 -1.111 TD 0.006 Tw [( )255(accurately and uniformly characterized)]TJ 9.9 0 0 9.9 288.4 163 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 290.8 163 Tm 0 Tc 0.006 Tw [( )255( but their optical property data are usually limited to)]TJ -17.2 -1.111 TD 0.099 Tw [( )348(wavelengths below 1)]TJ 9.9 0 0 9.9 218.2 153 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 220.6 153 Tm 0 Tc -0.248 Tw [( 06)]TJ /F13 1 Tf 1.222 0 TD -0.248 Tc 0 Tw ( m)Tj /F15 1 Tf 0.667 0 TD ( m)Tj 9.9 0 0 9.9 245 153 Tm ( .)Tj 9 0 0 9 247.4 153 Tm 0 Tc 0.099 Tw [( )348( Owing to the preponderance of glasses)]TJ 9.9 0 0 9.9 406.2 153 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 408.6 153 Tm 0 Tc 0.099 Tw [( )348( only a representative)]TJ ET endstream endobj 24 0 obj << /ProcSet [ /PDF /Text ] /ColorSpace << /DefaultRGB 1 0 R >> /Font << /F7 5 0 R /F10 7 0 R /F12 12 0 R /F13 13 0 R /F15 14 0 R /F18 20 0 R >> >> endobj 25 0 obj << /Type /Page /Parent 8 0 R /Resources 27 0 R /Contents 26 0 R /CropBox [ 43 94 552 748 ] /Thumb 648 0 R /B [ 846 0 R ] >> endobj 26 0 obj << /Length 13841 >> stream BT /F10 1 Tf 8 0 0 8 76 710 Tm 0 Tr 0 g ( )Tj 0 0 TD [(33)-13( )]TJ 1.125 0 TD (.6)Tj /F15 1 Tf 7 0 0 7 105.6 710 Tm 0.25 Tw [( )499(OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS)]TJ 9 0 0 9 136 683 Tm 0.297 Tw [( )546(small fraction of available glasses are included below)]TJ 9.9 0 0 9.9 360.4 683 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 362.8 683 Tm 0 Tc 0.297 Tw [( )546( SI derived units)]TJ 9.9 0 0 9.9 434.5 683 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 436.9 683 Tm 0 Tc 0.297 Tw [( )546( as commonly)]TJ -33.433 -1.111 TD 0.083 Tw [( )332(applied in material characterization)]TJ 9.9 0 0 9.9 276.9 673 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 279.3 673 Tm 0 Tc 0.083 Tw [( )332( are used)]TJ 9.9 0 0 9.9 315.8 673 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 663 Tm 0 Tc 0.157 Tw [( )406(Property data are accompanied with brief explanations and useful functional relation-)]TJ -1.333 -1.111 TD -0.248 Tw [( ships)]TJ 9.9 0 0 9.9 155.5 653 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 157.9 653 Tm 0 Tc 0.353 Tw [( )602( We have extracted property data from past compilations)]TJ 6 0 0 6 405.7 657 Tm ( )Tj 6 0 0 5 405.7 657 Tm (1)Tj 6 0 0 6 408.7 657 Tm ( )Tj 6 0 0 5 408.7 657 Tm (\320)Tj 6 0 0 6 411.7 657 Tm ( )Tj 6 0 0 5 411.7 657 Tm (1)Tj 6 0 0 6 414.7 657 Tm ( )Tj 6 0 0 5 414.7 657 Tm (1)Tj 9 0 0 9 417.7 653 Tm [( )602( as well as recent)]TJ -31.3 -1.111 TD -0.248 Tw [( literature)]TJ 9.9 0 0 9.9 172.4 643 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 174.8 643 Tm 0 Tc -0.248 Tw [( )-283(Unfortunately)]TJ 9.9 0 0 9.9 233.3 643 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 235.7 643 Tm 0 Tc 0.035 Tw [( )284( property data are somewhat sparse)]TJ 9.9 0 0 9.9 376 643 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 378.4 643 Tm 0 Tc 0.035 Tw [( )284( For example)]TJ 9.9 0 0 9.9 430.5 643 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 432.9 643 Tm 0 Tc 0.035 Tw [( )284( index data may)]TJ -32.989 -1.111 TD 0.056 Tw [( )305(be available for only a portion of the transparent region or the temperature dependence of)]TJ T* 0.084 Tw [( )333(the index may not be known)]TJ 9.9 0 0 9.9 250.5 623 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 252.9 623 Tm 0 Tc 0.084 Tw [( )333( Strength of many materials is poorly characterized)]TJ 9.9 0 0 9.9 456.9 623 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 459.3 623 Tm 0 Tc -0.248 Tw [( )-332(Thermal)]TJ -35.922 -1.111 TD 0.083 Tw [( )332(conductivity is frequently unavailable and other thermal properties are usually sketchy)]TJ 9.9 0 0 9.9 481 613 Tm -0.248 Tc 0 Tw ( .)Tj /F10 1 Tf 10 0 2.126 10 76 575.8 Tm ( )Tj 0 0 TD -0.005 Tc (3 )Tj 0.55 0 TD (3 )Tj 0.55 0 TD -0.007 Tc (. )Tj 0.27 0 TD 0.994 Tc (3 )Tj 1.55 0 TD 0 Tc 0.222 Tw (OPTICAL MATERIALS)Tj ET 0 G 1 i 0 J 0 j 0.3 w 10 M []0 d 76.7 570.8 m 495.2 570.8 l S BT /F15 1 Tf 9 0 0 9 136 550 Tm 0.09 Tw [( )339(Crystalline and amorphous \(including glass\) materials are dif)63( )339(ferentiated by their structural)]TJ 0 -1.111 TD -0.248 Tw [( \(crystallographic\) )-548(order)]TJ 9.9 0 0 9.9 231.4 540 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 233.8 540 Tm 0 Tc 0.3 Tw [( )549( The distinguishing structural characteristic of amorphous sub-)]TJ -10.867 -1.111 TD 0.093 Tw [( )342(stances is the absence of long-range order )342(;)-6( )342( the distinguishing characteristics of crystals are)]TJ T* 0.063 Tw [( )312(the presence of long-range order)]TJ 9.9 0 0 9.9 265.7 520 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 268.1 520 Tm 0 Tc 0.063 Tw [( )312( This order)]TJ 9.9 0 0 9.9 312.2 520 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 314.6 520 Tm 0 Tc 0.063 Tw [( )312( in the form of a periodic structure)]TJ 9.9 0 0 9.9 452.7 520 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 455.1 520 Tm 0 Tc 0.063 Tw [( )312( can cause)]TJ -35.456 -1.111 TD 0.272 Tw [( )521(directional-dependent \(anisotropic\) properties that require a more complex description)]TJ T* 0.093 Tw [( )342(than needed for isotropic)]TJ 9.9 0 0 9.9 236.7 500 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 239.1 500 Tm 0 Tc 0.093 Tw [( )342( amorphous materials)]TJ 9.9 0 0 9.9 325.2 500 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 327.6 500 Tm 0 Tc 0.093 Tw [( )342( The periodic features of crystals are used)]TJ -21.289 -1.111 TD 0.076 Tw [( )325(to classify them into six crystal systems)]TJ 9.9 0 0 9.9 291 490 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 293.4 490 Tm 0 Tc 0.076 Tw [( )325(* and further arrange them into 14 \(Bravais\) space)]TJ -17.489 -1.111 TD -0.248 Tw [( lattices)]TJ 9.9 0 0 9.9 163.4 480 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 165.8 480 Tm 0 Tc 0.251 Tw [( )500( 32 point groups)]TJ 9.9 0 0 9.9 235.3 480 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 237.7 480 Tm 0 Tc 0.251 Tw [( )500( and 230 space groups based on the characteristic symmetries)]TJ -11.3 -1.111 TD 0.083 Tw [( )332(found in a crystal)]TJ 9.9 0 0 9.9 205.5 470 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 460 Tm 0 Tc 0.247 Tw [( )496(Glass is by far the most widely used optical material)]TJ 9.9 0 0 9.9 370.2 460 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 372.6 460 Tm 0 Tc 0.247 Tw [( )496( accounting for more than 90)]TJ -26.289 -1.111 TD 0.099 Tw [( )348(percent of all optical elements manufactured)]TJ 9.9 0 0 9.9 314.6 450 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 317 450 Tm 0 Tc -0.248 Tw [( )-347(Traditionally)]TJ 9.9 0 0 9.9 371.1 450 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 373.5 450 Tm 0 Tc 0.099 Tw [( )348( glass has been the material of)]TJ -26.389 -1.111 TD 0.39 Tw [( )639(choice for optical systems designers)]TJ 9.9 0 0 9.9 288.5 440 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 290.9 440 Tm 0 Tc 0.39 Tw [( )639( owing to its high transmittance in the visible-)]TJ -17.211 -1.111 TD -0.248 Tw [( wavelength )-338(region)]TJ 9.9 0 0 9.9 208.5 430 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 210.9 430 Tm 0 Tc 0.09 Tw [( )339( high degree of homogeneity)]TJ 9.9 0 0 9.9 325.6 430 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 328 430 Tm 0 Tc 0.09 Tw [( )339( ease of molding)]TJ 9.9 0 0 9.9 394.1 430 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 396.5 430 Tm 0 Tc -0.248 Tw [( )-338(shaping)]TJ 9.9 0 0 9.9 429.5 430 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 431.9 430 Tm 0 Tc 0.09 Tw [( )339( and machining)]TJ 9.9 0 0 9.9 493 430 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 136 420 Tm 0 Tc 0.083 Tw [( )332(relatively low cost)]TJ 9.9 0 0 9.9 207.9 420 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 210.3 420 Tm 0 Tc 0.083 Tw [( )332( and the wide variety of index and dispersion characteristics available)]TJ 9.9 0 0 9.9 487.3 420 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 410 Tm 0 Tc 0.357 Tw [( )606(Under the proper conditions)]TJ 9.9 0 0 9.9 269.4 410 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 271.8 410 Tm 0 Tc 0.357 Tw [( )606( glass can be formed from many dif)61( )606(ferent inorganic)]TJ -15.089 -1.111 TD -0.248 Tw [( mixtures)]TJ 9.9 0 0 9.9 169.9 400 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 172.3 400 Tm 0 Tc 0.443 Tw [( )692( Hundreds of dif)57( )692(ferent optical glasses are available commercially)]TJ 9.9 0 0 9.9 455.6 400 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 458 400 Tm 0 Tc -0.248 Tw [( )-691(Primary)]TJ -35.778 -1.111 TD 0.48 Tw [( )729(glass-forming compounds include oxides)]TJ 9.9 0 0 9.9 306.7 390 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 309.1 390 Tm 0 Tc -0.248 Tw [( )-728(halides)]TJ 9.9 0 0 9.9 343.1 390 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 345.5 390 Tm 0 Tc 0.48 Tw [( )729( and chalcogenides with the most)]TJ -23.278 -1.111 TD 0.218 Tw [( )467(common mixtures being the oxides of silicon)]TJ 9.9 0 0 9.9 321.2 380 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 323.6 380 Tm 0 Tc -0.248 Tw [( )-466(boron)]TJ 9.9 0 0 9.9 351.3 380 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 353.7 380 Tm 0 Tc 0.218 Tw [( )467( and phosphorous used for glasses)]TJ -24.189 -1.111 TD 0.352 Tw [( )601(transmitting in the visible spectrum)]TJ 9.9 0 0 9.9 286.1 370 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 288.5 370 Tm 0 Tc 0.352 Tw [( )601( By varying the chemical composition of glasses)]TJ -16.944 -1.111 TD 0.165 Tw [( )414(\(glasses are not \336xed stoichiometrically\))]TJ 9.9 0 0 9.9 298.4 360 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 300.8 360 Tm 0 Tc 0.165 Tw [( )414( the properties of the glass can be varied)]TJ 9.9 0 0 9.9 469.7 360 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 472.1 360 Tm 0 Tc -0.248 Tw [( )-413(Most)]TJ -37.344 -1.111 TD 0.067 Tw [( )316(notably for optical applications)]TJ 9.9 0 0 9.9 259 350 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 261.4 350 Tm 0 Tc 0.067 Tw [( )316( glass compositions are altered to vary the refractive index)]TJ 9.9 0 0 9.9 493.5 350 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 136 340 Tm 0 Tc -0.248 Tw [( dispersion)]TJ 9.9 0 0 9.9 176 340 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 178.4 340 Tm 0 Tc 0.083 Tw [( )332( and thermo-optic coef)66( )332(\336cient)]TJ 9.9 0 0 9.9 292.7 340 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 330 Tm 0 Tc 0.201 Tw [( )450(Early glass technologists found that adding BaO of)60( )450(fered a high-refractive-index glass)]TJ -1.333 -1.111 TD 0.048 Tw [( )297(with lower than normal dispersion)]TJ 9.9 0 0 9.9 271.2 320 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 273.6 320 Tm [( )-296(B)]TJ 6 0 0 6 282.7 318.5 Tm ( )Tj 6 0 0 5 282.7 318.5 Tm (2)Tj 9 0 0 9 285.7 320 Tm ( O)Tj 6 0 0 6 293.1 318.5 Tm ( )Tj 6 0 0 5 293.1 318.5 Tm (3)Tj 9 0 0 9 296.1 320 Tm 0 Tc 0.048 Tw [( )297( of)64( )297(fered low index and very low dispersion)]TJ 9.9 0 0 9.9 463.8 320 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 466.2 320 Tm 0 Tc 0.048 Tw [( )297( and by)]TJ -36.689 -1.111 TD 0.055 Tw [( )304(replacing oxides with \337uorides)]TJ 9.9 0 0 9.9 256.2 310 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 258.6 310 Tm 0 Tc 0.055 Tw [( )304( glasses could be obtained with very low index and very low)]TJ -13.622 -1.111 TD -0.248 Tw [( dispersion)]TJ 9.9 0 0 9.9 176 300 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 178.4 300 Tm 0 Tc -0.248 Tw [( )-358(Later)]TJ 9.9 0 0 9.9 203.1 300 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 205.5 300 Tm 0 Tc 0.11 Tw [( )359( others developed very high index glasses with relatively low dispersions)]TJ -7.722 -1.111 TD 0.271 Tw [( )520(by introducing rare-earth elements)]TJ 9.9 0 0 9.9 279 290 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 281.4 290 Tm 0 Tc 0.271 Tw [( )520( especially lanthanum)]TJ 9.9 0 0 9.9 370.7 290 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 373.1 290 Tm 0 Tc 0.271 Tw [( )520( to glass compositions)]TJ 9.9 0 0 9.9 465.1 290 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 467.5 290 Tm 0 Tc -0.248 Tw [( )-519(Other)]TJ -36.833 -1.111 TD 0.221 Tw [( )470(compounds are added to silica-based glass mixtures to help with chemical stabilization)]TJ 9.9 0 0 9.9 493.5 280 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 136 270 Tm 0 Tc 0.22 Tw [( )469(typically the alkaline earth oxides and in particular Al)]TJ 6 0 0 6 361.8 268.5 Tm ( )Tj 6 0 0 5 361.8 268.5 Tm (2)Tj 9 0 0 9 364.8 270 Tm -0.248 Tc 0 Tw ( O)Tj 6 0 0 6 372.2 268.5 Tm ( )Tj 6 0 0 5 372.2 268.5 Tm (3)Tj 9 0 0 9 375.2 270 Tm 0 Tc 0.22 Tw [( )469( to improve the resistance of)]TJ -26.578 -1.111 TD 0.083 Tw [( )332(glasses to attack by water)]TJ 9.9 0 0 9.9 237.9 260 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 250 Tm 0 Tc 0.161 Tw [( )410(To extend the transmission range of glasses into the ultraviolet)]TJ 9.9 0 0 9.9 405.3 250 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 407.7 250 Tm 0 Tc 0.161 Tw [( )410( a number of \337uoride)]TJ -30.189 -1.111 TD 0.114 Tw [( )363(and \337uorophosphate glasses have been developed)]TJ 9.9 0 0 9.9 335.4 240 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 337.8 240 Tm 0 Tc 0.114 Tw [( )363( Nonoxide glasses are used for infrared)]TJ -22.422 -1.111 TD 0.112 Tw [( )361(applications requiring transmission beyond the transmission limit of typical optical glasses)]TJ T* -0.248 Tw [( \(2)]TJ 9.9 0 0 9.9 144 220 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 146.4 220 Tm 0 Tc -0.248 Tw [( 4 )-342(to )-342(2)]TJ 9.9 0 0 9.9 169.5 220 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 171.9 220 Tm ( 7)Tj /F13 1 Tf 0.722 0 TD ( m)Tj /F15 1 Tf 0.667 0 TD 0 Tc 0.094 Tw [( )343(m for an absorption coef)56( )343(\336cient of 1)-211( )343(cm)]TJ /F13 1 Tf 6 0 0 6 339.3 224 Tm ( )Tj 6 0 0 5 339.3 224 Tm (2)Tj /F15 1 Tf 6 0 0 6 344.2 224 Tm ( )Tj 6 0 0 5 344.2 224 Tm (1)Tj 9 0 0 9 347.2 220 Tm -0.248 Tc 0 Tw ( \))Tj 9.9 0 0 9.9 350.7 220 Tm ( .)Tj 9 0 0 9 353.1 220 Tm 0 Tc 0.094 Tw [( )343( These materials include chalcogen-)]TJ -24.122 -1.111 TD 0.083 Tw [( )332(ides such as As)]TJ 6 0 0 6 197 208.5 Tm ( )Tj 6 0 0 5 197 208.5 Tm (2)Tj 9 0 0 9 200 210 Tm -0.248 Tc 0 Tw ( S)Tj 6 0 0 6 205 208.5 Tm ( )Tj 6 0 0 5 205 208.5 Tm (3)Tj 9 0 0 9 208 210 Tm 0 Tc 0.083 Tw [( )332( glass and heavy-metal \337uorides such as ZrF)]TJ 6 0 0 6 385 208.5 Tm ( )Tj 6 0 0 5 385 208.5 Tm (4)Tj 9 0 0 9 388 210 Tm -0.248 Tw [( -based )-331(glasses)]TJ 9.9 0 0 9.9 443 210 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 200 Tm 0 Tc 0.237 Tw [( )486(Crystalline materials include naturally occurring minerals and manufactured crystals)]TJ 9.9 0 0 9.9 493.5 200 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 136 190 Tm 0 Tc 0.155 Tw [( )404(Both single crystals and polycrystalline forms are available for many materials)]TJ 9.9 0 0 9.9 453.9 190 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 456.3 190 Tm 0 Tc -0.248 Tw [( )-403(Polycrys-)]TJ -35.589 -1.111 TD 0.313 Tw [( )562(talline optical materials are typically composed of many small \(cf)]TJ 9.9 0 0 9.9 414 180 Tm -0.248 Tw [( .,)]TJ 9 0 0 9 418.9 180 Tm [( )-561(50)]TJ /F13 1 Tf 1.778 0 TD -0.248 Tc 0 Tw ( m)Tj /F15 1 Tf 0.667 0 TD 0 Tc -0.248 Tw [( m\) )-561(individual)]TJ ET 136.2 170.1 m 207.7 170.1 l S BT /F15 1 Tf 7 0 0 7 148 161 Tm [( *)-229( Cubic )-376(\(or )-376(isometric\))]TJ 7.7 0 0 7.7 216.3 161 Tm -0.248 Tc 0 Tw ( ,)Tj 7 0 0 7 218.2 161 Tm 0 Tc 0.128 Tw [( )377( hexagonal \(including rhombohedral\))]TJ 7.7 0 0 7.7 334.3 161 Tm -0.248 Tc 0 Tw ( ,)Tj 7 0 0 7 336.2 161 Tm 0 Tc -0.248 Tw [( )-376(tetragonal)]TJ 7.7 0 0 7.7 369.9 161 Tm -0.248 Tc 0 Tw ( ,)Tj 7 0 0 7 371.8 161 Tm 0 Tc -0.248 Tw [( )-376(orthorhombic)]TJ 7.7 0 0 7.7 416.4 161 Tm -0.248 Tc 0 Tw ( ,)Tj 7 0 0 7 418.3 161 Tm 0 Tc -0.248 Tw [( )-376(monoclinic)]TJ 7.7 0 0 7.7 454.4 161 Tm -0.248 Tc 0 Tw ( ,)Tj 7 0 0 7 456.3 161 Tm 0 Tc 0.128 Tw [( )377( and triclinic)]TJ -45.757 -1.143 TD 0.083 Tw [( )332(are the crystallographic systems)]TJ 7.7 0 0 7.7 234 153 Tm -0.248 Tc 0 Tw ( .)Tj ET endstream endobj 27 0 obj << /ProcSet [ /PDF /Text ] /ColorSpace << /DefaultRGB 1 0 R >> /Font << /F10 7 0 R /F13 13 0 R /F15 14 0 R >> >> endobj 28 0 obj << /Type /Page /Parent 8 0 R /Resources 30 0 R /Contents 29 0 R /CropBox [ 43 94 552 748 ] /Thumb 650 0 R /B [ 847 0 R ] >> endobj 29 0 obj << /Length 12680 >> stream BT /F15 1 Tf 7 0 0 7 306.3 710 Tm 0 Tr 0 g 0 Tc 0.25 Tw [( )499(PROPERTIES OF CRYSTALS AND GLASSES)]TJ /F10 1 Tf 8 0 0 8 480.2 710 Tm ( )Tj 0 0 TD [(33)-13( )]TJ 1.125 0 TD (.7)Tj /F15 1 Tf 9 0 0 9 136 683 Tm 0.418 Tw [( )667(crystals with random orientations and )]TJ /F12 1 Tf 18.667 0 TD -0.248 Tw [( grain )-666(boundaries )]TJ /F15 1 Tf 8.333 0 TD [( between )-666(them)]TJ 9.9 0 0 9.9 438 683 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 440.4 683 Tm 0 Tc 0.418 Tw [( )667( These grain)]TJ -33.822 -1.111 TD 0.343 Tw [( )592(boundaries are a form of material defect arising from the lattice mismatch between)]TJ T* -0.248 Tw [( individual )-479(grains)]TJ 9.9 0 0 9.9 202.8 663 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 205.2 663 Tm 0 Tc 0.231 Tw [( )480( Polycrystalline materials are made by diverse means such as pressing)]TJ -7.689 -1.111 TD 0.39 Tw [( )639(powders \(usually with heat applied\))]TJ 9.9 0 0 9.9 289.5 653 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 291.9 653 Tm 0 Tc -0.248 Tw [( )-638(sintering)]TJ 9.9 0 0 9.9 331.6 653 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 334 653 Tm 0 Tc 0.39 Tw [( )639( or chemical vapor deposition)]TJ 9.9 0 0 9.9 463.5 653 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 465.9 653 Tm 0 Tc -0.248 Tw [( )-638(Single)]TJ -36.656 -1.111 TD 0.468 Tw [( )717(crystals are typically grown from dissolved or molten material using a variety of)]TJ T* -0.248 Tw [( techniques)]TJ 9.9 0 0 9.9 178 633 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 180.4 633 Tm 0 Tc -0.248 Tw [( )-471(Usually)]TJ 9.9 0 0 9.9 214.6 633 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 217 633 Tm 0 Tc 0.223 Tw [( )472( polycrystalline materials of)65( )472(fer greater hardness and strength at the)]TJ -9 -1.111 TD 0.083 Tw [( )332(expense of increased scatter)]TJ 9.9 0 0 9.9 247.4 623 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 613 Tm 0 Tc 0.112 Tw [( )361(Uniformity of the refractive index throughout an optical element is a prime considera-)]TJ -1.333 -1.111 TD 0.1 Tw [( )349(tion in selecting materials for high-performance lenses)]TJ 9.9 0 0 9.9 352.9 603 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 355.3 603 Tm 0 Tc 0.1 Tw [( )349( elements for coherent optics)]TJ 9.9 0 0 9.9 471.9 603 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 474.3 603 Tm 0 Tc -0.248 Tw [( )-348(laser)]TJ -37.589 -1.111 TD [( harmonic )-417(generation)]TJ 9.9 0 0 9.9 218.7 593 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 221.1 593 Tm 0 Tc 0.169 Tw [( )418( and acousto-optical devices)]TJ 9.9 0 0 9.9 334.9 593 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 337.3 593 Tm 0 Tc 0.169 Tw [( )418( In general)]TJ 9.9 0 0 9.9 382.3 593 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 384.7 593 Tm 0 Tc 0.169 Tw [( )418( highly pure)]TJ 9.9 0 0 9.9 434.2 593 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 436.6 593 Tm 0 Tc 0.169 Tw [( )418( single crystals)]TJ -33.4 -1.111 TD 0.478 Tw [( )727(achieve the best uniformity)]TJ 9.9 0 0 9.9 255.1 583 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 257.5 583 Tm 0 Tc 0.478 Tw [( )727( followed by glasses \(especially those selected by the)]TJ -13.5 -1.111 TD 0.079 Tw [( )328(manufacturer for homogeneity\))]TJ 9.9 0 0 9.9 260.9 573 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 263.3 573 Tm 0 Tc 0.079 Tw [( )328( and lastly polycrystalline materials)]TJ 9.9 0 0 9.9 403.1 573 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 405.5 573 Tm 0 Tc -0.248 Tw [( )-327(Similarly)]TJ 9.9 0 0 9.9 443.4 573 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 445.8 573 Tm 0 Tc -0.248 Tw [( )-327(high-quality)]TJ -34.422 -1.111 TD 0.083 Tw [( )332(single crystals have very low scatter)]TJ 9.9 0 0 9.9 277.9 563 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 280.3 563 Tm 0 Tc 0.083 Tw [( )332( typically one-tenth that of glasses)]TJ 9.9 0 0 9.9 416.2 563 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 553 Tm 0 Tc 0.251 Tw [( )500(Applications requiring optical elements with direction-dependent properties)]TJ 9.9 0 0 9.9 459.1 553 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 461.5 553 Tm 0 Tc 0.251 Tw [( )500( such as)]TJ -36.167 -1.111 TD 0.264 Tw [( )513(polarizers and index-matching materials for harmonic generation)]TJ 9.9 0 0 9.9 403.7 543 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 406.1 543 Tm 0 Tc 0.264 Tw [( )513( frequently use single)]TJ -30.011 -1.111 TD -0.248 Tw [( crystals)]TJ 9.9 0 0 9.9 164.9 533 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 523 Tm 0 Tc 0.243 Tw [( )492(Purity of starting materials is a prime factor in determining the quality of the \336nal)]TJ -1.333 -1.111 TD -0.248 Tw [( product)]TJ 9.9 0 0 9.9 166.5 513 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 168.9 513 Tm 0 Tc 0.126 Tw [( )375( High material quality and uniformity of processing is required to avoid impurity)]TJ -3.656 -1.111 TD -0.248 Tw [( absorption)]TJ 9.9 0 0 9.9 178 503 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 180.4 503 Tm 0 Tc 0.152 Tw [( )401( index nonuniformity)]TJ 9.9 0 0 9.9 265.6 503 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 268 503 Tm 0 Tc -0.248 Tw [( )-400(voids)]TJ 9.9 0 0 9.9 292.1 503 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 294.5 503 Tm 0 Tc -0.248 Tw [( )-400(cracks)]TJ 9.9 0 0 9.9 322.6 503 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 325 503 Tm 0 Tc 0.152 Tw [( )401( and bubbles)]TJ 9.9 0 0 9.9 377.2 503 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 379.6 503 Tm 0 Tc 0.152 Tw [( )401( and excess scatter)]TJ 9.9 0 0 9.9 455.4 503 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 457.8 503 Tm 0 Tc -0.248 Tw [( )-400(Practical)]TJ -35.756 -1.111 TD 0.123 Tw [( )372(manufacturing techniques limit the size of optics of a given material \(glasses are typically)]TJ T* 0.525 Tw [( )774(limited by the moduli)]TJ 9.9 0 0 9.9 233.9 483 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 236.3 483 Tm [( )-773(i)]TJ 9.9 0 0 9.9 245.7 483 Tm ( .)Tj 9 0 0 9 248.1 483 Tm ( e)Tj 9.9 0 0 9.9 252.6 483 Tm 0 Tc -0.248 Tw [( .,)]TJ 9 0 0 9 257.5 483 Tm 0.525 Tw [( )774( deformation caused the weight of the piece\))]TJ 9.9 0 0 9.9 464.3 483 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 466.7 483 Tm 0 Tc -0.248 Tw [( )-773(Some)]TJ -36.744 -1.111 TD [( manufacturing )-566(methods)]TJ 9.9 0 0 9.9 231.6 473 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 234 473 Tm 0 Tc 0.318 Tw [( )567( such as hot pressing)]TJ 9.9 0 0 9.9 324.9 473 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 327.3 473 Tm 0 Tc 0.318 Tw [( )567( also produce signi\336cantly lower quality)]TJ -21.256 -1.111 TD 0.145 Tw [( )394(material when size becomes large \(especially when the thinnest dimension is signi\336cantly)]TJ T* -0.248 Tw [( increased\))]TJ 9.9 0 0 9.9 176.5 453 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 178.9 453 Tm 0 Tc 0.04 Tw [( )289( Cost of \336nished optical elements is a function of size)]TJ 9.9 0 0 9.9 388.5 453 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 390.9 453 Tm 0 Tc 0.04 Tw [( )289( raw material cost)]TJ 9.9 0 0 9.9 461.2 453 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 463.6 453 Tm 0 Tc 0.04 Tw [( )289( and the)]TJ -36.4 -1.111 TD -0.248 Tw [( dif)66( \336culty )-397(of )-397(machining)]TJ 9.9 0 0 9.9 225.5 443 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 227.9 443 Tm 0 Tc -0.248 Tw [( )-397(polishing)]TJ 9.9 0 0 9.9 267 443 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 269.4 443 Tm 0 Tc 0.149 Tw [( )398( and coating the material)]TJ 9.9 0 0 9.9 371.7 443 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 374.1 443 Tm 0 Tc 0.149 Tw [( )398( Any one of these factors can)]TJ -26.456 -1.111 TD -0.248 Tw [( dominate )-331(cost)]TJ 9.9 0 0 9.9 191.4 433 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 423 Tm 0 Tc 0.062 Tw [( )311(General information on the manufacturing methods for glasses and crystalline materials)]TJ -1.333 -1.111 TD 0.089 Tw [( )338(is available in several sources)]TJ 9.9 0 0 9.9 253.2 413 Tm -0.248 Tc 0 Tw ( .)Tj 6 0 0 6 255.6 417 Tm ( )Tj 6 0 0 5 255.6 417 Tm (9)Tj 6 0 0 6 258.6 417 Tm ( )Tj 6 0 0 5 258.6 417 Tm (\320)Tj 6 0 0 6 261.6 417 Tm ( )Tj 6 0 0 5 261.6 417 Tm (1)Tj 6 0 0 6 264.6 417 Tm ( )Tj 6 0 0 5 264.6 417 Tm (1)Tj 9 0 0 9 267.6 413 Tm 0 Tc 0.089 Tw [( )338( Information on cutting and polishing of optical elements)]TJ -14.622 -1.111 TD 0.083 Tw [( )332(can be found in the literature)]TJ 9.9 0 0 9.9 253.5 403 Tm -0.248 Tc 0 Tw ( .)Tj 6 0 0 6 255.9 407 Tm ( )Tj 6 0 0 5 255.9 407 Tm (2)Tj 6.6 0 0 6.6 258.9 407 Tm ( )Tj 6.6 0 0 5.499 258.9 407 Tm (,)Tj 6 0 0 6 260.5 407 Tm ( )Tj 6 0 0 5 260.5 407 Tm (1)Tj 6 0 0 6 263.5 407 Tm ( )Tj 6 0 0 5 263.5 407 Tm (2)Tj 6.6 0 0 6.6 266.5 407 Tm ( )Tj 6.6 0 0 5.499 266.5 407 Tm (,)Tj 6 0 0 6 268.1 407 Tm ( )Tj 6 0 0 5 268.1 407 Tm (1)Tj 6 0 0 6 271.1 407 Tm ( )Tj 6 0 0 5 271.1 407 Tm (3)Tj /F10 1 Tf 10 0 2.126 10 76 369.4 Tm ( )Tj 0 0 TD -0.005 Tc (3 )Tj 0.55 0 TD (3 )Tj 0.55 0 TD -0.007 Tc (. )Tj 0.27 0 TD 0.994 Tc (4 )Tj 1.55 0 TD 0 Tc 0.222 Tw (PROPERTIES OF MATERIALS)Tj ET 0 G 1 i 0 J 0 j 0.3 w 10 M []0 d 76.7 364.4 m 495.2 364.4 l S BT /F10 1 Tf 9 0 0 9 76 346.1 Tm ( )Tj T* 0.055 Tw (Symmetry Properties)Tj /F15 1 Tf 6.667 -1.856 TD 0.089 Tw [( )338(The description of the properties of solids depends on structural symmetry)]TJ 9.9 0 0 9.9 434.5 329.4 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 436.9 329.4 Tm 0 Tc 0.089 Tw [( )338( The structural)]TJ -33.433 -1.111 TD 0.244 Tw [( )493(symmetry crystalline materials dictate the number of appropriate directional-dependent)]TJ T* 0.149 Tw [( )398(terms that describe a property)]TJ 9.9 0 0 9.9 258.8 309.4 Tm -0.248 Tc 0 Tw ( .)Tj 6 0 0 6 261.2 313.4 Tm ( )Tj 6 0 0 5 261.2 313.4 Tm (1)Tj 6 0 0 6 264.2 313.4 Tm ( )Tj 6 0 0 5 264.2 313.4 Tm (4)Tj 9 0 0 9 267.2 309.4 Tm ( )Tj /F12 1 Tf 0.389 0 TD 0 Tc -0.248 Tw [( Neumann)]TJ /F15 1 Tf 4.267 0 TD -0.248 Tc 0 Tw ( \325)Tj /F12 1 Tf 0.278 0 TD 0 Tc -0.248 Tw [( s )-397(principle )]TJ /F15 1 Tf 4.956 0 TD 0.149 Tw [( )398(states that physical properties of a)]TJ -24.467 -1.111 TD 0.155 Tw [( )404(crystal must possess at least the symmetry of the point group of the crystal)]TJ 9.9 0 0 9.9 442.9 299.4 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 445.3 299.4 Tm 0 Tc -0.248 Tw [( )-403(Amorphous)]TJ -34.367 -1.111 TD [( \(glassy\) )-499(materials)]TJ 9.9 0 0 9.9 206.5 289.4 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 208.9 289.4 Tm 0 Tc 0.251 Tw [( )500( having no long-range symmetry)]TJ 9.9 0 0 9.9 343.4 289.4 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 345.8 289.4 Tm 0 Tc 0.251 Tw [( )500( are generally considered isotropic)]TJ 9.9 0 0 9.9 488.8 289.4 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 491.2 289.4 Tm ( *)Tj -39.467 -1.111 TD 0 Tc 0.112 Tw [( )361(and require the least number of property terms)]TJ 9.9 0 0 9.9 326.8 279.4 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 329.2 279.4 Tm 0 Tc 0.112 Tw [( )361( Macroscopic material properties are best)]TJ -21.467 -1.111 TD 0.104 Tw [( )353(described in tensor notation )353(;)-6( )353( the rank of the property tensors can range from zero \(scalar)]TJ T* 0.093 Tw [( )342(property\) up to large rank)]TJ 9.9 0 0 9.9 241.3 259.4 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 243.7 259.4 Tm 0 Tc 0.093 Tw [( )342( Table 1 summarizes common material properties and the rank)]TJ -11.967 -1.111 TD 0.083 Tw [( )332(of the tensor that describes them)]TJ 9.9 0 0 9.9 267.4 249.4 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 148 239.4 Tm 0 Tc 0.155 Tw [( )404(The rank of the property tensor and the symmetry of the material \(as determined by)]TJ -1.333 -1.111 TD 0.349 Tw [( )598(the point group for crystals\) determines the number of terms needed to describe a)]TJ T* -0.248 Tw [( property)]TJ 9.9 0 0 9.9 170 219.4 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 172.4 219.4 Tm 0 Tc 0.048 Tw [( )297( Table 2 summarizes both the number of terms needed to describe a property and)]TJ -4.044 -1.111 TD 0.306 Tw [( )555(the number of unique terms as a function of property tensor rank and point group)]TJ 9.9 0 0 9.9 493.6 209.4 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 136 199.4 Tm 0 Tc 0.08 Tw [( )329(Another important term in the de\336nition of tensor characteristics is the )]TJ /F12 1 Tf 31.956 0 TD -0.248 Tw [( principal )]TJ /F13 1 Tf 8.5 0 1.807 8.5 460.8 199.4 Tm ( )Tj 8.5 0 1.807 9.376 460.8 199.4 Tm (y)Tj /F12 1 Tf 9 0 0 9 465.4 199.4 Tm [( alues )]TJ /F15 1 Tf 2.489 0 TD [( of)]TJ ET 136.2 186.1 m 207.7 186.1 l S BT /F15 1 Tf 7 0 0 7 148 177 Tm 0.045 Tw [( )294(*)-229( )294(Glass properties are dependent on cooling rate)]TJ 7.7 0 0 7.7 297.4 177 Tm -0.248 Tc 0 Tw ( .)Tj 7 0 0 7 299.3 177 Tm 0 Tc 0.045 Tw [( )294( Nonuniform cooling will result in density variation and residual)]TJ -23.329 -1.143 TD 0.082 Tw [( )331(stress which cause anisotropy in all properties)]TJ 7.7 0 0 7.7 277.9 169 Tm -0.248 Tc 0 Tw ( .)Tj 7 0 0 7 279.8 169 Tm 0 Tc 0.082 Tw [( )331( Such nonisotropic behavior is dif)46( )331(ferent from that of crystals in that it)]TJ -20.543 -1.143 TD 0.101 Tw [( )350(arises from thermal gradients rather than periodic structure order)]TJ 7.7 0 0 7.7 340.4 161 Tm -0.248 Tc 0 Tw ( .)Tj 7 0 0 7 342.3 161 Tm 0 Tc -0.248 Tw [( )-349(Hence)]TJ 7.7 0 0 7.7 364.5 161 Tm -0.248 Tc 0 Tw ( ,)Tj 7 0 0 7 366.4 161 Tm 0 Tc 0.101 Tw [( )350( the nature of anisotropy in glasses varies)]TJ -32.914 -1.143 TD 0.083 Tw [( )332(from sample to sample)]TJ 7.7 0 0 7.7 206.7 153 Tm -0.248 Tc 0 Tw ( .)Tj ET endstream endobj 30 0 obj << /ProcSet [ /PDF /Text ] /ColorSpace << /DefaultRGB 1 0 R >> /Font << /F10 7 0 R /F12 12 0 R /F13 13 0 R /F15 14 0 R >> >> endobj 31 0 obj << /Type /Page /Parent 39 0 R /Resources 33 0 R /Contents 32 0 R /CropBox [ 43 94 552 748 ] /Thumb 652 0 R /B [ 848 0 R ] >> endobj 32 0 obj << /Length 16364 >> stream BT /F10 1 Tf 8 0 0 8 76 710 Tm 0 Tr 0 g ( )Tj 0 0 TD 0 Tc [(33)-13( )]TJ 1.125 0 TD (.8)Tj /F15 1 Tf 7 0 0 7 105.6 710 Tm 0.25 Tw [( )499(OPTICAL AND PHYSICAL PROPERTIES OF MATERIALS)]TJ /F10 1 Tf 8 0 0 8 76 682.5 Tm ( )Tj T* 0.055 Tw (TABLE 1)Tj /F15 1 Tf 5.05 0 TD 0.083 Tw [( )332(Tensor Characteristics and De\336nitions of Properties)]TJ ET 0 G 1 i 0 J 0 j 1 w 10 M []0 d 76 673.5 m 496 673.5 l S BT /F15 1 Tf 8 0 0 8 91.4 661.5 Tm -0.248 Tw [( Tensor )-323(rank)-8942( Property)-10954( Symbol)-3983( Units)-4336( Relationship)]TJ ET 0.3 w 76.7 655.1 m 495.2 655.1 l S BT /F15 1 Tf 8 0 0 8 111 643.5 Tm [( 0)-4375( Enthalpy )-323(\(energy\))]TJ 4.875 -1.188 TD [( Temperature)]TJ T* [( Heat )-323(capacity)]TJ /F12 1 Tf 22.75 2.375 TD -0.248 Tc 0 Tw ( U)Tj 0 -1.188 TD ( T)Tj T* ( C)Tj /F15 1 Tf 4.375 2.375 TD ( J)Tj 10 0 0 10 370.9 642.5 Tm ( /)Tj 8 0 0 8 374 643.5 Tm 0 Tc -0.248 Tw [( mole)]TJ -0.875 -1.188 TD -0.248 Tc 0 Tw ( K)Tj T* ( J)Tj 10 0 0 10 370.9 623.5 Tm ( /)Tj 8 0 0 8 374 624.5 Tm 0 Tc -0.248 Tw [( \(mole)]TJ /F13 1 Tf 2.775 0 TD -0.248 Tc 0 Tw ( ?)Tj /F15 1 Tf 0.55 0 TD 0 Tc -0.248 Tw [( K\))]TJ 6.738 2.375 TD -0.248 Tc 0 Tw ( \321)Tj 0 -1.188 TD ( \321)Tj /F12 1 Tf -1.95 -1.188 TD ( C)Tj /F13 1 Tf 0.925 0 TD 0.167 Tc -0.415 Tw [( 5 \255)]TJ /F12 1 Tf 1.487 0 TD -0.248 Tc 0 Tw ( U)Tj /F15 1 Tf 10 0 0 10 465.3 623.5 Tm ( /)Tj /F13 1 Tf 8 0 0 8 468.4 624.5 Tm ( \255)Tj /F12 1 Tf 0.488 0 TD ( T)Tj /F15 1 Tf -45.163 -1.562 TD 0 Tc -0.248 Tw [( 1)-4375( Displacement)]TJ 4.875 -1.188 TD [( Heat )-323(\337ow)]TJ T* [( Electric )-323(\336eld)]TJ T* [( Electric )-323(polarization)]TJ T* [( Electric )-323(displacement)]TJ T* [( Pyroelectric )-323(constant)]TJ /F12 1 Tf 22.75 5.938 TD -0.248 Tc 0 Tw ( x)Tj 0 -1.188 TD ( h)Tj /F7 1 Tf T* ( E)Tj T* ( P)Tj T* ( D)Tj /F12 1 Tf T* ( p)Tj /F15 1 Tf 4.375 5.937 TD ( m)Tj 0 -1.188 TD ( W)Tj 10 0 0 10 375.3 601.5 Tm ( /)Tj 8 0 0 8 378.4 602.5 Tm ( m)Tj 6 0 0 6 385 606 Tm ( )Tj 6 0 0 5 385 606 Tm (2)Tj 8 0 0 8 367 593 Tm ( V)Tj 10 0 0 10 373.6 592 Tm ( /)Tj 8 0 0 8 376.7 593 Tm ( m)Tj -1.212 -1.188 TD ( C)Tj 10 0 0 10 373.1 582.5 Tm ( /)Tj 8 0 0 8 376.2 583.5 Tm ( m)Tj 6 0 0 6 382.8 587 Tm ( )Tj 6 0 0 5 382.8 587 Tm (2)Tj 8 0 0 8 367 574 Tm ( C)Tj 10 0 0 10 373.1 573 Tm ( /)Tj 8 0 0 8 376.2 574 Tm ( m)Tj 6 0 0 6 382.8 577.5 Tm ( )Tj 6 0 0 5 382.8 577.5 Tm (2)Tj 8 0 0 8 367 564.5 Tm ( C)Tj 10 0 0 10 373.1 563.5 Tm ( /)Tj 8 0 0 8 376.2 564.5 Tm 0 Tc -0.248 Tw [( \(m)]TJ 6 0 0 6 385.9 568 Tm ( )Tj 6 0 0 5 385.9 568 Tm (2)Tj /F13 1 Tf 8 0 0 8 390.7 564.5 Tm -0.248 Tc 0 Tw ( ?)Tj /F15 1 Tf 0.55 0 TD 0 Tc -0.248 Tw [( K\))]TJ 7.425 5.937 TD -0.248 Tc 0 Tw ( \321)Tj 0 -1.188 TD ( \321)Tj T* ( \321)Tj /F7 1 Tf -1.587 -1.187 TD ( P)Tj /F13 1 Tf 0.825 0 TD ( 5)Tj 8 0 1.7 8 456.4 583.5 Tm ( e)Tj /F15 1 Tf 6 0 0 6 460.6 581.8 Tm ( )Tj 6 0 0 5 460.6 581.8 Tm (0)Tj /F18 1 Tf 8 0 1.7 8 464 583.5 Tm ( c)Tj /F7 1 Tf 8 0 0 8 469.1 583.5 Tm ( E)Tj -4.062 -1.188 TD ( D)Tj /F13 1 Tf 1 0 TD ( 5)Tj 8 0 1.7 8 452.5 574 Tm ( e)Tj /F15 1 Tf 6 0 0 6 456.7 572.3 Tm ( )Tj 6 0 0 5 456.7 572.3 Tm (0)Tj /F7 1 Tf 8 0 0 8 459.7 574 Tm ( E)Tj /F13 1 Tf 0.875 0 TD ( 1)Tj /F7 1 Tf 1 0 TD ( P)Tj /F13 1 Tf -4.362 -1.188 TD ( D)Tj /F7 1 Tf 0.662 0 TD ( P)Tj /F13 1 Tf 0.825 0 TD ( 5)Tj /F12 1 Tf 1 0 TD ( p)Tj /F13 1 Tf 0.825 0 TD ( D)Tj /F12 1 Tf 0.662 0 TD ( T)Tj /F15 1 Tf -45.075 -1.563 TD 0 Tc -0.248 Tw [( 2)-4375( Stress)]TJ 4.875 -1.188 TD [( Strain)]TJ T* [( Thermal )-323(expansion)]TJ T* [( Thermal )-323(conductivity)]TJ T* 0.083 Tw [( )332(Dielectric constant \(relative permittivity\))]TJ T* 0.081 Tw [( )330(Inverse dielectric tensor)]TJ T* -0.248 Tw [( Susceptibility)]TJ /F13 1 Tf 8 0 1.7 8 332 552 Tm -0.248 Tc 0 Tw ( s)Tj /F12 1 Tf 8 0 0 8 332 542.5 Tm ( e)Tj /F13 1 Tf 8 0 1.7 8 332 533 Tm ( a)Tj 0.252 -1.188 TD ( k)Tj 0.252 -1.188 TD ( e)Tj /F12 1 Tf 6 0 0 6 335.8 512.3 Tm ( )Tj 6 0 0 5 335.8 512.3 Tm (r)Tj /F7 1 Tf 8 0 0 8 332 504.5 Tm ( B)Tj /F18 1 Tf 8 0 1.7 8 332 495 Tm ( c)Tj /F15 1 Tf 8 0 0 8 367 552 Tm 0 Tc -0.248 Tw [( Pa)]TJ 2.625 -1.188 TD -0.248 Tc 0 Tw ( \321)Tj -2.625 -1.188 TD ( K)Tj /F13 1 Tf 6 0 0 6 373.2 536.5 Tm ( )Tj 6 0 0 5 373.2 536.5 Tm (2)Tj /F15 1 Tf 6 0 0 6 378.1 536.5 Tm ( )Tj 6 0 0 5 378.1 536.5 Tm (1)Tj 8 0 0 8 367 523.5 Tm ( W)Tj 10 0 0 10 375.3 522.5 Tm ( /)Tj 8 0 0 8 378.4 523.5 Tm 0 Tc -0.248 Tw [( \(m)]TJ /F13 1 Tf 1.438 0 TD -0.248 Tc 0 Tw ( ?)Tj /F15 1 Tf 0.55 0 TD 0 Tc -0.248 Tw [( K\))]TJ -0.787 -1.188 TD -0.248 Tc 0 Tw ( \321)Tj T* ( \321)Tj T* ( \321)Tj 8.312 7.125 TD ( \321)Tj 0 -1.188 TD ( \321)Tj /F12 1 Tf -1 -1.188 TD ( e)Tj /F13 1 Tf 0.663 0 TD ( 5)Tj 8 0 1.7 8 459.7 533 Tm ( a)Tj /F12 1 Tf 8 0 0 8 464.9 533 Tm ( T)Tj -4.225 -1.188 TD ( h)Tj /F13 1 Tf 0.775 0 TD 0.154 Tc -0.402 Tw [( 5 2)]TJ 8 0 1.7 8 451.8 523.5 Tm -0.248 Tc 0 Tw ( k)Tj /F15 1 Tf 8 0 0 8 457.1 523.5 Tm ( \()Tj /F13 1 Tf 0.388 0 TD ( \255)Tj /F12 1 Tf 0.487 0 TD ( T)Tj /F15 1 Tf 10 0 0 10 470.7 522.5 Tm ( /)Tj /F13 1 Tf 8 0 0 8 473.8 523.5 Tm ( \255)Tj /F12 1 Tf 0.487 0 TD ( x)Tj /F15 1 Tf 0.55 0 TD ( \))Tj /F7 1 Tf -5.212 -1.188 TD ( D)Tj /F13 1 Tf 0.988 0 TD ( 5)Tj 8 0 1.7 8 456.3 514 Tm ( e)Tj /F15 1 Tf 6 0 0 6 460.5 512.3 Tm ( )Tj 6 0 0 5 460.5 512.3 Tm (0)Tj /F13 1 Tf 8 0 1.7 8 463.9 514 Tm ( e)Tj /F12 1 Tf 6 0 0 6 467.8 512.3 Tm ( )Tj 6 0 0 5 467.8 512.3 Tm (r)Tj /F7 1 Tf 8 0 0 8 470.5 514 Tm ( E)Tj -3.212 -1.188 TD ( B)Tj /F13 1 Tf 0.875 0 TD ( 5)Tj 8 0 1.7 8 459.7 504.5 Tm ( e)Tj 6 0 0 6 464 508 Tm ( )Tj 6 0 0 5 464 508 Tm (2)Tj /F15 1 Tf 6 0 0 6 468.9 508 Tm ( )Tj 6 0 0 5 468.9 508 Tm (1)Tj /F12 1 Tf 6 0 0 6 464 502.8 Tm ( )Tj 6 0 0 5 464 502.8 Tm (r)Tj /F13 1 Tf 8 0 1.7 8 441.2 495 Tm ( e)Tj /F12 1 Tf 6 0 0 6 445.1 493.3 Tm ( )Tj 6 0 0 5 445.1 493.3 Tm (r)Tj /F13 1 Tf 8 0 0 8 449.1 495 Tm ( 5)Tj /F18 1 Tf 8 0 1.7 8 457.1 495 Tm ( c)Tj /F13 1 Tf 8 0 0 8 463.5 495 Tm ( 1)Tj /F15 1 Tf 0.987 0 TD ( 1)Tj -45.05 -1.563 TD 0 Tc -0.248 Tw [( 3)-4375( Piezoelectric )-329(coef)56( \336cient )-329(\(modulus\))]TJ 4.875 -1.188 TD 0.081 Tw [( )330(\(converse piezoelectric ef)68( )330(fect\))]TJ T* -0.248 Tw [( Electro-optic )-329(coef)60( \336cient )-329(\(linear\))]TJ T* [( Second-order )-323(susceptibility)]TJ /F12 1 Tf 22.75 3.563 TD -0.248 Tc 0 Tw ( d)Tj 0 -1.188 TD ( d)Tj T* ( r)Tj /F18 1 Tf 8 0 1.7 8 332 454 Tm ( c)Tj /F15 1 Tf 6 0 0 6 337.1 457.5 Tm ( )Tj 6 0 0 5 337.1 457.5 Tm (\()Tj 6 0 0 6 339.4 457.5 Tm ( )Tj 6 0 0 5 339.4 457.5 Tm (2)Tj 6 0 0 6 342.4 457.5 Tm ( )Tj 6 0 0 5 342.4 457.5 Tm (\))Tj 8 0 0 8 367 482.5 Tm ( m)Tj 10 0 0 10 374 481.5 Tm ( /)Tj 8 0 0 8 377.1 482.5 Tm ( V)Tj /F20 1 Tf 0.95 0 TD ( ;)Tj /F15 1 Tf 0.988 0 TD ( C)Tj 10 0 0 10 398.7 481.5 Tm ( /)Tj 8 0 0 8 401.9 482.5 Tm ( N)Tj -4.362 -1.188 TD ( m)Tj 10 0 0 10 374 472 Tm ( /)Tj 8 0 0 8 377.1 473 Tm ( V)Tj /F20 1 Tf 0.95 0 TD ( ;)Tj /F15 1 Tf 0.987 0 TD ( C)Tj 10 0 0 10 398.7 472 Tm ( /)Tj 8 0 0 8 401.9 473 Tm ( N)Tj -4.362 -1.188 TD ( m)Tj 10 0 0 10 374 462.5 Tm ( /)Tj 8 0 0 8 377.1 463.5 Tm ( V)Tj -1.262 -1.188 TD ( m)Tj 10 0 0 10 374 453 Tm ( /)Tj 8 0 0 8 377.1 454 Tm ( V)Tj /F7 1 Tf 8.237 3.562 TD ( P)Tj /F13 1 Tf 0.825 0 TD ( 5)Tj /F12 1 Tf 0.988 0 TD ( d)Tj /F21 1 Tf 0.825 0 TD ( ?)Tj /F13 1 Tf 8 0 1.7 8 468.5 482.5 Tm ( s)Tj /F12 1 Tf 8 0 0 8 443.4 473 Tm ( e)Tj /F13 1 Tf 0.65 0 TD ( 5)Tj /F12 1 Tf 1 0 TD ( d)Tj /F21 1 Tf 0.825 0 TD ( ?)Tj /F7 1 Tf 0.55 0 TD ( E)Tj /F13 1 Tf -3.387 -1.188 TD ( D)Tj /F7 1 Tf 0.663 0 TD ( B)Tj /F13 1 Tf 0.875 0 TD ( 5)Tj /F12 1 Tf 0.987 0 TD ( r)Tj /F21 1 Tf 0.675 0 TD ( ?)Tj /F7 1 Tf 0.538 0 TD ( E)Tj -4.787 -1.188 TD ( P)Tj /F13 1 Tf 0.825 0 TD ( 5)Tj 8 0 1.7 8 446.6 454 Tm ( e)Tj /F15 1 Tf 6 0 0 6 450.8 452.3 Tm ( )Tj 6 0 0 5 450.8 452.3 Tm (0)Tj /F18 1 Tf 8 0 1.7 8 454.3 454 Tm ( c)Tj /F15 1 Tf 6 0 0 6 459.4 457.5 Tm ( )Tj 6 0 0 5 459.4 457.5 Tm (\()Tj 6 0 0 6 461.7 457.5 Tm ( )Tj 6 0 0 5 461.7 457.5 Tm (2)Tj 6 0 0 6 464.7 457.5 Tm ( )Tj 6 0 0 5 464.7 457.5 Tm (\))Tj /F7 1 Tf 8 0 0 8 467 454 Tm ( E)Tj /F15 1 Tf 6 0 0 6 472.7 452.3 Tm ( )Tj 6 0 0 5 472.7 452.3 Tm (1)Tj /F7 1 Tf 8 0 0 8 475.7 454 Tm ( E)Tj /F15 1 Tf 6 0 0 6 481.4 452.3 Tm ( )Tj 6 0 0 5 481.4 452.3 Tm (2)Tj 8 0 0 8 111 441.5 Tm 0 Tc -0.248 Tw [( 4)-4375( Elastic )-323(stif)64( fness)]TJ 4.875 -1.188 TD [( Elastic )-323(compliance)]TJ T* [( Elasto-optic )-323(tensor)]TJ T* [( Piezo-optic )-323(tensor)]TJ /F7 1 Tf 22.75 3.563 TD -0.248 Tc 0 Tw ( c)Tj 0 -1.188 TD ( s)Tj T* ( p)Tj T* ( q)Tj /F15 1 Tf 4.375 3.563 TD 0 Tc -0.248 Tw [( Pa)]TJ 0 -1.188 TD [( Pa)]TJ /F13 1 Tf 6 0 0 6 375.8 435.5 Tm ( )Tj 6 0 0 5 375.8 435.5 Tm (2)Tj /F15 1 Tf 6 0 0 6 380.7 435.5 Tm ( )Tj 6 0 0 5 380.7 435.5 Tm (1)Tj 8 0 0 8 388 422.5 Tm -0.248 Tc 0 Tw ( \321)Tj -2.625 -1.188 TD 0 Tc -0.248 Tw [( Pa)]TJ /F13 1 Tf 6 0 0 6 375.8 416.5 Tm ( )Tj 6 0 0 5 375.8 416.5 Tm (2)Tj /F15 1 Tf 6 0 0 6 380.7 416.5 Tm ( )Tj 6 0 0 5 380.7 416.5 Tm (1)Tj /F13 1 Tf 8 0 1.7 8 429.8 441.5 Tm -0.248 Tc 0 Tw ( s)Tj 8 0 0 8 436.8 441.5 Tm ( 5)Tj /F12 1 Tf 0.988 0 TD ( c)Tj /F13 1 Tf 0.712 0 TD ( ?)Tj /F12 1 Tf 0.55 0 TD ( e)Tj /F15 1 Tf 0.512 0 TD ( ;)Tj /F12 1 Tf 0.462 0 TD ( c)Tj /F13 1 Tf 0.663 0 TD ( 5)Tj /F15 1 Tf 0.988 0 TD ( 1)Tj 10 0 0 10 480.2 440.5 Tm ( /)Tj /F7 1 Tf 8 0 0 8 483.3 441.5 Tm ( s)Tj /F12 1 Tf -6.6 -1.188 TD ( e)Tj /F13 1 Tf 0.663 0 TD ( 5)Tj /F7 1 Tf 0.988 0 TD ( s)Tj /F21 1 Tf 0.612 0 TD ( ?)Tj /F13 1 Tf 8 0 1.7 8 452.9 432 Tm ( s)Tj /F15 1 Tf 8 0 0 8 458.7 432 Tm ( ;)Tj /F7 1 Tf 0.462 0 TD ( s)Tj /F13 1 Tf 0.562 0 TD ( 5)Tj /F15 1 Tf 0.988 0 TD ( 1)Tj 10 0 0 10 479.1 431 Tm ( /)Tj /F12 1 Tf 8 0 0 8 482.3 432 Tm ( c)Tj /F13 1 Tf -7.163 -1.188 TD ( D)Tj /F7 1 Tf 0.663 0 TD ( B)Tj /F13 1 Tf 0.875 0 TD ( 5)Tj /F7 1 Tf 0.988 0 TD ( p)Tj /F21 1 Tf 0.775 0 TD ( ?)Tj /F12 1 Tf 0.55 0 TD ( e)Tj /F15 1 Tf 0.512 0 TD ( ;)Tj /F7 1 Tf 0.462 0 TD ( p)Tj /F13 1 Tf 0.713 0 TD ( 5)Tj /F7 1 Tf 1 0 TD ( q)Tj /F21 1 Tf 0.762 0 TD ( ?)Tj /F12 1 Tf 0.55 0 TD ( c)Tj /F13 1 Tf -7.938 -1.188 TD ( D)Tj /F7 1 Tf 0.662 0 TD ( B)Tj /F13 1 Tf 0.875 0 TD ( 5)Tj /F7 1 Tf 1 0 TD ( q)Tj /F21 1 Tf 0.763 0 TD ( ?)Tj /F13 1 Tf 8 0 1.7 8 455.1 413 Tm ( s)Tj /F15 1 Tf 8 0 0 8 460.9 413 Tm ( ;)Tj /F7 1 Tf 0.462 0 TD ( q)Tj /F13 1 Tf 0.725 0 TD ( 5)Tj /F7 1 Tf 0.988 0 TD ( p)Tj /F21 1 Tf 0.775 0 TD ( ?)Tj /F7 1 Tf 0.538 0 TD ( s)Tj ET 1 w 76 407 m 496 407 l S BT /F15 1 Tf 9 0 0 9 136 380.3 Tm 0 Tc 0.376 Tw [( )625(a second-rank tensor property)]TJ 9.9 0 0 9.9 263.9 380.3 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 266.3 380.3 Tm 0 Tc 0.376 Tw [( )625( The principal values of a property are those values)]TJ -14.478 -1.111 TD 0.231 Tw [( )480(referenced to \(measured along\) the crystal axes as de\336ned in Table 2)]TJ 9.9 0 0 9.9 426.6 370.3 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 429 370.3 Tm 0 Tc 0.231 Tw [( )480( For example)]TJ 9.9 0 0 9.9 484.6 370.3 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 487 370.3 Tm [( )-479(a)]TJ -39 -1.111 TD 0 Tc 0.293 Tw [( )542(second-rank tensor of a triclinic crystal has nine nonzero coef)65( )542(\336cients)]TJ 9.9 0 0 9.9 425.3 360.3 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 427.7 360.3 Tm 0 Tc 0.293 Tw [( )542( and because of)]TJ -32.411 -1.111 TD -0.248 Tw [( symmetry)]TJ 9.9 0 0 9.9 174.4 350.3 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 176.8 350.3 Tm 0 Tc 0.237 Tw [( )486( six independent coef)62( )486(\336cients)]TJ 9.9 0 0 9.9 292.8 350.3 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 295.2 350.3 Tm 0 Tc 0.237 Tw [( )486( These six coef)60( )486(\336cients can be separated into \(1\))]TJ -17.689 -1.111 TD 0.408 Tw [( )657(three principal values of the quantity \(e)]TJ 9.9 0 0 9.9 312 340.3 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 314.4 340.3 Tm ( g)Tj 9.9 0 0 9.9 318.9 340.3 Tm 0 Tc -0.248 Tw [( .,)]TJ 9 0 0 9 323.8 340.3 Tm 0.408 Tw [( )657( thermal expansion coef)63( )657(\336cient)]TJ 9.9 0 0 9.9 451.4 340.3 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 453.8 340.3 Tm 0 Tc -0.248 Tw [( )-656(dielectric)]TJ -35.311 -1.111 TD [( constant)]TJ 9.9 0 0 9.9 168.9 330.3 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 171.3 330.3 Tm 0 Tc 0.136 Tw [( )385( refractive index)]TJ 9.9 0 0 9.9 237.2 330.3 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 239.6 330.3 Tm 0 Tc 0.136 Tw [( )385( and stress\))]TJ 9.9 0 0 9.9 286 330.3 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 288.4 330.3 Tm 0 Tc 0.136 Tw [( )385( and \(2\) the three angles describing the orientation)]TJ -16.933 -1.111 TD 0.083 Tw [( )332(of the crystal axes \()]TJ /F13 1 Tf 9 0 1.913 9 214.4 320.3 Tm -0.248 Tc 0 Tw ( a)Tj /F12 1 Tf 9 0 0 9 220.7 320.3 Tm ( ,)Tj /F13 1 Tf 9 0 1.913 9 224.9 320.3 Tm ( b)Tj /F12 1 Tf 9 0 0 9 231.3 320.3 Tm ( ,)Tj /F13 1 Tf 9 0 1.913 9 235.5 320.3 Tm ( g)Tj /F15 1 Tf 9 0 0 9 241.5 320.3 Tm ( \))Tj /F12 1 Tf 0.411 0 TD ( .)Tj /F15 1 Tf -10.8 -1.111 TD 0 Tc 0.047 Tw [( )296(Properties of materials depend on several fundamental constants that are listed in Table)]TJ -1.333 -1.111 TD -0.248 Tc 0 Tw ( 3)Tj 9.9 0 0 9.9 140.5 300.3 Tm ( .)Tj 6 0 0 6 142.9 304.2 Tm ( )Tj 6 0 0 5 142.9 304.2 Tm (1)Tj 6 0 0 6 145.9 304.2 Tm ( )Tj 6 0 0 5 145.9 304.2 Tm (5)Tj 9 0 0 9 148.9 300.3 Tm 0 Tc 0.083 Tw [( )332( These constants are de\336ned as follows)]TJ 9.9 0 0 9.9 304.4 300.3 Tm -0.248 Tc 0 Tw ( .)Tj /F10 1 Tf 9 0 0 9 76 271.3 Tm ( )Tj 0 0 TD 0 Tc 0.055 Tw [(Optical Properties)-9( )]TJ 8.622 0 TD 0.011 Tc (: )Tj 0.289 0 TD 0 Tc [( Introduction)]TJ /F23 1 Tf -2.244 -3.256 TD ( )Tj 0 0 TD (Refracti)Tj /F21 1 Tf 8.5 0 1.807 8.5 168.1 242 Tm ( )Tj 8.5 0 1.807 9.376 168.1 242 Tm (y)Tj /F23 1 Tf 9 0 0 9 173.9 242 Tm ( )Tj T* 0.078 Tw (e Index)Tj /F7 1 Tf 3.367 0 TD -0.248 Tc 0 Tw ( .)Tj /F15 1 Tf 1.3 0 TD 0 Tc 0.105 Tw [( )354(Important optical properties)]TJ 9.9 0 0 9.9 328.7 242 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 331.1 242 Tm 0 Tc -0.248 Tw [( )-353(de\336nitions)]TJ 9.9 0 0 9.9 375.3 242 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 377.7 242 Tm 0 Tc -0.248 Tw [( )-353(formulas)]TJ 9.9 0 0 9.9 415.3 242 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 417.7 242 Tm 0 Tc 0.105 Tw [( )354( and basic concepts)]TJ -31.3 -1.111 TD 0.463 Tw [( )712(are derived from a classical description of propagation based on the macroscopic)]TJ T* -0.248 Tw [( Maxwell\325s )-345(equations)]TJ 9.9 0 0 9.9 216.6 222 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 219 222 Tm 0 Tc 0.097 Tw [( )346( The standard wave equation for the electric \336eld )]TJ /F7 1 Tf 22.4 0 TD -0.248 Tw [( E )]TJ /F15 1 Tf 1.067 0 TD 0.097 Tw [( )346(is obtained from)]TJ -32.689 -1.111 TD -0.248 Tw [( the )-331(Faraday)]TJ 9.9 0 0 9.9 183.4 212 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 185.8 212 Tm 0 Tc -0.248 Tw [( )-331(Gauss)]TJ 9.9 0 0 9.9 212.7 212 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 215.1 212 Tm 0 Tc 0.083 Tw [( )332( and Ampere Laws in Maxwell\325s form )332(:)-6( )332(*)]TJ /F13 1 Tf 5.622 -2 TD -0.248 Tc 0 Tw ( =)Tj /F15 1 Tf 6 0 0 6 271.7 198 Tm ( )Tj 6 0 0 5 271.7 198 Tm (2)Tj /F7 1 Tf 9 0 0 9 274.7 194 Tm ( E)Tj /F13 1 Tf 0.878 0 TD ( 5)Tj /F15 1 Tf 0.989 0 TD ( \()Tj /F13 1 Tf 0.389 0 TD ( 2)Tj /F12 1 Tf 0.822 0 TD ( i)Tj /F13 1 Tf 9 0 1.913 9 304.9 194 Tm 0.044 Tc -0.292 Tw [( v m)-11( s)]TJ 9 0 0 9 325.6 194 Tm -0.248 Tc 0 Tw ( 2)Tj 9 0 1.913 9 334.5 194 Tm ( v)Tj /F15 1 Tf 6 0 0 6 341.4 198 Tm ( )Tj 6 0 0 5 341.4 198 Tm (2)Tj /F13 1 Tf 9 0 1.913 9 344.4 194 Tm 0.044 Tc -0.292 Tw [( m e)]TJ /F15 1 Tf 9 0 0 9 355.6 194 Tm -0.248 Tc 0 Tw ( \))Tj /F7 1 Tf 0.389 0 TD ( E)Tj /F15 1 Tf 13.933 0 TD 0 Tc -0.248 Tw [( \(1\))]TJ ET 0.3 w 136.2 178.1 m 207.7 178.1 l S BT /F15 1 Tf 7 0 0 7 148 169 Tm 0.091 Tw [( )340(*)-229( )340(The de\336nition of the dielectric constant and refractive index in this section is based on a harmonic \336eld of the)]TJ -1.714 -1.143 TD -0.248 Tw [( form )-422(exp)-209( \()]TJ /F13 1 Tf 4.686 0 TD -0.248 Tc 0 Tw ( 2)Tj /F12 1 Tf 0.829 0 TD ( i)Tj /F13 1 Tf 7 0 1.488 7 176.5 161 Tm ( v)Tj /F12 1 Tf 7 0 0 7 181.4 161 Tm ( t)Tj /F15 1 Tf 0.329 0 TD ( \))Tj /F12 1 Tf 0.414 0 TD 0 Tc -0.248 Tw [( . )]TJ /F15 1 Tf 0.671 0 TD 0.174 Tw [( )423(Other de\336nitions lead to dif)39( )423(ferent sign conventions \(e)]TJ 7.7 0 0 7.7 362.3 161 Tm -0.248 Tc 0 Tw ( .)Tj 7 0 0 7 364.2 161 Tm ( g)Tj 7.7 0 0 7.7 367.7 161 Tm 0 Tc -0.248 Tw [( .,)]TJ 7 0 0 7 371.5 161 Tm -0.248 Tc 0 Tw ( )Tj /F12 1 Tf 0.414 0 TD ( n)Tj /F24 1 Tf 8.5 0 1.807 8.5 374.4 161 Tm ( )Tj 8.5 0 1.807 7 374.4 161 Tm (#)Tj /F13 1 Tf 7 0 0 7 379.7 161 Tm ( 5)Tj /F12 1 Tf 0.986 0 TD ( n)Tj /F13 1 Tf 0.771 0 TD ( 2)Tj /F12 1 Tf 1 0 TD 0 Tc -0.248 Tw [( ik)]TJ /F15 1 Tf 0.871 0 TD 0.174 Tw [( 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-1.188 TD -0.248 Tc 0 Tw ( 0)Tj T* ( 0)Tj T* 0 Tc -0.248 Tw [( 1)-200( \(1\))]TJ T* -0.248 Tc 0 Tw ( 0)Tj 5 4.75 TD 0 Tc -0.248 Tw [( 3)-200( \(2\))]TJ 0 -1.188 TD [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ 4.5 4.75 TD [( 13)-200( \(6\))]TJ 0.5 -1.188 TD -0.248 Tc 0 Tw ( 0)Tj T* 0 Tc -0.248 Tw [( 5)-200( \(2\))]TJ T* [( 8)-200( \(4\))]TJ T* -0.248 Tc 0 Tw ( 0)Tj 6.25 4.75 TD 0 Tc -0.248 Tw [( 24)-200( \(7\))]TJ 0 -1.188 TD [( 24)-200( \(7\))]TJ T* [( 18)-200( \(6\))]TJ T* [( 18)-200( \(6\))]TJ T* [( 18)-200( \(6\))]TJ -65.75 -1.188 TD [( \(6-fold )-323(axis\))-11674( P)-5602( 6)]TJ 0 10 -10 0 336 349.1 Tm -0.248 Tc 0 Tw ( /)Tj 0 8 -8 0 335 352.2 Tm ( m)Tj -0.937 -3.563 TD ( 6)Tj 0 10 -10 0 364.5 349.1 Tm ( /)Tj 0 8 -8 0 363.5 352.2 Tm 0 Tc -0.248 Tw [( mmm)]TJ 6.563 3.562 TD -0.248 Tc 0 Tw ( C)Tj 0 6 -6 0 336.7 410.4 Tm ( )Tj 0 6 -5 0 336.7 410.4 Tm (6)Tj 0 8 -8 0 344.5 404.7 Tm ( C)Tj 0 6 -6 0 346.2 410.4 Tm ( )Tj 0 6 -5 0 346.2 410.4 Tm (3)Tj 0 6 -6 0 346.2 413.4 Tm ( )Tj 0 6 -5 0 346.2 413.4 Tm (h)Tj 0 8 -8 0 354 404.7 Tm ( C)Tj 0 6 -6 0 355.7 410.4 Tm ( )Tj 0 6 -5 0 355.7 410.4 Tm (6)Tj 0 6 -6 0 355.7 413.4 Tm ( )Tj 0 6 -5 0 355.7 413.4 Tm (h)Tj 0 8 -8 0 363.5 404.7 Tm ( D)Tj 0 6 -6 0 365.2 411.3 Tm ( )Tj 0 6 -5 0 365.2 411.3 Tm (6)Tj 0 8 -8 0 373 404.7 Tm ( C)Tj 0 6 -6 0 374.7 410.4 Tm ( )Tj 0 6 -5 0 374.7 410.4 Tm (6)Tj 0 6 -6 0 374.7 413.4 Tm ( )Tj 0 6 -5 0 374.7 413.4 Tm (v)Tj 0 8 -8 0 382.5 404.7 Tm ( D)Tj 0 6 -6 0 384.2 411.3 Tm ( )Tj 0 6 -5 0 384.2 411.3 Tm (3)Tj 0 6 -6 0 384.2 414.3 Tm ( )Tj 0 6 -5 0 384.2 414.3 Tm (h)Tj 0 8 -8 0 392 404.7 Tm ( D)Tj 0 6 -6 0 393.7 411.3 Tm ( )Tj 0 6 -5 0 393.7 411.3 Tm (6)Tj 0 6 -6 0 393.7 414.3 Tm ( )Tj 0 6 -5 0 393.7 414.3 Tm (h)Tj 0 8 -8 0 335 443 Tm ( 6)Tj 0 -1.188 TD ( 6)Tj /F24 1 Tf 0 9.5 -9.5 0 342.5 443.4 Tm ( )Tj 0 9.5 -8 0 342.5 443.4 Tm (#)Tj /F15 1 Tf 0 8 -8 0 354 443 Tm ( 6)Tj 0 10 -10 0 355 447.3 Tm ( /)Tj 0 8 -8 0 354 450.4 Tm ( m)Tj -0.925 -1.188 TD 0 Tc -0.248 Tw [( 622)]TJ T* [( 6mm)]TJ T* -0.248 Tc 0 Tw ( 6)Tj /F24 1 Tf 0 9.5 -9.5 0 380.5 443.4 Tm ( )Tj 0 9.5 -8 0 380.5 443.4 Tm (#)Tj /F15 1 Tf 0 8 -8 0 382.5 446.9 Tm 0 Tc -0.248 Tw [( 2m)]TJ -0.487 -1.188 TD -0.248 Tc 0 Tw ( 6)Tj 0 10 -10 0 393 447.3 Tm ( /)Tj 0 8 -8 0 392 450.4 Tm 0 Tc -0.248 Tw [( mmm)]TJ 6.013 7.125 TD [( 168)-50( \320)-38( 173)]TJ 1.062 -1.188 TD [( 174)]TJ -1.062 -1.188 TD [( 175)-50( \320)-38( 176)]TJ T* [( 177)-50( \320)-38( 182)]TJ T* [( 183)-50( \320)-38( 186)]TJ T* [( 187)-50( \320)-38( 190)]TJ T* [( 191)-50( \320)-38( 194)]TJ 7.062 7.125 TD [( 1)-200( \(1\))]TJ 0 -1.188 TD -0.248 Tc 0 Tw ( 0)Tj T* ( 0)Tj T* ( 0)Tj T* 0 Tc -0.248 Tw [( 1)-200( \(1\))]TJ T* -0.248 Tc 0 Tw ( 0)Tj T* ( 0)Tj 5 7.125 TD 0 Tc -0.248 Tw [( 3)-200( \(2\))]TJ 0 -1.188 TD [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ T* [( 3)-200( \(2\))]TJ 5 7.125 TD [( 7)-200( \(4\))]TJ 0 -1.188 TD [( 6)-200( \(2\))]TJ T* -0.248 Tc 0 Tw ( 0)Tj T* 0 Tc -0.248 Tw [( 2)-200( \(1\))]TJ T* [( 5)-200( \(3\))]TJ T* [( 3)-200( \(1\))]TJ T* -0.248 Tc 0 Tw ( 0)Tj 6.25 7.125 TD 0 Tc -0.248 Tw [( 12)-200( \(5\))]TJ 0 -1.188 TD [( 12)-200( \(5\))]TJ T* [( 12)-200( \(5\))]TJ T* [( 12)-200( \(5\))]TJ T* [( 12)-200( \(5\))]TJ T* [( 12)-200( \(5\))]TJ T* [( 12)-200( \(5\))]TJ -65.75 -1.188 TD [( Cubic)]TJ T* [( \(isometric\))]TJ T* [( \(4)-274( 3-fold)-269( axes\))]TJ 0 -3.562 TD [( Isotropic)]TJ 10.075 5.938 TD -0.248 Tc 0 Tw ( a)Tj /F13 1 Tf 0.663 0 TD ( 5)Tj /F15 1 Tf 0.987 0 TD ( b)Tj /F13 1 Tf 0.712 0 TD ( 5)Tj /F15 1 Tf 1 0 TD ( c)Tj /F13 1 Tf 0 8 -8 1.7 411 227.3 Tm ( a)Tj 0 8 -8 0 411 234.3 Tm ( 5)Tj 0 8 -8 1.7 411 242.2 Tm ( b)Tj 0 8 -8 0 411 249.2 Tm ( 5)Tj 0 8 -8 1.7 411 257.1 Tm ( g)Tj 0 8 -8 0 411 263.6 Tm ( 5)Tj /F15 1 Tf 1 0 TD 0 Tc -0.248 Tw [( 90)]TJ /F13 1 Tf 0.987 0 TD -0.248 Tc 0 Tw ( 8)Tj /F15 1 Tf -5.675 -4.75 TD 0 Tc -0.248 Tw [( Amorphous)]TJ 7.612 5.937 TD -0.248 Tc 0 Tw ( P)Tj 0 8.8 -8.8 0 401.5 299.8 Tm ( ,)Tj 0 8 -8 0 401.5 303.7 Tm ( I)Tj 0 8.8 -8.8 0 401.5 306.8 Tm ( ,)Tj 0 8 -8 0 401.5 310.8 Tm ( F)Tj -0.475 -5.938 TD ( \321)Tj 4.713 5.938 TD 0 Tc -0.248 Tw [( m3)]TJ 0 -2.375 TD [( m3m)]TJ 1.537 -3.562 TD -0.248 Tc 0 Tw ( \321)Tj 5.963 5.938 TD ( T)Tj 0 -1.188 TD ( T)Tj 0 6 -6 0 412.7 410 Tm ( )Tj 0 6 -5 0 412.7 410 Tm (h)Tj 0 8 -8 0 420.5 404.7 Tm ( O)Tj T* ( T)Tj 0 6 -6 0 431.7 410 Tm ( )Tj 0 6 -5 0 431.7 410 Tm (d)Tj 0 8 -8 0 439.5 404.7 Tm ( O)Tj 0 6 -6 0 441.2 411.3 Tm ( )Tj 0 6 -5 0 441.2 411.3 Tm (h)Tj 0 8 -8 0 449 404.7 Tm ( \321)Tj 4.787 5.937 TD 0 Tc -0.248 Tw [( 23)]TJ 0 -1.188 TD [( m3)]TJ T* [( 432)]TJ T* -0.248 Tc 0 Tw ( 4)Tj /F24 1 Tf 0 9.5 -9.5 0 428 443.4 Tm ( )Tj 0 9.5 -8 0 428 443.4 Tm (#)Tj /F15 1 Tf 0 8 -8 0 430 446.9 Tm 0 Tc -0.248 Tw [( 3m)]TJ -0.487 -1.188 TD [( m3m)]TJ 1.5 -1.188 TD -0.248 Tc 0 Tw ( \321)Tj 5.438 5.938 TD 0 Tc -0.248 Tw [( 195)-50( \320)-38( 199)]TJ 0 -1.188 TD [( 200)-50( \320)-38( 206)]TJ T* [( 207)-50( \320)-38( 224)]TJ T* [( 215)-50( \320)-38( 220)]TJ T* [( 221)-50( \320)-38( 230)]TJ 1.312 -1.188 TD -0.248 Tc 0 Tw ( \321)Tj 5.75 5.938 TD ( 0)Tj 0 -1.188 TD ( 0)Tj T* ( 0)Tj T* ( 0)Tj T* ( 0)Tj T* ( 0)Tj 5 5.938 TD 0 Tc -0.248 Tw [( 3)-200( \(1\))]TJ 0 -1.188 TD [( 3)-200( \(1\))]TJ T* [( 3)-200( \(1\))]TJ T* [( 3)-200( \(1\))]TJ T* [( 3)-200( \(1\))]TJ T* [( 3)-200( \(1\))]TJ 5 5.938 TD [( 3)-200( \(1\))]TJ 0 -1.188 TD -0.248 Tc 0 Tw ( 0)Tj T* ( 0)Tj T* 0 Tc -0.248 Tw [( 3)-200( \(1\))]TJ T* -0.248 Tc 0 Tw ( 0)Tj T* ( 0)Tj 6.25 5.938 TD 0 Tc -0.248 Tw [( 12)-200( \(3\))]TJ 0 -1.188 TD [( 12)-200( \(3\))]TJ T* [( 12)-200( \(3\))]TJ T* [( 12)-200( \(3\))]TJ T* [( 12)-200( \(3\))]TJ T* [( 12)-200( \(2\))]TJ ET 1 w 455 159 m 455 719 l S BT /F15 1 Tf 0 7 -7 0 467 171 Tm 0.099 Tw [( )348(*)-229( )348(Values are the number of nonzero coef)41( )348(\336cients in \(equilibrium\) property tensors and the values in parentheses are the numbers of independent coef)46( )348(\336cients in the tensor)]TJ 0 7.7 -7.7 0 467 699.7 Tm -0.248 Tc 0 Tw ( .)Tj 0 7 -7 0 467 701.6 Tm 0 Tc -0.248 Tw [( )-347(Note)]TJ -77.514 -1.143 TD 0.046 Tw [( )295(that the elasto-optic and piezo-optic tensors have lower symmetry than the rank-4 tensors de\336ned in this table and therefore have more independent coef)25( )295(\336cients than shown)]TJ 0 7.7 -7.7 0 475 688.9 Tm -0.248 Tc 0 Tw ( .)Tj 0 7 -7 0 475 690.8 Tm 0 Tc -0.248 Tw [( )-294(Second-)]TJ 0 7.7 -7.7 0 475 717.3 Tm -0.248 Tc 0 Tw ( ,)Tj 0 7 -7 0 483 159 Tm 0 Tc -0.248 Tw [( third-)]TJ 0 7.7 -7.7 0 483 176.1 Tm -0.248 Tc 0 Tw ( ,)Tj 0 7 -7 0 483 178 Tm 0 Tc 0.083 Tw [( )332( and fourth-rank tensors are given in the usual reduced index format \(see text\))]TJ 0 7.7 -7.7 0 483 423 Tm -0.248 Tc 0 Tw ( .)Tj ET endstream endobj 42 0 obj << /ProcSet [ /PDF /Text ] /ColorSpace << /DefaultRGB 1 0 R >> /Font << /F8 6 0 R /F10 7 0 R /F13 13 0 R /F15 14 0 R /F24 37 0 R /F26 43 0 R >> >> endobj 43 0 obj << /Type /Font /Subtype /Type1 /Name /F26 /FirstChar 0 /LastChar 255 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618.9 Tm (19)Tj 8 0 0 8 339.6 606 Tm -0.248 Tc 0 Tw ( 4)Tj /F18 1 Tf 8 0 1.7 8 343.5 606 Tm ( p)Tj /F13 1 Tf 8 0 0 8 350.4 606 Tm ( ?)Tj /F15 1 Tf 0.55 0 TD 0 Tc -0.248 Tw [( 10)]TJ /F13 1 Tf 6 0 0 6 362.7 609.4 Tm ( )Tj 6 0 0 5 362.7 609.4 Tm (2)Tj /F15 1 Tf 6 0 0 6 367.6 609.4 Tm ( )Tj 6 0 0 5 367.6 609.4 Tm (7)Tj /F13 1 Tf 8 0 0 8 371.9 606 Tm -0.248 Tc 0 Tw ( 5)Tj /F15 1 Tf -6.062 -1.188 TD 0 Tc -0.248 Tw [( 12)]TJ /F12 1 Tf 1.012 0 TD -0.248 Tc 0 Tw ( .)Tj /F15 1 Tf 0.238 0 TD 0 Tc -0.248 Tw [( 566)-213( 370)-213( 614)]TJ /F13 1 Tf 5.125 0 TD -0.248 Tc 0 Tw ( ?)Tj /F15 1 Tf 0.55 0 TD 0 Tc -0.248 Tw [( 10)]TJ /F13 1 Tf 6 0 0 6 386.7 599.9 Tm ( )Tj 6 0 0 5 386.7 599.9 Tm (2)Tj /F15 1 Tf 6 0 0 6 391.6 599.9 Tm ( )Tj 6 0 0 5 391.6 599.9 Tm (7)Tj 8 0 0 8 327.4 587 Tm -0.248 Tc 0 Tw ( 8)Tj /F12 1 Tf 0.512 0 TD ( .)Tj /F15 1 Tf 0.238 0 TD 0 Tc -0.248 Tw [( 854)-213( 187)-200( 187)]TJ /F13 1 Tf 5.125 0 TD -0.248 Tc 0 Tw ( ?)Tj /F15 1 Tf 0.55 0 TD 0 Tc -0.248 Tw [( 10)]TJ /F13 1 Tf 6 0 0 6 386.7 590.4 Tm ( )Tj 6 0 0 5 386.7 590.4 Tm (2)Tj /F15 1 Tf 6 0 0 6 391.6 590.4 Tm ( )Tj 6 0 0 5 391.6 590.4 Tm (12)Tj 8 0 0 8 335.4 577.5 Tm -0.248 Tc 0 Tw ( 6)Tj /F12 1 Tf 0.512 0 TD ( .)Tj /F15 1 Tf 0.238 0 TD 0 Tc -0.248 Tw [( 626)-213( 075)-200( 5)]TJ /F13 1 Tf 4.125 0 TD -0.248 Tc 0 Tw ( ?)Tj /F15 1 Tf 0.55 0 TD 0 Tc -0.248 Tw [( 10)]TJ /F13 1 Tf 6 0 0 6 386.7 580.9 Tm ( )Tj 6 0 0 5 386.7 580.9 Tm (2)Tj /F15 1 Tf 6 0 0 6 391.6 580.9 Tm ( )Tj 6 0 0 5 391.6 580.9 Tm (34)Tj 8 0 0 8 340.2 568 Tm [( 299)-212( 792)-200( 458)]TJ 10.1 9.5 TD [( kg)]TJ 0 -1.188 TD [( mole)]TJ /F13 1 Tf 6 0 0 6 438.3 637.9 Tm ( )Tj 6 0 0 5 438.3 637.9 Tm (2)Tj /F15 1 Tf 6 0 0 6 443.2 637.9 Tm ( )Tj 6 0 0 5 443.2 637.9 Tm (1)Tj 8 0 0 8 421 625 Tm -0.248 Tc 0 Tw ( J)Tj 10 0 0 10 424.9 624 Tm ( /)Tj 8 0 0 8 428 624.9 Tm ( K)Tj -0.875 -1.175 TD ( C)Tj 0 -1.188 TD ( N)Tj 10 0 0 10 427.6 605 Tm ( /)Tj 8 0 0 8 430.7 605.9 Tm ( A)Tj 6 0 0 6 437.4 609.4 Tm ( )Tj 6 0 0 5 437.4 609.4 Tm (2)Tj 8 0 0 8 442.7 606 Tm 0 Tc -0.248 Tw [( or)-267( H)]TJ 10 0 0 10 459.4 605 Tm -0.248 Tc 0 Tw ( /)Tj 8 0 0 8 462.6 605.9 Tm ( m)Tj -5.2 -2.363 TD ( F)Tj 10 0 0 10 426.2 586 Tm ( /)Tj 8 0 0 8 429.3 586.9 Tm ( m)Tj -1.037 -1.175 TD ( J)Tj /F13 1 Tf 0.65 0 TD ( ?)Tj /F15 1 Tf 0.55 0 TD ( s)Tj -1.2 -1.188 TD ( m)Tj 10 0 0 10 428 567 Tm ( /)Tj 8 0 0 8 431.1 567.9 Tm ( s)Tj ET 1 w 154 562 m 478 562 l S BT /F15 1 Tf 9 0 0 9 136 533 Tm 0 Tc -0.248 Tw [( where )]TJ /F13 1 Tf 9 0 1.913 9 164 533 Tm -0.248 Tc 0 Tw ( s)Tj /F12 1 Tf 9 0 0 9 170.3 533 Tm 0 Tc -0.248 Tw [( , )]TJ /F13 1 Tf 9 0 1.913 9 176.6 533 Tm -0.248 Tc 0 Tw ( e)Tj /F12 1 Tf 9 0 0 9 181.5 533 Tm 0 Tc -0.248 Tw [( , )]TJ /F15 1 Tf 0.7 0 TD [( and )]TJ /F13 1 Tf 9 0 1.913 9 206.3 533 Tm -0.248 Tc 0 Tw ( m)Tj /F12 1 Tf 9 0 0 9 212.8 533 Tm ( )Tj /F15 1 Tf 0.444 0 TD 0 Tc 0.202 Tw [( )451(are the frequency-dependent conductivity)]TJ 9.9 0 0 9.9 385.5 533 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 387.9 533 Tm 0 Tc -0.248 Tw [( )-450(permeability)]TJ 9.9 0 0 9.9 441.4 533 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 443.8 533 Tm 0 Tc 0.202 Tw [( )451( and permit-)]TJ -34.2 -1.111 TD -0.248 Tw [( tivity)]TJ 9.9 0 0 9.9 155.9 523 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 158.3 523 Tm 0 Tc -0.248 Tw [( )-611(respectively)]TJ 9.9 0 0 9.9 210.3 523 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 212.7 523 Tm 0 Tc 0.363 Tw [( )612( These quantities are scalars in an isotropic medium)]TJ 9.9 0 0 9.9 440.3 523 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 442.7 523 Tm 0 Tc 0.363 Tw [( )612( To simplify)]TJ -34.078 -1.111 TD -0.248 Tw [( notation)]TJ 9.9 0 0 9.9 169 513 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 171.4 513 Tm 0 Tc 0.083 Tw [( )332( a generalized permittivity is sometimes de\336ned as )332(:)]TJ /F13 1 Tf 9 0 1.913 9 261 489.4 Tm -0.248 Tc 0 Tw ( e)Tj /F12 1 Tf 6 0 0 6 265.3 487.9 Tm ( )Tj 6 0 0 5 265.3 487.9 Tm (c)Tj /F15 1 Tf 9 0 0 9 268.4 489.3 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 271.9 489.3 Tm ( v)Tj /F15 1 Tf 9 0 0 9 278.8 489.3 Tm ( \))Tj /F13 1 Tf 0.556 0 TD ( 5)Tj 9 0 1.913 9 292.7 489.3 Tm ( e)Tj /F12 1 Tf 6 0 0 6 297 487.9 Tm ( )Tj 6 0 0 5 297 487.9 Tm (r)Tj /F15 1 Tf 9 0 0 9 299.8 489.3 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 303.3 489.3 Tm ( v)Tj /F15 1 Tf 9 0 0 9 310.2 489.3 Tm ( \))Tj /F20 1 Tf 22 0 0 22 313.7 488.4 Tm ( F)Tj /F15 1 Tf 9 0 0 9 318.5 489.3 Tm ( 1)Tj /F13 1 Tf 0.667 0 TD ( 1)Tj /F12 1 Tf 0.989 0 TD ( i)Tj /F13 1 Tf 9 0 1.913 9 340.2 495.8 Tm ( s)Tj /F15 1 Tf 9 0 0 9 346.6 495.8 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 350.1 495.8 Tm ( v)Tj /F15 1 Tf 9 0 0 9 357 495.8 Tm ( \))Tj ET 0.3 w 337.7 492.4 m 362.7 492.4 l S BT /F13 1 Tf 9 0 1.913 9 337.4 482.9 Tm ( v)Tj /F19 1 Tf 0.7 0 TD ( \310)Tj /F15 1 Tf 9 0 0 9 348.5 482.9 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 352 482.9 Tm ( v)Tj /F15 1 Tf 9 0 0 9 358.9 482.9 Tm ( \))Tj /F20 1 Tf 22 0 0 22 362.9 488.4 Tm ( G)Tj /F15 1 Tf 9 0 0 9 484.5 489.4 Tm 0 Tc -0.248 Tw [( \(2\))]TJ -38.722 -2.622 TD [( where )]TJ /F13 1 Tf 9 0 1.913 9 165.3 465.8 Tm -0.248 Tc 0 Tw ( e)Tj /F12 1 Tf 6 0 0 6 169.6 464.3 Tm ( )Tj 6 0 0 5 169.6 464.3 Tm (c)Tj /F15 1 Tf 9 0 0 9 172.7 465.8 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 176.2 465.8 Tm ( v)Tj /F15 1 Tf 9 0 0 9 183.1 465.8 Tm 0 Tc 0.342 Tw [( )591(\) is a generalized relative permittivity of dielectric constant \(i)]TJ 9.9 0 0 9.9 448.4 465.8 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 450.8 465.8 Tm ( e)Tj 9.9 0 0 9.9 455.3 465.8 Tm 0 Tc -0.248 Tw [( .,)]TJ 9 0 0 9 460.2 465.8 Tm [( )-590(with )]TJ /F19 1 Tf 9 0 1.913 9 487.8 465.8 Tm -0.248 Tc 0 Tw ( \310)Tj /F15 1 Tf 6 0 0 6 492.4 464.3 Tm ( )Tj 6 0 0 5 492.4 464.3 Tm (0)Tj 9 0 0 9 136 455.8 Tm 0 Tc -0.248 Tw [( removed )-335(from )]TJ /F13 1 Tf 9 0 1.913 9 195.5 455.8 Tm -0.248 Tc 0 Tw ( e)Tj 9 0 0 9 201.8 455.8 Tm ( 5)Tj 9 0 1.913 9 210.7 455.8 Tm ( e)Tj /F15 1 Tf 6 0 0 6 215.3 454.3 Tm ( )Tj 6 0 0 5 215.3 454.3 Tm (0)Tj /F13 1 Tf 9 0 1.913 9 218.8 455.8 Tm ( e)Tj /F12 1 Tf 6 0 0 6 223.1 454.3 Tm ( )Tj 6 0 0 5 223.1 454.3 Tm (c)Tj /F15 1 Tf 9 0 0 9 226.2 455.8 Tm 0 Tc 0.087 Tw [( )336(\) that includes contributions from free charges [via the conductivity)]TJ /F13 1 Tf 9 0 1.913 9 136 445.8 Tm -0.248 Tc 0 Tw ( s)Tj /F15 1 Tf 9 0 0 9 142.3 445.8 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 145.8 445.8 Tm ( v)Tj /F15 1 Tf 9 0 0 9 152.7 445.8 Tm 0 Tc -0.248 Tw [( \)])]TJ /F12 1 Tf 0.711 0 TD -0.248 Tc 0 Tw ( )Tj /F15 1 Tf 0.422 0 TD 0 Tc 0.175 Tw [( )424(and bound charges [via the relative permittivity)]TJ 9.9 0 0 9.9 357.3 445.8 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 359.7 445.8 Tm ( )Tj /F13 1 Tf 9 0 1.913 9 363.5 445.8 Tm ( e)Tj /F12 1 Tf 6 0 0 6 367.8 444.3 Tm ( )Tj 6 0 0 5 367.8 444.3 Tm (r)Tj /F15 1 Tf 9 0 0 9 370.6 445.8 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 374.1 445.8 Tm ( v)Tj /F15 1 Tf 9 0 0 9 381 445.8 Tm 0 Tc -0.248 Tw [( \)])]TJ /F12 1 Tf 0.744 0 TD [( . )]TJ /F15 1 Tf 0.667 0 TD 0.175 Tw [( )424(Assuming a nonmagnetic)]TJ -28.633 -1.111 TD -0.248 Tw [( material )-376(\()]TJ /F13 1 Tf 9 0 1.913 9 175.3 435.8 Tm -0.248 Tc 0 Tw ( m)Tj /F12 1 Tf 6 0 0 6 181.7 434.3 Tm ( )Tj 6 0 0 5 181.7 434.3 Tm (r)Tj /F13 1 Tf 9 0 0 9 186 435.8 Tm ( 5)Tj /F15 1 Tf 0.989 0 TD 0 Tc -0.248 Tw [( 1\))]TJ /F12 1 Tf 0.944 0 TD [( , )]TJ /F15 1 Tf 0.622 0 TD 0.128 Tw [( )377(and using the preceding generalized dielectric constant)]TJ 9.9 0 0 9.9 429.4 435.8 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 431.8 435.8 Tm 0 Tc 0.128 Tw [( )377( the plane-wave)]TJ -32.867 -1.111 TD 0.083 Tw [( )332(solution to the wave equation is)]TJ /F7 1 Tf 12.178 -1.889 TD -0.248 Tc 0 Tw ( E)Tj /F15 1 Tf 0.711 0 TD ( \()Tj /F12 1 Tf 0.389 0 TD 0.067 Tc -0.315 Tw [( z ,)]TJ /F13 1 Tf 9 0 1.913 9 264.8 408.8 Tm -0.248 Tc 0 Tw ( v)Tj /F15 1 Tf 9 0 0 9 271.7 408.8 Tm ( \))Tj /F13 1 Tf 0.556 0 TD ( 5)Tj /F7 1 Tf 0.989 0 TD ( E)Tj /F15 1 Tf 0.711 0 TD 0 Tc -0.248 Tw [( \(0\))-222( exp)-222( [)]TJ /F12 1 Tf 3.6 0 TD -0.248 Tc 0 Tw ( i)Tj /F15 1 Tf 0.333 0 TD ( \()Tj /F13 1 Tf 9 0 1.913 9 330.9 408.8 Tm ( v)Tj /F12 1 Tf 9 0 0 9 337.3 408.8 Tm ( z)Tj /F15 1 Tf 11 0 0 11 342.8 407.8 Tm ( /)Tj /F12 1 Tf 9 0 0 9 346.3 408.7 Tm ( c)Tj /F15 1 Tf 0.489 0 TD ( \))Tj /F27 1 Tf 0.389 0.089 TD ( 4)Tj ET 361.7 417 m 382.7 417 l S BT /F19 1 Tf 9 0 1.913 9 361.3 408.8 Tm ( \310)Tj /F12 1 Tf 6 0 0 6 365.6 407.3 Tm ( )Tj 6 0 0 5 365.6 407.3 Tm (c)Tj /F15 1 Tf 9 0 0 9 368.7 408.7 Tm ( \()Tj /F13 1 Tf 9 0 1.913 9 372.2 408.7 Tm ( v)Tj /F15 1 Tf 9 0 0 9 379.1 408.7 Tm 0 Tc -0.248 Tw [( \)])]TJ 11.711 0.011 TD [( \(3\))]TJ -37.389 -1.9 TD [( In )-393(optics)]TJ 9.9 0 0 9.9 183 391.7 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 185.4 391.7 Tm 0 Tc 0.145 Tw [( )394( it is frequently convenient to de\336ne a )]TJ /F12 1 Tf 17.767 0 TD -0.248 Tw [( complex )-393(refracti)]TJ /F13 1 Tf 8.5 0 1.807 8.5 408.6 391.7 Tm ( )Tj 8.5 0 1.807 9.376 408.6 391.7 Tm (y)Tj /F12 1 Tf 9 0 0 9 413.2 391.7 Tm 0.145 Tw [( )394(e index n)]TJ /F24 1 Tf 10.5 0 2.232 10.5 445.5 391.7 Tm ( )Tj 10.5 0 2.232 9 445.5 391.7 Tm (#)Tj /F12 1 Tf 9 0 0 9 450.1 391.7 Tm -0.248 Tc 0 Tw ( )Tj /F15 1 Tf 0.389 0 TD 0 Tc -0.248 Tw [( the )-393(square)]TJ -35.289 -1.111 TD 0.244 Tw [( )493(root of the complex dielectric constant \(henceforth)]TJ 9.9 0 0 9.9 347.6 381.7 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 350 381.7 Tm 0 Tc 0.244 Tw [( )493( the symbol )]TJ /F13 1 Tf 9 0 1.913 9 403.8 381.7 Tm -0.248 Tc 0 Tw ( e)Tj /F12 1 Tf 9 0 0 9 408.1 381.7 Tm ( )Tj /F15 1 Tf 0.489 0 TD 0 Tc 0.244 Tw [( )493(will be used for the)]TJ -30.722 -1.111 TD 0.083 Tw [( )332(relative complex dielectric constant\) )332(:)]TJ 38.722 -4.4 TD -0.248 Tw [( \(4\))]TJ /F12 1 Tf -24.678 2.5 TD -0.248 Tc 0 Tw ( n)Tj /F24 1 Tf 10.5 0 2.232 10.5 262.6 354.6 Tm ( )Tj 10.5 0 2.232 9 262.6 354.6 Tm (#)Tj /F13 1 Tf 9 0 0 9 269.2 354.6 Tm ( 5)Tj /F12 1 Tf 0.989 0 TD ( n)Tj /F13 1 Tf 0.778 0 TD ( 1)Tj /F12 1 Tf 0.989 0 TD 0 Tc -0.248 Tw [( ik)]TJ /F13 1 Tf 1.056 0 TD -0.248 Tc 0 Tw ( 5)Tj /F27 1 Tf 0.989 0.078 TD ( 4)Tj ET 319.9 362.9 m 324.4 362.9 l S BT /F13 1 Tf 9 0 1.913 9 319.9 354.6 Tm ( e)Tj 9 0 0 9 325.7 354.6 Tm ( 5)Tj /F27 1 Tf 0.989 0.078 TD ( 4)Tj ET 342.1 362.9 m 370.6 362.9 l S BT /F13 1 Tf 9 0 1.913 9 341.8 354.6 Tm ( e)Tj 9 0 0 9 346.5 354.6 Tm 0.156 Tc -0.404 Tw [( 9 1)]TJ /F12 1 Tf 1.478 0 TD -0.248 Tc 0 Tw ( i)Tj /F13 1 Tf 9 0 1.913 9 362.3 354.6 Tm ( e)Tj 9 0 0 9 367.1 354.6 Tm ( 0)Tj 9 0 1.913 9 259.5 340.1 Tm ( e)Tj 9 0 0 9 264.3 340.1 Tm 0.156 Tc -0.404 Tw [( 9 5)]TJ /F12 1 Tf 1.478 0 TD -0.248 Tc 0 Tw ( n)Tj /F15 1 Tf 6 0 0 6 283.1 344 Tm ( )Tj 6 0 0 5 283.1 344 Tm (2)Tj /F13 1 Tf 9 0 0 9 287.6 340.1 Tm ( 2)Tj /F12 1 Tf 0.989 0 TD ( k)Tj /F15 1 Tf 6 0 0 6 302 344 Tm ( )Tj 6 0 0 5 302 344 Tm (2)Tj 9 0 0 9 305.1 340.1 Tm ( ;)Tj /F13 1 Tf 9 0 1.913 9 325.4 340.1 Tm ( e)Tj 9 0 0 9 330.2 340.1 Tm 0.156 Tc -0.404 Tw [( 0 5)]TJ /F15 1 Tf 1.478 0 TD -0.248 Tc 0 Tw ( 2)Tj /F12 1 Tf 0.5 0 TD 0 Tc -0.248 Tw [( nk)]TJ -9.9 -1.622 TD -0.248 Tc 0 Tw ( n)Tj /F15 1 Tf 6 0 0 6 264.4 329.5 Tm ( )Tj 6 0 0 5 264.4 329.5 Tm (2)Tj /F13 1 Tf 9 0 0 9 268.9 325.5 Tm ( 5)Tj /F15 1 Tf 6 0 0 6 278.3 329.5 Tm ( )Tj 6 0 0 5 278.3 329.5 Tm (1)Tj 6 0 0 6 278.4 327.3 Tm ( )Tj 6 0 0 5 278.4 327.3 Tm (\320)Tj 6 0 0 6 278.5 324 Tm ( )Tj 6 0 0 5 278.5 324 Tm (2)Tj 9 0 0 9 282 325.5 Tm ( [)Tj /F13 1 Tf 9 0 1.913 9 284.9 325.5 Tm ( e)Tj 9 0 0 9 289.7 325.5 Tm 0.156 Tc -0.404 Tw [( 9 1)]TJ /F27 1 Tf 1.478 0.078 TD -0.248 Tc 0 Tw ( 4)Tj ET 310.5 333.8 m 342.5 333.8 l S BT /F13 1 Tf 9 0 1.913 9 310.1 325.5 Tm ( e)Tj 9 0 0 9 314.8 325.5 Tm ( 9)Tj /F15 1 Tf 6 0 0 6 317.7 329.5 Tm ( )Tj 6 0 0 5 317.7 329.5 Tm (2)Tj /F13 1 Tf 9 0 0 9 322.2 325.5 Tm ( 1)Tj 9 0 1.913 9 331.1 325.5 Tm ( e)Tj 9 0 0 9 335.9 325.5 Tm ( 0)Tj /F15 1 Tf 6 0 0 6 338.8 329.5 Tm ( )Tj 6 0 0 5 338.8 329.5 Tm (2)Tj 9 0 0 9 341.8 325.5 Tm ( ])Tj /F12 1 Tf -9.211 -1.611 TD ( k)Tj /F15 1 Tf 6 0 0 6 264.4 314.9 Tm ( )Tj 6 0 0 5 264.4 314.9 Tm (2)Tj /F13 1 Tf 9 0 0 9 268.9 311 Tm ( 5)Tj /F15 1 Tf 6 0 0 6 278.3 314.9 Tm ( )Tj 6 0 0 5 278.3 314.9 Tm (1)Tj 6 0 0 6 278.4 312.7 Tm ( )Tj 6 0 0 5 278.4 312.7 Tm (\320)Tj 6 0 0 6 278.5 309.5 Tm ( )Tj 6 0 0 5 278.5 309.5 Tm (2)Tj 9 0 0 9 282 310.9 Tm ( [)Tj /F13 1 Tf 0.322 0 TD ( 2)Tj 9 0 1.913 9 292.3 310.9 Tm ( e)Tj 9 0 0 9 297.1 310.9 Tm 0.156 Tc -0.404 Tw [( 9 1)]TJ /F27 1 Tf 1.478 0.089 TD -0.248 Tc 0 Tw ( 4)Tj ET 317.9 319.2 m 349.9 319.2 l S BT /F13 1 Tf 9 0 1.913 9 317.5 311 Tm ( e)Tj 9 0 0 9 322.2 311 Tm ( 9)Tj /F15 1 Tf 6 0 0 6 325.1 314.9 Tm ( )Tj 6 0 0 5 325.1 314.9 Tm (2)Tj /F13 1 Tf 9 0 0 9 329.6 311 Tm ( 1)Tj 9 0 1.913 9 338.5 311 Tm ( e)Tj 9 0 0 9 343.3 311 Tm ( 0)Tj /F15 1 Tf 6 0 0 6 346.2 314.9 Tm ( )Tj 6 0 0 5 346.2 314.9 Tm (2)Tj 9 0 0 9 349.2 311 Tm ( ])Tj -23.689 -1.922 TD 0 Tc -0.248 Tw [( where )]TJ /F12 1 Tf 2.978 0 TD [( n )]TJ /F15 1 Tf 0.867 0 TD 0.068 Tw [( )317(is the \(real\) )]TJ /F12 1 Tf 5.444 0 TD [( )317(index of refraction )]TJ /F15 1 Tf 8.333 0 TD -0.248 Tw [( and )]TJ /F12 1 Tf 1.922 0 TD [( k )]TJ /F15 1 Tf 0.867 0 TD [( is )-316(the )]TJ /F12 1 Tf 2.689 0 TD 0.068 Tw [( )317(index of absorption )]TJ /F15 1 Tf 8.778 0 TD [( )317(\(or imaginary part)]TJ -31.878 -1.111 TD 0.195 Tw [( )444(of the complex refractive index\))]TJ 9.9 0 0 9.9 268 283.7 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 270.4 283.7 Tm 0 Tc 0.195 Tw [( )444( \(The index of absorption is also called the absorption)]TJ -14.933 -1.111 TD -0.248 Tw [( constant)]TJ 9.9 0 0 9.9 168.9 273.7 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 171.3 273.7 Tm 0 Tc 0.317 Tw [( )566( index of extinction)]TJ 9.9 0 0 9.9 255 273.7 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 257.4 273.7 Tm 0 Tc 0.317 Tw [( )566( or some other combination of these terms)]TJ 9.9 0 0 9.9 442.5 273.7 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 444.9 273.7 Tm 0 Tc 0.317 Tw [( )566(\) Using this)]TJ -34.322 -1.111 TD 0.152 Tw [( )401(de\336nition of the complex index of refraction and the solution of the wave equation [Eq)]TJ 9.9 0 0 9.9 493.6 263.7 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 136 253.7 Tm 0 Tc -0.248 Tw [( \(3\)])]TJ 9.9 0 0 9.9 150.4 253.7 Tm -0.248 Tc 0 Tw ( ,)Tj 9 0 0 9 152.8 253.7 Tm 0 Tc 0.083 Tw [( )332( the optical power density \(proportional to )]TJ 6 0 0 6 326.8 257.6 Tm ( )Tj 6 0 0 5 326.8 257.6 Tm (1)Tj 6 0 0 6 326.9 255.4 Tm ( )Tj 6 0 0 5 326.9 255.4 Tm (\320)Tj 6 0 0 6 327 252.2 Tm ( )Tj 6 0 0 5 327 252.2 Tm (2)Tj /F20 1 Tf 9 0 0 9 332.5 253.6 Tm ( )Tj 9 0 0 7.5 332.5 253.6 Tm (u)Tj /F7 1 Tf 9 0 0 9 334.4 253.6 Tm -0.248 Tc 0 Tw ( E)Tj /F20 1 Tf 0.711 0 TD ( )Tj 9 0 0 7.5 340.8 253.6 Tm (u)Tj /F15 1 Tf 6 0 0 6 342.7 257.6 Tm ( )Tj 6 0 0 5 342.7 257.6 Tm (2)Tj 9 0 0 9 345.7 253.7 Tm 0 Tc 0.083 Tw [( )332( from Poynting\325s vector\) is)]TJ -17.689 -1.922 TD -0.248 Tw [( Power)-266( density)]TJ /F13 1 Tf 6.322 0 TD -0.248 Tc 0 Tw ( 5)Tj /F15 1 Tf 6 0 0 6 252.8 240.3 Tm ( )Tj 6 0 0 5 252.8 240.3 Tm (1)Tj 6 0 0 6 253 238.1 Tm ( )Tj 6 0 0 5 253 238.1 Tm (\320)Tj 6 0 0 6 253.1 234.9 Tm ( )Tj 6 0 0 5 253.1 234.9 Tm (2)Tj /F27 1 Tf 9 0 0 9 256.5 237.1 Tm ( 4)Tj ET 264 244.6 m 285.5 244.6 l S BT /F13 1 Tf 9 0 1.913 9 263.9 236.4 Tm ( m)Tj /F15 1 Tf 6 0 0 6 270.5 234.9 Tm ( )Tj 6 0 0 5 270.5 234.9 Tm (0)Tj 11 0 0 11 274 235.4 Tm ( /)Tj /F13 1 Tf 9 0 1.913 9 277.5 236.3 Tm ( e)Tj /F15 1 Tf 6 0 0 6 282.2 234.9 Tm ( )Tj 6 0 0 5 282.2 234.9 Tm (0)Tj /F20 1 Tf 9 0 0 9 287.2 236.3 Tm ( )Tj 9 0 0 7.5 287.2 236.3 Tm (u)Tj /F7 1 Tf 9 0 0 9 289.1 236.3 Tm ( E)Tj /F15 1 Tf 0.711 0 TD ( \()Tj /F12 1 Tf 0.389 0 TD ( z)Tj /F15 1 Tf 0.556 0 TD ( \))Tj /F20 1 Tf 0.389 0 TD ( )Tj 9 0 0 7.5 307.5 236.3 Tm (u)Tj /F15 1 Tf 6 0 0 6 309.4 240.3 Tm ( )Tj 6 0 0 5 309.4 240.3 Tm (2)Tj /F13 1 Tf 9 0 0 9 313.9 236.4 Tm ( 5)Tj /F15 1 Tf 6 0 0 6 323.3 240.3 Tm ( )Tj 6 0 0 5 323.3 240.3 Tm (1)Tj 6 0 0 6 323.5 238.1 Tm ( )Tj 6 0 0 5 323.5 238.1 Tm (\320)Tj 6 0 0 6 323.6 234.9 Tm ( )Tj 6 0 0 5 323.6 234.9 Tm (2)Tj /F27 1 Tf 9 0 0 9 327 237.1 Tm ( 4)Tj ET 334.5 244.6 m 356 244.6 l S BT /F13 1 Tf 9 0 1.913 9 334.4 236.4 Tm ( m)Tj /F15 1 Tf 6 0 0 6 341 234.9 Tm ( )Tj 6 0 0 5 341 234.9 Tm (0)Tj 11 0 0 11 344.5 235.4 Tm ( /)Tj /F13 1 Tf 9 0 1.913 9 348 236.3 Tm ( e)Tj /F15 1 Tf 6 0 0 6 352.7 234.9 Tm ( )Tj 6 0 0 5 352.7 234.9 Tm (0)Tj /F20 1 Tf 9 0 0 9 357.7 236.3 Tm ( )Tj 9 0 0 7.5 357.7 236.3 Tm (u)Tj /F7 1 Tf 9 0 0 9 359.6 236.3 Tm ( E)Tj /F15 1 Tf 0.711 0 TD 0 Tc -0.248 Tw [( \(0\))]TJ /F20 1 Tf 1.278 0 TD ( )Tj 9 0 0 7.5 377.5 236.3 Tm (u)Tj /F15 1 Tf 6 0 0 6 379.4 240.3 Tm ( )Tj 6 0 0 5 379.4 240.3 Tm (2)Tj 9 0 0 9 384.4 236.4 Tm [( exp)-222( \()]TJ /F13 1 Tf 2.167 0 TD -0.248 Tc 0 Tw ( 2)Tj /F15 1 Tf 0.822 0 TD ( 2)Tj /F13 1 Tf 9 0 1.913 9 415.8 236.4 Tm ( v)Tj /F12 1 Tf 9 0 0 9 422.2 236.4 Tm 0 Tc -0.248 Tw [( kz)]TJ /F15 1 Tf 11 0 0 11 432.7 235.4 Tm -0.248 Tc 0 Tw ( /)Tj /F12 1 Tf 9 0 0 9 436.2 236.3 Tm ( c)Tj /F15 1 Tf 0.489 0 TD ( \))Tj 4.878 0.011 TD 0 Tc -0.248 Tw [( \(5\))]TJ -38.722 -1.922 TD 0.08 Tw [( )329(where the exponential function represents the attenuation of the wave)]TJ 9.9 0 0 9.9 416.2 219.1 Tm -0.248 Tc 0 Tw ( .)Tj 9 0 0 9 418.6 219.1 Tm 0 Tc 0.08 Tw [( )329( The meanings of )]TJ /F12 1 Tf 8.033 0 TD -0.248 Tc 0 Tw ( n)Tj /F15 1 Tf -39.433 -1.111 TD 0 Tc -0.248 Tw [( and )]TJ /F12 1 Tf 2.1 0 TD [( k )]TJ /F15 1 Tf 1.044 0 TD [( are )-491(clear)-7( :)-6( )]TJ /F12 1 Tf 4.744 0 TD [( n )]TJ /F15 1 Tf 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transmittance over a)]TJ -17.744 -1.1 TD -0.248 Tw [( distance )]TJ /F12 1 Tf 3.878 0 TD 0.056 Tc -0.304 Tw [( z ,)56( )]TJ /F15 1 Tf 1.133 0 TD -0.248 Tc 0 Tw ( i)Tj 9.9 0 0 9.9 183.6 179.1 Tm ( .)Tj 9 0 0 9 186 179.1 Tm ( e)Tj 9.9 0 0 9.9 190.5 179.1 Tm 0 Tc -0.248 Tw [( .,)]TJ /F18 1 Tf 9 0 1.913 9 249.4 159.5 Tm -0.248 Tc 0 Tw ( t)Tj /F13 1 Tf 9 0 0 9 255.7 159.5 Tm ( 5)Tj /F20 1 Tf 1.822 0.722 TD ( )Tj 9 0 0 7.5 272.1 166 Tm (u)Tj /F7 1 Tf 9 0 0 9 274 166 Tm ( E)Tj /F15 1 Tf 0.711 0 TD ( \()Tj /F12 1 Tf 0.389 0 TD ( z)Tj /F15 1 Tf 0.556 0 TD ( \))Tj /F20 1 Tf 0.389 0 TD ( )Tj 9 0 0 7.5 292.4 166 Tm (u)Tj /F15 1 Tf 6 0 0 6 294.3 170 Tm ( )Tj 6 0 0 5 294.3 170 Tm (2)Tj ET 264.5 162.6 m 304.5 162.6 l S BT /F20 1 Tf 9 0 0 9 264 153 Tm ( )Tj 9 0 0 7.5 264 153 Tm (u)Tj /F7 1 Tf 9 0 0 9 265.9 153 Tm ( E)Tj /F15 1 Tf 0.711 0 TD ( \()Tj /F12 1 Tf 0.389 0 TD ( z)Tj /F13 1 Tf 0.711 0 TD ( 5)Tj /F15 1 Tf 0.989 0 TD 0 Tc -0.248 Tw [( 0\))]TJ /F20 1 Tf 0.889 0 TD ( )Tj 9 0 0 7.5 299.1 153 Tm 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