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Refractive Index and Dispersion TIE-29 Technical Information 1 Advanced Optics Version February 2016 TIE-29 Refractive Index and Dispersion Introduction 1. Refractive Index . 1 The most important property of optical glass is the refractive index and its dispersion behavior. 2. Wavelenght Dependence of This technical information gives an overview of the Refractive Index: Dispersion . 2 following topics: 3. Temperature Dependence of Refractive Index . 6 • Dispersion – Principal Dispersion 4. Influence of the Fine Annealing Process on the – Secondary Spectrum Refractive Index and Abbe number . 7 – Sellmeier Dispersion Equation 5. Tolerances . 9 • Temperature Dependence of Refractive Index • Influence of the Fine Annealing Process on the 6. Refractive Index Measurement . 11 Refractive Index and Abbe number 7. Literature . 12 • Tolerances • Refractive Index Measurement 1. Refractive Index If light enters a non-absorbing homogeneous material Practically speaking the refractive index is a measure for the reflection and refraction occurs at the boundary surface. strength of deflection occurring at the boundary surface due The refractive index n is given by the ratio of the velocity to the refraction of the light beam. The equation describing of light in vacuum c to that of the medium v the amount of deflection is called Snell’s law: c n = (1) n1 · sin(a1) = n2 · sin(a2) (2) v The refractive index data given in the data sheets are The refractive index is a function of the wavelength. The measured relative to the refractive index measured in air. most common characteristic quantity for characterization of The refractive index of air is very close to 1. an optical glass is the refractive index n in the middle range of the visible spectrum. This principal refractive index is usually denoted as nd – the refractive index at the wavelength 587.56 nm or in many cases as ne at the wavelength 546.07 nm. ➜ Technical Information 2 Advanced Optics TIE-29 Refractive Index and Dispersion 2. Wavelength Dependence of Refractive Index: 1 Dispersion 3.5 10 3.0 The dispersion is a measure of the change of the refractive 100 ) n λ ( index with wavelength. Dispersion can be explained by apply- ) 2.5 λ k ( k ing the electromagnetic theory to the molecular structure of n 10–1 matter. If an electromagnetic wave impinges on an atom or 2.0 a molecule the bound charges vibrate at the frequency of the 1.5 10–2 incident wave. Refractive Index 1.0 Absorption Constant 10–3 The bound charges have resonance frequency at a certain 0.5 wavelength. A plot of the refractive index as a function of the 0 10–4 wavelength for fused silica can be seen in figure 1. It can be 10–1 100 101 seen that in the main spectral transmission region the refractive Wavelength λ/µm index increases towards shorter wavelength. Additionally the Fig. 1: Measured optical constants of fused silica (SiO glass) [1]. dotted line shows the absorption constant as a function of the 2 wavelength. 2.1 Principal Dispersion The difference (nF – nC) is called the principal dispersion. Traditionally optical glasses in the range of nd > 50 are called nF and nC are the refractive indices at the 486.13 nm and crown glasses, the other ones as flint glasses. 656.27 nm wavelength. The most common characterization of the dispersion of optical Glasses having a low refractive index in general also have a glasses is the Abbe number. The Abbe number is defined as low dispersion behavior e. g. a high Abbe number. Glasses having a high refractive index have a high dispersion behavior nd = (nd – 1)/(nF – nC) (3) and a low Abbe number. Sometimes the Abbe number is defined according to the e line as ne = (ne – 1)/(nF' – nC') (4) ➜ ➜ Back to index Technical Information 3 Advanced Optics TIE-29 Refractive Index and Dispersion 2.2 Secondary Spectrum The characterization of optical glass through refractive index The deviations ΔPx,y from the ”normal lines” are listed for the and Abbe number alone is insufficient for high quality optical following five relative partial dispersions for each glass type in systems. A more accurate description of the glass properties is the data sheets. achievable with the aid of the relative partial dispersions. PC,t = (nC – nt)/(nF – nC) The relative partial dispersion Px,y for the wavelengths x and y PC,s = (nC – ns)/(nF – nC) is defined by the equation: PF,e = (nF – ne)/(nF – nC) (8) Pg,F = (ng – nF)/(nF – nC) Px,y = (nx – ny)/(nF – nC) (5) Pi,g = (ni – ng)/(nF – nC) As Abbe demonstrated, the following linear relationship will The position of the normal lines is determined based on value approximately apply to the majority of glasses, the so-called pairs of the glass types K7 and F2. The explicit formulas for the ”normal glasses” deviations ΔPx,y of the above-mentioned five relative partial dis- persions are: Px,y ≈ axy + bxy · nd (6) ΔPC,t = (nC – nt)/(nF – nC) – (0.5450 + 0.004743 · nd) axy and bxy are specific constants for the given relative partial ΔPC,s = (nC – ns)/(nF – nC) – (0.4029 + 0.002331 · nd) dispersion. Δ PF,e = (nF – ne)/(nF – nC) – (0.4884 – 0.000526 · nd) (9) In order to correct the secondary spectrum (i. e. color correc- Δ Pg,F = (ng – nF)/(nF – nC) – (0.6438 – 0.001682 · nd) tion for more than two wavelengths) glasses are required Δ Pi,g = (ni – ng)/(nF – nC) – (1.7241 – 0.008382 · nd) which do not conform to this rule. Therefore glass types having deviating partial dispersion from Abbe’s empirical rule are Figure 2 shows the Pg,F versus the Abbe number nd especially interesting. diagram. As a measure of the deviation of the partial dispersion from The relative partial dispersions listed in the catalog were Abbe’s rule the ordinate difference ΔP is introduced. Instead cal culated from refractive indices to 6 decimal places. The of relation (6) the following generally valid equation is used: dispersion formula (10) can be used to interpolate additional unlisted refractive indices and relative partial dispersions Px,y = axy + bxy · nd + ΔPx,y (7) (see chapter 2.3). The term ΔPx,y therefore quantitatively describes a dispersion behavior that deviates from that of the ”normal glasses”. ➜ ➜ Back to index Technical Information 4 Advanced Optics TIE-29 Refractive Index and Dispersion νd 100 90 80 70 60 50 40 30 20 10 0.65 N-SF66 0.65 P-SF68 0.64 P -Diagram 0.64 F F C g,F C n n n n – – – Description of Symbols – g g F F n n n n 0.63 N-glasses 0.63 = = N-SF57 g,F g,F P-glasses g,F P SF11 P SF57* Classical crown and int glasses N-SF11N-SF6 0.62 0.62 Glasses suitable for precision molding N-SF14 P-SF69 N-SF4 N-SF10 HT – High transmittance glasses P-SF8 SF10 N-SF15N-SF1 0.61 HTultra – Ultra high transmittance glasses 0.61 N-LASF46AN-SF5*N-SF8 * Available in step 0.5 N-LASF9 N-SF2 SF5 SF6 0.60 N-BASF2N-LAF7SF2* SF56A 0.60 N-LASF45 N-F2 SF4 LASF35 N-BASF64 SF1 0.59 0.59 N-LASF46B LF5 N-BAF52 N-BAF4 0.58 N-BAF51 0.58 N-KZFS8* LAFN7 N-BAF10 LLF1 F2 N-LASF40 F5 0.57 N-SSK8 0.57 N-SSK5 N-KZFS5* N-KF9 N-LASF43 N-BALF5N-SSK2 N-LAK22N-SK2* N-BALF4 N-LASF31A N-LAK12 N-LAF2 0.56 N-LASF41 P-LASF50 0.56 N-SK4 N-BAK4 N-KZFS11* P-LASF47 N-SK14 N-BAK1 N-PSK53A* N-KZFS4* P-LASF51 N-SK5 K7 P-LAF37 N-BAK2N-K5 N-LASF44* N-LAF33 N-PK51* N-LAF21 0.55 N-PK52A N-SK11 0.55 N-FK51A* N-LAF35 N-LAF34 N-FK58 N-PSK3N-ZK7 N-LAK10 N-BK7* N-LAK33B P-BK7 K10 0.54 N-LAK8 0.54 N-BK10 N-LAK34 N-KZFS2* N-FK5* N-LAK14 P-SK60 P-LAK35 N-LAK7 P-SK57 N-LAK21 N-LAK9* 0.53 P-SK58A 0.53 P-SK57Q1 N-SK16 0.52 0.52 0.51 0.51 February 2016 100 90 80 70 60 50 40 30 20 10 νd Fig. 2: Pg,F as a function of the Abbe number for SCHOTT’s optical glass assortment. Additionally the normal line is given. ➜ ➜ Back to index Technical Information 5 Advanced Optics TIE-29 Refractive Index and Dispersion 2.3 Sellmeier Dispersion Equation Wavelength [nm] Designation Spectral Line Used Element The Sellmeier Equation is especially suitable for the progres- 2325.42 infrared mercury line Hg sion of refractive index in the wavelength range from the UV through the visible to the IR area (to 2.3 µm). It is derived 1970.09 infrared mercury line Hg from the classical dispersion theory and allows the description 1529.582 infrared mercury line Hg of the progression of refractive index over the total transmis- 1060.0 neodymium glass laser Nd sion region with one set of data and to calculate accurate 1013.98 t infrared mercury line Hg intermediate values. 852.11 s infrared cesium line Cs 706.5188 r red helium line He B · λ2 B · λ2 B · λ2 n 2(λ) – 1 = 1 + 2 + 3 656.2725 C red hydrogen line H (λ2 – C ) (λ2 – C ) (λ2 – C ) (10) 1 2 3 643.8469 C' red cadmium line Cd 632.8 helium-neon-gas-laser He-Ne The determination of the coefficients was performed for all 589.2938 D center of double sodium line Na glass types on the basis of precision measurements by fitting 587.5618 d yellow helium line He the dispersion equation to the measurement values.
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