Skip to main content
SpringerLink
Log in

Refractive Index of Optical Materials

  • Chapter
Springer Handbook of Glass

Part of the book series: Springer Handbooks ((SHB))

Abstract

This chapter deals with the use of methods for measuring the refractive index of optical materials. It contains five sections:

The first section recalls some bases of the electromagnetic theory of light leading to the main characteristics of the index of refraction, and their consequences in geometrical optics (Snell–Descartes laws), in the spectral transmission and absorption of optical media, or the polarization of light beams at interfaces between optical media.

The second section describes the more or less classical panel of methods that have been devised to measure refractive indices of bulk materials: these are essentially based upon either the refraction or reflection of light inside prisms (minimum deviation angle, Littrow methods,…) polarizing properties of optical boundaries (ellipsometric, Brewster configurations).

While the previous section consists of refractive index characterization at a given temperature, the third section is dedicated to the dependence of the refractive index upon the temperature: the normalized thermo-optic coefficient (NTOC) is defined here and an experimental set-up specially designed for this purpose by one of the authors is described in detail.

The last section is concerned with the fact that most optical components are thin film coated in order to improve their performance in transmission, reflection or absorption. Since spectrophotometry is extensively used to characterize these coatings, the operating principle of spectrophotometers is recalled, as well as the main parameters of these deposited films that one can expect to extract by using this technology from spectrophotometric measurements. Various spectrophotometric procedures are described to determine the optical constants of optical ‘‘systems'' (bulk and thin film compounds) in the case of homogeneous or inhomogeneous films, slightly absorbing or not.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • SCHOTT AG: Interactive Abbe diagram, https://www.schott.com/advanced_optics/english/knowledge-center/technical-articles-and-tools/abbe-diagramm.html (2018)

  • N.G. Van Kampen, F. Lurçat: Causalité et relations de Kramers-Kronig, J. Phys. Radium 22, 179–191 (1961)

    Article  Google Scholar 

  • V. Lucarini, J.J. Saarinen, K.-E. Peiponen, M.E. Vartiainen: Kramers-Kronig Relations in Optical Materials (Springer, Berlin, Heidelberg 2005)

    Google Scholar 

  • J.F. Ogilvie, G.J. Fee: Equivalence of Kramers-Kronig and Fourier transforms to convert between optical dispersion and optical spectra, MATCH Commun. Math. Comput. Chem. 69, 249–262 (2013)

    CAS  Google Scholar 

  • M. Born, E. Wolf: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, Cambridge 1999)

    Book  Google Scholar 

  • A. Hadni: Essentials of Modern Physics Applied to the Study of the Infrared (Pergamon, Oxford 1967)

    Google Scholar 

  • H.A. Macleod: Thin-Film Optical Filters, 4th edn. (CRC, Boca Raton 2010)

    Book  Google Scholar 

  • F.S. Forman, A.V. Tikhonravov: Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-sur-Yvette 1992)

    Google Scholar 

  • National Metrology Institute of Germany: https://www.ptb.de/cms/en.html (2015)

  • D. Tentori, J.R. Lerma: Refractometry by minimum deviation accuracy analysis, Opt. Eng. 29(2), 160–168 (1990)

    Article  Google Scholar 

  • D.B. Leviton, B.J. Frey, T.K. Kvamme: High accuracy, absolute, cryogenic refractive index measurements of infrared lens materials for JWST NIRcam using CHARMS, Proc. SPIE 5904, 222–233 (2005)

    Google Scholar 

  • B.J. Frey, D.B. Leviton: Cryogenic High Accuracy Refraction Measuring System (CHARMS): A new facility for cryogenic infrared through farultraviolet refractive index measurements, Proc. SPIE 5494, 492–504 (2004)

    Article  CAS  Google Scholar 

  • C. Véret: Réfractométrie, Tech. Ing. R 6300, 1–12 (1995)

    Google Scholar 

  • J. Mangin: Indice de réfraction des matériaux optiques massifs. In: CNRS/ROP Workshop on metrology of refractive indices, Paris, 24-25/11/2008 (2009), http://www.rop.cnrs.fr/IMG/pdf/Indices_de_refraction.pdf

    Google Scholar 

  • R.M.A. Azzam, N.M. Bashara: Ellipsometry and Polarized Light (Elsevier, Amsterdam 1987)

    Book  Google Scholar 

  • G. Tompkins, W.A. McGahan: Spectroscopic Ellipsometry and Reflectometry: A User's Guide (Wiley, New York 1999)

    Google Scholar 

  • H.G. Tompkins, E.A. Irene (Eds.): Handbook of Ellipsometry (William Andrew, Norwich, New York 2005)

    Google Scholar 

  • A. Rothen: The ellipsometer, an apparatus to measure thicknesses of thin surface films, Rev. Sci. Instrum. 16, 26–30 (1945)

    Article  CAS  Google Scholar 

  • F. Abeles: Surface electromagnetic waves ellipsometry, Surf. Sci. 56, 237–251 (1976)

    Article  CAS  Google Scholar 

  • D.E. Aspnes, J.B. Theeten, F. Hottier: Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry, Phys. Rev. B 20(8), 3292 (1979)

    Article  CAS  Google Scholar 

  • E.D. Palik: Handbook of Optical Constants of Solids (Academic, New York 1985)

    Google Scholar 

  • J.A. Faucher, G.M. McManus, H.J. Trurnit: Simplified Treatment of Ellipsometry, J. Opt. Soc. Am. 48(1), 51–54 (1958)

    Article  CAS  Google Scholar 

  • S. Huard: Polarisation de la lumière (Ed Masson, Paris 1994)

    Google Scholar 

  • R.C. Jones: A new calculus for the treatment of optical systems Part I, J. Opt. Soc. Am. 31, 486–493 (1941)

    Google Scholar 

  • R.C. Jones: A new calculus for the treatment of optical systems Part III, J. Opt. Soc. Am. 31, 500–503 (1941)

    Article  Google Scholar 

  • R.C. Jones: A new calculus for the treatment of optical systems Part IV, J. Opt. Soc. Am. 32, 488–493 (1942)

    Article  Google Scholar 

  • D.E. Aspnes: Spectroscopic ellipsometry — Past, present, and future, Thin Solid Films 571, 334–344 (2014)

    Article  CAS  Google Scholar 

  • J.M. Frigerio: Détermination des indices par ellipsométrie: Principes théoriques et limitations. In: CNRS/ROP Workshop Metrol. Refract. Indices, Paris, 24–25.11.2008 (2009), http://www.rop.cnrs.fr/spip.php?article349

    Google Scholar 

  • F. Bernoux, J.P. Piel, B. Castellon, C. Defranoux, J.H. Lecat, P. Boher, J.L. Stehle: Ellipsométrie – Théorie, Tech. Ing. R 6490, 1–13 (2003)

    Google Scholar 

  • L. Prod'homme: A new approach to the thermal change in the refractive index with temperature, Phys. Chem. Glasses 1, 145–153 (1960)

    Google Scholar 

  • A.J. Bosman, E.E. Havinga: Temperature dependence of dielectric constants of cubic ionic compounds, Phys. Rev. 129, 1593–1600 (1963)

    Article  CAS  Google Scholar 

  • E.E. Havinga, A.J. Bosman: Temperature dependence of dielectric constant of crystals with NaCl and CsCl structure, Phys. Rev. 140, A292–A303 (1965)

    Article  Google Scholar 

  • J.M. Jewell: Model for the thermo-optic behavior of sodium borate and aluminosilicate, J. Non-Cryst. Solids 146, 145–153 (1992)

    Article  CAS  Google Scholar 

  • G. Gosh: Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses, Appl. Opt. 36, 1540–1546 (1997)

    Article  Google Scholar 

  • T. Zhang, M.-Q. Wu, S.-R. Zhang, J. Xiong, J.-M. Wang, D.-H. Zhang, F.-M. He, Z.-P. Li: Permittivity and its temperature dependence in hexagonal structure BN dominated by the local electric field, Chin. Phys. B 21, 077701-1–077701-8 (2012)

    Google Scholar 

  • G.N. Ramachandran: Thermo-optic of solids, Proc. Indian Acad. Sci. 25A, 498–515 (1947)

    Article  CAS  Google Scholar 

  • K.F. Trost: Die thermische Ausdehnung der Alkalihalogenide vom NaCl-Typ bei hohen und tiefen Temperaturen, Z. Naturforsch. 18b, 662–664 (1963)

    Article  CAS  Google Scholar 

  • H.H. Li: Refractive index of alkali halides and its temperature derivatives, J. Phys. Chem. Ref. Data 5, 329–528 (1976)

    Article  CAS  Google Scholar 

  • Korth Kristalle: http://www.korth.de

  • S. Kumar: Thermal expansion of simple ionic crystals, Proc. Natl. Inst. Sci. India A25, 364–372 (1959)

    Google Scholar 

  • J.E. Rapp, H.D. Merchant: Thermal expansion of alkali halides from 70 to 570 K, J. Appl. Phys. 44, 3919–3923 (1973)

    Article  CAS  Google Scholar 

  • Corning Incorporated: https://www.corning.com

  • M. Lallemand, J. Martinet: Influence de la température sur le coefficient thermo-optique des fluorures alcalino-terreux, Rev. Phys. Appl. 17, 111–117 (1982)

    Article  CAS  Google Scholar 

  • Amorphous Materials Inc.: http://www.amorphousmaterials.com

  • Fiberlabs Inc.: https://www.fiberlabs-inc.com/

  • SCHOTT AG: http://www.schott.com/advanced_optics

  • HOYA CORPORATION USA Optics Division: http://www.hoyaoptics.com

  • HIKARI GLASS Co., Ltd.: http://www.hikari-g.co.jp

  • OHARA Inc.: http://www.ohara-inc.co.jp

  • UMICORE Electro Optic Materials: http://www.opticalmaterials.umicore.com

  • VITRON: www.vitron.de/english/

  • D.B. Sirdeshmukh, L. Sirdeshmukh, K.G. Subhadra: Alkali Halides: A Handbok of Physical Properties (Springer, Berlin 2001)

    Book  Google Scholar 

  • D.B. Leviton, B.J. Frey: Temperature dependent absolute refractive index measurements of fused silica, Proc. SPIE 6273, 6273K (2006)

    Google Scholar 

  • B.D. Frey, D.B. Leviton: Automation, operation and data analysis in the cryogenic, high accuracy, refraction measuring system (CHARMS), Proc. SPIE 5904, 212–221 (2005)

    Google Scholar 

  • J.F. Nye: Physical Properties of Crystals (Clarendon, Oxford 1976)

    Google Scholar 

  • S. Fossier, S. Salaün, J. Mangin, O. Bidault, I. Thénot, J.-J. Zondy, W. Chen, F. Rotermund, V. Petrov, J. Heningsen, A. Yelisseiev, L. Isaenko, S. Lobanov, O. Balachninaite, G. Slekys, V. Sirutkaitis: Optical, vibrational, thermal, electrical, damage and phase-matching properties of lithium thioindate, J. Opt. Soc. Am. B 21, 1981–2007 (2004)

    Article  CAS  Google Scholar 

  • J. Mangin, G. Mennerat, G. Gadret, V. Badikov, J.-C. de Miscault: Comprehensive formulation of the temperature dependence dispersion of optical materials; illustration with case of temperature tuning of a mid-IR HgGa2S4 OPO, J. Opt. Soc. Am. B 26, 1702–1709 (2009)

    Article  CAS  Google Scholar 

  • J. Mangin, P. Strimer, L. Lahlou-Kassi: An interferometric dilatometer for the determination of thermo-optic coefficients of NLO materials, Meas. Sci. Technol. 4, 826–834 (1993)

    Article  CAS  Google Scholar 

  • G.E. Merritt: The interference method of measuring thermal expansion, J. Res. Natl. Bur. Stand. (US) 10, 59–76 (1932)

    Article  Google Scholar 

  • R.M. Walker, G.W. Cleek, I.H. Malitson, M.J. Dodge, T.A. Hahn: Optical and mechanical properties of some neodymium-doped glasses, J. Res. Natl. Bur. Stand. (US) 75A, 163–174 (1971)

    Article  Google Scholar 

  • R.M. Walker, G.W. Cleek: Refractive index of fused silica at low temperatures, J. Res. Natl. Bur. Stand. (US) 75A, 279–281 (1971)

    Article  Google Scholar 

  • R.M. Walker, G.W. Cleek: The effect of temperature and pressure on the refractive index of some oxide glasses, J. Res. Natl. Bur. Stand. (US) 77A, 755–763 (1973)

    Article  Google Scholar 

  • M. Okaji, H. Imai: A practical measurement system for accurate determination of linear thermal expansion coefficients, J. Phys. E Sci. Instrum. 17, 669–673 (1984)

    Article  CAS  Google Scholar 

  • P. Hariharan, D. Sen: Double-passed two-beam interferometers. II. Effect of specimen absorption and finite path difference, J. Opt. Soc. Am. 51, 1212–1218 (1961)

    Article  Google Scholar 

  • A.P. Müller, A. Cezairlaiyan: Interferometric technique for the subsecond measurement of thermal expansion at high temperatures: application to refractory metals, Int. J. Thermophys. 12, 643–656 (1991)

    Article  Google Scholar 

  • G. Gosh: Model for the thermo-optic coefficients of some standard optical glasses, J. Non-Cryst. Solids 189, 191–196 (1995)

    Article  Google Scholar 

  • W.J. Tropf, M.E. Thomas, T.J. Harris: Optical and physical properties of crystals and glasses. In: Handbook of Optics, Vol. II, ed. by M. Bass (McGraw-Hill, New York 1995)

    Google Scholar 

  • M.V. Hobden, J. Warner: The temperature dependence of the refractive indices of pure lithium niobate, Phys. Lett. 22, 243–244 (1966)

    Article  CAS  Google Scholar 

  • D.H. Jundt: Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate, Opt. Lett. 22, 1553–1555 (1997)

    Article  CAS  Google Scholar 

  • I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, G. Gadret: Linear and nonlinear optical properties of MgO:LiTaO3, Appl. Phys. B 96, 423–432 (2009)

    Article  CAS  Google Scholar 

  • J. Mangin, G. Mennerat, P. Villeval: Thermal expansion, normalized thermo-optic-coefficients, and condition for second harmonic generation of a Nd:YAG laser with wide temperature bandwidth in RbTiOPO4, J. Opt. Soc. Am. B 28, 873–881 (2011)

    Article  CAS  Google Scholar 

  • W. Tropf, M.E. Thomas: Infrared refractive index and thermo-optic coefficient measurement at APL, Johns Hopkins APL Tech. Dig. 19, 293–298 (1998)

    CAS  Google Scholar 

  • O.S. Heavens: Measurement of optical constants of thin films. In: Physics of Thin Films (Academic, New York 1964)

    Google Scholar 

  • M. Cathelinaud: Les méthodes spectrophotométriques pour la détermination d'indice de couches minces. In: CNRS/ROP Workshop Metrol. Refract. Indices, Paris, 24–25.11.2008 (2009), http://www.rop.cnrs.fr/spip.php?article349

    Google Scholar 

  • P. Bousquet, F. Flory, P. Roche: Scattering from multilayer thin films: theory and experiment, J. Opt. Soc. Am. 71(9), 1115–1123 (1981)

    Article  CAS  Google Scholar 

  • A. Piegari, F. Flory: Optical Thin Films and Coatings: From Materials to Applications (Woodhead, Oxford 2013)

    Google Scholar 

  • C. Amra: Light scattering from multilayer optics. I. Tools of investigation, J. Opt. Soc. Am. A 11, 197–210 (1994)

    Article  Google Scholar 

  • S. Adachi: Model dielectric constants of GaP, GaAs, Gasb, InP, InAs, and InSb, Phys. Rev. B 35(14), 7454–7463 (1987)

    Article  CAS  Google Scholar 

  • V. Kumar, S.K. Sharma, T.P. Sharma, V. Singh: Band gap determination in thick films from reflectance measurements, Opt. Mater. 12, 115–119 (1999)

    Article  CAS  Google Scholar 

  • P.S. Hauge: Polycrystalline silicon film thickness measurement from analysis of visible reflectance spectra, J. Opt. Soc. Am. 69(8), 1143–1152 (1979)

    Article  CAS  Google Scholar 

  • J.C. Manifacier, J. Gassiot, J.P. Fillard: A simple method for the determination of the optical constants, n, k and the thickness of a weakly absorbing thin film, J. Phys. E Sci. Instrum. 9, 1002–1004 (1976)

    Article  CAS  Google Scholar 

  • I. Ohlidal, K. Navrfitil, E. Schmidt: Simple method for the complete optical analysis of very thick and weakly absorbing films, Appl. Phys. A 29, 157–162 (1982)

    Article  Google Scholar 

  • R. Jacobsson: Inhomogeneous and coevaporated homogeneous films for optical applications, Phys. Thin Films 8, 51–98 (1975)

    CAS  Google Scholar 

  • J.P. Borgogno, B. Lazarides, E. Pelletier: Automatic determination of the optical constants of inhomogeneous thin films, Appl. Opt. 21, 4020–4029 (1982)

    Article  CAS  Google Scholar 

  • J.A. Dobrowolski, F.C. Ho, A. Waldorf: Determination of optical constants of thin film coating materials based on inverse synthesis, Appl. Opt. 22(20), 3191–3200 (1983)

    Article  CAS  Google Scholar 

  • F. Abeles: Methods for determining optical parameters of thin films. In: Progress in Optics, Vol. 2, ed. by E. Wolf (Elsevier, Amsterdam 1963)

    Google Scholar 

  • S.G. Tomlin: Optical reflection and transmission formulae for thin films, J. Phys. D 1, 1667–1671 (1968)

    Article  Google Scholar 

  • H. Wolter: Zur Optik dünner Metallfilme, Z. Phys. 105(5), 269–308 (1937)

    Article  CAS  Google Scholar 

  • M. Cathelinaud, F. Lemarquis, J. Loesel, B. Cousin: Metal-dielectric light absorbers manufactured by ion plating, Proc. SPIE 5250, 5250–5250–8 (2004)

    Google Scholar 

  • G. Hass, L. Hadley: Optical Constants of metals. In: American Institute of Physics Handbook, ed. by D.E. Gray (McGraw-Hill, New York 1972)

    Google Scholar 

  • M. Cathelinaud, F. Lemarquis, C. Amra: Index determination of opaque and semitransparent metallic films: Application to light absorbers, Appl. Opt. 41, 2546–2554 (2002)

    Article  CAS  Google Scholar 

  • W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery: Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge University Press, Cambridge 1992)

    Google Scholar 

  • R.E. Denton, R.D. Campbell, S.G. Tomlin: The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence, J. Phys. D 5(4), 852–863 (1972)

    Article  CAS  Google Scholar 

  • B. Badoil, M. Cathelinaud, F. Lemarchand, F. Lemarquis, M. Lequime: Development of a Real-Time Reflectance and Transmittance Monitoring System for the Manufacturing of Metal-Dielectric Light Absorber. In: Proc. ESA/CNES ICSO (2006), https://doi.org/10.1117/12.2308179

    Chapter  Google Scholar 

  • D.P. Arndt, R.M.A. Azzam, J.M. Bennett, J.P. Borgogno, C.K. Carniglia, W.E. Case, J.A. Dobrowolski, U.J. Gibson, T. Tuttle Hart, F.C. Ho, V.A. Hodgkin, W.P. Klapp, H.A. Macleod, E. Pelletier, M.K. Purvis, D.M. Quinn, D.H. Strome, R. Swenson, P.A. Temple, T.F. Thonn: Multiple determination of the optical constants of thin-film coating materials, Appl. Opt. 23(20), 3571–3596 (1984)

    Article  CAS  Google Scholar 

  • A. Duparré, D. Ristau: Optical interference coatings, Meas. Probl. Appl. Opt. 47(13), C179–C184 (2007)

    Article  Google Scholar 

  • A. Duparré, D. Ristau: Optical interference coatings measurement problem, Appl. Opt. 53(4), A281–A286 (2013)

    Article  Google Scholar 

  • F. Lemarchand, C. Deumié, M. Zerrad, L. Abel-Tiberini, B. Bertussi, G. Georges, B. Lazaridès, M. Cathelinaud, M. Lequime, C. Amra: Optical characterization of an unknown single layer: Institut Fresnel contribution to the Optical Interference Coatings 2004 Topical Meeting Measurement Problem, Appl. Opt. 45(7), 1312–1318 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut d’Optique Graduate School, Palaiseau, France

    Jean-Louis Meyzonnette

  2. Laboratoire Interdisciplinaire Carnot de Bourgogne, Dijon, France

    Jacques Mangin

  3. Institute of Chemical Sciences Rennes, UMR CNRS 6226, University of Rennes 1, Rennes, France

    Michel Cathelinaud

Authors
  1. Jean-Louis Meyzonnette
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacques Mangin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michel Cathelinaud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michel Cathelinaud .

Editor information

Editors and Affiliations

  1. Rochester Precision Optics, LLC, West Henrietta, NY, USA

    J. David Musgraves

  2. Dept. of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Juejun Hu

  3. UMR 6226 – Institut des Sciences Chimiques de Rennes, University of Rennes I, Rennes, France

    Laurent Calvez

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Cite this chapter

Meyzonnette, JL., Mangin, J., Cathelinaud, M. (2019). Refractive Index of Optical Materials. In: Musgraves, J.D., Hu, J., Calvez, L. (eds) Springer Handbook of Glass. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-93728-1_29

Download citation

Publish with us

Policies and ethics

Search

Navigation