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On Ludvig Lorenz and his 1890 treatise on light scattering by spheres

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Abstract

This paper offers background and perspective on a little-known memoir by Ludvig Lorenz on light scattering by spheres, which was published in Danish in 1890. It is a companion to an English translation of the memoir appearing separately. Apart from introducing Lorenz and some of his contributions to optics and electrodynamics, the paper focuses on the emergence, content and reception of the 1890 memoir and its role in what is often called the Lorenz-Mie theory. In addition to the historical analysis, the paper illuminates aspects of modern Lorenz-Mie theory and its many applications, with an eye to Lorenz’s original work.

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References

  1. Abildgaard, O. H. A., Frisvad, J. R., Falster, V., Parker, A., Christensen, N. J., Dahl, A. B., and Larsen, R. 2016. Noninvasive particle sizing using camera-based diffuse reflectance spectroscopy. Appl. Opt. 55(14): 3840–3846.

    Article  ADS  Google Scholar 

  2. Aden, A. L. and Kerker, M. 1951. Scattering of electromagnetic waves from two concentric spheres. J. Appl. Phys. 22(10): 1242–1246.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Arfken, G. B., Weber, H. J., and Harris, F. E. 2013. Mathemaical Methods for Physicists: A Comprehensive Guide, seventh edn. Academic Print/Elsevier, Massachusetts.

  4. Barton, J. P., Alexander, D. R., and Schaub, S. A. 1988. Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam. J. Appl. Phys. 64(4): 1632–1639.

    Article  ADS  Google Scholar 

  5. Bateman, H. 1915. The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwell’s Equations. Cambridge University Press, Cambridge.

  6. Bauer, G. 1826. Von den Coefficienten der Reihen von Kugelfunctionen einer Variablen. J. Reinen Angew. Math. 56(2): 101–121.

    MathSciNet  Google Scholar 

  7. Belokopytov, G. V. and Vasil’ev, E. N. 2006. Scattering of a plane inhomogeneous electromagnetic wave by a spherical particle. Radiophys. Quant. Electr. 49(1): 65–73. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 72–81, January 2006.

    Article  ADS  Google Scholar 

  8. Born, M. and Wolf, E. 1999. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, seventh (expanded) edn. Cambridge University Press.

  9. Box, G. P., Sealey, K. M., and Box, M. A. 1992. Inversion of Mie extinction measurements using analytic eigenfunction theory. J. Atmos. Sci. 49(22): 2074–2081.

    Article  ADS  Google Scholar 

  10. Callet, P. 1996. Pertinent data for modelling pigmented materials in realistic rendering. Comput. Graph. Forum 15(2): 119–127.

    Article  Google Scholar 

  11. Castanet, G., Delconte, A., Lemoine, F., Mees, L., and Gréhan, G. 2005. Evaluation of temperature gradients within combusting droplets in linear stream using two colors laser-induced fluorescence. Exp. Fluids 39(2): 431–440.

    Article  Google Scholar 

  12. Chandrasekhar, S. 1950. Radiative Transfer. Oxford University Press, Oxford. Unabridged and slightly revised version published by Dover, New York, 1960.

  13. Chew, H., McNulty, P. J., and Kerker, M. 1976. Model for raman and fluorescent scatteringby molecules embedded in small particles. Phys. Rev. A 13(1): 396–404.

    Article  ADS  Google Scholar 

  14. Christiansen, C. 1896. Lorenz, ludvig valentin. In Dansk biografisk Lexikon, edited by C. F. Bricka. Copenhagen, 376–381.

  15. Chýlek, P. 1977. Light scattering by small particles in an absorbing medium. J. Opt. Soc. Am. 67(4): 561–563.

    Article  ADS  Google Scholar 

  16. Clebsch, A. 1863. Ueber die Reflexion an einer Kugelfläche. J. Reinen Angew. Math. 61: 195–262.

    MathSciNet  Google Scholar 

  17. Dal Corso, A., Frisvad, J. R., Kjeldsen, T. K., and Bærentzen, J. A. 2016. Interactive appearance prediction for cloudy beverages. In Workshop on Material Appearance Modeling (MAM 2016). The Eurographics Association, 1–4.

  18. Darrigol, O. 2010. James MacCullagh’s ether: An optical route to Maxwell’s equations? Eur. Phys. J. H 35(2): 133–172.

    Article  Google Scholar 

  19. Darrigol, O. 2012. A History of Optics from Greek Antiquity to the Nineteenth Century. Oxford University Press, Oxford.

  20. Debye, P. 1909a. Der Lichtdruck auf Kugeln von beliebigem Material. Ann. Phys. 335(11): 57–136.

    Article  MATH  Google Scholar 

  21. Debye, P. 1909b. Näherungsformeln für die Zylinderfunktionen für große Werte des Arguments und unbeschränkt veränderliche Werte des Index. Math. Ann. 67(4): 535–558.

    Article  MathSciNet  MATH  Google Scholar 

  22. Dusel, P. W., Kerker, M., and Cooke, D. D. 1979. Distribution of absorption centers within irradiated spheres. J. Opt. Soc. Am. 69(1): 55–59.

    Article  ADS  Google Scholar 

  23. Frisvad, J. R. 2018. Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave. J. Opt. Soc. Am. A 35(4): 669–680.

    Article  ADS  Google Scholar 

  24. Frisvad, J. R., Christensen, N. J., and Falster, P. 2007a. The Aristotelian rainbow: From philosophy to computer graphics. In Proceedings of GRAPHITE 2007. ACM, 119–128+311.

  25. Frisvad, J. R., Christensen, N. J., and Jensen, H. W. 2007b. Computing the scatteringproperties of participating media using Lorenz-Mie theory. ACM Trans. Graph. 26(3): 60:1–60:10.

    Article  Google Scholar 

  26. Frisvad, J. R., Christensen, N. J., and Jensen, H. W. 2012. Predicting the appearance of materials using Lorenz-Mie theory. In The Mie Theory: Basics and Applications, edited by W. Hergert and T. Wriedt. Springer Series in Optical Sciences, Vol. 169. Chap. 4, pp. 101–133.

  27. Fry, T. C. 1927. Plane waves of light I. Electromagnetic behavior. J. Opt. Soc. Am. 15(3): 137–161.

    Article  ADS  Google Scholar 

  28. Galejs, J. 1962. Scattering from a conducting sphere embedded in a semi-infinite dissipative medium. J. Res. Natl. Bur. Stand. D. Radio Propag. 66D(5): 607–612.

    Article  MATH  Google Scholar 

  29. Gouesbet, G. 2012. From theories by Lorenz and Mie to ontological underdetermination of theories by experiments. In The Mie Theory: Basics and Applications, edited by W. Hergert and T. Wriedt. Springer Series in Optical Sciences, Vol. 169. Chap. 3, pp. 73–100.

  30. Gouesbet, G. 2019. Generalized Lorenz-Mie theories and mechanical effects of laser light, on the occasion of Arthur Ashkin’s receipt of the 2018 Nobel prize in physics for his pioneering work in optical levitation and manipulation: A review. J. Quant. Spectr. Radiat. Transf. 225: 258–277.

    Article  ADS  Google Scholar 

  31. Gouesbet, G. and Gréhan, G. 1982. Sur la généralisation de la théorie de Lorenz-Mie. J. Opt. 13(2): 97–103.

    Article  ADS  Google Scholar 

  32. Gouesbet, G. and Gréhan, G. 2017. Generalized Lorenz-Mie Theories, second edn. Springer, Berlin.

  33. Gouesbet, G., Maheu, B., and Gréhan, G. 1988. Light scattering from a sphere arbitrarily located in a Gaussian beam. J. Opt. Soc. Am. A 5(9): 1427–1443.

    Article  ADS  Google Scholar 

  34. Grenfell, T. C. and Warren, S. G. 1999. Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation. J. Geophys. Res. 104(D24): 31, 697–31, 709.

    Article  Google Scholar 

  35. Hansen, J. and Nazarenko, L. 2004. Soot climate forcing via snow and ice albedos. Proc. Natl. Acad. Sci. USA 101(2): 423–428.

    Article  ADS  Google Scholar 

  36. Helmholtz, H. v. 1867. Handbuch der Physiologischen Optik. Leopold Voss, Leipzig. Three volumes published 1856–1866 and published together in Algemeine Encyklopädie der Physik, Vol. 9, 1867.

  37. Hergert, W. 2012. Gustav Mie: From electromagnetic scattering to an electromagnetic view of matter. In The Mie Theory: Basics and Applications, edited by W. Hergert and T. Wriedt. Springer Series in Optical Sciences, Vol. 169. Chap. 1, pp. 1–51.

  38. Horvath, H. 2009. Gustav Mie and the scattering and absorption of light by particles: Historic developments and basics. J. Quant. Spectr. Radiat. Transf. 110(11): 787–799.

    Article  ADS  Google Scholar 

  39. Howell, J. R., Mengüç, M. P., and Siegel, R. 2016. Thermal Radiation Heat Transfer, sixth edn. CRC Press/Taylor & Francis, Boca Raton.

  40. Ishimaru, A. 1978. Wave Propagation in Random Media. Academic Press, New York. Reissued by IEEE Press and Oxford University Press, 1997.

  41. Ishimaru, A. 2017. Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications, second edn. John Wiley & Sons, Hoboken.

  42. Jackèl, D. and Walter, B. 1997. Modeling and rendering of the atmosphere using Mie-scattering. Comput. Graph. Forum 16(4): 201–210.

    Article  Google Scholar 

  43. Jackson, J. D. and Okun, L. B. 2001. Historical roots of gauge invariance. Rev. Mod. Phys. 73(3): 663–680.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. Kaiser, W. 1981. Theorien der Elektrodynamik im 19. Jahrhundert. Gerstenberg, Hildesheim.

  45. Keller, O. 2002. Optical works of L. V. Lorenz. In Progress in Optics, edited by E. Wolf. Vol. 43. Elsevier, Amsterdam, Chap. 3, pp. 195–294.

  46. Kerker, M. 1969. The Scattering of Light and Other Electromagnetic Radiation. Academic Press, New York.

  47. Kerker, M. 1982. Lorenz-Mie scattering by spheres: some newly recognized phenomena. Aeros. Sci. Technol. 1(3): 275–291.

    Article  ADS  Google Scholar 

  48. Kerker, M. and Cooke, D. D. 1973. Radiation pressure on absorbing spheres and photophoresis. Appl. Opt. 12(7): 1378–1379.

    Article  ADS  Google Scholar 

  49. Kerker, M. and Cooke, D. D. 1982. Photophoretic force on aerosol particles in the free-molecule regime. J. Opt. Soc. Am. 72(9): 1267–1272.

    Article  ADS  Google Scholar 

  50. Killian, J. L., Ye, F., and Wang, M. D. 2018. Optical tweezers: A force to be reckoned with. Cell 175(6): 1445–1448.

    Article  Google Scholar 

  51. Kim, I., Lee, K.-S., Lee, T.-S., Jung, D. S., Lee, W.-S., Kim, W. M., and Lee, K.-S. 2015. Size dependence of spherical metal nanoparticles on absorption enhancements of plasmonic organic solar cells. Syn. Metals 199: 174–178.

    Article  Google Scholar 

  52. Kirchhoff, G. 1857. Ueber die Bewegung der Elektricität in Drähten. Ann. Phys. Chem. 176(2): 193–217.

    Article  ADS  Google Scholar 

  53. Kragh, H. 2018a. The Lorenz-Lorentz formula: Origin and early history. Substantia 2(2): 7–18.

    MathSciNet  Google Scholar 

  54. Kragh, H. 2018b. Ludvig Lorenz: A Nineteenth-Century Theoretical Physicist. Royal Danish Academy of Sciences and Letters, Copenhagen.

  55. Kragh, H. 2018c. Ludvig Lorenz and his non-Maxwellian electrical theory of light. Phys. Perspect. 20(3): 221–253.

    Article  ADS  Google Scholar 

  56. Logan, N. A. 1962. Early history of the Mie solution. J. Opt. Soc. Am. 52(3): 342–343.

    Article  Google Scholar 

  57. Logan, N. A. 1965. Survey of some early studies of the scattering of plane waves by a sphere. Proc. IEEE 53(8): 773–785.

    Article  Google Scholar 

  58. Lorentz, H. A. 1880. Ueber dieBeziehung zwischen der Fortpflanzungsgeschwindigkeit des Lichtes und der Körperdichte. Ann. Phys. Chem. 245(4): 641–665.

    Article  ADS  MATH  Google Scholar 

  59. Lorenz, L. V. 1861. Bestimmung der Schwingungsrichtung des Lichtäthers durch die Reflexion und Brechung des Lichtes. Ann. Phys. Chem. 190(10): 238–250.

    Article  ADS  Google Scholar 

  60. Lorenz, L. V. 1863. Ueber die Theorie des Lichts. Ann. Phys. Chem. 194(1): 111–145.

    Article  ADS  Google Scholar 

  61. Lorenz, L. V. 1867. On the identity of the vibrations of light with electrical currents. Philos. Mag. 34(230): 287–301.

    Article  Google Scholar 

  62. Lorenz, L. V. 1869. Experimentale og theoretiske Undersøgelser over Legemers Brydningsforhold. Det kongelige danske Videnskabernes Selskabs Skrifter 5(8): 203–248.

    Google Scholar 

  63. Lorenz, L. V. 1877. Die Lehre vom Licht. Teubner, Leipzig.

  64. Lorenz, L. V. 1880. Ueber die Refractionsconstante. Ann. Phys. Chem. 247(9): 70–103.

    Article  ADS  MATH  Google Scholar 

  65. Lorenz, L. V. 1883. Theorie der Dispersion. Ann. Phys. Chem. 256(9): 1–21.

    Article  ADS  MATH  Google Scholar 

  66. Lorenz, L. V. 1890. Lysbevægelser i og uden for en af plane Lysbølger belyst Kugle. Det kongelige danske Videnskabernes Selskabs Skrifter 6(6): 1–62.

    Google Scholar 

  67. Lorenz, L. V. 1898–1904. Oeuvres Scientifiques de L. Lorenz. Vol. 1–2. Lehmann & Stage, Copenhagen.

  68. Luan, F., Gu, B., Gomes, A. S. L., Yong, K.-T., Wen, S., and Prasad, P. N. 2015. Lasing in nanocomposite random media. Nano Today 10(2): 168–192.

    Article  Google Scholar 

  69. Ma, L. X., Xie, B. W., Wang, C. C., and Liu, L. H. 2019. Radiative transfer in dispersed media: Considering the effect of host medium absorption on particle scattering. J. Quant. Spectr. Radiat. Transf. 230: 24–35.

    Article  ADS  Google Scholar 

  70. Maxwell Garnett, J. C. 1904. Colours in metal glasses and in metallic films. Philos. Trans. 203(359–371): 385–420.

    Article  ADS  MATH  Google Scholar 

  71. McCartney, E. J. 1976. Optics of the Atmosphere: Scattering by Molecules and Particles. John Wiley & Sons, New York.

  72. Mie, G. 1908. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Ann. Phys. 330(3): 377–445.

    Article  MATH  Google Scholar 

  73. Mobley, C. D. 1994. Light and Water: Radiative Transfer in Natural Waters. Academic Press, San Diego.

  74. Mourant, J. R., Fuselier, T., Boyer, J., Johnson, T. M., and Bigio, I. J. 1997. Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms. Appl. Opt. 36(4): 949–957.

    Article  ADS  Google Scholar 

  75. Mundy, W. C., Roux, J. A., and Smith, A. M. 1974. Mie scattering by spheres in an absorbing medium. J. Opt. Soc. Am. 64(12): 1593–1597.

    Article  ADS  Google Scholar 

  76. Nicholson, J. W. 1910. The asymptotic expansions of Bessel functions. Philos. Mag. 19(110): 228–249.

    Article  MATH  Google Scholar 

  77. Pitari, G., Di Genova, G., and De Luca, N. 2015. A modelling study of the impact of on-road diesel emissions on arctic black carbon and solar radiation transfer. Atmosphere 6(3): 318–340.

    Article  ADS  Google Scholar 

  78. Polimeno, P., Magazzù, A., Iatì, M. A., Patti, F., Saija, R., Boschi, C. D. E., Donato, M. G., Gucciardi, P. G., Jones, P. H., Volpe, G., and Maragò, O. M. 2018. Optical tweezers and their applications. J. Quant. Spectr. Radiat. Transf. 218: 131–150.

    Article  ADS  Google Scholar 

  79. Postelmans, A., Aernouts, B., and Saeys, W. 2018. Estimation of particle size distributions from bulk scattering spectra: sensitivity to distribution type and spectral noise. Opt. Express 26(12): 15015–15038.

    Article  ADS  Google Scholar 

  80. Poynting, J. H. 1884. On the transfer of energy in the electromagnetic field. Philos. Trans. 175: 343–361.

    Article  MATH  Google Scholar 

  81. Prieve, D. C. and Walz, J. Y. 1993. Scattering of an evanescent surface wave by a microscopic dielectric sphere. Appl. Opt. 32(9): 1629–1641.

    Article  ADS  Google Scholar 

  82. Rakovich, Y. P. and Donegan, J. F. 2010. Photonic atoms and molecules. Laser Photonics Rev. 4(2): 179–191.

    Article  ADS  Google Scholar 

  83. Rayleigh, Lord. 1871a. On the light from the sky, its polarization and colours. Philos. Mag. 41(271): 107–120.

    Article  Google Scholar 

  84. Rayleigh, Lord. 1871b. On the light from the sky, its polarization and colours. Philos. Mag. 41(273): 274–279.

    Article  Google Scholar 

  85. Rayleigh, Lord. 1871c. On the scattering of light by small particles. Philos. Mag. 41(275): 447–454.

    Article  Google Scholar 

  86. Rayleigh, Lord. 1881. On the electromagnetic theory of light. Philos. Mag. 12(73): 81–101.

    Article  Google Scholar 

  87. Rayleigh, Lord. 1899. On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky. Philos. Mag. 47(287): 375–384.

    Article  MATH  Google Scholar 

  88. Sadeghi, I., Muñoz, A., Laven, P., Jarosz, W., Seron, F., Gutierrez, D., and Jensen, H. W. 2012. Physically-based simulation of rainbows. ACM Trans. Graph. 31(1): 3:1–3:12.

    Article  Google Scholar 

  89. Schaub, S. A., Alexander, D. R., Barton, J. P., and Emanuel, M. A. 1989. Focused laser beam interactions with methanol droplets: effects of relative beam diameter. Appl. Opt. 28(9): 1666–1669.

    Article  ADS  Google Scholar 

  90. Schuster, A. 1909. An Introduction to the Theory of Optics. Edward Arnold, London.

  91. Stiles, W. S. and Burche, J. M. 1959. N.P.L. colour-matching investigation: Final report (1958). Opt. Acta 6: 1–26.

    Article  ADS  Google Scholar 

  92. Stockman, A. and Sharpe, L. T. 2000. The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype. Vis. Res. 40(13): 1711–1737.

    Article  Google Scholar 

  93. Stratton, J. A. 1941. Electromagn. Theory. McGraw-Hill, New York.

  94. Todhunter, I. 1893. A History of the Theory of Elasticity and of the Strength of Materials: From Galilei to the Present Time. Vol. II. Saint-Venant to Lord Kelvin. Cambridge University Press, Cambridge.

  95. Tuchin, V. 2015. Tissue Optics: Light Scattering Models and Instruments for Medical Diagnosis, third edn. SPIE Press, Washington.

  96. van de Hulst, H. C. 1957. Light Scattering by Small Particles. John Wiley & Sons, New York.

  97. Vizgin, V. P. 1994. Unified Field Theories: in the First Third of the 20th Century. Birkhäuser, Basel.

  98. Wait, J. R. 1962. Electromagnetic scattering from a radially inhomogeneous sphere. Appl. Sci. Res., Section B 10(5–6): 441–450.

    Article  MATH  Google Scholar 

  99. Wait, J. R. 1998. The ancient and modern history of EM ground-wave propagation. IEEE Antennas Propag. Mag. 40(5): 7–24.

    Article  ADS  Google Scholar 

  100. Wang, L. V. and Wu, H. 2007. Biomedical Optics: Principles and Imaging. John Wiley & Sons, Hoboken.

  101. Ward, J. and Benson, O. 2011. Wgm microresonators: sensing, lasing and fundamental optics with microspheres. Laser Photon. Rev. 5(4): 553–570.

    Article  ADS  Google Scholar 

  102. Watson, G. N. 1922. A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge.

  103. Whittaker, E. 1958. A History of the Theories of Aether and Electricity: Vol. I: The Classical Theories, 2nd revised edn. Thomas Nelson, London.

  104. Wiscombe, W. J. 1980. Improved Mie scattering algorithms. Appl. Opt. 19(9): 1505–1509.

    Article  ADS  Google Scholar 

  105. Wriedt, T. 2012. Mie theory: A review. In The Mie Theory: Basics and Applications, edited by W. Hergert and T. Wriedt. Springer Series in Optical Sciences, Vol. 169. Chap. 2, pp. 53–71.

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Frisvad, J.R., Kragh, H. On Ludvig Lorenz and his 1890 treatise on light scattering by spheres. EPJ H 44, 137–160 (2019). https://doi.org/10.1140/epjh/e2019-100022-y

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