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Modeling the Dispersion of Light

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Singularities and Oscillations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 91))

Abstract

This note discusses the modeling of dispersive phenomena in optics. The basic question is “Is there a reasonable differential equations model which explains the dispersive behavior of a prism?” Alternatively, “ Is there a differential equation model which includes the experimentally observed fact that the speed of light depends on its frequency?” The index of refraction is equal to 1/speed2so this is equivalent to studying the dependence of the index on frequency.

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References

  1. R. Boyd, Nonlinear Optics, Academic Press, 1992.

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  2. P. Donnat, Quelque contributions mathématiques en optiques nonlinéaire, These doctoral de L’Ecole Poytechnique, Palaiseau, 1994.

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  3. P. Donnat and J. Rauch, Dispersive nonlinear geometric optics, Jour. Math. Phys., to appear.

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  4. R.P. Feynmann, R. Leighton, and M. Sands, The Feynmann Lectures on Physics Vols. I., II., Addison-Wesley Pub., 1964.

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  5. H.A. Lorentz, Theory of Electrons, Teubner 1908, reprinted by Dover, 1952.

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  6. E. Purcell, Electricity and Magnetism, McGraw-Hill, 1965.

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  7. J. Rauch, Partial Differential Equations, Sringer-Verlag, 1991.

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  8. G. Whitham, Linear and Nonlinear Waves, John Wiley and Sons Inc., 1974.

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Author information

Authors and Affiliations

  1. Commissariat de l’Energie Atomique, Centre d’Etude de Limeil Valenton, Villeneuve St. Georges, 94195, France

    Phillipe Donnat

  2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1003, USA

    Jeffrey Rauch

Authors
  1. Phillipe Donnat
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  2. Jeffrey Rauch
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1003, USA

    Jeffrey Rauch

  2. Department of Mathematics, University of North Carolina, Chapel Hill, Chapel Hill, NC, 27599, USA

    Michael Taylor

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© 1997 Springer Science+Business Media New York

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Donnat, P., Rauch, J. (1997). Modeling the Dispersion of Light. In: Rauch, J., Taylor, M. (eds) Singularities and Oscillations. The IMA Volumes in Mathematics and its Applications, vol 91. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1972-9_2

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  • DOI: https://doi.org/10.1007/978-1-4612-1972-9_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7362-2

  • Online ISBN: 978-1-4612-1972-9

  • eBook Packages: Springer Book Archive

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