Skip to main content
SpringerLink
Log in

Diffraction by periodic structures

  • Conference paper
  • First Online:
Inverse Problems in Mathematical Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 422))

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bellout, H., Friedman, A.: Scattering by strip grating. J. Math. Anal. Applic. 147 (1990) 228–248.

    Google Scholar 

  2. Bensoussan, A., Lions, J. L., Papanicolaou, G.: Asymptotic analysis for periodic structures. Studies in Mathematics and its applications 5. North Holland, 1978.

    Google Scholar 

  3. Brackhage, H., Werner, P.: Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung. Arch. Math. 16 (1965) 325–329.

    Google Scholar 

  4. Cadilhac, M.: Some mathematical aspects of the grating theory. In: Petit, R. (ed.): Electromagnetic theory of gratings, Springer, 1980, 53–62.

    Google Scholar 

  5. Chen, X., Friedman, A.: Maxwell's equations in a periodic structure. Trans. Amer. Math. Soc. 323 (1991) 456–507.

    Google Scholar 

  6. Colton, D., Kress, R.: Integral equation methods in scattering theory. Wiley, New York 1983.

    Google Scholar 

  7. Gilbarg, D., Trudinger, N. S.: Elliptic partial differential equations of second order. Springer, Berlin 1983.

    Google Scholar 

  8. Hörmander, L.: An introduction to complex analysis in several variables. D. Van Nostrand, 1966.

    Google Scholar 

  9. Kato, T.: Perturbation theory for linear operators. Springer, Berlin 1976.

    Google Scholar 

  10. Kirsch, A.: The domain derivative and two applications in inverse scattering theory. To appear in Inverse Problems.

    Google Scholar 

  11. Millar, R. F.: The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers. Radio Science 8 (1973) 785–796.

    Google Scholar 

  12. Millar, R. F.: On the Rayleigh assumption in scattering by a periodic surface. Proc. Camb. Phil. Soc. 65 (1969) 773–791.

    Google Scholar 

  13. Millar, R. F.: On the Rayleigh assumption in scattering by a periodic surface: Part II. Proc. Camb. Phil. Soc. 69 (1971) 217–225.

    Google Scholar 

  14. Nedelec, J. C., Starling, F.: Integral equation methods in a quasi-periodic diffraction problem for the time harmonic Maxwell's equations. SIAM J. Math. Anal. 22 (1991) 1679–1701.

    Google Scholar 

  15. Petit, R.: Electromagnetic theory of gratings. Springer, Berlin 1980.

    Google Scholar 

  16. Pironneau, O.: Optimal shape design for elliptic systems. Springer, Berlin 1984.

    Google Scholar 

  17. Wilcox, C. H.: Scattering Theory for Diffraction Gratings. Lecture Notes in Mathematics, Springer, Berlin 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, 8520, Erlangen, Germany

    Andreas Kirsch

Authors
  1. Andreas Kirsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Lassi Päivärinta Erkki Somersalo

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this paper

Cite this paper

Kirsch, A. (1993). Diffraction by periodic structures. In: Päivärinta, L., Somersalo, E. (eds) Inverse Problems in Mathematical Physics. Lecture Notes in Physics, vol 422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57195-7_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-57195-7_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57195-7

  • Online ISBN: 978-3-540-47947-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation