A rigorous method for solving the problems of diffraction of monochromatic electromagnetic waves by periodic structures


We present a rigorous method for solving the problems of diffraction of monochromatic electromagnetic waves on periodic structures of many types. The method is based on transformation of the Helmholtz equation and the boundary conditions to a certain system of integral equations and a subsequent rigorous solution of this system.


Integral Equation Plane Wave Dielectric Permittivity Periodic Structure Homogenous Region 


  1. 1.
    A. Sommerfeld, Math. Ann., 47, 317 (1896).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    M. Born and E. Wolf, Principles of Optics, Cambridge. Univ. Press, Cambridge (1999).Google Scholar
  3. 3.
    A. I. Potekhin, Some Problems of Diffraction of Electromagnetic Waves [in Russian], Sovetskoe Radio, Moscow (1948), p. 69, 105.Google Scholar
  4. 4.
    R. B. Vaganov and B. Z. Katzenelenbaum, Fundamentals of the Diffraction Theory [in Russian], Nauka, Moscow (1982), p. 43.Google Scholar
  5. 5.
    L. A. Weinstein, The Theory of Diffraction and the Factorization Method, Golem Press, Boulder, Colo. (1969).Google Scholar
  6. 6.
    A. Taflove and M. E. Brodwin, IEEE Trans. Microwave Theory Techn., MTT-23, 623 (1975).ADSCrossRefGoogle Scholar
  7. 7.
    S. Peng and G. M. Morris, J. Opt. Soc. Am. A, 12, 1087 (1995).ADSCrossRefGoogle Scholar
  8. 8.
    Yu.A. Eremin and A. G. Sveshnikov, Method of Discrete Sources in the Problems of Electromagnetic Diffraction, Moscow State Univ. Press, Moscow (1992).Google Scholar
  9. 9.
    S. V. Zymovetz and P. I. Geshev, Tech. Phys., 51, No. 3, 291 (2006).CrossRefGoogle Scholar
  10. 10.
    L. A. Weinstein and A. I. Sukov, Radiotekh. Élektron., 29, 1472 (1984).ADSGoogle Scholar
  11. 11.
    E. V. Koposova, Radiophys. Quantum Electron., 53, No. 4, 244 (2010).ADSCrossRefGoogle Scholar
  12. 12.
    M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Theory of Waves [in Russian], Nauka, Moscow (1979), p. 246.Google Scholar
  13. 13.
    G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1968).Google Scholar
  14. 14.
    R. Petit, ed., Electromagnetic theory of gratings, Springer-Verlag, New York (1980), p. 23Google Scholar
  15. 15.
    V. P. Shestopalov, A. A. Kirilenkov, S. A. Masalov, and Yu.K. Sirenko, Resonance Wave Scattering, Vol. 1, Diffraction Gratings [in Russian], Naukova Dumka, Kiev (1986), p. 37.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Institute of Applied Physics of the Russian Academy of SciencesNizhny NovgorodRussia

Personalised recommendations