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A modification of the Kummer\'s method for computation of the three-dimensional Green\'s function for one-dimensional periodic structures


S.P. Skobelev – Dr. Sc. (Phys.-Math.), Leading Research Scientist, PJSC «Radiofizika» (Moscow); Associate Professor, Moscow Institute of Physics and Technology (State University) E-mail:

A brief review of some available approaches to effective computation of the Green\'s function for singly periodic structures in the form of potential corresponding to an infinite linear arrays of point sources is made. Some inconveniences associated with practical application of the existing approaches including bulkiness, multiplicity of parameters, and necessity of combining with each other are noted. A new modification of the Kummer\'s method with involving complex coordinates and Poisson summation formula avoiding the indicated inconveniences is proposed.


  1. Boag A., Leviatan Y., Boag A. Analysis of electromagnetic scattering from linear periodic arrays of perfectly conducting bodies using a cylindrical-current model // IEEE Trans. Antennas Propagat. 1991. V. 39. № 9. P. 1332−1337.
  2. Craeye C., Tijhuis A.G., Schaubert D.H. An efficient MoM formulation for finite-by-infinite arrays of two-dimensional antennas arranged in a three-dimensional structure // IEEE Trans. Antennas Propagat. 2004. V. 52. № 1. P. 271−282.
  3. Fructos A.L., Boix R.R., Mesa F. Application of Kummer\'s transformation to the efficient computation of the 3-D Green\'s functions with 1-D periodicity // IEEE Trans. Antennas Propag. 2010. V. 58. № 1. P. 95−106.
  4. Skobelev S.P. Modifikacija metoda Kummera dlja ehffektivnogo vychislenija dvumernojj i trekhmernojj funkcijj Grina dlja odnomerno-periodicheskikh struktur // Antenny. 2011. № 10. S. 58−64.
  5. Skobelev S.P. A Modification of the Kummer\'s method for efficient computation of the 2-D and 3-D Green\'s functions for 1-D Periodic Structures // IEEE Trans. Antennas Propagat. 2012. V. 60. № 1. P. 412−416.
  6. Ivanishin M.M. Primenenie integralnykh uravnenijj k zadache o cilindre v prjamougolnom volnovode // Radiotekhnika i ehlektronika. 1984. T. 29. № 10. S. 1887−1895.
  7. Valerio G., Baccarelli P., Burghignoli P., Galli A. Comparative analysis of acceleration techniques for 2-D and 3-D Green’s functions in periodic structures along one and two directions // IEEE Trans. Antennas Propagat. 2007. V. 55. № 6. Pt. 1. P. 1630−1643.
  8. Ivanishin M.M., Skobelev S.P. A modification of the Kummer\'s method for efficient computation of the Green\'s function for doubly periodic structures // IEEE Trans. Antennas Propagat. 2009. V. 57. № 9. P. 2794−2798.


June 24, 2020
May 29, 2020

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