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Il Nuovo Cimento B (1971-1996)

, Volume 71, Issue 1, pp 65–74 | Cite as

Diffraction by perfectly conducting plane screens

II.—Plane-screen diffraction
  • W. D. Montgomery
Article

Summary

The unique solution to the general vector problem of electromagnetic diffraction by a perfectly conducting plane screen of arbitrary configuration is obtained in the form of a convergent series. The radiation impinging on the plane screen originates from a spatially bounded source which is also of arbitrary configuration. The mathematical context used to obtain this solution is the Hilbert-space formulation of the angular-spectrum representation of plane waves.

Дифракция на идеально проводящих плоских экранах.-II

Резюме

В форме сходящегося ряда получается единственное решение общей векторной проблемы электромагнитной дифракции на идеально проводящем плоском экране произвольной конфигуации. Излучение, падающее на плоский экран, происходит из пространственно ограниченного источника, который также также имеет произвольную конфигурацию. Математический подход, использованный для получения этого решения, представляет формулировку в гильбертовом пространстве представления углового спектра плоских волн.

Riassunto

L’unica soluzione al problema generale vettoriale della diffrazione elettromagnetica mediante uno schermo piano a conduzione perfetta di configurazione arbitraria si ottiene in forma di serie convergente. La radiazione che colpisce lo schermo piano deriva da una fonte spazialmente limitata, anch’essa di configurazione arbitraria. Il contesto matematico usato per ottenere questa soluzione è la formulazione nello spazio di Hilbert della rappresentazione dello spettro angolare delle onde piane.

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References

  1. (1).
    W. D. Montgomery:Nuovo Cimento B,4, 275 (1971).ADSCrossRefMATHGoogle Scholar
  2. (2).
    W. D. Montgomery:J. Opt. Soc. Am. A,58, 720 (1968). Verbal presentation.Google Scholar
  3. (3).
    W. D. Montgomery:J. Opt. Soc. Am.,58, 1112 (1968).ADSCrossRefMATHGoogle Scholar
  4. (4).
    We define\(f = (\hat f_1 ,\hat f_2 ,\hat f_3 )\) as the Fourier transform of itsx, y, z components, and\(f \cdot \varrho = \xi \hat f_1 + \eta \hat f_2 + \zeta \hat f_3 \) Google Scholar
  5. (5).
    There is also a left-propagating reflected boundary fieldr=[r, s], Using the results of ref. (8) we can show that the power interaction betweena andr, together withf, provides the screen with no net power loss or gain.ADSCrossRefMATHGoogle Scholar
  6. (6).
    R. Sikorski:Boolean Algebras (Berlin, 1964), p. 5.Google Scholar
  7. (7).
    TheD σ,K σ and ℛσ denote the domain, kernel and range, respectively, of the transformationJ which maps the inputa into the outputf (see I).Google Scholar
  8. (8).
    W. D. Montgomery:Nuovo Cimento B,15, 94 (1973). Note the change of notation fromG e toG m and fromG h toG e.ADSCrossRefGoogle Scholar
  9. (9).
    W. D. Montgomery:Nuovo Cimento B,46, 33 (1978).ADSCrossRefGoogle Scholar
  10. (10).
    This result was presented at the meeting onIntegral-Equation Methods in Engineering December 7–12, 1980 held at the Mathematical Research Institute, Oberwolfach, Federal Republic of Germany.Google Scholar
  11. (11).
    W. D. Montgomery:J. Opt. Soc. Am.,67, 1437 (1977). Verbal presentation.ADSGoogle Scholar
  12. (12).
    P. R. Halmos:A Hilbert Space Problem Book (Princeton, N. J., 1967), p. 257.Google Scholar
  13. (13).
    D. C. Youla:IEEE Trans. Circuits Syst., CAS-25, 694 (1978).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1982

Authors and Affiliations

  • W. D. Montgomery
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada

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