The diffraction of a plane wave by an infinite slit. I
Author:
Robert J. Spahn
Journal:
Quart. Appl. Math. 40 (1982), 105-110
MSC:
Primary 78A45
DOI:
https://doi.org/10.1090/qam/652055
MathSciNet review:
652055
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Abstract: The diffraction of a normally incident plane wave by an infinite slit of finite width in a perfectly conducting screen is solved using a Lebedev integral transform theorem and the Wiener-Hopf technique. This technique leads to an infinite system of equations to which the method of successive approximation is applied. In particular, an expression for the transmission coefficient (defined as the ratio of the transmitted to the incident power per unit length) is obtained for $a \ll \lambda$ where $2a$ is the slit width and $\lambda$ is the wave length of the incident wave. There is exact agreement with the known result [3] except for a constant, which has been difficult to determine because of the slow convergence of the series involved; however, a new term has been obtained.
A. Sommerfeld, Vorlesungen über theoretische Physik, vol. 4, Wiesbaden, Dieterich, 1950
P. M. Morse and P. J. Rubenstein, The diffraction of waves by ribbons and by slits, Phys. Rev. 54, 895–898 (1938)
- C. J. Bouwkamp, Diffraction theory, Reports on Progress in Physics 17 (1954), 35–100. MR 63923, DOI https://doi.org/10.1088/0034-4885/17/1/302
- F. Oberhettinger, Diffraction of waves by a wedge, Comm. Pure Appl. Math. 7 (1954), 551–563. MR 63284, DOI https://doi.org/10.1002/cpa.3160070306
- N. N. Lebedev, Sur un formule d’inversion, C. R. (Doklady) Acad. Sci. URSS (N.S.) 52 (1946), 655–658 (French). MR 0021144
- Paul B. Bailey and George E. Barr, Diffraction by a slit or strip, J. Mathematical Phys. 10 (1969), 1906–1913. MR 250563, DOI https://doi.org/10.1063/1.1664780
A. Sommerfeld, Vorlesungen über theoretische Physik, vol. 4, Wiesbaden, Dieterich, 1950
P. M. Morse and P. J. Rubenstein, The diffraction of waves by ribbons and by slits, Phys. Rev. 54, 895–898 (1938)
C. J. Bouwkamp, Diffraction theory, Reports on Progress in Physics 17, 35–100 (1954)
F. Oberhettinger, Diffraction of waves by a wedge, Comm. Pure and Appl. Math 7, 551–563 (1954)
N. N. Lebedev, Sur une formule d’inversion, Comptes Rendus (Doklady) de l’Academie des Sciences de l’URSS (M8)52, 655–658 (1946)
P. B. Bailey and G. E. Barr, Diffraction by a slit or strip, J. Math. Physics 10, 1906–1913 (1969)
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Article copyright:
© Copyright 1982
American Mathematical Society