Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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.

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DOI: https://doi.org/10.1090/qam/652055
Article copyright: © Copyright 1982 American Mathematical Society

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