Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Diffraction of a dipole field by a unidirectionally conducting semi-infinite screen

Author: James Radlow
Journal: Quart. Appl. Math. 17 (1959), 113-127
MSC: Primary 78.00
DOI: https://doi.org/10.1090/qam/106678
MathSciNet review: 106678
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Abstract: An exact solution is obtained for the diffraction of a dipole field by a unidirectionally conducting semi-infinite plane screen. Double Laplace transforms are applied to Maxwell's equations, and the defining conditions of the unidirectionality lead to an equation between two complex functions of two complex variables. This equation is solved by an extension of the usual function-theoretical method, and we can then express the electro-magnetic field in terms of certain complex triple integrals. These are transformed into real integrals, so that it is possible to discuss the field behavior in the neighborhood of the diffracting edge. The variation of singularity along the edge of the screen is given.

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DOI: https://doi.org/10.1090/qam/106678
Article copyright: © Copyright 1959 American Mathematical Society

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