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The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(4):549-583; doi:10.1093/qjmam/54.4.549
© 2001 by Oxford University Press
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Diffraction by a Dielectric Wedge at Skew Incidence

Christian Bergljung1 and Svend Berntsen2

( 1 Department of Applied Electronics, Lund University, PO Box 118, S-221 00 Lund, Sweden 2 Department of Mathematics, Aalborg University, Fredrik Bajers vej 7E, DK-9220 Aalborg Ø, Denmark )

The problem of diffraction by a homogeneous dielectric wedge irradiated by a time-harmonic plane wave at skew incidence is represented by uncoupled Fredholm integral equations of the second kind. It is shown that there exists a unique solution if the wave numbers of the exterior and interior media are suitably restricted; the result covers also the case in which the wave numbers are real and the wedge is optically denser. A complete asymptotic expansion is obtained for the solution in the neighbourhood of the edge. The electric field transverse to the edge becomes singular at the edge, and the singularity exponent does not depend on the skewness of the incidence. Finally, it is shown that lateral waves appear along the wedge faces also for plane-wave incidence.


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