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The Sommerfeld half‐plane problem revisited, IV: Variations on a theme of Carlson and Heins
Author(s) -
Heins A. E.,
Pond J. M.
Publication year - 1988
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670100307
Subject(s) - mathematics , specular reflection , reflection (computer programming) , mathematical analysis , plane (geometry) , boundary (topology) , neumann boundary condition , boundary value problem , dirichlet problem , plane wave , geometry , optics , physics , computer science , programming language
A plane wave is incident upon an infinite set of equally spaced, semi‐infinite parallel and staggered plates. The boundary conditions on the plates alternate between the Dirichlet and Neumann ones. This problem is formulated as a pair of coupled Wiener‐Hopf integral equations and solved by a method proposed by A. E. Heins in 1950. For the case of specular reflection, that is, a single reflected plane wave, the magnitudes of the reflection coefficient and the transmission coefficients are determined.