Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Phenomenological theory of multimode surface waves for plane structures

Authors: Samuel N. Karp and Jr. Karal
Journal: Quart. Appl. Math. 24 (1966), 239-247
DOI: https://doi.org/10.1090/qam/99919
MathSciNet review: QAM99919
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Abstract: The notion of impedance boundary condition is generalized and illustrated by the discussion of the electromagnetic field arising from a magnetic line dipole source located above a plane structure. The generalized impedance boundary condition contains a set of parameters whose totality offers a physical description of the configuration. By suitably selecting these parameters, the configuration may be made to correspond to a structure that supports surface waves. We give an exact solution for a plane structure that supports one, two and three surface waves. The magnitudes of the surface waves are obtained and simple formulas for the radiated far field patterns are given. We also show how the methods employed can be extended to the case of any number of surface waves. This involves an $ n$th order mixed boundary condition for a second order partial differential equation.

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DOI: https://doi.org/10.1090/qam/99919
Article copyright: © Copyright 1966 American Mathematical Society

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