The field of a dipole above an infinite corrugated plane

Authors:
T. S. Chu and S. N. Karp

Journal:
Quart. Appl. Math. **21** (1964), 257-268

DOI:
https://doi.org/10.1090/qam/154546

MathSciNet review:
154546

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Abstract | References | Additional Information

Abstract: We investigate the excitation and propagation of the three dimensional electromagnetic field over an infinite corrugated plane which is approximated by an anisotropic impedance boundary condition. Emphasis is placed upon effects of surface anisotropy which are not evident in two dimensional treatments. In particular we consider the excitation by a magnetic point dipole in detail. It turns out that the fields are determined by a scalar wave function which satisfies a mixed boundary condition involving a linear combination of the wave function, its normal derivative and its second order tangential derivative. The exact formal solution is first derived, and then the radiated far field and the surface wave far field are evaluated separately. Both the phase and the amplitude of the excited surface wave are dependent upon the direction of observation. Numerical results are given. The physical significance of this solution is discussed. A comparison is made between this problem and the theory of ship waves.

**[1]**R. W. Hougardy and R. C. Hansen, Scanning*surface wave antennas--oblique surface waves over a corrugated conductor*, Trans. I. R. E.**AP-6**, 370 (1958). Comments by L. O. Goldstone and A. A. Oliner, ibid.,**AP-7**, 274 (1959). Comments by R. E. Collins,**AP-7**, 276 (1959).**[2]**A. L. Cullen,*The excitation of plane surface waves*, Proc. I. E. E. (4)**101**, 225 (1954).**[3]**B. Friedman and W. E. Williams,*Excitation of surface waves*, Proc. I. E. E.**105C**, 252 (1958).**[4]**S. N. Karp and F. C. Karal,*Surface waves on a right-angled wedge*, Comm. Pure Appl. Math.**12**, 435 (1959) [see also Wescon 1958]. MR**0108210****[5]**S. N. Karp,*Two-dimensional Green's function for a right-angled wedge under an impedance boundary condition*, Comm. Pure Appl. Math.**13**, 203 (1960). MR**0118276****[6]**S. N. Karp and F. C. Karal,*A new method for the determination of far fields with application to the problem of radiation of a line source at the tip of an absorbing wedge*, Trans. I. R. E.**AP-7**, S91 (1959).**[7]**F. C. Karal, S. N. Karp, T. S. Chu and R. G. Kouyoumjian,*Scattering of a surface wave by a discontinuity in the surface reactance on a right-angled wedge*, Comm. Pure Appl. Math.**14**, 35 (1961). MR**0119790****[8]**A. S. Peters,*A new treatment of the ship wave problem*, Comm. Pure Appl. Math.**2**, 123 (1949). MR**0033716****[9]**J. K. Lunde,*On the linearized theory of wave resistance for displacement ships in steady and accelerated motion*, A technical report published by the Society of Naval Architects and Marine Engineers in 1951.

Additional Information

DOI:
https://doi.org/10.1090/qam/154546

Article copyright:
© Copyright 1964
American Mathematical Society