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
Full-text PDF Free Access
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.
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).
A. L. Cullen, The excitation of plane surface waves, Proc. I. E. E. (4) 101, 225 (1954).
B. Friedman and W. E. Williams, Excitation of surface waves, Proc. I. E. E. 105C, 252 (1958).
- Samuel N. Karp and Frank C. Karal Jr., Vertex excited surface waves on both faces of a right-angled wedge, Comm. Pure Appl. Math. 12 (1959), 435–455. MR 108210, DOI https://doi.org/10.1002/cpa.3160120304
- Samuel N. Karp, Two dimensional Green’s function for a right angled wedge under an impedance boundary condition, Comm. Pure Appl. Math. 13 (1960), 203–216. MR 118276, DOI https://doi.org/10.1002/cpa.3160130204
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).
- F. C. Karal Jr., S. N. Karp, Ta-Shing 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 (1961), 35–48. MR 119790, DOI https://doi.org/10.1002/cpa.3160140103
- A. S. Peters, A new treatment of the ship wave problem, Comm. Pure Appl. Math. 2 (1949), 123–148. MR 33716, DOI https://doi.org/10.1002/cpa.3160020202
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.
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).
A. L. Cullen, The excitation of plane surface waves, Proc. I. E. E. (4) 101, 225 (1954).
B. Friedman and W. E. Williams, Excitation of surface waves, Proc. I. E. E. 105C, 252 (1958).
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].
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).
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).
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).
A. S. Peters, A new treatment of the ship wave problem, Comm. Pure Appl. Math. 2, 123 (1949).
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
Article copyright:
© Copyright 1964
American Mathematical Society
