Surface wave incidence on a plane structure having a multi-mode discontinuity in impedance
Authors:
Richard C. Morgan and Samuel N. Karp
Journal:
Quart. Appl. Math. 30 (1972), 299-310
MSC:
Primary 78.45
DOI:
https://doi.org/10.1090/qam/400919
MathSciNet review:
400919
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Abstract: The phenomenological theory of multi-mode surface wave propagation is applied to a plane structure having a multi-mode discontinuity in impedance. The resulting boundary-value problem is reduced to the solution of a Wiener–Hopf equation whose factorization is given in terms of the factorization that occurred in the one-mode case. Despite the complexity of the solution, the magnitudes of the surface wave excitation coefficients are elementary functions, as is the cylindrical power flow.
S. N. Karp and F. C. Karal, Phenonenological theory of muliti-mode surface wave structures, in Quasi-optics symposium, Brooklyn Polytechnic Institute, John Wiley, New York, 1964.
F. C. Karal and S. N. Karp, Phenomenological theory of multi-mode surface waves for plane structures, Res. Rep. EM-198, Courant Institute of Mathematical Sciences, New York University, New York, 1964; condensed version, Quart. Appl. Math. 24, 239–247 (1966)
R. C. Morgan, S. N. Karp, and F. C. Karal, Solution to the phenomenological problem of a magnetic line source above a plane structure that supports N excited modes, SIAM J. Appl. Math. 15, 1363–1377 (1967)
S. N. Karp and F. C. Karal, Generalized impedance boundary conditions with applications to surface wave structures, in Proc. URSI, Comm. VI Conference, Delft, The Netherlands, 1965.
R. C. Morgan, S. N. Karp and F. C. Karal, Multi-mode surface wave diffraction by a right-angled wedge, Quart. Appl. Math. 24, 263–266 (1966)
A. F. Kay, Scattering of a surface wave by a discontinuity in reactance, IEEE Trans. Antennas and Propagation AP-7, 22–31 (1959)
J. Kane and S. N. Karp, Radio propagation past a pair of dielectric interfaces, Res. Rep. EM-154, Courant Institute of Mathematical Sciences, New York University, New York, 1960.
J. Kane, Surface waves on a reactive half plane, Res. Rep. EM-159, Courant Institute of Mathematical Sciences, New York University, 1960.
- V. Fock, Sur certaines équations intégrales de physique mathématique, Rec. Math. [Mat. Sbornik] N.S. 14(56) (1944), 3–50 (Russian, with French summary). MR 0012190
J. Bazer and S. N. Karp, Propagation of plane electromagnetic waves past a shoreline, J. Res. Nat. Bur. Standards. 66D, 319–334 (1962)
- R. C. Morgan, Uniqueness theorem for a multi-mode surface wave diffraction problem, Quart. Appl. Math. 26 (1968/69), 601–604. MR 236535, DOI https://doi.org/10.1090/S0033-569X-1969-0236535-4
R. E. Collin and F. J. Zucker, Antenna theory, pt. 2, McGraw-Hill, New York, 1969, p. 304.
- Samuel N. Karp and Richard C. Morgan, Multi-mode surface wave phenomena, Internat. J. Engrg. Sci. 13 (1975), 687–698 (English, with French, German and Italian summaries). MR 0441078, DOI https://doi.org/10.1016/0020-7225%2875%2990007-5
S. N. Karp and F. C. Karal, Phenonenological theory of muliti-mode surface wave structures, in Quasi-optics symposium, Brooklyn Polytechnic Institute, John Wiley, New York, 1964.
F. C. Karal and S. N. Karp, Phenomenological theory of multi-mode surface waves for plane structures, Res. Rep. EM-198, Courant Institute of Mathematical Sciences, New York University, New York, 1964; condensed version, Quart. Appl. Math. 24, 239–247 (1966)
R. C. Morgan, S. N. Karp, and F. C. Karal, Solution to the phenomenological problem of a magnetic line source above a plane structure that supports N excited modes, SIAM J. Appl. Math. 15, 1363–1377 (1967)
S. N. Karp and F. C. Karal, Generalized impedance boundary conditions with applications to surface wave structures, in Proc. URSI, Comm. VI Conference, Delft, The Netherlands, 1965.
R. C. Morgan, S. N. Karp and F. C. Karal, Multi-mode surface wave diffraction by a right-angled wedge, Quart. Appl. Math. 24, 263–266 (1966)
A. F. Kay, Scattering of a surface wave by a discontinuity in reactance, IEEE Trans. Antennas and Propagation AP-7, 22–31 (1959)
J. Kane and S. N. Karp, Radio propagation past a pair of dielectric interfaces, Res. Rep. EM-154, Courant Institute of Mathematical Sciences, New York University, New York, 1960.
J. Kane, Surface waves on a reactive half plane, Res. Rep. EM-159, Courant Institute of Mathematical Sciences, New York University, 1960.
V. Fock, Sur certaines equations integrales de physique mathematique, Recueil Math. Nouvelle T.A. 56 (1944)
J. Bazer and S. N. Karp, Propagation of plane electromagnetic waves past a shoreline, J. Res. Nat. Bur. Standards. 66D, 319–334 (1962)
R. C. Morgan, Uniqueness theorem for a multi-mode surface wave diffraction problem, Quart. Appl. Math. 26, 601–604 (1969)
R. E. Collin and F. J. Zucker, Antenna theory, pt. 2, McGraw-Hill, New York, 1969, p. 304.
R. C. Morgan and S. N. Karp, Multi-mode surface wave phenomena, to appear.
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Article copyright:
© Copyright 1972
American Mathematical Society
