Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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.

References [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] 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)
  • [3] 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)
  • [4] 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.
  • [5] 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)
  • [6] A. F. Kay, Scattering of a surface wave by a discontinuity in reactance, IEEE Trans. Antennas and Propagation AP-7, 22-31 (1959)
  • [7] 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.
  • [8] J. Kane, Surface waves on a reactive half plane, Res. Rep. EM-159, Courant Institute of Mathematical Sciences, New York University, 1960.
  • [9] 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
  • [10] J. Bazer and S. N. Karp, Propagation of plane electromagnetic waves past a shoreline, J. Res. Nat. Bur. Standards. 66D, 319-334 (1962)
  • [11] R. C. Morgan, Uniqueness theorem for a multi-mode surface wave diffraction problem., Quart. Appl. Math. 26 (1968/1969), 601–604. MR 0236535, https://doi.org/10.1090/S0033-569X-1969-0236535-4
  • [12] R. E. Collin and F. J. Zucker, Antenna theory, pt. 2, McGraw-Hill, New York, 1969, p. 304.
  • [13] 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, https://doi.org/10.1016/0020-7225(75)90007-5

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DOI: https://doi.org/10.1090/qam/400919
Article copyright: © Copyright 1972 American Mathematical Society

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