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.

**[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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Additional Information

DOI:
https://doi.org/10.1090/qam/400919

Article copyright:
© Copyright 1972
American Mathematical Society