Phenomenological theory of multimode surface waves for plane structures

Authors:
Samuel N. Karp and Jr. Karal

Journal:
Quart. Appl. Math. **24** (1966), 239-247

DOI:
https://doi.org/10.1090/qam/99919

MathSciNet review:
QAM99919

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Abstract | References | Additional Information

Abstract: The notion of impedance boundary condition is generalized and illustrated by the discussion of the electromagnetic field arising from a magnetic line dipole source located above a plane structure. The generalized impedance boundary condition contains a set of parameters whose totality offers a physical description of the configuration. By suitably selecting these parameters, the configuration may be made to correspond to a structure that supports surface waves. We give an exact solution for a plane structure that supports one, two and three surface waves. The magnitudes of the surface waves are obtained and simple formulas for the radiated far field patterns are given. We also show how the methods employed can be extended to the case of any number of surface waves. This involves an th order mixed boundary condition for a second order partial differential equation.

**[1]**Barlow, H. M., and Cullen, A. L., Surface Waves, Proc. Inst. Elec. Engrgs. Part III, Vol. 100, 1953, p. 329.**[2]**Barlow, H. M., and Karbowiak, A. E., An Experimental Investigation of the Properties of Corrugated Cylindrical Surface Waveguides, Proc. Inst. Elec. Engrgs. Part III, Vol. 101, 1954, pp. 182-188.**[3]**Bazer, J., and Karp, S. N., Propagation of Plane Electromagnetic Waves Past a Shoreline, Jour. of Res. Nat. Bureau of Standards, Vol. 66D, 1962, pp. 319-334.**[4]**D. B. Brick,*The radiation of a Hertzian dipole over a coated conductor*, Proc. Inst. Elec. Engrs. C.**102**(1955), 104–121. MR**0072014****[5]**Chu, T. S., Kouyounjain, R. G., Karal, F. C. and Karp, S. N., The Diffraction of Surface Waves by a Terminated Structure in the Form of a Right-Angle Bend, I.R.E. Trans, on Antennas and Propagation, Vol. AP-10, 1962, pp. 679-686.**[6]**T. S. Chu and S. N. Karp,*The field of a dipole above an infinite corrugated plane*, Quart. Appl. Math.**21**(1963/1964), 257–268. MR**0154546**, https://doi.org/10.1090/S0033-569X-1964-0154546-X**[7]**Robert E. Collin,*Field theory of guided waves*, International Series in Pure and Applied Physics, Mc-Graw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR**0116872****[8]**Cottony, H. V. et. al., Antennas and Waveguides and Annotated Bibliography, I.R.E. Trans, on Antennas and Propagation, Vol. AP-7, 1959, pp. 87-98.**[9]**Cullen, A. L., The Excitation of Plane Surface Waves, Proc. Inst. Elec. Engrgs. Part IV, Vol. 101, 1954, pp. 225-234.**[10]**Felsen, L. B., Diffraction by an Imperfectly Conducting Wedge, McGill Symposium on Microwave Optics, Part II, 1959, pp. 287-292.**[11]**Felsen, L. B., Field Solutions for a Class of Corrugated Wedges and Cone Surfaces, Polytech. Inst. Brooklyn, Memo No. 32, July, 1957.**[12]**Fernando, W. M. G., and Barlow, H. M., An Investigation of the Properties of Radical Cylindrical Surface Waves Launched over Flat Reactive Surfaces, Proc. Inst. Elec. Engrgs., Vol. 103B, 1956, pp. 307-318.**[13]**Friedman, B., and Williams, W. E., Excitation of Surface Waves, Proc. Inst. Elec. Engrgs., Vol. 105C, 1958, pp. 252-258.**[14]**G. Grünberg,*Suggestions for a theory of the coastal refraction*, Phys. Rev. (2)**63**(1943), 185–189. MR**0007866****[15]**Kane, J., A Surface Wave Antenna as a Boundary Value Problem, Electromagnetic Theory and Antennas, Edited by E. C. Jordan, Pergamon Press, New York, 1963, pp. 891-894.**[16]**Frank C. Karal Jr. and Samuel N. Karp,*Diffraction of a skew plane electromagnetic wave by an absorbing right-angled wedge*, Comm. Pure Appl. Math.**11**(1958), 495–533. MR**0099202**, https://doi.org/10.1002/cpa.3160110404**[17]**Frank C. Karal Jr. and Samuel N. Karp,*Diffraction of a plane wave by a right angled wedge which sustains surface waves on one face*, Quart. Appl. Math.**20**(1962/1963), 97–106. MR**0151112**, https://doi.org/10.1090/S0033-569X-1962-0151112-1**[18]**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**0119790**, https://doi.org/10.1002/cpa.3160140103**[19]**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**0118276**, https://doi.org/10.1002/cpa.3160130204**[20]**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**0108210**, https://doi.org/10.1002/cpa.3160120304**[21]**S. N. Karp and F. C. Karal Jr.,*Vertex excited surface waves on one face of a right angled wedge*, Quart. Appl. Math.**18**(1960/1961), 235–243. MR**0115596**, https://doi.org/10.1090/S0033-569X-1960-0115596-7**[22]**Karp, S. N., and Karal, F. C., 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, I.R.E. Trans, on Antennas and Propagation, Toronto Symposium on Electromagnetic Theory, Vol. AP-7, 1959, pp. S91-S102.**[23]**Kay, A. F., Scattering of a Surface Wave by a Discontinuity in Reactance, I.R.E. Trans, on Antennas and Propagation, Vol. AP-7, 1959, pp. 22-31.**[24]**Maluzhinets, G. D., The Excitation, Reflection and Emission of Surface Waves from a Wedge with Given Face Impedances, Soviet Physics, Dokl, Vol. 3, 1958, pp. 752-755.**[25]**F. J. Zucker,*Progress during the past three years in surface and leaky wave antennas*, J. Res. Nat. Bur. Standards Sect. D**64D**(1960), 746–749. MR**0134385****[26]**Karp, S. N., and Karal, F. C., Generalized Impedance Boundary Conditions with Applications to Surface Wave Structures, to appear in the Proceedings of the Delft Symposium on Electromagnetic Theory (U.R.S.I. Comm. VI Conference, Delft, the Netherlands, 1965).

Additional Information

DOI:
https://doi.org/10.1090/qam/99919

Article copyright:
© Copyright 1966
American Mathematical Society