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IEEE Transactions on Antennas and Propagation
Volume 48 Number 9, September 2000

Table of Contents for this issue

Complete paper in PDF format

The Failure of"Classic"Perturbation Theory at a Rough Neumann Boundary Near Grazing

Donald E. Barrick and Rosa Fitzgerald

Page 1452.

Abstract:

Rice's"classic"perturbation theory predicts an erroneous limit at grazing for vertically polarized plane wave scatter from an infinite perfectly conducting rough surface; likewise, the attendant result for the specularly reflected mode also fails at grazing. We show where and why in the system of perturbational equations this difficulty occurs. We then reformulate the perturbational approach to handle the low-incidence angle region for a one-dimensionally (1-D) rough Neumann boundary (vertical polarization from a perfectly conducting surface). The result for scattered fields vanishes in direct proportion to incidence angle above grazing and the result for the normalized roughness-modified surface impedance becomes constant with angle near grazing. For completeness and comparison, we give results for the horizontal polarization at a Dirichlet boundary, where perturbation results encounter no difficulties. Scatter dependence on grazing angle is explained in terms of the"classic"perturbation result multiplied by a propagation factor to the cell. The latter includes the sum of the direct and specularly reflected waves at the surface. This quantity can be replaced by the appropriate surface-wave propagation factor for radiation from dipole antennas, thereby explaining the strong observed vertically polarized sea scatter at high frequency (HF) on and below the horizon.

References

  1. J. R. Wait, Electromagnetic Waves in Stratified Media, New York: Pergamon, 1962.
  2. J. R. Wait, "On the theory of radio propagation over a slightly roughened curved earth,"in Electromagnetic Probing in Geophysics , J. R. Wait, Ed. Boulder, CO: Golem, 1971, pp.  370-381. 
  3. D. E. Barrick, "Theory of HF/VHF propagation across the rough sea", Radio Sci., vol. 6, pp.  517-533, 1971.
  4. E. Feynberg, "On the propagation of radio waves along an imperfect surface", J. Phys., vol. 9, pp.  317-330, 1944.
  5. L. Rayleigh, Theory of Sound, London: U.K.: Macmillan, 1929,vol. II, pp.  89-96. 
  6. S. O. Rice, "Reflection of electromagnetic waves from slightly rough surfaces,"in Theory of Electromagnetic Waves, M. Kline, Ed. New York: Wiley, 1951, pp.  351-378. 
  7. V. I. Tatarskii and M. Charnotskii, "Universal behavior of scattering amplitudes from a plane in an average rough surface for small grazing angles", Waves Random Media, vol. 8, pp.  29-40, 1998.
  8. V. I. Tatarskii and M. Charnotskii, "On the universal behavior of scattering from a rough surface for small grazing angles", IEEE Trans. Antennas Propagat., vol. 46, pp.  67-72, Jan.  1998.
  9. D. E. Barrick, "Grazing behavior of scatter and propagation above any rough surface", IEEE Trans. Antennas Propagat., vol. 46, pp.  73-83,  Jan.  1998.
  10. D. E. Barrick, "Near-grazing illumination and shadowing of rough surfaces", Radio Sci., vol. 30, pp.  563-580, 1995.
  11. D. E. Barrick, "First-order theory and analysis of MF/HF/VHF scatter from the sea", IEEE Trans. Antennas Propagat., vol.  AP-20, pp.  2-10, Jan.  1972.
  12. A. N. Sommerfeld, "The propagation of waves in wireless telegraphy", Ann. Phys., vol. 28, pp.  665 -682, 1907.
  13. K. A. Norton, "Propagation of radio waves over a plane earth", Nature, vol. 135, pp.  954-955, 1935.
  14. G. D. Monteath, "Application of the compensation theorem to certain radiation and propagation problems", Proc. Inst. Elect. Eng., vol. 98, pp.  23-30, 1951.
  15. I. M. Fuks, V. I. Tatarskii and D. E. Barrick, "Behavior of scattering from a rough surface at small grazing angles", Waves Random Media, vol. 9, pp.  295-305,  1999.
  16. R. Fitzgerald, "Reconstruction of the surface power spectrum from reflectivity data", Opt. Lett., vol. 24, pp.  364-366, 1999.
  17. J. Shen and A. Maradudin, "Multiple scattering of waves from random rough surfaces", Phys. Rev. B, vol. 22, pp.  4234 -4240, 1980.
  18. J. Sanchez-Gil, A. Maradudin and E. Mendez, "Limits of validity of three perturbation theories of the specular scattering of light from one-dimensional, randomly rough, dielectric surfaces", J. Opt. Soc. Amer. A, vol. 12, pp.  1547-1558, 1995.