OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2538–2550

Electromagnetic wave scattering from moving surfaces with high-amplitude corrugated pattern

Peter De Cupis  »View Author Affiliations

JOSA A, Vol. 23, Issue 10, pp. 2538-2550 (2006)

View Full Text Article

Acrobat PDF (237 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



This paper deals with the problem of electromagnetic wave scattering from rough surfaces. By means of a generalized Floquet modal representation an analytic solution can be found that is valid for any Fourier-expandable surface pattern, with no limitation on the corrugation amplitude. By means of the special relativistic frame-hopping method, the motionless solution is generalized to the case of uniform translational relative motion between the surface and the observer. Plane-wave simplification techniques are employed to minimize the algebraic complexity of the field covariance transformations. A detailed signal analysis of the electromagnetic scattered field is performed in both the frequency and the time domains.

© 2006 Optical Society of America

OCIS Codes
(240.5770) Optics at surfaces : Roughness
(290.5880) Scattering : Scattering, rough surfaces
(350.5720) Other areas of optics : Relativity

ToC Category:

Original Manuscript: December 9, 2005
Revised Manuscript: April 7, 2006
Manuscript Accepted: April 11, 2006

Peter De Cupis, "Electromagnetic wave scattering from moving surfaces with high-amplitude corrugated pattern," J. Opt. Soc. Am. A 23, 2538-2550 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. J. Van Bladel, Relativity and Engineering (Springer-Verlag, 1984).
  2. D. Censor, "Scattering in velocity-dependent systems," Radio Sci. 7, 331-337 (1972).
  3. D. Censor, "The mathematical elements of relativistic free-space scattering," J. Electromagn. Waves Appl. 19, 907-923 (2005).
  4. P. De Cupis, G. Gerosa, and G. Schettini, "Electromagnetic scattering by uniformly moving bodies," J. Electromagn. Waves Appl. 14, 1037-1062 (2000).
  5. P. De Cupis, P. Burghignoli, G. Gerosa, and M. Marziale, "Electromagnetic wave scattering by a perfectly conducting wedge in uniform translational motion," J. Electromagn. Waves Appl. Vol. 16, 345-364 (2002).
  6. P. De Cupis, D. Anatriello, and G. Gerosa, "An asymptotically exact technique for electromagnetic scattering by uniformly moving objects with arbitrary geometry," XXVIIth Union Radio-Scientifique Internationale General Assembly, Maastricht (the Netherlands), August 17-24, 2002. PDF available at http://www.die.uniromal.it/personale/gerosa/bibliografia/2002URSIlowbarp509.pdf.
  7. G. Valenzuela, "Scattering of electromagnetic waves from a slightly rough surface moving with uniform velocity," Radio Sci. 3, 1154-1157 (1968).
  8. A. Tzikas, D. Chrissoulidis, and E. Kriezis, "Relativistic bistatic scattering by a uniformly moving random rough surface," IEEE Trans. Microwave Theory Tech. 34, 1046-1052 (1986).
  9. P. De Cupis, "Relativistic scattering by moving rough surfaces," VIth Società Italiana di Matematica Applicata e Industriale (SIMAI) National Congress, Domus de Maria (CA), Italy, May 27-31, 2002. PDF available at http://www.die.uniromal.it/personale/gerosa/bibliografia/2002SIMAI.pdf.
  10. D. P. Chrissoulidis, L. P. Ivrissimtzis, and E. E. Kriezis, "Relativistic scattering by a random rough Kirchhoff surface in uniform motion," Radio Sci. 22, 803-814 (1986).
  11. S. L. Chuang and J. A. Kong, "Scattering of waves from periodic surfaces," Proc. IEEE 69, 1132-1144 (1981).
  12. S. Savaidis, P. Frangos, D. L. Jaggard, and K. Hizanidis, "Scattering from fractally corrugated surfaces: an exact approach," Opt. Lett. 20, 2357-2359 (1995).
  13. S. Savaidis, P. Frangos, D. L. Jaggard, and K. Hizanidis, "Scattering from fractally corrugated surfaces with use of the extended boundary method," J. Opt. Soc. Am. A 14, 475-485 (1997).
  14. P. De Cupis, "Relativistic scattering by moving rough surfaces," Opt. Lett. 28, 849-850 (2003).
  15. P. De Cupis and G. Gerosa, "Relativistic scattering by moving rough surfaces," in Electromagnetics in a Complex World, I.Pinto, ed. (Springer-Verlag, 2004). PDF draft http://www.die.uniromal.it/personale/gerosa/bibliografia/2003lowbarbenevento.pdf.
  16. For instance, in the case of a periodical pattern with roughness parameters given by Eq. 13, different indices Q not = L epsilon Z^M should redundantly assign the same Floquet mode (i.e., K'_Q = K'_L) if Sigma^M _m=1(qm−lm)jm=0.
  17. D. Censor, "The Doppler effect—now you see it, now you don't," J. Math. Phys. 25, 309-316 (1984).
  18. Within the proposed relativistic extension of the EBC methodology, the influence on the Doppler spectrum profile of the shape of the diffractive corrugation is summarized through the following theoretical chain: The surface geometric features are directly represented by the Fourier parameters fm,Xim, varphim, m=1-M, given by Eq. . Their values determine the algebraic linear system obtainable from Eq. , whose solutions furnish the amplitudes {CP′,DP′} of the various Floquet modes in the co-moving frame Σ′. Then, after covariance transformation to the laboratory frame Σ, the amplitude coefficients of any given Floquet mode, i.e., {CP,DP}, set the magnitude level of its associated Doppler-shifted tune; see Eq. . Also the exponential term exp[i(kp∙r)], whose magnitude is not = 1 for an evanescent Floquet mode, is directly dependent on K′={xim}m=1−M, as one can infer from Eqs. .
  19. Y. Ben Shimol and D. Censor, "Contribution to the problem of near-zone inverse Doppler effect," Radio Sci. 33, 463-474 (1998).
  20. D. Censor, "Theory of the Doppler effect: fact, fiction and approximation," Radio Sci. 19, 1027-1040 (1984).
  21. Main aliases are shifted by Deltax′=l2π/xi_1, l epsilon Z−{0}, where xi_1 is the slowest spatial "tune" used in Eq. , and are in general dissimilar with respect to the actual peak, since the Riemann approximate summation is in general not periodical, i.e., usually xi_m not = mxi_1, m=2,3...,M in Eq. .
  22. J. A. Kong, Electromagnetic Wave Theory (Wiley, 1986), Chap. 6.3.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited