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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • 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)
http://dx.doi.org/10.1364/JOSAA.23.002538


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Abstract

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:
Scattering

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

Citation
Peter De Cupis, "Electromagnetic wave scattering from moving surfaces with high-amplitude corrugated pattern," J. Opt. Soc. Am. A 23, 2538-2550 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-10-2538


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References

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  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. .
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  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.

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