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

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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- 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.
- D. Censor, "The Doppler effect—now you see it, now you don't," J. Math. Phys. 25, 309-316 (1984).
- 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. .
- Y. Ben Shimol and D. Censor, "Contribution to the problem of near-zone inverse Doppler effect," Radio Sci. 33, 463-474 (1998).
- D. Censor, "Theory of the Doppler effect: fact, fiction and approximation," Radio Sci. 19, 1027-1040 (1984).
- 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. .
- J. A. Kong, Electromagnetic Wave Theory (Wiley, 1986), Chap. 6.3.

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