Abstract

The solution to the problem of optical or electromagnetic-wave scattering from perfectly conducting rough surfaces modeled by a multiscale fractal function is generalized to the case of relative uniform translating motion with respect to the observer. The presence of motion can be treated by the relativistic frame hopping method by means of plane-wave simplification techniques, since the solution relevant to the static case is expressed in terms of a generalized expansion of Floquet modes.

© 2003 Optical Society of America

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References

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  1. J. Van Bladel, Relativity and Engineering (Springer-Verlag, New York, 1984).
    [CrossRef]
  2. D. Censor, Radio Sci. 7, 331 (1972).
    [CrossRef]
  3. P. De Cupis, G. Gerosa, and G. Schettini, J. Electromagn. Waves Appl. 14, 1037 (2000).
    [CrossRef]
  4. G. Valenzuela, Radio Sci. 3, 1154 (1968).
  5. S. Savaidis, P. Frangos, D. L. Jaggard, and K. Hizanidis, Opt. Lett. 20, 2357 (1995).
    [CrossRef]
  6. S. Savaidis, P. Frangos, D. L. Jaggard, and K. Hizanidis, J. Opt. Soc. Am. A 14, 475 (1997).
    [CrossRef]
  7. D. L. Jaggard and X. Sun, J. Opt. Soc. Am. A 7, 1131 (1997).
    [CrossRef]

2000

P. De Cupis, G. Gerosa, and G. Schettini, J. Electromagn. Waves Appl. 14, 1037 (2000).
[CrossRef]

1997

1995

1972

D. Censor, Radio Sci. 7, 331 (1972).
[CrossRef]

1968

G. Valenzuela, Radio Sci. 3, 1154 (1968).

Censor, D.

D. Censor, Radio Sci. 7, 331 (1972).
[CrossRef]

De Cupis, P.

P. De Cupis, G. Gerosa, and G. Schettini, J. Electromagn. Waves Appl. 14, 1037 (2000).
[CrossRef]

Frangos, P.

Gerosa, G.

P. De Cupis, G. Gerosa, and G. Schettini, J. Electromagn. Waves Appl. 14, 1037 (2000).
[CrossRef]

Hizanidis, K.

Jaggard, D. L.

Savaidis, S.

Schettini, G.

P. De Cupis, G. Gerosa, and G. Schettini, J. Electromagn. Waves Appl. 14, 1037 (2000).
[CrossRef]

Sun, X.

Valenzuela, G.

G. Valenzuela, Radio Sci. 3, 1154 (1968).

Van Bladel, J.

J. Van Bladel, Relativity and Engineering (Springer-Verlag, New York, 1984).
[CrossRef]

J. Electromagn. Waves Appl.

P. De Cupis, G. Gerosa, and G. Schettini, J. Electromagn. Waves Appl. 14, 1037 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Radio Sci.

G. Valenzuela, Radio Sci. 3, 1154 (1968).

D. Censor, Radio Sci. 7, 331 (1972).
[CrossRef]

Other

J. Van Bladel, Relativity and Engineering (Springer-Verlag, New York, 1984).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Log amplitude of the various PW components of the scattered electric field EsϖP;r=log10BP expiκP·r versus normalized frequency shift ϖP/ω-1 for various values of r=0,0,ξσC. Parameters of the scattering surface: M=2; σC/λ=1, b=1.1, α=0.9, Λ/λ=1, Φ=0,π/8; incidence angle, θ=π/2; relative velocity, β=0.01; truncation subset of the Floquet expansion, Ξ2=p0,p1p0,p1-6,-5,,6.

Equations (13)

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Eir,t=yˆ ReA expiκi·r-ωt,
Eir,t=yˆ ReA expiκi·r-ωt,
ω,A=γ1-βκix/ωc-1ω,A,
κi=xˆκix-zˆκiz,    κix=γκix-βωc-1,κiz=ωc-12-κix21/2.
z=fx=σCn=0M-1αn sinbnKx+φn,
Esr,t=ReyˆPZMBP expiκP·r-ωt,
BP=-iωc-14πκzPQZM-1χP+QaQ expiP-Q·Φ×n=0M-1Jpn-qnκzPσCαn;
Eir,t=ReyˆPZMAP expiκP-·r-ωt,
AP=iωc-14πκzPQZMaQ expiP-Q·Φ×n=0M-1Jpn-qnκzPσCαn;
Esr,t=ReyˆPZMBP expiκP·r-ϖPt,
ϖP,BP=γ1+βκxP/ωc-1ω,BP,
κP=xˆκxP+zˆκzP,    κxP=γκxP+βωc-1,κzP=ϖPc-12-κxP21/2.
ϖP/ω-1=γβλΛn=0M-1pnbn.

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