Abstract

Iterative methods offer a practical means for the calculation of wave scattering from two-dimensional surfaces. We present what is to our knowledge the first calculation of the scattering of an electromagnetic beam from a two-dimensional, randomly rough, perfectly conducting surface, using an iterative approach. We also examine a bootstrapping scheme of iteration that can further reduce computing time.

© 1994 Optical Society of America

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References

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  1. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a grating,” Ann. Phys. 203, 255–307 (1990), and references therein.
    [CrossRef]
  2. P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
    [CrossRef]
  3. P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: Dirichlet and Neumann boundary conditions,” Appl. Opt. 32, 2848–2851 (1993).
    [CrossRef] [PubMed]
  4. C. Macaskill, B. J. Kachoyan, “Iterative methods for scattering from rough surfaces varying in either one or two dimensions,” presented at the ICO Topical Meeting on Atmospheric and Surface Scattering and Propagation, Florence, Italy, August 1991.
  5. C. Macaskill, B. J. Kachoyan, “Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces,” Appl. Opt. 32, 2839–2847 (1993).
    [CrossRef] [PubMed]
  6. N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
    [CrossRef]
  7. K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  8. A. J. Stoddard, “An iterative method for scattering from rough dielectric or conducting interfaces,” Waves Random Media 2, 235–251 (1992), and references therein.
    [CrossRef]

1993 (2)

1992 (2)

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

A. J. Stoddard, “An iterative method for scattering from rough dielectric or conducting interfaces,” Waves Random Media 2, 235–251 (1992), and references therein.
[CrossRef]

1990 (1)

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a grating,” Ann. Phys. 203, 255–307 (1990), and references therein.
[CrossRef]

1987 (1)

1984 (1)

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Garcia, N.

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Kachoyan, B. J.

C. Macaskill, B. J. Kachoyan, “Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces,” Appl. Opt. 32, 2839–2847 (1993).
[CrossRef] [PubMed]

C. Macaskill, B. J. Kachoyan, “Iterative methods for scattering from rough surfaces varying in either one or two dimensions,” presented at the ICO Topical Meeting on Atmospheric and Surface Scattering and Propagation, Florence, Italy, August 1991.

Macaskill, C.

C. Macaskill, B. J. Kachoyan, “Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces,” Appl. Opt. 32, 2839–2847 (1993).
[CrossRef] [PubMed]

C. Macaskill, B. J. Kachoyan, “Iterative methods for scattering from rough surfaces varying in either one or two dimensions,” presented at the ICO Topical Meeting on Atmospheric and Surface Scattering and Propagation, Florence, Italy, August 1991.

Maradudin, A. A.

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: Dirichlet and Neumann boundary conditions,” Appl. Opt. 32, 2848–2851 (1993).
[CrossRef] [PubMed]

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a grating,” Ann. Phys. 203, 255–307 (1990), and references therein.
[CrossRef]

McGurn, A. R.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a grating,” Ann. Phys. 203, 255–307 (1990), and references therein.
[CrossRef]

Mendez, E. R.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a grating,” Ann. Phys. 203, 255–307 (1990), and references therein.
[CrossRef]

K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

Michel, T.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a grating,” Ann. Phys. 203, 255–307 (1990), and references therein.
[CrossRef]

O’Donnell, K. A.

Stoddard, A. J.

A. J. Stoddard, “An iterative method for scattering from rough dielectric or conducting interfaces,” Waves Random Media 2, 235–251 (1992), and references therein.
[CrossRef]

Stoll, E.

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Tran, P.

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: Dirichlet and Neumann boundary conditions,” Appl. Opt. 32, 2848–2851 (1993).
[CrossRef] [PubMed]

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

Ann. Phys. (1)

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a grating,” Ann. Phys. 203, 255–307 (1990), and references therein.
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Phys. Rev. B (1)

P. Tran, A. A. Maradudin, “Scattering of a scalar beam from a two-dimensional randomly rough hard wall: enhanced backscattering,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

Phys. Rev. Lett. (1)

N. Garcia, E. Stoll, “Monte Carlo calculation for electromagnetic wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Waves Random Media (1)

A. J. Stoddard, “An iterative method for scattering from rough dielectric or conducting interfaces,” Waves Random Media 2, 235–251 (1992), and references therein.
[CrossRef]

Other (1)

C. Macaskill, B. J. Kachoyan, “Iterative methods for scattering from rough surfaces varying in either one or two dimensions,” presented at the ICO Topical Meeting on Atmospheric and Surface Scattering and Propagation, Florence, Italy, August 1991.

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Figures (2)

Fig. 1
Fig. 1

Plot of the differential reflection coefficient (DRC) for the scattering of a p-polarized beam from a rough surface characterized by rms height σ = 1.0λ and lateral correlation length a = 2.0λ. The iteration uses the inhomogeneous term as the initial guess. The result is the average of 100 surface realizations. The dashed curve is the first iteration, and the solid curves are the sixth and the tenth iterations, (a) In-plane scattering (φ = 0°), p-polarized outgoing wave; (b) out-of-plane (φ = 90°) scattering, s-polarized outgoing wave; (c) in-plane scattering, s-polarized outgoing wave; (d) out-of-plane scattering, p-polarized outgoing wave.

Fig. 2
Fig. 2

Plot of the DRC for the same surface as in Fig. 1. The solid curve is the sixth iteration of Fig. 1, and the dashed curve is the second iteration of the iteration scheme in which the result from the surface with rms height σ − dσ is used as the initial guess for the iteration. ME is the mean error, the percentage difference between the two results averaged over the number of scattering angles; Max is the maximum error.

Equations (8)

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B inc ( r ) + 1 4 π G o × [ n × B ( r ) ] d S = { B ( r ) z > ζ ( r ) 0 z < ζ ( r ) ,
j ( r ) = 2 j inc ( r ) + 1 2 π n ( r ) × P G o × j ( r ) d S ,
j x ( R i ) = 2 j x inc ( R i ) + 1 2 π L 2 N 2 i j C ( R j ) C ( R j ) × α [ j x ( R j ) ( z x ζ x j ζ y i ) + j y ( R j ) x ( ζ y i ζ y j ) ] , j x ( R i ) = 2 j y inc ( R i ) + 1 2 π L 2 N 2 i j C ( R j ) C ( R i ) × α [ j y ( R j ) ( z ζ y j x ζ x i ) + j x ( R j ) ( ζ x i ζ x j ) ] ,
B s c ( r ) = K , γ b ̂ γ ( K ) B γ ( K , z ) e i K · R e ipz ,
R γ Ω = L 4 ( 2 π ) 2 ( ω c ) 3 ( cos θ ) 2 f inc [ | B γ ( K ) | 2 | B γ ( K ) | 2 ] ,
B inc ( r ) = 2 π W 2 L 2 K ( ω / c ) b ̂ inc ( K ) e i K · R e ipz × exp [ ( K K o ) 2 W 2 / 2 ] ,
b ̂ p inc ( K x , K y , p ) = 1 ( ω / c ) ( K x 2 + p 2 ) 1 / 2 × [ K x K y , ( K x 2 + p 2 ) K y p ] , b ̂ s inc ( K x , K y , p ) = 1 ( K x 2 + p 2 ) 1 / 2 ( p , 0 , K x ) .
f inc = 4 π 2 W 4 L 2 K ω / c p exp [ ( K K o ) 2 W 2 ] .

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