Abstract

In this article, the fields scattered by coated cylinders, a rough layer, and an object below a rough surface are computed by the efficient propagation-inside-layer-expansion (PILE) method combined with the physical optics (PO) approximation to accelerate the calculation of the local interactions on the non-illuminated scatterer, which is assumed to be perfectly conducting. The PILE method is based on the method of moments, and the impedance matrix of the two scatterers is then inverted by blocks from a Taylor series expansion of the inverse of the Schur complement. Its main interest is that it is rigorous, with a simple formulation and a straightforward physical interpretation. In addition, one of the advantages of PILE is to be able to hybridize methods (rigorous or asymptotic) valid for a single scatterer. Then, in high frequencies, the hybridization with PO allows us to significantly reduce the complexity in comparison to a direct lower–upper inversion of the impedance matrix of the two scatterers without loss in accuracy.

© 2013 Optical Society of America

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    [CrossRef]
  2. D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
    [CrossRef]
  3. X. Wang, C.-F. Wang, Y.-B. G. Gan, and L.-W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Progr. Electromagn. Res. 40, 207–227 (2003).
  4. N. Déchamps, N. De Beaucoudrey, C. Bourlier, and S. Toutain, “Fast numerical method for electromagnetic scattering by rough layered interfaces: propagation-inside-layer expansion method,” J. Opt. Soc. Am. A 23, 359–369 (2006).
    [CrossRef]
  5. C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
    [CrossRef]
  6. N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to an updated BMIA/CAG approach,” IEEE Trans. Antennas Propag. 55, 2790–2802 (2007).
    [CrossRef]
  7. N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration,” IEEE Trans. Antennas Propag. 55, 3576–3586 (2007).
    [CrossRef]
  8. C. Bourlier, G. Kubické, and N. Déchamps, “A fast method to compute scattering by a buried object under a randomly rough surface: PILE combined to FB-SA,” J. Opt. Soc. Am. A 25, 891–902 (2008).
    [CrossRef]
  9. S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Progr. Electromagn. Res. 78, 25–38 (2008).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. H. T. Chou and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward–backward method,” Radio Sci. 33, 1277–1287 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. D. Torrungrueng, J. T. Johnson, and H. T. Chou, “Some issues related to the novel spectral acceleration method for the fast computation of radiation/scattering from one-dimensional extremely large scale quasi-planar structures,” Radio Sci. 37(2):3, 1–20 (2002).
    [CrossRef]
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  26. L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
    [CrossRef]
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    [CrossRef]
  28. G. Kubické, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined to FB-SA,” IEEE Trans. Antennas Propag. 18, 495–519 (2008).
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    [CrossRef]
  30. G. Kubické and C. Bourlier, “A fast hybrid method for scattering from a large object with dihedral effects above a large rough surface,” IEEE Trans. Antennas Propag. 59, 189–198 (2011).
    [CrossRef]
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    [CrossRef]
  33. L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).
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2013

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophysics 11, 177–183 (2013).
[CrossRef]

G. P. Zouros, “Oblique electromagnetic scattering from lossless or lossy composite elliptical dielectric cylinders,” J. Opt. Soc. Am. A 30, 196–205 (2013).
[CrossRef]

2012

A. F. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

2011

2010

G. Kubické, C. Bourlier, and J. Saillard, “Scattering from canonical objects above a sea-like 1D rough surface from a rigorous fast method,” Waves Random Complex Media 20, 156–178 (2010).
[CrossRef]

F. Frezza, C. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

2008

S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Progr. Electromagn. Res. 78, 25–38 (2008).

C. Bourlier, G. Kubické, and N. Déchamps, “A fast method to compute scattering by a buried object under a randomly rough surface: PILE combined to FB-SA,” J. Opt. Soc. Am. A 25, 891–902 (2008).
[CrossRef]

G. Kubické, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined to FB-SA,” IEEE Trans. Antennas Propag. 18, 495–519 (2008).

2007

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to an updated BMIA/CAG approach,” IEEE Trans. Antennas Propag. 55, 2790–2802 (2007).
[CrossRef]

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration,” IEEE Trans. Antennas Propag. 55, 3576–3586 (2007).
[CrossRef]

2006

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

N. Déchamps, N. De Beaucoudrey, C. Bourlier, and S. Toutain, “Fast numerical method for electromagnetic scattering by rough layered interfaces: propagation-inside-layer expansion method,” J. Opt. Soc. Am. A 23, 359–369 (2006).
[CrossRef]

2003

X. Wang, C.-F. Wang, Y.-B. G. Gan, and L.-W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Progr. Electromagn. Res. 40, 207–227 (2003).

2002

J. T. Johnson, “A numerical study of scattering from an object above a rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2002).
[CrossRef]

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

A. Iodice, “Forward–backward method for scattering from dielectric rough surfaces,” IEEE Trans. Antennas Propag. 50, 901–911 (2002).
[CrossRef]

D. Torrungrueng, J. T. Johnson, and H. T. Chou, “Some issues related to the novel spectral acceleration method for the fast computation of radiation/scattering from one-dimensional extremely large scale quasi-planar structures,” Radio Sci. 37(2):3, 1–20 (2002).
[CrossRef]

2000

H. T. Chou and J. T. Johnson, “Formulation of the forward-backward method using novel spectra acceleration for the modeling of scattering from impedance rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 605–607 (2000).
[CrossRef]

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656–1668 (2000).
[CrossRef]

1998

H. T. Chou and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward–backward method,” Radio Sci. 33, 1277–1287 (1998).
[CrossRef]

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward–backward method for scattering from imperfect conductors,” IEEE Trans. Antennas Propag. 46, 101–107 (1998).
[CrossRef]

1996

D. A. Kapp and G. S. Brown, “A new numerical method for rough-surface scattering calculations,” IEEE Trans. Antennas Propag. 44, 711–722 (1996).
[CrossRef]

R. J. Adams and G. S. Brown, “An iterative solution of one-dimensional rough surface scattering problems based on a factorization of the Helmholtz operator,” IEEE Trans. Antennas Propag. 47, 765–767 (1996).
[CrossRef]

1995

L. Tsang, C. H. Chang, K. Pak, and H. Sangani, “Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method,” IEEE Trans. Antennas Propag. 43, 851–859 (1995).
[CrossRef]

1993

L. Tsang, C. H. Chang, and H. Sangani, “A banded matrix iterative approach to Monte Carlo simulations of scattering of waves by large scale random rough surface problems: TM case,” Electron. Lett. 29, 1666–1667 (1993).
[CrossRef]

L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
[CrossRef]

1988

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

Adams, R. J.

R. J. Adams and G. S. Brown, “An iterative solution of one-dimensional rough surface scattering problems based on a factorization of the Helmholtz operator,” IEEE Trans. Antennas Propag. 47, 765–767 (1996).
[CrossRef]

Ahmed, S.

S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Progr. Electromagn. Res. 78, 25–38 (2008).

Ao, C. O.

L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).

Beaucoudrey, N. De

Bourlier, C.

G. Kubické and C. Bourlier, “A fast hybrid method for scattering from a large object with dihedral effects above a large rough surface,” IEEE Trans. Antennas Propag. 59, 189–198 (2011).
[CrossRef]

G. Kubické, C. Bourlier, and J. Saillard, “Scattering from canonical objects above a sea-like 1D rough surface from a rigorous fast method,” Waves Random Complex Media 20, 156–178 (2010).
[CrossRef]

C. Bourlier, G. Kubické, and N. Déchamps, “A fast method to compute scattering by a buried object under a randomly rough surface: PILE combined to FB-SA,” J. Opt. Soc. Am. A 25, 891–902 (2008).
[CrossRef]

G. Kubické, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined to FB-SA,” IEEE Trans. Antennas Propag. 18, 495–519 (2008).

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to an updated BMIA/CAG approach,” IEEE Trans. Antennas Propag. 55, 2790–2802 (2007).
[CrossRef]

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration,” IEEE Trans. Antennas Propag. 55, 3576–3586 (2007).
[CrossRef]

N. Déchamps, N. De Beaucoudrey, C. Bourlier, and S. Toutain, “Fast numerical method for electromagnetic scattering by rough layered interfaces: propagation-inside-layer expansion method,” J. Opt. Soc. Am. A 23, 359–369 (2006).
[CrossRef]

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media, 2nd ed. (Academic, 1980).

Brown, G. S.

D. A. Kapp and G. S. Brown, “A new numerical method for rough-surface scattering calculations,” IEEE Trans. Antennas Propag. 44, 711–722 (1996).
[CrossRef]

R. J. Adams and G. S. Brown, “An iterative solution of one-dimensional rough surface scattering problems based on a factorization of the Helmholtz operator,” IEEE Trans. Antennas Propag. 47, 765–767 (1996).
[CrossRef]

Chang, C. H.

L. Tsang, C. H. Chang, K. Pak, and H. Sangani, “Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method,” IEEE Trans. Antennas Propag. 43, 851–859 (1995).
[CrossRef]

L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
[CrossRef]

L. Tsang, C. H. Chang, and H. Sangani, “A banded matrix iterative approach to Monte Carlo simulations of scattering of waves by large scale random rough surface problems: TM case,” Electron. Lett. 29, 1666–1667 (1993).
[CrossRef]

Chou, H. T.

D. Torrungrueng, J. T. Johnson, and H. T. Chou, “Some issues related to the novel spectral acceleration method for the fast computation of radiation/scattering from one-dimensional extremely large scale quasi-planar structures,” Radio Sci. 37(2):3, 1–20 (2002).
[CrossRef]

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656–1668 (2000).
[CrossRef]

H. T. Chou and J. T. Johnson, “Formulation of the forward-backward method using novel spectra acceleration for the modeling of scattering from impedance rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 605–607 (2000).
[CrossRef]

H. T. Chou and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward–backward method,” Radio Sci. 33, 1277–1287 (1998).
[CrossRef]

Déchamps, N.

C. Bourlier, G. Kubické, and N. Déchamps, “A fast method to compute scattering by a buried object under a randomly rough surface: PILE combined to FB-SA,” J. Opt. Soc. Am. A 25, 891–902 (2008).
[CrossRef]

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration,” IEEE Trans. Antennas Propag. 55, 3576–3586 (2007).
[CrossRef]

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to an updated BMIA/CAG approach,” IEEE Trans. Antennas Propag. 55, 2790–2802 (2007).
[CrossRef]

N. Déchamps, N. De Beaucoudrey, C. Bourlier, and S. Toutain, “Fast numerical method for electromagnetic scattering by rough layered interfaces: propagation-inside-layer expansion method,” J. Opt. Soc. Am. A 23, 359–369 (2006).
[CrossRef]

DeRaad, L. L.

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward–backward method for scattering from imperfect conductors,” IEEE Trans. Antennas Propag. 46, 101–107 (1998).
[CrossRef]

Ding, K.-H.

L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).

Fiaz, A. F.

A. F. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Fiaz, M. A.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophysics 11, 177–183 (2013).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teutolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies, 2nd ed. (Cambridge University, 1992).

Frezza, F.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophysics 11, 177–183 (2013).
[CrossRef]

A. F. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, C. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

Gan, Y.-B. G.

X. Wang, C.-F. Wang, Y.-B. G. Gan, and L.-W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Progr. Electromagn. Res. 40, 207–227 (2003).

Holliday, D.

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward–backward method for scattering from imperfect conductors,” IEEE Trans. Antennas Propag. 46, 101–107 (1998).
[CrossRef]

Iodice, A.

A. Iodice, “Forward–backward method for scattering from dielectric rough surfaces,” IEEE Trans. Antennas Propag. 50, 901–911 (2002).
[CrossRef]

Ishimaru, A.

L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
[CrossRef]

Johnson, J. T.

D. Torrungrueng, J. T. Johnson, and H. T. Chou, “Some issues related to the novel spectral acceleration method for the fast computation of radiation/scattering from one-dimensional extremely large scale quasi-planar structures,” Radio Sci. 37(2):3, 1–20 (2002).
[CrossRef]

J. T. Johnson, “A numerical study of scattering from an object above a rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2002).
[CrossRef]

H. T. Chou and J. T. Johnson, “Formulation of the forward-backward method using novel spectra acceleration for the modeling of scattering from impedance rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 605–607 (2000).
[CrossRef]

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656–1668 (2000).
[CrossRef]

H. T. Chou and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward–backward method,” Radio Sci. 33, 1277–1287 (1998).
[CrossRef]

Kapp, D. A.

D. A. Kapp and G. S. Brown, “A new numerical method for rough-surface scattering calculations,” IEEE Trans. Antennas Propag. 44, 711–722 (1996).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).

Kubické, G.

G. Kubické and C. Bourlier, “A fast hybrid method for scattering from a large object with dihedral effects above a large rough surface,” IEEE Trans. Antennas Propag. 59, 189–198 (2011).
[CrossRef]

G. Kubické, C. Bourlier, and J. Saillard, “Scattering from canonical objects above a sea-like 1D rough surface from a rigorous fast method,” Waves Random Complex Media 20, 156–178 (2010).
[CrossRef]

C. Bourlier, G. Kubické, and N. Déchamps, “A fast method to compute scattering by a buried object under a randomly rough surface: PILE combined to FB-SA,” J. Opt. Soc. Am. A 25, 891–902 (2008).
[CrossRef]

G. Kubické, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined to FB-SA,” IEEE Trans. Antennas Propag. 18, 495–519 (2008).

Kuo, C.-H.

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Lawrence, D. E.

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

Lee, S.-C.

Li, L.-W.

X. Wang, C.-F. Wang, Y.-B. G. Gan, and L.-W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Progr. Electromagn. Res. 40, 207–227 (2003).

Moghaddam, M.

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Naqvi, Q. A.

S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Progr. Electromagn. Res. 78, 25–38 (2008).

Pajewski, C.

Pajewski, L.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophysics 11, 177–183 (2013).
[CrossRef]

A. F. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Pak, K.

L. Tsang, C. H. Chang, K. Pak, and H. Sangani, “Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method,” IEEE Trans. Antennas Propag. 43, 851–859 (1995).
[CrossRef]

Pawliuk, P.

Phu, P.

L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
[CrossRef]

Ponti, C.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophysics 11, 177–183 (2013).
[CrossRef]

A. F. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, C. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teutolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies, 2nd ed. (Cambridge University, 1992).

Saillard, J.

G. Kubické, C. Bourlier, and J. Saillard, “Scattering from canonical objects above a sea-like 1D rough surface from a rigorous fast method,” Waves Random Complex Media 20, 156–178 (2010).
[CrossRef]

G. Kubické, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined to FB-SA,” IEEE Trans. Antennas Propag. 18, 495–519 (2008).

Sangani, H.

L. Tsang, C. H. Chang, K. Pak, and H. Sangani, “Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method,” IEEE Trans. Antennas Propag. 43, 851–859 (1995).
[CrossRef]

L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
[CrossRef]

L. Tsang, C. H. Chang, and H. Sangani, “A banded matrix iterative approach to Monte Carlo simulations of scattering of waves by large scale random rough surface problems: TM case,” Electron. Lett. 29, 1666–1667 (1993).
[CrossRef]

Sarabandi, K.

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

Schettini, G.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophysics 11, 177–183 (2013).
[CrossRef]

A. F. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, C. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

St-Cyr, G. J.

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward–backward method for scattering from imperfect conductors,” IEEE Trans. Antennas Propag. 46, 101–107 (1998).
[CrossRef]

Teutolsky, S. A.

W. H. Press, S. A. Teutolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies, 2nd ed. (Cambridge University, 1992).

Thorsos, E. I.

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

Torrungrueng, D.

D. Torrungrueng, J. T. Johnson, and H. T. Chou, “Some issues related to the novel spectral acceleration method for the fast computation of radiation/scattering from one-dimensional extremely large scale quasi-planar structures,” Radio Sci. 37(2):3, 1–20 (2002).
[CrossRef]

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656–1668 (2000).
[CrossRef]

Toutain, S.

Tsang, L.

L. Tsang, C. H. Chang, K. Pak, and H. Sangani, “Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method,” IEEE Trans. Antennas Propag. 43, 851–859 (1995).
[CrossRef]

L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
[CrossRef]

L. Tsang, C. H. Chang, and H. Sangani, “A banded matrix iterative approach to Monte Carlo simulations of scattering of waves by large scale random rough surface problems: TM case,” Electron. Lett. 29, 1666–1667 (1993).
[CrossRef]

L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).

Vetterling, W. T.

W. H. Press, S. A. Teutolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies, 2nd ed. (Cambridge University, 1992).

Wang, C.-F.

X. Wang, C.-F. Wang, Y.-B. G. Gan, and L.-W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Progr. Electromagn. Res. 40, 207–227 (2003).

Wang, X.

X. Wang, C.-F. Wang, Y.-B. G. Gan, and L.-W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Progr. Electromagn. Res. 40, 207–227 (2003).

Yedlin, M.

Zouros, G. P.

Electron. Lett.

L. Tsang, C. H. Chang, and H. Sangani, “A banded matrix iterative approach to Monte Carlo simulations of scattering of waves by large scale random rough surface problems: TM case,” Electron. Lett. 29, 1666–1667 (1993).
[CrossRef]

IEEE Trans. Antennas Propag.

D. A. Kapp and G. S. Brown, “A new numerical method for rough-surface scattering calculations,” IEEE Trans. Antennas Propag. 44, 711–722 (1996).
[CrossRef]

R. J. Adams and G. S. Brown, “An iterative solution of one-dimensional rough surface scattering problems based on a factorization of the Helmholtz operator,” IEEE Trans. Antennas Propag. 47, 765–767 (1996).
[CrossRef]

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward–backward method for scattering from imperfect conductors,” IEEE Trans. Antennas Propag. 46, 101–107 (1998).
[CrossRef]

A. Iodice, “Forward–backward method for scattering from dielectric rough surfaces,” IEEE Trans. Antennas Propag. 50, 901–911 (2002).
[CrossRef]

L. Tsang, C. H. Chang, K. Pak, and H. Sangani, “Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method,” IEEE Trans. Antennas Propag. 43, 851–859 (1995).
[CrossRef]

G. Kubické, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined to FB-SA,” IEEE Trans. Antennas Propag. 18, 495–519 (2008).

G. Kubické and C. Bourlier, “A fast hybrid method for scattering from a large object with dihedral effects above a large rough surface,” IEEE Trans. Antennas Propag. 59, 189–198 (2011).
[CrossRef]

J. T. Johnson, “A numerical study of scattering from an object above a rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2002).
[CrossRef]

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

A. F. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to an updated BMIA/CAG approach,” IEEE Trans. Antennas Propag. 55, 2790–2802 (2007).
[CrossRef]

N. Déchamps and C. Bourlier, “Electromagnetic scattering from a rough layer: propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration,” IEEE Trans. Antennas Propag. 55, 3576–3586 (2007).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

H. T. Chou and J. T. Johnson, “Formulation of the forward-backward method using novel spectra acceleration for the modeling of scattering from impedance rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 605–607 (2000).
[CrossRef]

D. Torrungrueng, H. T. Chou, and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656–1668 (2000).
[CrossRef]

J. Acoust. Soc. Am.

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

J. Electromagn. Waves Appl.

L. Tsang, C. H. Chang, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to monte carlo simulations of large scale random rough surface scattering: TE case,” J. Electromagn. Waves Appl. 29, 1185–1200 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Near Surf. Geophysics

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophysics 11, 177–183 (2013).
[CrossRef]

Progr. Electromagn. Res.

S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Progr. Electromagn. Res. 78, 25–38 (2008).

X. Wang, C.-F. Wang, Y.-B. G. Gan, and L.-W. Li, “Electromagnetic scattering from a circular target above or below rough surface,” Progr. Electromagn. Res. 40, 207–227 (2003).

Radio Sci.

D. Torrungrueng, J. T. Johnson, and H. T. Chou, “Some issues related to the novel spectral acceleration method for the fast computation of radiation/scattering from one-dimensional extremely large scale quasi-planar structures,” Radio Sci. 37(2):3, 1–20 (2002).
[CrossRef]

H. T. Chou and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward–backward method,” Radio Sci. 33, 1277–1287 (1998).
[CrossRef]

Waves Random Complex Media

G. Kubické, C. Bourlier, and J. Saillard, “Scattering from canonical objects above a sea-like 1D rough surface from a rigorous fast method,” Waves Random Complex Media 20, 156–178 (2010).
[CrossRef]

Other

W. H. Press, S. A. Teutolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipies, 2nd ed. (Cambridge University, 1992).

L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2000).

L. M. Brekhovskikh, Waves in Layered Media, 2nd ed. (Academic, 1980).

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Figures (10)

Fig. 1.
Fig. 1.

Scattering from two scatterers where only one is illuminated. The source (incident field) is defined in medium Ω0.

Fig. 2.
Fig. 2.

RCS in decibel scale versus the scattering angle θsca. The radii of the two concentric circular cylinders are a1=3λ0 and a2=2λ0; their centers are C1=C2=(0,0); the relative permittivities of media {Ω0,Ω1,Ω2} are {εr0=1,εr1=2,εr2=4+0.05j}, respectively; and the wavelength inside Ω0 is λ0=1m. The incidence angle is θinc=0, and the polarization is TE. For the MoM, the number of samples per wavelength is Nλ0={10,20}.

Fig. 3.
Fig. 3.

Results for the same parameters as in Fig. 2, but for the TM polarization.

Fig. 4.
Fig. 4.

Ratio RCSLU/RCSAnalytical in decibels (difference in decibels) versus the scattering angle θsca. The parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Ratio RCSLU/RCSAnalytical in decibels (difference in decibels) versus the scattering angle θsca. The parameters are the same as in Fig. 3.

Fig. 6.
Fig. 6.

(a) Coated elliptical cylinder: semi-major axis a1=6λ0, a2=3λ0, semi-minor axis b1=4λ0, b2=λ0, centers C1=(0,0), C2=(1,1)λ0, and rotation angles α1=0, α2=10°. (b) Elliptical cylinder below a rough surface: a2=4λ0, b2=2λ0, C2=(0,3)λ0, α2=0, surface length L1=80λ0, center C1=(0,0)λ0, height standard deviation σz1=0.5λ0, correlation length Lc1=2λ0; the surface height autocorrelation function is Gaussian, and the parameter of the Thorsos wave is g=L1/4. (c) Rough layer: L1=L2=80λ0, σz1=0.5λ0, σz2=0.1λ0, Lc1=2λ0, Lc2=λ0, C1=(0,0)λ0, C2=(0,2)λ0; the surface height autocorrelation function for both surfaces is Gaussian, and the parameter of the Thorsos wave is g=L1/4. In addition; for the three scenarios, the incidence angle is θinc=30°, the relative permittivities of media {Ω0,Ω1,Ω2} are {1,2+0.1j,j(PC)}, and the total number of unknowns are N={1047,2434,3040}, for scenarios (a), (b), and (c), respectively.

Fig. 7.
Fig. 7.

(a) RCS in dBm versus the scattering angle θsca; (b) NRCS in dB versus the scattering angle θsca; (c) NRCS in dB versus the scattering angle θsca. The parameters of the three scenarios are given in the caption of Fig. 6, and the polarization is TE.

Fig. 8.
Fig. 8.

Same results as in Fig. 7, but the results with hybridization are added.

Fig. 9.
Fig. 9.

Computation time versus the number of unknowns. Scenario 1 is chosen, and to increase the number of unknowns, the problem size artificially increases by applying a scaling on the sizes of the cylinders.

Fig. 10.
Fig. 10.

Same results as in Fig. 8, but with the following changes: (a) Fig. 10(a): scenario 1 of Fig. 6(a) but a1=2λ0, a2=λ0, b1=2λ0, b2=λ0 (smaller cylinders) and C1=(0.5,0.5)λ0; (b) Fig. 10(b): Scenario 3 of Fig. 6(c) but σz2=0.5λ0 (rougher lower surface).

Tables (2)

Tables Icon

Table 1. Computation Times in Seconds to Obtain the Results of Figs. 2 and 3

Tables Icon

Table 2. Values of the Norm M¯c of the Characteristic Matrix Defined by Eq. (13)

Equations (37)

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X=[X1X2],
X1=[ψ1(r1)ψ1(rN1)ψ1(r1)nψ1(rN1)n]T,rp[1;N1]S1,
X2=[ψ2(r1)ψ2(rN2)ψ2(r2)nψ2(rN2)n]T,rp[1;N2]S2,
b=[b1b2]=[ψinc(r1)ψinc(rN1)00N1timesb1T,rS1002N2timesb2T,rS2]T.
Z¯=[A¯1B¯10¯0¯C¯11ρ01D¯1A¯21B¯21A¯121ρ01B¯12A¯2B¯20¯0¯C¯21ρ12D¯2]=[Z¯1Z¯21Z¯12Z¯2],
Z¯1=[A¯1B¯1C¯11ρ01D¯1],Z¯2=[A¯2B¯2C¯21ρ12D¯2],
Z¯21=[0¯0¯A¯21B¯21],Z¯12=[A¯121ρ01B¯120¯0¯].
{ψsca,0(r)=S1[ψ0(r)g0(r,r)ng0(r,r)ψ0(r)n]dSψsca,1(r)=p=1p=2spSp[ψp(r)g1(r,r)ng1(r,r)ψp(r)n]dSψsca,2(r)=S2[ψ2(r)g2(r,r)ng2(r,r)ψ2(r)n]dS,
RCS=limr2πr|ψsca,0ψinc,0|2=|ψsca,0|24|k0|,
ψsca,0=1ψinc,0S1[jksca·n^0ψ0(r)+ψ0(r)n]ejksca·rdS,
X1=[p=0p=PPILEM¯cp]Z¯11b1=p=0p=PPILEY1(p),
{Y1(0)=Z¯11b1forp=0Y1(p)=M¯cY1(p1)forp>0,
M¯c=Z¯11Z¯21Z¯21Z¯12.
NRCS(θinc,θsca)=limrrpsca,0Pinc=116πη0k0|ψsca,0|2Pinc,
Pinc=gcosθinc2η0π2[11+2tan2θinc2k02g2cos2θinc],
εPILE=normθsca(RCSPILERCSLU)normθsca(RCSLU),
ψ2(r)=2{ψinc,1(r)rS2,Ill0rS2,Shaandψ2(r)n=0S2,TMpolarization,
ψ2(r)n=2{ψinc,1(r)nrS2,Ill0rS2,Shaandψ2(r)=0S2,TEpolarization,
Z12,mn=Z12,mn1sgn[(r2,mr1,n)·n^2,m]2=Z12,mn1+sgn[(x2,mx1,n)v2,mγ2,m(z2,mz1,n)v2,m]2.
v=Z¯21u=Z¯21Z¯12Y1(0)=D¯[A¯121ρ01B¯12][w1w2]=D¯[A¯12w1+1ρ01B¯12w2],
A1,mn={jk0vn|Δn|4H1(1)(k0rnrm)rnrm×[γn(xnxm)(znzm)]formn+12vn|Δn|4πγ(xn)1+γ2(xn)form=n,
B1,mn=j|Δn|1+γn24{[1+2jπln(0.164k01+γn2|Δn|)]form=nH0(1)(k0rnrm)fornm,
C1,mn={jk1vn|Δn|4H1(1)(k1rnrm)rnrm[γn(xnxm)(znzm)]formn12vn|Δn|4πγ(xn)1+γ2(xn)form=n,
D1,mn=j|Δn|1+γn24{[1+2jπln(0.164k11+γn2|Δn|)]form=nH0(1)(k1rnrm)formn,
{A12,mn=jk1v1,n|Δ1,n|4H1(1)(k1r1,nr2,m)r1,nr2,m×[γ1,n(x1,nx2,m)(z1,nz2,m)]A21,mn=jk1v2,n|Δ2,n|4H1(1)(k1r2,nr1,m)r2,nr1,m×[γ2,n(x2,nx1,m)(z2,nz1,m)]B12,mn=j|Δ1,n|1+γ1,n24H0(1)(k1r1,nr2,m)B21,mn=j|Δ2,n|1+γ2,n24H0(1)(k1r2,nr1,m).
TE:Z¯2=B¯2,X2=ψ2n.
TM:Z¯2=A¯2,X2=ψ2.
{TE:Z¯12=[A¯121ρ01B¯12],Z¯21=[0¯B¯21]TM:Z¯12=[A¯121ρ01B¯12],Z¯21=[0¯A¯21].
ψ0(r,θ)=n=n=+[AnJn(k0r)+BnHn(1)(k0r)]ejnθwithAn=ψinc,0ejnθinc,
ψ1(r,θ)=n=n=+[CnJn(k1r)+DnHn(1)(k1r)]ejnθ,
ψ2(r,θ)=n=n=+EnJn(k2r)ejnθ,
{ψ0(a1,θ)=ψ1(a1,θ)ψ1(a2,θ)=ψ2(a2,θ)ψ0r|r=a1=ρ01ψ1r|r=a1ψ1r|r=a2=ρ12ψ2r|r=a2.
[Hn(1)(k0a1)Jn(k1a1)Hn(1)(k1a1)0k0Hn(1)(k0a1)ρ01k1Jn(k1a1)ρ01k1Hn(1)(k1a1)00Jn(k1a2)Hn(1)(k1a2)Jn(k2a2)0k1Jn(k1a2)k1Hn(1)(k1a2)k2ρ12Jn(k2a2)][BnCnDnEn]=[AnJn(k0a1)Ank0Jn(k0a1)00].
RCS(θinc,θsca)=4k0|n=n=+Bnejn(θinc+θscaπ)|2.
B12,mnn|r2,m=jk1v2,m|Δ1,n|1+γ1,n2H114r121+γ2,m2(z12γ2,mx12)
A12,mnn|r2,m=jk1v1,n|Δ1,n|v2,m41+γ2,m2[w00+w10(γ1,n+γ2,m)+w11γ1,nγ2,m],
{w00=k1z122H10r122+(x122z122)H11r123w10=x12z12r123(2H11H10k1r12)w11=k1x122H10r122+(z122x122)H11r123,

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