Abstract

The forward–backward method with a novel spectral acceleration algorithm (FB/NSA) has been shown to be a highly efficient O(Ntot) iterative method of moments, where Ntot is the total number of unknowns to be solved, for the computation of electromagnetic (EM) wave scattering from both one-dimensional and two-dimensional (2-D) rough surfaces. The efficiency of the method makes studies of backscattering enhancement from moderately rough impedance surfaces at large incident angles tractable. Variations in the characteristics of backscattering enhancement with incident angle, surface impedance, polarization, and surface statistics are investigated by use of the 2-D FB/NSA method combined with parallel computing techniques. The surfaces considered are Gaussian random processes with an isotropic Gaussian spectrum and root-mean-square surface heights and slopes ranging from 0.5λ to λ and from 0.5 to 1.0, respectively, where λ is the EM wavelength in free space. Incident angles ranging from normal incidence up to 70° are considered in this study. It is found that backscattering enhancement depends strongly on all parameters of interest.

© 2001 Optical Society of America

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References

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  1. A. Ishimaru, “Experimental and theoretical studies on enhanced backscattering from scatterers and rough surfaces,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 1–15.
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    [Crossref]
  3. K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering from random rough surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [Crossref]
  4. M. J. Kim, J. Dainty, A. Friberg, A. Sant, “Experimental study of enhanced backscattering from one- and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
    [Crossref]
  5. A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).
  6. P. Phu, A. Ishimaru, Y. Kuga, “Co-polarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
    [Crossref]
  7. A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).
  8. C. Hsieh, A. K. Fung, “Application of an extended IEM to multiple surface scattering and backscatter enhancement,” J. Electromagn. Waves Appl. 13, 121–135 (1999).
    [Crossref]
  9. E. Bahar, M. El-Shenawee, “Enhanced backscatter from one dimensional random rough surfaces—stationary phase approximations to full wave solutions,” J. Opt. Soc. Am. A 12, 151–161 (1995).
    [Crossref]
  10. P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
    [Crossref]
  11. J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
    [Crossref]
  12. K. Pak, L. Tsang, C. H. Chan, J. T. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995).
    [Crossref]
  13. K. Pak, L. Tsang, J. T. Johnson, “Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (1997).
    [Crossref]
  14. R. L. Wagner, J. M. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
    [Crossref]
  15. V. Jandhyala, E. Michielssen, S. Balasubramaniam, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
    [Crossref]
  16. R. F. Harrington, Field Computation by Moment Methods (Krieger, Malarbar, Fla., 1982).
  17. H.-T. Chou, 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]
  18. H.-T. Chou, J. T. Johnson, “Formulation of forward–backward method using novel spectral acceleration for the modeling of scattering from impedance rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 605–607 (2000).
    [Crossref]
  19. D. Torrungrueng, H.-T. Chou, 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]
  20. D. Torrungrueng, J. T. Johnson, H.-T. Chou, “Some issues related to the novel spectral acceleration (NSA) method for the fast computation of radiation/scattering from one-dimensional extremely large-scale quasi-planar structures,” manuscript available from the authors.
  21. D. Torrungrueng, J. T. Johnson, “The forward–backward method with a novel acceleration algorithm (FB/NSA) for the computation of scattering from two-dimensional large-scale impedance random rough surfaces,” Microwave Opt. Technol. Lett. 29, 232–236 (2001).
    [Crossref]
  22. D. Torrungrueng, “Applications of the novel spectral acceleration (NSA) algorithm for the computation of scattering from rough surfaces,” Ph.D. dissertation (Ohio State University, Columbus, Ohio, 2000).
  23. J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
    [Crossref]
  24. T. B. A. Senior, “Impedance boundary conditions for imperfectly conducting surface,” Appl. Sci. Res. Sect. B 8, 418–436 (1960).
    [Crossref]
  25. A. A. Maradudin, “The impedance boundary condition at a two-dimensional rough metal surface,” Opt. Commun. 116, 452–467 (1995).
    [Crossref]
  26. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  27. A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).
  28. S. T. McDaniel, “Acoustic and radar scattering from directional seas,” Waves Random Media 9, 537–549 (1999).
    [Crossref]

2001 (1)

D. Torrungrueng, J. T. Johnson, “The forward–backward method with a novel acceleration algorithm (FB/NSA) for the computation of scattering from two-dimensional large-scale impedance random rough surfaces,” Microwave Opt. Technol. Lett. 29, 232–236 (2001).
[Crossref]

2000 (2)

H.-T. Chou, J. T. Johnson, “Formulation of forward–backward method using novel spectral 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, 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]

1999 (3)

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
[Crossref]

S. T. McDaniel, “Acoustic and radar scattering from directional seas,” Waves Random Media 9, 537–549 (1999).
[Crossref]

C. Hsieh, A. K. Fung, “Application of an extended IEM to multiple surface scattering and backscatter enhancement,” J. Electromagn. Waves Appl. 13, 121–135 (1999).
[Crossref]

1998 (2)

V. Jandhyala, E. Michielssen, S. Balasubramaniam, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[Crossref]

H.-T. Chou, 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]

1997 (2)

R. L. Wagner, J. M. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
[Crossref]

K. Pak, L. Tsang, J. T. Johnson, “Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (1997).
[Crossref]

1996 (2)

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).

1995 (3)

1994 (2)

P. Phu, A. Ishimaru, Y. Kuga, “Co-polarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[Crossref]

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[Crossref]

1992 (1)

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

1991 (1)

A. Ishimaru, “Backscattering enhancement: from radar cross sections to electron and light localizations to rough-surface scattering,” IEEE Antennas Propag. Mag. 33, 7–11 (1991).
[Crossref]

1990 (1)

1987 (1)

1960 (1)

T. B. A. Senior, “Impedance boundary conditions for imperfectly conducting surface,” Appl. Sci. Res. Sect. B 8, 418–436 (1960).
[Crossref]

Bahar, E.

Balasubramaniam, S.

V. Jandhyala, E. Michielssen, S. Balasubramaniam, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[Crossref]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Celli, V.

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[Crossref]

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Chan, C. H.

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

K. Pak, L. Tsang, C. H. Chan, J. T. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995).
[Crossref]

Chan, T. K.

A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).

Chew, W. C.

V. Jandhyala, E. Michielssen, S. Balasubramaniam, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[Crossref]

R. L. Wagner, J. M. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
[Crossref]

Chou, H.-T.

H.-T. Chou, J. T. Johnson, “Formulation of forward–backward method using novel spectral 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, 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, 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]

Dainty, J.

Dainty, J. C.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

El-Shenawee, M.

Friberg, A.

Fung, A. K.

C. Hsieh, A. K. Fung, “Application of an extended IEM to multiple surface scattering and backscatter enhancement,” J. Electromagn. Waves Appl. 13, 121–135 (1999).
[Crossref]

Gu, Z. H.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Krieger, Malarbar, Fla., 1982).

Hsieh, C.

C. Hsieh, A. K. Fung, “Application of an extended IEM to multiple surface scattering and backscatter enhancement,” J. Electromagn. Waves Appl. 13, 121–135 (1999).
[Crossref]

Ishimaru, A.

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).

P. Phu, A. Ishimaru, Y. Kuga, “Co-polarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[Crossref]

A. Ishimaru, “Backscattering enhancement: from radar cross sections to electron and light localizations to rough-surface scattering,” IEEE Antennas Propag. Mag. 33, 7–11 (1991).
[Crossref]

A. Ishimaru, “Experimental and theoretical studies on enhanced backscattering from scatterers and rough surfaces,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 1–15.

Jandhyala, V.

V. Jandhyala, E. Michielssen, S. Balasubramaniam, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[Crossref]

Johnson, J. T.

D. Torrungrueng, J. T. Johnson, “The forward–backward method with a novel acceleration algorithm (FB/NSA) for the computation of scattering from two-dimensional large-scale impedance random rough surfaces,” Microwave Opt. Technol. Lett. 29, 232–236 (2001).
[Crossref]

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

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
[Crossref]

H.-T. Chou, 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]

K. Pak, L. Tsang, J. T. Johnson, “Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (1997).
[Crossref]

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

K. Pak, L. Tsang, C. H. Chan, J. T. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995).
[Crossref]

Kim, M. J.

Kong, J. A.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
[Crossref]

Kuga, Y.

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).

P. Phu, A. Ishimaru, Y. Kuga, “Co-polarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[Crossref]

Le, C.

A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).

Lu, J. Q.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Maradudin, A. A.

A. A. Maradudin, “The impedance boundary condition at a two-dimensional rough metal surface,” Opt. Commun. 116, 452–467 (1995).
[Crossref]

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[Crossref]

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

McDaniel, S. T.

S. T. McDaniel, “Acoustic and radar scattering from directional seas,” Waves Random Media 9, 537–549 (1999).
[Crossref]

McGurn, A. R.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Mendez, E. R.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

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

Michel, T.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Michielssen, E.

V. Jandhyala, E. Michielssen, S. Balasubramaniam, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[Crossref]

Nieto-Vesperinas, M.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

O’Donnell, K. A.

Pak, K.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
[Crossref]

K. Pak, L. Tsang, J. T. Johnson, “Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (1997).
[Crossref]

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

K. Pak, L. Tsang, C. H. Chan, J. T. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995).
[Crossref]

Phu, P.

P. Phu, A. Ishimaru, Y. Kuga, “Co-polarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[Crossref]

Sant, A.

Sant, A. J.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Sengers, L. A.

A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).

Senior, T. B. A.

T. B. A. Senior, “Impedance boundary conditions for imperfectly conducting surface,” Appl. Sci. Res. Sect. B 8, 418–436 (1960).
[Crossref]

Shin, R. T.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
[Crossref]

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

Song, J. M.

R. L. Wagner, J. M. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
[Crossref]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Torrungrueng, D.

D. Torrungrueng, J. T. Johnson, “The forward–backward method with a novel acceleration algorithm (FB/NSA) for the computation of scattering from two-dimensional large-scale impedance random rough surfaces,” Microwave Opt. Technol. Lett. 29, 232–236 (2001).
[Crossref]

D. Torrungrueng, H.-T. Chou, 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]

D. Torrungrueng, “Applications of the novel spectral acceleration (NSA) algorithm for the computation of scattering from rough surfaces,” Ph.D. dissertation (Ohio State University, Columbus, Ohio, 2000).

Tran, P.

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[Crossref]

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Tsang, L.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
[Crossref]

K. Pak, L. Tsang, J. T. Johnson, “Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (1997).
[Crossref]

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

K. Pak, L. Tsang, C. H. Chan, J. T. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995).
[Crossref]

Voronovich, A. G.

A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).

Wagner, R. L.

R. L. Wagner, J. M. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
[Crossref]

Wallis, R. F.

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Appl. Sci. Res. Sect. B (1)

T. B. A. Senior, “Impedance boundary conditions for imperfectly conducting surface,” Appl. Sci. Res. Sect. B 8, 418–436 (1960).
[Crossref]

IEE Trans. Geosci. Remote Sens. (1)

V. Jandhyala, E. Michielssen, S. Balasubramaniam, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[Crossref]

IEEE Antennas Propag. Mag. (1)

A. Ishimaru, “Backscattering enhancement: from radar cross sections to electron and light localizations to rough-surface scattering,” IEEE Antennas Propag. Mag. 33, 7–11 (1991).
[Crossref]

IEEE Trans. Antennas Propag. (2)

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[Crossref]

R. L. Wagner, J. M. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (3)

H.-T. Chou, J. T. Johnson, “Formulation of forward–backward method using novel spectral 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, 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. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, K. Pak, “A numerical study of ocean polarimetric thermal emission,” IEEE Trans. Geosci. Remote Sens. 37, 8–20 (1999).
[Crossref]

J. Electromagn. Waves Appl. (1)

C. Hsieh, A. K. Fung, “Application of an extended IEM to multiple surface scattering and backscatter enhancement,” J. Electromagn. Waves Appl. 13, 121–135 (1999).
[Crossref]

J. Opt. Soc. Am. A (6)

Microwave Opt. Technol. Lett. (1)

D. Torrungrueng, J. T. Johnson, “The forward–backward method with a novel acceleration algorithm (FB/NSA) for the computation of scattering from two-dimensional large-scale impedance random rough surfaces,” Microwave Opt. Technol. Lett. 29, 232–236 (2001).
[Crossref]

Opt. Commun. (1)

A. A. Maradudin, “The impedance boundary condition at a two-dimensional rough metal surface,” Opt. Commun. 116, 452–467 (1995).
[Crossref]

Prog. Electromagn. Res. (1)

A. Ishimaru, C. Le, Y. Kuga, L. A. Sengers, T. K. Chan, “Polarimetric scattering theory for high slope rough surfaces,” Prog. Electromagn. Res. 14, 1–36 (1996).

Radio Sci. (2)

P. Phu, A. Ishimaru, Y. Kuga, “Co-polarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave frequencies,” Radio Sci. 29, 1275–1291 (1994).
[Crossref]

H.-T. Chou, 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]

Rev. Mex. Fis. (1)

A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 38, 343–397 (1992).

Waves Random Media (1)

S. T. McDaniel, “Acoustic and radar scattering from directional seas,” Waves Random Media 9, 537–549 (1999).
[Crossref]

Other (6)

D. Torrungrueng, “Applications of the novel spectral acceleration (NSA) algorithm for the computation of scattering from rough surfaces,” Ph.D. dissertation (Ohio State University, Columbus, Ohio, 2000).

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).

A. Ishimaru, “Experimental and theoretical studies on enhanced backscattering from scatterers and rough surfaces,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 1–15.

D. Torrungrueng, J. T. Johnson, H.-T. Chou, “Some issues related to the novel spectral acceleration (NSA) method for the fast computation of radiation/scattering from one-dimensional extremely large-scale quasi-planar structures,” manuscript available from the authors.

R. F. Harrington, Field Computation by Moment Methods (Krieger, Malarbar, Fla., 1982).

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Figures (14)

Fig. 1
Fig. 1

2-D rough-surface profile S illuminated by a tapered incident field Ei(x, y, z) centered at the origin and propagating in direction kˆi=xˆ sin θi cos ϕi+yˆ sin θi sin ϕi-zˆ cos θi.

Fig. 2
Fig. 2

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various incident angles (0°θi40°) for PEC Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 3
Fig. 3

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various incident angles (60°θi70°) for PEC Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 4
Fig. 4

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various incident angles (0°θi40°) for IBC Gaussian surfaces with relative permittivity r1=10.0+i10.0 and an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 5
Fig. 5

Comparison of Monte-Carlo 2-D FB–NSA results (150 realizations) with various incident angles (60°θi70°) for IBC Gaussian surfaces with relative permittivity r1=10.0+i10.0 and an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 6
Fig. 6

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various incident angles (0°θi40°) for PEC Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=0.5 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 7
Fig. 7

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various incident angles (60°θi70°) for PEC Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=0.5 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 8
Fig. 8

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various surface materials at θi=0° for Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 9
Fig. 9

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various surface materials at θi=40° for Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 10
Fig. 10

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various surface materials at θi=70° for Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 11
Fig. 11

Comparison of the normalized incoherent backscattering RCS (in decibels) computed by the Monte Carlo 2-D FB–NSA method (150 realizations) averaged over the three consecutive angles in 1-deg steps (including the backscattering angle) nearby the backscattering direction of interest with various surface materials for Gaussian surfaces with an isotropic Gaussian spectrum h/λ=σs=1.0 and lx=ly=2λ: (a) co-polarization, (b) cross polarization.

Fig. 12
Fig. 12

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various rms surface slopes at θi=20° for PEC Gaussian surfaces with an isotropic Gaussian spectrum lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 13
Fig. 13

Comparison of Monte Carlo 2-D FB–NSA results (150 realizations) with various rms surface slopes at θi=70° for PEC Gaussian surfaces with an isotropic Gaussian spectrum lx=ly=2λ: (a) HH polarization, (b) VH polarization, (c) HV polarization, (d) VV polarization.

Fig. 14
Fig. 14

Comparison of the normalized incoherent backscattering RCS (in decibels) computed by the Monte Carlo 2-D FB–NSA method (150 realizations) averaged over the three consecutive angles in 1-deg steps (including the backscattering angle) nearby the backscattering direction of interest and the Monte Carlo SSA (up to second order and for 100 realizations) with various rms surface slopes for PEC Gaussian surfaces with an isotropic Gaussian spectrum lx=ly=2λ: (a) co-polarization, (b) cross polarization.

Equations (9)

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W(kx, ky)=l2h24πexp-14(kx2+ky2)l2,
Lx=3.5λ,γ=0.08 rad,amax=1.0,kz,tail=0.24k,
ky,tail=0.24 Re[κ],Cz=8.0,Cy=14.0.
Lx=4.0λ,γ=0.08 rad,amax=2.0,kz,tail=0.2k,
ky,tail=0.24 Re[κ],Cz=11.0,Cy=14.0.
Lx=4.5λ,γ=0.08 rad,amax=2.0,kz,tail=0.20k,
ky,tail=0.20 Re[κ],Cz=10.0,Cy=15.0.
σαβi(θs, θi)=limr 4πr2|Eαβs˜-Eαβs˜|2cos θi,
Eαβs˜=Eαβs(2η S Sβi·nˆinds)1/2,

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