## Investigation on wide-band scattering of a 2-D target above 1-D randomly rough surface by FDTD method |

Optics Express, Vol. 19, Issue 2, pp. 1091-1100 (2011)

http://dx.doi.org/10.1364/OE.19.001091

Acrobat PDF (1265 KB)

### Abstract

Finite-difference time-domain (FDTD) algorithm with a pulse wave excitation is used to investigate the wide-band composite scattering from a two-dimensional(2-D) infinitely long target with arbitrary cross section located above a one-dimensional(1-D) randomly rough surface. The FDTD calculation is performed with a pulse wave incidence, and the 2-D representative time-domain scattered field in the far zone is obtained directly by extrapolating the currently calculated data on the output boundary. Then the 2-D wide-band scattering result is acquired by transforming the representative time-domain field to the frequency domain with a Fourier transform. Taking the composite scattering of an infinitely long cylinder above rough surface as an example, the wide-band response in the far zone by FDTD with the pulsed excitation is computed and it shows a good agreement with the numerical result by FDTD with the sinusoidal illumination. Finally, the normalized radar cross section (NRCS) from a 2-D target above 1-D rough surface versus the incident frequency, and the representative scattered fields in the far zone versus the time are analyzed in detail.

© 2011 OSA

## 1. Introduction

1. E. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. **83**(1), 78–92 (1988). [CrossRef]

3. T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media **14**(4), R1–R40 (2004). [CrossRef]

4. N. Geng, A. Sullivan, and L. Carin, “Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space,” IEEE Trans. Antenn. Propag. **49**(5), 740–748 (2001). [CrossRef]

6. X. Wang and L. W. Li, “Numerical characterization of bistatic scattering from PEC cylinder partially embedded in a dielectric rough surface interface: horizontal polarization,” Prog. Electromagn. Res. **91**, 35–51 (2009). [CrossRef]

7. X. D. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM Case,” IEEE Antennas Wirel. Propag. Lett. **2**(22), 319–322 (2003). [CrossRef]

8. Y. Zhang, J. Lu, J. Pacheco, C. D Jr, C. O Moss, T. M Ao, Grzegorczyk, and J. A Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antenn. Propag. **53**(5), 1631–1639 (2005). [CrossRef]

9. D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microw. Opt. Technol. Lett. **49**(1), 241–247 (2007). [CrossRef]

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

11. T. Lu, W. Cai, and P. Zhang, “Discontinuous galerkin time-domain method for GPR simulation in dispersive media,” IEEE Trans. Geosci. Rem. Sens. **43**(1), 72–80 (2005). [CrossRef]

13. F. Frezza, P. Martinelli, L. Pajewski, and G. Schettini, “Short-pulse electromagnetic scattering by buried perfectly conducting cylinders,” IEEE Trans. Geosci. Remote Sens. Lett. **4**(4), 611–615 (2007). [CrossRef]

14. J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from two-dimensional rough surface with UPML absorbing condition,” Waves Random Complex Media **19**(3), 418–429 (2009). [CrossRef]

15. J. Li, L. X. Guo, H. Zeng, and X. B. Han, “Message-passing-interface-based parallel FDTD investigation on the EM scattering from a 1-D rough sea surface using uniaxial perfectly matched layer absorbing boundary,” J. Opt. Soc. Am. A **26**(6), 1494–1502 (2009). [CrossRef]

16. J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. **88**, 197–211 (2008). [CrossRef]

18. L. X. Guo, J. Li, and H. Zeng, “Bistatic scattering from a three-dimensional object above a two-dimensional randomly rough surface modeled with the parallel FDTD approach,” J. Opt. Soc. Am. A **26**(11), 2383–2392 (2009). [CrossRef]

## 2. Wide-band scattering of composite model

**, which makes angle**

*k*_{i}*y*-axis. And the scattered direction

**is rotated clockwise by the angle**

*k*_{s}*y*-axis. And one-dimensional randomly rough surface profile with Gaussian spectrum is simulated by Monte Carlo method [19].

17. J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough a sea surface,” Waves Random Complex Media **18**(4), 641–650 (2008). [CrossRef]

### 2.1 Near fields

*et al*. [22

22. A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three- dimensional randomly rough surfaces,” IEEE Trans. Geosci. Rem. Sens. **32**(5), 986–994 (1994). [CrossRef]

*T*is a constant which determines the tapering width of the window function so chosen that the tapering drops from unity to

23. I. Ahmed, E. Li, and K. Krohne, “Convolutional perfectly matched layer for an unconditionally stable LOD-FDTD method,” IEEE Microw. Wirel. Compon. Lett. **17**(12), 816–818 (2007). [CrossRef]

23. I. Ahmed, E. Li, and K. Krohne, “Convolutional perfectly matched layer for an unconditionally stable LOD-FDTD method,” IEEE Microw. Wirel. Compon. Lett. **17**(12), 816–818 (2007). [CrossRef]

*x*- and

*y*-directions. It is assumed that the thickness of the CPML is

*d*, with the front planar interface located in the

*M*,

23. I. Ahmed, E. Li, and K. Krohne, “Convolutional perfectly matched layer for an unconditionally stable LOD-FDTD method,” IEEE Microw. Wirel. Compon. Lett. **17**(12), 816–818 (2007). [CrossRef]

### 2.2 Far fields

24. R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A Finite-Difference Time-Domain near zone to far zone transformation,” IEEE Trans. Antenn. Propag. **39**(4), 429–433 (1991). [CrossRef]

*k*is the incident wavenumber) in the 2-D frequency domain far zone transformation equations [25

25. R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to far-zone transformation,” IEEE Trans. Antenn. Propag. **40**(7), 848–851 (1992). [CrossRef]

*z*variation and the 2-D far zone fields is given bywhere,

*ω*is the incident angular frequency. Thus, the 2-D time domain transformation of near zone fields to the far zone can be obtained by the modifications to the 3-D transient transformation. The 3-D time-domain electric vector potential

*j*and

*r*is the distance from the origin in the reference coordinate to the observed point in the far zone. The corresponding equations for the 3-D time-domain far zone scattered fields are where

*z*variable over a unit distance, and the representative 2-D time-domain far zone scattered fields

**Simultaneously, the incident pulse wave**

*L*is the length of rough surface.

## 3. Numerical results and discussions

*τ*determines the width of Gaussian pulse wave. In performing the calculations, some parameters are given as following:

17. J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough a sea surface,” Waves Random Complex Media **18**(4), 641–650 (2008). [CrossRef]

*ε*is shown in Fig. 4 . Where the incident angle is

*ε*for both the backward and specular direction. This phenomenon should be not surprising, and the primary reason for this is that the scattering from the rough surface becomes stronger with the increase of

*ε*.

*δ*and

*l*with the s-polarized wave illumination. The incident angle is

*δ*except for the low frequency. We attribute this behavior to the fact that the roughness of rough surface increases with increasing of

*δ*. Consequently, the incoherent scattering enhances with increasing of the surface roughness, which leads to the smaller specular scattering. In addition, it is also seen that the NRCS in the specular direction become gently larger with the increase of

*l*in Fig. 5(b). This is due to the fact that by keeping the rms height constant and by increasing the correlation length, the electromagnetic roughness is constant, but the rms slope decreases, leading to a narrower distribution of the scattered energy, which implies an increase of the scattered energy in the specular direction.

## 4. Conclusion

## Acknowledgments

## References and links

1. | E. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. |

2. | C. Bourlier and N. Pinel, “Numerical implementation of local unified models for backscattering from random rough sea surfaces,” Waves in Random and Complex Media |

3. | T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media |

4. | N. Geng, A. Sullivan, and L. Carin, “Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space,” IEEE Trans. Antenn. Propag. |

5. | B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. |

6. | X. Wang and L. W. Li, “Numerical characterization of bistatic scattering from PEC cylinder partially embedded in a dielectric rough surface interface: horizontal polarization,” Prog. Electromagn. Res. |

7. | X. D. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM Case,” IEEE Antennas Wirel. Propag. Lett. |

8. | Y. Zhang, J. Lu, J. Pacheco, C. D Jr, C. O Moss, T. M Ao, Grzegorczyk, and J. A Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antenn. Propag. |

9. | D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microw. Opt. Technol. Lett. |

10. | G. Kubické, C. Bourlier, and J. Saillard, “Scattering from canonical objects above a sea-like one-dimensional rough surface from a rigorous fast method,” Waves Random Complex Media |

11. | T. Lu, W. Cai, and P. Zhang, “Discontinuous galerkin time-domain method for GPR simulation in dispersive media,” IEEE Trans. Geosci. Rem. Sens. |

12. | J. T. Johnson and R. J. Burkholder, “A study of scattering from an object below a rough surface,” IEEE Trans. Geosci. Rem. Sens. |

13. | F. Frezza, P. Martinelli, L. Pajewski, and G. Schettini, “Short-pulse electromagnetic scattering by buried perfectly conducting cylinders,” IEEE Trans. Geosci. Remote Sens. Lett. |

14. | J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from two-dimensional rough surface with UPML absorbing condition,” Waves Random Complex Media |

15. | J. Li, L. X. Guo, H. Zeng, and X. B. Han, “Message-passing-interface-based parallel FDTD investigation on the EM scattering from a 1-D rough sea surface using uniaxial perfectly matched layer absorbing boundary,” J. Opt. Soc. Am. A |

16. | J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. |

17. | J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough a sea surface,” Waves Random Complex Media |

18. | L. X. Guo, J. Li, and H. Zeng, “Bistatic scattering from a three-dimensional object above a two-dimensional randomly rough surface modeled with the parallel FDTD approach,” J. Opt. Soc. Am. A |

19. | Y. Kuga and P. Phu, “Experimental studies of millimeter wave scattering in discrete random media and from rough surfaces,” Prog. Electromagn. Res. |

20. | A. Taflove, and S. C. Hagness, |

21. | J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microw. Theory Tech. |

22. | A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three- dimensional randomly rough surfaces,” IEEE Trans. Geosci. Rem. Sens. |

23. | I. Ahmed, E. Li, and K. Krohne, “Convolutional perfectly matched layer for an unconditionally stable LOD-FDTD method,” IEEE Microw. Wirel. Compon. Lett. |

24. | R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A Finite-Difference Time-Domain near zone to far zone transformation,” IEEE Trans. Antenn. Propag. |

25. | R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to far-zone transformation,” IEEE Trans. Antenn. Propag. |

26. | J. A. Kong, |

**OCIS Codes**

(290.5880) Scattering : Scattering, rough surfaces

**ToC Category:**

Scattering

**History**

Original Manuscript: November 12, 2010

Revised Manuscript: December 18, 2010

Manuscript Accepted: December 20, 2010

Published: January 10, 2011

**Citation**

Juan Li, Li-Xin Guo, Yong-Chang Jiao, and Ke Li, "Investigation on wide-band scattering of a 2-D target above 1-D randomly rough
surface by FDTD method," Opt. Express **19**, 1091-1100 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1091

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### References

- E. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83(1), 78–92 (1988). [CrossRef]
- C. Bourlier and N. Pinel, “Numerical implementation of local unified models for backscattering from random rough sea surfaces,” Waves in Random and Complex Media 19(3), 455–479 (2009). [CrossRef]
- T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media 14(4), R1–R40 (2004). [CrossRef]
- N. Geng, A. Sullivan, and L. Carin, “Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space,” IEEE Trans. Antenn. Propag. 49(5), 740–748 (2001). [CrossRef]
- B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. 47, 3399–3405 (2009).
- X. Wang and L. W. Li, “Numerical characterization of bistatic scattering from PEC cylinder partially embedded in a dielectric rough surface interface: horizontal polarization,” Prog. Electromagn. Res. 91, 35–51 (2009). [CrossRef]
- X. D. Wang, Y. B. Gan, and L. W. Li, “Electromagnetic scattering by partially buried PEC cylinder at the dielectric rough surface interface: TM Case,” IEEE Antennas Wirel. Propag. Lett. 2(22), 319–322 (2003). [CrossRef]
- Y. Zhang, J. Lu, J. Pacheco, C. D Jr, C. O Moss, T. M Ao, Grzegorczyk, and J. A Kong, “Mode-expansion method for calculating electromagnetic waves scattered by objects on rough ocean surfaces,” IEEE Trans. Antenn. Propag. 53(5), 1631–1639 (2005). [CrossRef]
- D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microw. Opt. Technol. Lett. 49(1), 241–247 (2007). [CrossRef]
- G. Kubické, C. Bourlier, and J. Saillard, “Scattering from canonical objects above a sea-like one-dimensional rough surface from a rigorous fast method,” Waves Random Complex Media 20(1), 156–178 (2010). [CrossRef]
- T. Lu, W. Cai, and P. Zhang, “Discontinuous galerkin time-domain method for GPR simulation in dispersive media,” IEEE Trans. Geosci. Rem. Sens. 43(1), 72–80 (2005). [CrossRef]
- J. T. Johnson and R. J. Burkholder, “A study of scattering from an object below a rough surface,” IEEE Trans. Geosci. Rem. Sens. 42(1), 59–66 (2004). [CrossRef]
- F. Frezza, P. Martinelli, L. Pajewski, and G. Schettini, “Short-pulse electromagnetic scattering by buried perfectly conducting cylinders,” IEEE Trans. Geosci. Remote Sens. Lett. 4(4), 611–615 (2007). [CrossRef]
- J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from two-dimensional rough surface with UPML absorbing condition,” Waves Random Complex Media 19(3), 418–429 (2009). [CrossRef]
- J. Li, L. X. Guo, H. Zeng, and X. B. Han, “Message-passing-interface-based parallel FDTD investigation on the EM scattering from a 1-D rough sea surface using uniaxial perfectly matched layer absorbing boundary,” J. Opt. Soc. Am. A 26(6), 1494–1502 (2009). [CrossRef]
- J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on bistatic scattering from a target above two-layered rough surfaces using UPML absorbing condition,” Prog. Electromagn. Res. 88, 197–211 (2008). [CrossRef]
- J. Li, L. X. Guo, and H. Zeng, “FDTD investigation on the electromagnetic scattering from a target above a randomly rough a sea surface,” Waves Random Complex Media 18(4), 641–650 (2008). [CrossRef]
- L. X. Guo, J. Li, and H. Zeng, “Bistatic scattering from a three-dimensional object above a two-dimensional randomly rough surface modeled with the parallel FDTD approach,” J. Opt. Soc. Am. A 26(11), 2383–2392 (2009). [CrossRef]
- Y. Kuga and P. Phu, “Experimental studies of millimeter wave scattering in discrete random media and from rough surfaces,” Prog. Electromagn. Res. 14, 37–88 (1996).
- A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time- Domain Method (Boston: Artech House, 2005).
- J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microw. Theory Tech. 48(4), 582–588 (2000). [CrossRef]
- A. K. Fung, M. R. Shah, and S. Tjuatja, “Numerical simulation of scattering from three- dimensional randomly rough surfaces,” IEEE Trans. Geosci. Rem. Sens. 32(5), 986–994 (1994). [CrossRef]
- I. Ahmed, E. Li, and K. Krohne, “Convolutional perfectly matched layer for an unconditionally stable LOD-FDTD method,” IEEE Microw. Wirel. Compon. Lett. 17(12), 816–818 (2007). [CrossRef]
- R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A Finite-Difference Time-Domain near zone to far zone transformation,” IEEE Trans. Antenn. Propag. 39(4), 429–433 (1991). [CrossRef]
- R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to far-zone transformation,” IEEE Trans. Antenn. Propag. 40(7), 848–851 (1992). [CrossRef]
- J. A. Kong, Electromagnetic Wave Theory (New York: Wiley, 1986).

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