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Computer Simulations of Rough Surface Scattering

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Light Scattering and Nanoscale Surface Roughness

Part of the book series: Nanostructure Science and Technology ((NST))

Abstract

“Numerically exact” methods for rough surface scattering have increased in their relevance to surface scattering studies over the past quarter century. This increase in relevance follows the increase in computational power that has become readily available over the same period, along with developments in approaches for reducing the computational complexity of such methods. However, while computational power has increased by several orders of magnitude, and the range of surface scattering problems that can be studied numerically has followed directly, the overall impact of numerical studies has been decidedly less dramatic, while still of some import, as will be discussed throughout this chapter.

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References

  1. J.A. DeSanto and RJ. Wombell, “Rough surface scattering,” Waves Random Media 1, S41–S56 (1991).

    Article  ADS  Google Scholar 

  2. D. Maystre, M. Saillard, and J. Ingers, “Scattering by one or two dimensional randomly rough surfaces,” Waves Random Media 3, S143–S155 (1991).

    Article  Google Scholar 

  3. E.I. Thorsos and D.R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 3, S165–S190 (1991).

    Article  Google Scholar 

  4. M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, R103–R137 (2001).

    Article  MathSciNet  ADS  Google Scholar 

  5. K.M. Warnick and W.C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11, R1–R30 (2001).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. R.T. Marchand and G.S. Brown, “On the use of finite surfaces in the numerical prediction of rough surface scattering,” IEEE Trans. Antennas Propag. 47, 600–604 (1999).

    Article  ADS  Google Scholar 

  7. J.T. Johnson, “A numerical study of low grazing angle backscatter from ocean-like impedance surfaces with the canonical grid method,” IEEE Trans. Antennas Propag. 46, 114–120(1998).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  9. J.V. Toporkov, R. Awadallah, and G.S. Brown, “Issues related to the use of a Gaussian-like incident field for low-grazing-angle scattering,” J. Opt. Soc. Am. A 16, 176–187 (1999).

    Article  ADS  Google Scholar 

  10. H. Braunisch, Y. Zhang, C.O. Ao, S.E. Shin, Y.E. Yang, K.H. Ding, J.A. Kong, and L. Tsang, “Tapered wave with dominant polarization state for all angles of incidence,” IEEE Trans. Antennas Propag. 48, 1086–1096 (2000).

    Article  ADS  Google Scholar 

  11. H.X. Ye and Y.Q. Jin, “Parameterization of the tapered incident wave for numerical simulation of scattering from rough surfaces,” IEEE Trans. Antennas Propag. 53, 1234–1237 (2005).

    Article  ADS  Google Scholar 

  12. J.C. West, “On the control of edge diffraction in numerical rough surface scattering using resistive tapering,” IEEE Trans. Antennas Propag. 51, 3180–3183 (2003).

    Article  ADS  Google Scholar 

  13. Z.Q. Zhao and J.C. West, “Resistive suppression of edge effects in MLFMA scattering from finite conductivity surfaces,” IEEE Trans. Antennas Propag. 53, 1848–1852 (2005).

    Article  ADS  Google Scholar 

  14. J.V. Toporkov, R.T. Marchand, and G.S. Brown, “On the discretization of the integral equation describing scattering by rough conducting surfaces,” IEEE Trans. Antennas Propag. 46, 150–161 (1998).

    Article  ADS  Google Scholar 

  15. Q. Li, C.H. Chan, and L. Tsang, “Monte Carlo simulations of wave scattering from lossy dielectric random rough surfaces using the physics-based two-grid method and the canonical grid method,” IEEE Trans. Antennas Propag. 47, 752–769 (1999).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. J.T. Johnson, “Surface currents induced on a dielectric halfspace by a Gaussian beam: a useful validation for MOM codes,” Radio Sci. 32, 923–934 (1997).

    Article  ADS  Google Scholar 

  18. J.T. Johnson, R.T. Shin, J. Eidson, L. Tsang, and J.A. Kong, “A method of moments model for VHF propagation,” IEEE Trans. Antennas Propag. 45, 115–125 (1997).

    Article  ADS  Google Scholar 

  19. C.H. Chan, L. Tsang, and Q. Li, “Monte-Carlo simulation of large-scale one-dimensional random rough-surface scattering at near-grazing incidence: penetrable case,” IEEE Trans. Antennas Propag. 46, 142–149 (1998 Jan.).

    Google Scholar 

  20. J.T. Johnson and R.J. Burkholder, “Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface,” IEEE Trans. Geosci. Remote Sens. 39, 1214–1220 (2001).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. P. Tran and A.A. Maradudin, “The scattering of electromagnetic waves from a randomly rough 2-D metallic surface,” Opt. Commun. 110, 269–273 (1994).

    Article  ADS  Google Scholar 

  23. J.C. West, “Integral equation formulation for iterative calculation of scattering from lossy rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1609–1615 (2000).

    Article  ADS  Google Scholar 

  24. M.Y. Xia, C.H. Chan, S.Q. Li, B. Zhang, and L. Tsang, “An efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse-matrix canonical grid method,” IEEE Trans. Antennas Propag. 51, 1142–1149(2003).

    Article  MathSciNet  ADS  Google Scholar 

  25. J.T. Johnson, unpublished notes (2003).

    Google Scholar 

  26. L.S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dogarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R.C. Whaley, Scalapack Users’ Guide (SIAM Publications, Philadelphia, 1997).

    MATH  Google Scholar 

  27. R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eljkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, available at http://netlib2.cs.utk.edu/ linalg/htmLtemplates/Templates. html.

    Google Scholar 

  28. J.C. West and J.M. Sturm, “On iterative approaches for electromagnetic rough surface scattering problems,” IEEE Trans. Antennas Propag. 47, 1281–1288 (1999).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. L. Tsang, C.H. Chan, H. Sangani, A. Ishimaru, and P. Phu, “A banded matrix iterative approach to Monte Carlo simulations of scattering of waves by large-scale random rough surface scattering,” J. Electr. Waves Appl. 7, 185–200 (1993).

    Google Scholar 

  30. D. Holliday, L.L. Deraad, and G.J. St-Cyr, “Forward-backward: a new method for computing low grazing angle scattering,” IEEE Trans. Antennas Propag. 44, 722–729 (1996).

    Article  ADS  Google Scholar 

  31. D.A. Kapp and G.S. Brown, “A new numerical method for rough surface scattering calculations,” IEEE Trans. Antennas Propag. 44, 711–721 (1996).

    Article  ADS  Google Scholar 

  32. 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).

    Article  MathSciNet  ADS  Google Scholar 

  33. P. Tran, “Calculation of the scattering of electromagnetic waves from a two-dimensional perfectly conducting surface using the method of order multiple interactions,” Waves Random Media, 7, 295–302 (1997).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. R.J. Adams and G.S. Brown, “An iterative solution of one-dimensional rough surface scattering problems based on factorization of the Helmholtz equation,” IEEE Trans. Antennas Propag. 47, 765–767 (1999).

    Article  ADS  Google Scholar 

  35. P. Tran, V. Celli, and A.A. Maradudin, “Electromagnetic scattering from a 2-dimensional randomly rough perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A. 11, 1686–1689 (1994).

    Article  ADS  Google Scholar 

  36. D.J. Wingham and R.H. Devayya, “A note on the use of the Neumann expansion in calculating the scatter from rough surfaces,” IEEE Trans. Antennas Propag. 40, 560–563 (1992).

    Article  ADS  Google Scholar 

  37. L. Tsang, C.H. Chan, and K. Pak, “Monte Carlo simulations of a two-dimensional random rough surface using the sparse-matrix flat surface iterative approach,” Electron. Lett. 29, 1153–1154 (1993).

    Article  ADS  Google Scholar 

  38. J.C. West, “Preconditioned iterative solution of scattering from rough surfaces,” IEEE Trans. Antennas Propag. 48, 1001–1002 (2000).

    Article  ADS  Google Scholar 

  39. M. Saillard and G. Soriano, “Fast numerical solution for scattering from rough surfaces with small slopes,” IEEE Trans. Antennas Propag. 52, 2799–2802 (2004).

    Article  ADS  Google Scholar 

  40. J.T. Johnson, “On the canonical grid method for two dimensional scattering problems,” IEEE Trans. Antennas Propag. 46, 297–302 (1998).

    Article  ADS  Google Scholar 

  41. N. Engheta, W.D. Murphy, V. Rokhlin, and M.S. Vassiliou, “The fast multipole method for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  42. R.L. Wagner, J.M. Song and W.C. Chew, “Monte Carlo Simulation of Electromagnetic Scattering from Two-Dimensional Random Rough Surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).

    Article  ADS  Google Scholar 

  43. R.J. Adams and G.S. Brown, “Use of fast multipole method with method of ordered multiple interactions,” Electron. Lett. 34, 2219–2220 (1998).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. V. Jandhyala, B. Shanker, E. Michielssen and W.C. Chew, “Fast algorithm for the analysis of scattering by dielectric rough surfaces,” J. Opt. Soc. Am. A. 15, 1877–1885 (1998b).

    Article  MathSciNet  ADS  Google Scholar 

  46. L. Tsang, D. Chen, P. Xu, Q. Li, and V. Jandhyala, “Wave scattering with the UV multilevel partitioning method: parts 1 and 2,” Radio Sci. 39, RS5010–RS5011 (2004).

    Article  ADS  Google Scholar 

  47. L. Tsang, C.H. Chan, K. Pak, 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).

    Article  ADS  Google Scholar 

  48. K. Pak, L. Tsang, C.H. Chan, and 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).

    Article  ADS  Google Scholar 

  49. 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(5), 1277–1287 (1998).

    Article  ADS  Google Scholar 

  50. H.T. Chou and J.T Johnson, “Formulation of forward-backward method using novel spectral acceleration for the modeling of scattering from impedance rough rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38(1), 605–607 (2000).

    Article  ADS  Google Scholar 

  51. S.Q. Li, C.H. Chan, M.Y. Xia, B. Zhang, and L. Tsang, “Multilevel expansion of the sparse-matrix canonical grid method for two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 49, 1579–1589 (2001).

    Article  ADS  Google Scholar 

  52. D.M. Milder, “An improved formalism for wave scattering from rough surfaces,” J. Acoust. Soc. Am. 89, 529–541 (1991).

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  54. 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, 3(1)-3(20) (2002).

    Google Scholar 

  55. D. Torrungrueng, H.T. Chou, and J.T. Johnson, “A novel spectral acceleration algorithm for the computation of scattering from two-dimensional rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38(4), 1656–1668 (2000).

    Article  ADS  Google Scholar 

  56. D. Torrungrueng and 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. Techol. Lett. 29, 232–236(2001).

    Article  Google Scholar 

  57. D. Torrungrueng and J.T. Johnson, “An improved FB/NSA algorithm for the computation of scattering from two-dimensional large-scale rough surfaces,” J. Electromagn. Waves Appl. 15, 1337–1362 (2001).

    Article  MathSciNet  Google Scholar 

  58. H.C. Ku, R. Awadallah, R.L. McDonald, and N.E. Woods, “Fast and accurate algorithm for scattering from large-scale 2-D dielectric ocean surfaces,” Int’l Antennas and Propagation Symposium, conference proceedings, 3A, 454–457 (2005).

    Google Scholar 

  59. S.Q. Li, C.H. Chan, L. Tsang, Q. Li, and L. Zhou, “Parallel implementation of the sparse-matrix canonical grid method for the analysis of two-dimensional random rough surfaces (3-D scattering problem) on a Beowulf system,” IEEE Trans. Geosci. Remote Sens. 38, 1600–1608 (2000).

    Article  ADS  Google Scholar 

  60. H. Kim and J.T. Johnson, “Radar images of rough surface scattering: comparison of numerical and analytical models,” IEEE Trans. Antennas Propag. 50, 94–100 (2002).

    Article  ADS  Google Scholar 

  61. H.T. Ewe, J.T. Johnson, and K.S. Chen, “A comparison study of surface scattering models,” Int’l Geoscience and Remote Sensing Symposium (IGARSS 01), conference proceedings, 6, 2692–2694 (2001).

    Google Scholar 

  62. T. Wu, K.S. Chen, J. Shi, and A.K. Fung, “A transition model for the reflection coefficient in surface scattering,” IEEE Trans. Geosci. Remote Sens. 39, 2040–2050 (2001).

    Article  ADS  Google Scholar 

  63. J.T. Johnson, R.T. Shin, J.A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean scattering,” IEEE Trans. Geosci. Remote Sens. 36(1), 72–83 (1998).

    Article  ADS  Google Scholar 

  64. J.T. Johnson and H.T. Chou, “Numerical studies of low grazing angle backscatter from 1-D and 2-D impedance surfaces,” IGARSS’98 Conference Proceedings 4, 2295–2297 (1998).

    Google Scholar 

  65. A.A. Maradudin, E.R. Mendez, and T. Michel, “Backscattering effects in the elastic scattering of P-polarized light from a large amplitude random metallic grating,” Opt. Lett. 14, 151 (1989).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  67. J.T. Johnson, L. Tsang, R.T. Shin, K. Pak, C.H. Chan, A. Ishimaru, and 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).

    Article  ADS  Google Scholar 

  68. D. Torrungrueng and J.T. Johnson, “Numerical studies of backscattering enhancement of electromagnetic waves from two-dimensional random rough surfaces using the FB/NSA method,” J. Opt. Soc. Am. A. 18, 2518–2526 (2001).

    Article  ADS  Google Scholar 

  69. C. Bourlier and G. Berginc, “Multiple scattering in the high-frequency limit with second order shadowing function from 2-D anisotropic rough dielectric surfaces: parts I and II,” Waves Random Media 14, 229–276 (2004).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  70. T. Elfouhaily and C.A. Guerin, “A critical survey of approximate scattering theories from random rough surfaces,” Wave Random Media 14, R1–R40 (2004).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  71. G. Soriano, C.A. Guerin, and M. Saillard, “Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff, and small-slope approximations,” Waves Random Media 12, 63–83 (2002).

    Article  MATH  ADS  Google Scholar 

  72. C.A. Guerin, G. Soriano, and T. Elfouhaily, “Weight curvature approximation: numerical tests for 2-D dielectric surfaces,” Waves Random Media 14, 349–363 (2004).

    Article  MATH  ADS  Google Scholar 

  73. F.W. Millet and K.L. Warnick, “Validity of rough surface backscattering models,” Waves Random Media 14, 327–347 (2004).

    Article  MATH  ADS  Google Scholar 

  74. K. O’Neill, R.F. Lussky, and K.D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).

    Article  ADS  Google Scholar 

  75. G. F. Zhang, L. Tsang, and K. Pak, “Angular correlation function and scattering coefficient of electromagnetic waves scattered by a buried object under a two-dimensional rough surface,” J. Opt. Soc. Am. A. 15, 2995–3002 (1998).

    Article  ADS  Google Scholar 

  76. M. El-Shenawee, C. Rappaport, and M. Silevitch, “Monte Carlo simulations of electromagnetic wave scattering from a random rough surface with three dimensional buried object,” J. Opt. Soc. Am. A. 18, 3077–3084 (2001).

    Article  ADS  Google Scholar 

  77. J.T. Johnson, “A numerical study of scattering from an object above a rough surface,” IEEE Trans. Antennas Propag. 40, 1361–1367 (2002).

    Article  ADS  Google Scholar 

  78. J.T. Johnson and R.J. Burkholder, “A study of scattering from an object below a rough interface,” IEEE Trans. Geosci. Remote Sens. 42, 59–66 (2004).

    Article  ADS  Google Scholar 

  79. M. El-Shenawee, “Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects,” IEEE Trans. Geosci. Remote Sens. 42, 67–76 (2004).

    Article  ADS  Google Scholar 

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Johnson, J.T. (2007). Computer Simulations of Rough Surface Scattering. In: Maradudin, A.A. (eds) Light Scattering and Nanoscale Surface Roughness. Nanostructure Science and Technology. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35659-4_7

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