Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces

The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory.

[1]  S. Rice.  Reflection of electromagnetic waves from slightly rough surfaces , 1951 .

[2]  G. Valenzuela,et al.  Depolarization of EM waves by slightly rough surfaces , 1967 .

[3]  J. C. Leader.  Bidirectional Scattering of Electromagnetic Waves from Rough Surfaces , 1971 .

[4]  A. Fung,et al.  Numerical computation of scattering from a perfectly conducting random surface , 1978 .

[5]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[6]  V. Agranovich,et al.  Surface polaritons : electromagnetic waves at surfaces and interfaces , 1982 .

[7]  Om P. Gandhi,et al.  Fast-Fourier-Transform Method for Calculation of SAR Distributions in Finely Discretized Inhomogeneous Models of Biological Bodies , 1984 .

[8]  E. Stoll,et al.  Monte Carlo Calculation for Electromagnetic-Wave Scattering from Random Rough Surfaces , 1984 .

[9]  Arthur R. McGurn,et al.  Some aspects of light scattering from a randomly rough metal surface , 1985 .

[10]  J. Kong.  Electromagnetic Wave Theory , 1986 .

[11]  R. Larsen.  An introduction to mathematical statistics and its applications / Richard J. Larsen, Morris L. Marx , 1986 .

[12]  Arthur R. McGurn,et al.  Localization effects in the elastic scattering of light from a randomly rough surface , 1987 .

[13]  Eugenio R. Mendez,et al.  Experimental study of scattering from characterized random surfaces , 1987 .

[14]  Om P. Gandhi,et al.  Comparison of the FFT Conjugate Gradient Method and the Finite-Difference Time-Domain Method for the 2-D Absorption Problem , 1987 .

[15]  V. Rokhlin.  Rapid Solution of Integral Equations of Scattering Theory , 1990 .

[16]  K. J. Glover,et al.  The discrete Fourier transform method of solving differential-integral equations in scattering theory , 1989 .

[17]  W. Chew.  Waves and Fields in Inhomogeneous Media , 1990 .

[18]  A. Ishimaru,et al.  Backscattering enhancement: from radar cross sections, to electron and light localizations to rough surface scattering , 1991, IEEE Antennas and Propagation Magazine.

[19]  Backscattering enhancement from a dielectric surface , 1991 .

[20]  Tran,et al.  Scattering of a scalar beam from a two-dimensional randomly rough hard wall: Enhanced backscattering. , 1992, Physical review. B, Condensed matter.

[21]  R. Collin,et al.  Electromagnetic scattering from perfectly conducting rough surfaces (a new full wave method) , 1992 .

[22]  Stephen M. Wandzura,et al.  Electric Current Basis Functions for Curved Surfaces , 1992 .

[23]  Duncan J. Wingham,et al.  The numerical calculation of rough surface scattering by the conjugate gradient method , 1992, IEEE Trans. Geosci. Remote. Sens..

[24]  V. Rokhlin,et al.  The fast multipole method (FMM) for electromagnetic scattering problems , 1992 .

[25]  Akira Ishimaru,et al.  A Banded Matrix Iterative Approach to Monte Carlo Simulations Of Large-Scale Random Rough Surface Scattering: TE Case , 1993 .

[26]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[27]  Leung Tsang,et al.  Monte Carlo simulation of a two-dimensional random rough surface using the sparse-matrix flat-surface iterative approach , 1993 .

[28]  Scattering of a scalar beam from a two-dimensional randomly rough hard wall: Dirichlet and Neumann boundary conditions. , 1993, Applied optics.

[29]  W.C. Chew,et al.  A fast algorithm for solving hybrid integral equation , 1993, Proceedings of IEEE Antennas and Propagation Society International Symposium.

[30]  V. Rokhlin.  Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions , 1993 .

[31]  Yasuo Kuga,et al.  Millimetre-wave scattering from one-dimensional surfaces of different surface correlation functions , 1993 .

[32]  S. Wandzura,et al.  Scattering computation using the fast multipole method , 1993, Proceedings of IEEE Antennas and Propagation Society International Symposium.

[33]  Weng Cho Chew,et al.  Fast algorithm for solving hybrid integral equations , 1993 .

[34]  A. Maradudin,et al.  Enhanced backscattering of light from weakly rough, random metal surfaces. , 1993, Applied optics.

[35]  K. O'Donnell,et al.  Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness , 1994 .

[36]  Daniel Maystre,et al.  LOCALIZATION OF LIGHT BY RANDOMLY ROUGH SURFACES : CONCEPT OF LOCALITON , 1994 .

[37]  Akira Ishimaru,et al.  Monte Carlo simulations of large-scale composite random rough-surface scattering based on the banded-matrix iterative approach , 1994 .

[38]  Saibun Tjuatja,et al.  Numerical simulation of scattering from three-dimensional randomly rough surfaces , 1994, IEEE Trans. Geosci. Remote. Sens..

[39]  Ezekiel Bahar,et al.  Full wave solutions for rough-surface bistatic radar cross sections: Comparison with small perturbation, physical optics, numerical, and experimental results , 1994 .

[40]  Leung Tsang,et al.  Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations , 1994 .

[41]  Leung Tsang,et al.  A SMFSIA method for the electromagnetic scattering from a two-dimensional (3-D scattering problem) perfectly conducting random rough surface , 1994, Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting.

[42]  Alexei A. Maradudin,et al.  Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods , 1994 .

[43]  Weng Cho Chew,et al.  A ray‐propagation fast multipole algorithm , 1994 .

[44]  Weng Cho ChewDepartment.  A Multilevel Algorithm for Solving Boundary Integral Equation , 1994 .

[45]  Monte Carlo simulations and backscattering enhancement of random metallic rough surfaces at optical frequencies , 1994 .

[46]  Jiming Song,et al.  Fast multipole method solution using parametric geometry , 1994 .

[47]  M. Bleszynski,et al.  A fast integral-equation solver for electromagnetic scattering problems , 1994, Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting.

[48]  R. E. Collin.  Scattering of an incident Gaussian beam by a perfectly conducting rough surface , 1994 .

[49]  A ray propagation approach for accelerating the fast multipole method , 1994, Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting.

[50]  Alexei A. Maradudin,et al.  The scattering of electromagnetic waves from a randomly rough 2D metallic surface , 1994 .

[51]  Weng Cho Chew,et al.  Moment method solutions using parametric geometry , 1995 .

[52]  Weng Cho Chew,et al.  An FFT T‐matrix method for 3D microwave scattering solutions from random discrete scatterers , 1995 .

[53]  Leung Tsang,et al.  Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method , 1995 .

[54]  Leung Tsang,et al.  A sparse‐matrix canonical‐grid method for scattering by many scatterers , 1995 .

[55]  Jiming Song,et al.  Multilevel fast‐multipole algorithm for solving combined field integral equations of electromagnetic scattering , 1995 .

[56]  Michael A. Epton,et al.  Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations , 1995, SIAM J. Sci. Comput..

[57]  Akira Ishimaru,et al.  Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data , 1996 .