Scattering by Anisotropic Rough Layered 2D Interfaces

We propose a statistical study of the scattering of an incident plane wave by a stack of two two-dimensional rough interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fields are represented by Rayleigh expansions, and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes. For slightly rough interfaces with a finite extension, we show that the modulus of the co- and cross-polarized scattering amplitudes follows a Hoyt law and that the phase is not uniformly distributed. For interfaces with an infinite extension, the modulus follows a Rayleigh law and the phase is uniformly distributed. We show that these results are true for correlated or uncorrelated interfaces and for isotropic or anisotropic interfaces.

[1]  Nicolas Pinel,et al.  Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect , 2007 .

[2]  C Amra,et al.  Role of interface correlation in light scattering by a multilayer. , 1992, Applied optics.

[3]  R. Dusséaux,et al.  Effect of the illumination length on the statistical distribution of the field scattered from one-dimensional random rough surfaces: analytical formulae derived from the small perturbation method , 2007 .

[4]  Yuzhi Zhang,et al.  Diffuse like and cross-polarized fields scattered from irregular layered structures-full-wave analysis , 1999 .

[5]  Christophe Bourlier,et al.  Fast numerical method for electromagnetic scattering by rough layered interfaces: propagation-inside-layer expansion method. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[6]  Fawwaz T. Ulaby,et al.  Fluctuation statistics of millimeter-wave scattering from distributed targets , 1988 .

[7]  Alexander Yarovoy,et al.  Scattering properties of a statistically rough interface inside a multilayered medium , 2000 .

[8]  R. Dusseaux,et al.  On the Co-Polarized Scattered Intensity Ratio of Rough Layered Surfaces: The Probability Law Derived From the Small Perturbation Method , 2012, IEEE Transactions on Antennas and Propagation.

[9]  Ezekiel Bahar,et al.  A new unified full wave approach to evaluate the scatter cross sections of composite random rough surfaces , 1996, IEEE Trans. Geosci. Remote. Sens..

[10]  Giorgio Franceschetti,et al.  Scattering From Layered Structures With One Rough Interface: A Unified Formulation of Perturbative Solutions , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[11]  Nicolas Pinel,et al.  Scattering from very rough layers under the geometric optics approximation: further investigation. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  R. F. Millar.  On the Rayleigh assumption in scattering by a periodic surface. II , 1969, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  K. W. Lam,et al.  On the analysis of statistical distributions of UWB signal scattering by random rough surfaces based on Monte Carlo simulations of Maxwell equations , 2004 .

[14]  Eric Jakeman,et al.  Modeling fluctuations in scattered waves , 2006 .

[15]  C Amra,et al.  From light scattering to the microstructure of thin-film multilayers. , 1993, Applied optics.

[16]  Guangyou Fang,et al.  THEORETICAL MODEL OF ELECTROMAGNETIC SCATTERING FROM 3D MULTI-LAYER DIELECTRIC MEDIA WITH SLIGHTLY ROUGH SURFACES , 2009 .

[17]  C. Amra.  Light scattering from multilayer optics. II. Application to experiment , 1994 .

[18]  Eiichi Ogawa,et al.  An evaluation method for the reflection coefficient of building walls , 1990 .

[19]  P. Phu,et al.  Experimental studies of millimeter-wave scattering in discrete random media and from rough surfaces - Summary , 1996 .

[20]  R. Dusséaux,et al.  Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface , 2010 .

[21]  J. P. Rahn,et al.  Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties. , 1983, Applied optics.

[22]  C Amra,et al.  Theory and application of antiscattering single layers: antiscattering antireflection coatings. , 1986, Applied optics.

[23]  Mahta Moghaddam,et al.  Electromagnetic Scattering From Multilayer Rough Surfaces With Arbitrary Dielectric Profiles for Remote Sensing of Subsurface Soil Moisture , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[24]  Scattering by random rough surfaces: Study of direct and inverse problem , 2006 .

[25]  C Amra,et al.  Comparison of surface and bulk scattering in optical multilayers. , 1993, Applied optics.

[26]  D. Maystre,et al.  Sur la diffraction d'une onde plane par un reseau infiniment conducteur , 1971 .

[27]  C. Bourlier,et al.  Electromagnetic Scattering From a Rough Layer: Propagation-Inside-Layer Expansion Method Combined to the Forward-Backward Novel Spectral Acceleration , 2007, IEEE Transactions on Antennas and Propagation.

[28]  Mahta Moghaddam,et al.  Bistatic scattering from three-dimensional layered rough surfaces , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[29]  I. Fuks,et al.  Wave diffraction by a rough boundary of an arbitrary plane-layered medium , 2001 .

[30]  G. Toso,et al.  Electromagnetic scattering from bounded or infinite subsurface bodies , 1997 .

[31]  Antonio Iodice,et al.  Electromagnetic Wave Scattering From Layered Structures With an Arbitrary Number of Rough Interfaces , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[32]  C. Amra.  Light scattering from multilayer optics. I. Tools of investigation , 1994 .

[33]  R. Dusséaux,et al.  Statistical distribution of the field scattered by rough layered interfaces: formulae derived from the small perturbation method , 2010 .

[34]  F. Molinet,et al.  New perturbation theory of diffraction gratings and its application to the study of ghosts , 1995 .

[35]  The Rayleigh Hypothesis in the Theory of Diffraction by a Perturbation in a Plane Surface , 1980 .

[36]  Gérard Berginc,et al.  The Small-Slope Approximation Method Applied to a Three-Dimensional Slab with Rough Boundaries , 2007 .

[37]  C. Bourlier,et al.  Electromagnetic Scattering From a Rough Layer: Propagation-Inside-Layer Expansion Method Combined to an Updated BMIA/CAG Approach , 2007, IEEE Transactions on Antennas and Propagation.

[38]  Kamal Sarabandi,et al.  95-GHz scattering by terrain at near-grazing incidence , 1998 .

[39]  R. Dusseaux,et al.  On the Co-Polarized Phase Difference of Rough Layered Surfaces: Formulae Derived From the Small Perturbation Method , 2011, IEEE Transactions on Antennas and Propagation.

[40]  R. Dusséaux,et al.  Statistical study of radiation loss from planar optical waveguides: the curvilinear coordinate method and the small perturbation method. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[41]  R. Dusséaux,et al.  Statistical study of the radiation losses due to surface roughness for a dilectric slab deposited on a metal substrate , 2008 .

[42]  Yide Wang,et al.  Influence of layer roughness for road survey by Ground Penetrating Radar at nadir : theoretical study , 2011 .

[43]  R. Dusséaux.  Model with two roughness levels for diffraction gratings: the generalized Rayleigh expansion , 1998 .

[44]  A. Iodice,et al.  Transmission Through Layered Media With Rough Boundaries: First-Order Perturbative Solution , 2009, IEEE Transactions on Antennas and Propagation.

[45]  C. Amra,et al.  Interface roughness cross-correlation laws deduced from scattering diagram measurements on optical multilayers: effect of the material grain size , 1987, Annual Meeting Optical Society of America.

[46]  M. Moghaddam,et al.  Scattering From Multilayer Rough Surfaces Based on the Extended Boundary Condition Method and Truncated Singular Value Decomposition , 2006, IEEE Transactions on Antennas and Propagation.

[47]  J. Elson,et al.  Infrared light scattering from surfaces covered with multiple dielectric overlayers. , 1977, Applied optics.

[48]  Akira Ishimaru,et al.  Copolarized and cross‐polarized enhanced backscattering from two‐dimensional very rough surfaces at millimeter wave frequencies , 1994 .

[49]  Magda El-Shenawee.  Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects , 2004, IEEE Transactions on Geoscience and Remote Sensing.