We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic field in each medium is represented by a Rayleigh expansion and a perturbation method is used for solving the boundary value problem and determining the first-order scattering amplitudes by recurrence relations. The scattering amplitude under the first-order small slope approximation are deduced from results derived from the first-order small perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented.
2. Elson, J. M., J. P. Rahn, and J. M. Bennett, "Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties ," Appl. Opt., Vol. 22, No. 20, 3207-3219, 1983.
3. Amra, C., G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: Antiscattering antireflection coatings," Appl. Opt., Vol. 25, No. 16, 2695-2702, 1986.
4. Amra, C., J. H. Apfel, and E. Pelletier, "Role of interface correlation in light scattering by a multilayer," Appl. Opt., Vol. 31, No. 6, 3134-3151, 1992.
5. Afifi, S. and M. Diaf, "Scattering by random rough surfaces: Study of direct and inverse problem," Optics Comm., Vol. 265, 11-17, 2006.
6. Tabatabaeenejad, A. and M. Moghaddam, "Bistatic scattering from three-dimensional layered rough surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 44, No. 8, 2102-2114, 2006.
7. Brelet, Y. and C. Bourlier, "SPM numerical results from an effective surface impedance for a one-dimensional perfectly-conducting rough sea surface," Progress In Electromagnetics Research, Vol. 81, 413-436, 2008.
8. Imperatore, P., A. Iodice, and D. Riccio, "Electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces," IEEE Trans. Geosci. Remote Sens., Vol. 47, No. 4, 1056-1072, 2009.
9. Lin, Z. W., X. J. Zhang, and G. Y. Fang, "Theoretical model of electromagnetic scattering from 3D multi-layer dielectric media with slightly rough surfaces," Progress In Electromagnetics Research, Vol. 96, 37-62, 2009.
10. Afifi, S., R. Dusseaux, and R. de Oliveira, "Statistical distribution of the field scattered by roug layered interfaces: Formulae derived from the small perturbation method," Waves in Random and Complex Media, Vol. 20, No. 1, 1-22, 2010.
11. Afifi, S. and R. Dusseaux, "On the co-polarized phase difference of rough layered surfaces: Formulae derived from the small perturbation method," IEEE Trans. Antennas Propagat., Vol. 59, No. 7, 2607-2618, 2011.
12. Afifi, S. and R. Dusseaux, "On the co-polarized scattered intensity ratio of rough layered surfaces: The probability law derived from the small perturbation method," IEEE Trans. Antennas Propagat., Vol. 60, No. 4, 2133-2138, 2012.
13. Voronovich, G., Wave Scattering from Rough Surfaces, Springer, Berlin, 1994.
14. Berginc, G. and C. Bourrely, "The small-slope approximation method applied to a three-dimensional slab with rough boundaries," Progress In Electromagnetics Research, Vol. 73, 131-121, 2007.
15. Luo, G. and M. Zhang, "Investigation on the scattering from one-dimensional nonlinear fractal sea surface by second-order small-slope approximation," Progress In Electromagnetics Research, Vol. 133, 425-441, 2013.
16. Tsang, L., J. A. Kong, and K.-H. Ding, , Scattering of Electromagnetic Waves --- Theory and Application, Wiley-Interscience, New York, 2001.
17. Beckmann, P. , A. Spizzichino, and , The Scattering of Electromagnetic Waves from Rough Surface, Oxford, Pergamon, 1963.
18. Pinel, N. and C. Bourlier, "Scattering from very rough layers under the geometric optics approximation: Further investigation," J. Opt. Soc. Am. A., Vol. 25, No. 6, 1293-1306, 2008.
19. Dusseaux, R., P. Chambelin, and C. Faure, "Analysis of rectangular waveguide H-plane junctions in a nonorthogonal coordinate system," Progress In Electromagnetics Research, Vol. 28, 205-229, 2000.
20. Kuo, C.-H. and M. Moghaddam, "Electromagnetic scattering from multilayer rough surfaces with arbitrary dielectric pro¯les for remote sensing of subsurface soil moisture," IEEE Trans. Geosci. Remote Sens., Vol. 45, No. 2, 349-366, 2007.
21. Petit, R., Electromagnetic Theory of Gratings, Springer-Verlag, Heidelberg, 1980.
22. Van Den Berg, P. M. and J. T. Fokkema, "The Rayleigh hypothesis in the theory of diffraction by a perturbation in a plane surface," Radio Sci., Vol. 15, 723-732, 1980.
23. Baudier, C. and R. Dusseaux, "Scattering of an E==-polarized plane wave by one-dimensional rough surfaces: Numerical applicability domain of a Rayleigh method in the far-field zone," Progress In Electromagnetics Research, Vol. 34, 1-27, 2001.
24. Mainguy, S. and J. J. Greffet, "A numerical evaluation of Rayleigh theory applied to scattering by randomly rough dielectric surfaces," Waves in Random Media, Vol. 8, No. 1, 79-101, 1998.
25. Born, M. and E. Wolf, Principles of Optics --- Electromagnetic Theory of Propagation Interference and Di®raction of Light, Pergamon, Oxford, 1980.
26. Tsang, L., J. A. Kong, K. H. Ding, and C. O. Ao, "Scattering of Electromagnetic Waves --- Numerical Simulations," Wiley-Interscience, 2001.