We present a rigorous method giving the field scattered by a dielectric plane surface with a local cylindrical perturbation illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. A Method of Moments (PPMoM) with Pulses for basis and weighting functions is applied for solving in the spectral domain. For several deterministic profiles, we study the influence of polarization, incidence angle and perturbation depth and show that the distance defining the far-field approximation depends on the observation angle.
1. Chandezon, J., D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Optics (Paris), Vol. 11, 235-241, 1980. doi:10.1088/0150-536X/11/4/005
2. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, New York, 1941.
3. Elson, J. M. and R. H. Ritchie, "Photon interaction at a rough metal surface," Phys. Rev., Vol. B4, 4129-4138, 1971. doi:10.1103/PhysRevB.4.4129
4. Dusseaux, R. and R. de Oliveira, "Scattering of a plane wave by 1- dimensional rough surface — Study in a nonorthogonal coordinate system," Progress in Electromagnetic Research, Vol. 34, 63-88, 2001. doi:10.2528/PIER01030901
5. Harrington, R. F., Field Computation by Moment Methods, McMillan, London, 1968.
6. 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. doi:10.1029/RS015i004p00723
7. Millar, R. F., "The Rayleigh hypothesis and a related least-square solution to scattering problems for periodic surfaces and other scatterers," Radio Sci., Vol. 8, 785-796, 1973. doi:10.1029/RS008i008p00785
8. 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 Electromagnetic Research, Vol. 34, 1-27, 2001. doi:10.2528/PIER01010501
9. Baudier, C. and R. Dusseaux, "Diffraction par une surface rugueuse dielectrique: Domaine d’application num´erique d’une methode de Rayleigh," 12th OHD Symposium, 345-348, Le Mans, France, 2001.
10. Maystre, D., "Electromagnetic scattering from perfectly conducting rough surfaces in the resonance region," IEEE Trans. Antennas Propagat., Vol. 31, No. 6, 885-895, 1983. doi:10.1109/TAP.1983.1143159
11. Maystre, D., "Rigorous theory of light scattering from rough surfaces," J. Optics (Paris), Vol. 15, No. 1, 43-51, 1984. doi:10.1088/0150-536X/15/1/005
12. Maystre, D., O. Mata Mendez, and R. Roger, "A new electromagnetic theory for scattering shallow rough surfaces," Optica Acta, Vol. 30, No. 12, 1707-1723, 1983. doi:10.1080/713821125
13. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves — Advanced Topics, Ch. 1, Wiley Series in Remote Sensing, A Wiley-Interscience Publication, New York, 2001. doi:10.1002/0471224278