We consider the diffraction of time-harmonic electromagnetic waves by a perfectly conducting planar obstacle, coated by thin contrasted multi-layers of dielectric materials. A partial Fourier transform is used to derive an impedance condition that links the tangential components of the electric and magnetic fields, and transfers the boundary condition from the obstacle’s face to the other face of dielectric multi-layers.
We first determine the exact formula and construct approximations of the impedance condition for one dielectric thin layer; after that, we extend the obtained result to multi-layers.
N.Bartoli and A.Bendali, Numerical solving of electromagnetic scattering by coated perfectly conducting obstacles, Technical report TR/EMC/01/42, CERFACS, Toulouse, France, 2001.
2.
N.Bartoli and A.Bendali, Robust and high-order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer, IMA Journal of Applied Mathematics67 (2002), 479–508. doi:10.1093/imamat/67.5.479.
3.
A.Bendali, M.Fares, K.Lemrabet and S.Pernet, Recent Developments in the Scattering of an Electromagnetic Wave by a Coated Perfectly Conducting Obstacle, Waves 09, Pau, France, 2009.
4.
A.Bendali and K.Lemrabet, The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation, Society for Industrial and Applied Mathematics56(6) (1996), 1664–1693. doi:10.1137/S0036139995281822.
5.
A.Bendali and K.Lemrabet, Asymptotic analysis of the scattering of a time-harmonic wave by a perfectly conducting metal coated with a thin dielectric shell, Asymptotic Analysis57 (2008), 199–227.
6.
M.Duruflé, H.Haddar and P.Joly, Higher order generalized impedance boundary conditions in electromagnetic scattering problems, C. R. Physique7(5) (2006), 533–542. doi:10.1016/j.crhy.2006.03.010.
7.
B.Engquist and J.C.Nédélec, Effective boundary conditions for acoustic and electro-magnetic scattering in thin layers, Report, CMAP, Ecole Polytechnique, France, 1993.
8.
H.Haddar, P.Joly and H.Nguyen, Generalized impedance boundary conditions for scattering problems from strongly absorbing obstacles: The case of Maxwell’s equations, Mathematical Models and Methods in Applied Sciences18(10) (2008), 1787–1827. doi:10.1142/S0218202508003194.
9.
H.Haddar and A.Lechlieter, Electromagnetic wave scattering from rough penetrable layers, SIAM Journal on Mathematics Analysis43 (5) (2011), 2418–2443. doi:10.1137/100783613.
10.
P.L.Huddleston and D.S.Wang, An impedance boundary condition approach to radiation by uniformly coated antennas, Radio Sciences24 (1989), 427–432. doi:10.1029/RS024i004p00427.
11.
P.Joly and A.Semin, Propagation of an acoustic wave in a junction of two thin slots, Research Report RR-6708, INRIA, October 2008.
12.
P.Joly and S.Tordeux, Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots, ESAIM: M2AN40 (2006), 63–97.
13.
P.Joly and S.Tordeux, Matching of asymptotic expansions for wave propagation in media with thin slots. I: The asymptotic expansion, Multiscale Model. Simul.5(1) (2006), 304–336(electronic). doi:10.1137/05064494X.
14.
J.B.Keller and D.Givoli, Exact nonreflecting boundary conditions, J. Comput. Phys.82(1) (1989), 172–192. doi:10.1016/0021-9991(89)90041-7.
15.
M.A.Leontovich, Approximate Boundary Condition for Electromagnetic Field on the Surface of Good Conductor. Investigations on Radiowave Propagation. Part II, Academy of Sciences, Moscow, 1978.
16.
J.C.Nédélec, Acoustic and Electromagnetic Equations, Springer, 2001.
17.
T.B.A.Senior and J.L.Volakis, Approximate Boundary Conditions in Electromagnetics, IEE Electromagnetic Waves Series, Vol. 41, IEEE Press, New York, 1995.
18.
G.Soriano and M.Saillard, Scattering of electromagnetic waves from two-dimensional rough surfaces with impedance approximation, J. Opt. Soc. Amer. A18(1) (2001), 124–133. doi:10.1364/JOSAA.18.000124.
