A variational method for electromagnetic diffraction in biperiodic structures
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 4, p. 419-439
@article{M2AN_1994__28_4_419_0,
     author = {Dobson, D. C.},
     title = {A variational method for electromagnetic diffraction in biperiodic structures},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {28},
     number = {4},
     year = {1994},
     pages = {419-439},
     zbl = {0820.65087},
     mrnumber = {1288506},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_4_419_0}
}
Dobson, D. C. A variational method for electromagnetic diffraction in biperiodic structures. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 4, pp. 419-439. http://www.numdam.org/item/M2AN_1994__28_4_419_0/

[1] T. Abboud, J. Nédélec, 1992, Electromagnetic waves in an inhomogeneous medium, J, Math. Anal. Appl, 164, 40-58. | MR 1146575 | Zbl 0755.35134

[2] A. Bendali, 1984, Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method. Part 1 : The continuous problem., Math. of Computation, 167, 29-46. | MR 744923 | Zbl 0555.65082

[2] A. Bendali, 1984, Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method. Part 2 : The discrete problem, Math. of Computation, 167, 47-68. | MR 744924 | Zbl 0555.65083

[3] H. Bellout, A. Friedman, 1990, Scattering by stripe grating, J. Math. Anal. Appl., 147, 228-248. | MR 1044697 | Zbl 0716.35061

[4] M. Born, E. Wolf, 1980, Principles of Optics, sixth edition, Pergamon Press, Oxford.

[5] O. P. Bruno, F. Reitich, 1992, Solution of a boundary value problem for elmholtz equation via variation of the boundary into the complex domain, Proc. Royal Soc. Edinburgh, 122A, 317-340. | MR 1200203 | Zbl 0789.35042

[6] O. P. Bruno, F. Reitich, 1993, Numerical solution of diffraction problems : a method of variation of boundaries, J. Opt. Soc. America A, 10, 1168-1175.

[7] O. P. Bruno, F. Reitich, Numerical solution of diffraction problems : a method of variation of boundaries II. Dielectric gratings, Padé approximants and singularities ; III. Doubly periodic gratings, preprints. | MR 1817674

[8] X. Chen, A. Friedman, 1991, Maxwell's equations in a periodic structure, Trans. Amer. Math. Soc, 323, 465-507. | MR 1010883 | Zbl 0727.35131

[9] J. A. Cox, D. Dobson, 1991, An integral equation method for biperiodic diffraction structures, in J. Lerner and W. McKinney, ed., International Conference on the Application and Theory of Periodic Structures, Proc. SPIE 1545, 106-113.

[10] D. Dobson, A. Friedman, 1992, The time-harmonic Maxwell equations in a doubly periodic structure, J. Math. Anal. Appl., 166, 507-528. | MR 1160941 | Zbl 0759.35046

[11] B. Ducomet, D. Ha. Quang, 1992, Diffusion électromagnétique à basse fréquence par un réseau de cylindres diélectriques : étude numérique, RAIRO, Modél. Math. Anal. Numér. 26, 709-738. | Numdam | MR 1183414 | Zbl 0754.65103

[12] A. Friedman, 1990, Mathematics in Industrial Problems, Part 3, Springer-Verlag, Heidelberg. | MR 1074003 | Zbl 0731.00006

[13] D. Gilbarg, N. S. Trudinger, 1977, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Heidelberg. | MR 473443 | Zbl 0361.35003

[14] T. Kato, 1980, Perturbation Theory for Linear Operators (corrected second édition), Springer-Verlag, Berlin. | MR 407617 | Zbl 0435.47001

[15] J. C. Nédélec, F. Starling, 1988, Integral equation methods in quasi-periodic diffraction problems for the time-harmonic Maxwell's equations, in « Rapport Interne », Vol. 179, C.M.A.P., Ecole Polytechnique, Palaiseau. | Zbl 0756.35004

[16] Electromagnetic Theory of Gratings, 1980, Topics in Current Physics, Vol. 22, edited by R. Petit, Springer-Verlag, Heidelberg. | MR 609533

[17] M Taylor, 1981, Pseudodifferential Operators, Princeton University Press, Princeton, N. J. | MR 618463 | Zbl 0453.47026