A variational method for electromagnetic diffraction in biperiodic structures
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 4, pp. 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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {419--439},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {4},
     year = {1994},
     mrnumber = {1288506},
     zbl = {0820.65087},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_4_419_0/}
}
TY  - JOUR
AU  - Dobson, D. C.
TI  - A variational method for electromagnetic diffraction in biperiodic structures
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1994
SP  - 419
EP  - 439
VL  - 28
IS  - 4
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1994__28_4_419_0/
LA  - en
ID  - M2AN_1994__28_4_419_0
ER  - 
%0 Journal Article
%A Dobson, D. C.
%T A variational method for electromagnetic diffraction in biperiodic structures
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1994
%P 419-439
%V 28
%N 4
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1994__28_4_419_0/
%G en
%F M2AN_1994__28_4_419_0
Dobson, D. C. A variational method for electromagnetic diffraction in biperiodic structures. ESAIM: Modélisation mathématique et analyse numérique, Tome 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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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

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

[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 | Zbl

[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 | Zbl

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

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

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

[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

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

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