A. Lechleiter and D. Nguyen, On Uniqueness in Electromagnetic Scattering from Biperiodic Structures, accepted for ESAIM: Mathematical Modelling and Numerical Analysis

D. Nguyen, On Shape Identification of Diffraction Gratings from Spectral Data: The TM Case, preprint (to be submitted)

A. Lechleiter and D. Nguyen, Factorization Method for Inverse Electromagnetic Scattering from Biperiodic Structures, preprint (to be submitted)

]. T. Abboud, Electromagnetic waves in periodic media, Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, pp.1-9, 1993.

H. Alber, Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.3, issue.3-4, pp.251-272, 1979.
DOI : 10.1017/S0305004100028875

H. Ammari, Uniqueness theorems for an inverse problem in a doubly periodic structure, Inverse Problems, vol.11, issue.4, pp.823-833, 1995.
DOI : 10.1088/0266-5611/11/4/013

T. Arens, Scattering by biperiodic layered media: The integral equation approach, 2010.

T. Arens, Why linear sampling works, Inverse Problems, vol.20, issue.1, pp.163-173, 2004.
DOI : 10.1088/0266-5611/20/1/010

T. Arens, S. N. Chandler-wilde, and J. A. Desanto, On integral equation and least squares methods for scattering by diffraction gratings, Communications in Computational Physics, vol.1, pp.1010-1042, 2006.

T. Arens and N. Grinberg, A complete factorization method for scattering by periodic structures, Computing, pp.75-111, 2005.

T. Arens and A. Kirsch, The factorization method in inverse scattering from periodic structures, Inverse Problems, vol.19, issue.5, pp.1195-1211, 2003.
DOI : 10.1088/0266-5611/19/5/311

T. Arens and A. Lechleiter, The linear sampling method revisited, Journal of Integral Equations and Applications, vol.21, issue.2, pp.179-202, 2009.
DOI : 10.1216/JIE-2009-21-2-179

URL : https://hal.archives-ouvertes.fr/hal-00782985

G. Bao, Finite Element Approximation of Time Harmonic Waves in Periodic Structures, SIAM Journal on Numerical Analysis, vol.32, issue.4, pp.1155-1169, 1995.
DOI : 10.1137/0732053

G. Bao, Z. Chen, and H. Wu, Adaptive finite-element method for diffraction gratings, Journal of the Optical Society of America A, vol.22, issue.6, pp.1106-1114, 2005.
DOI : 10.1364/JOSAA.22.001106

G. Bao, L. Cowsar, and W. Masters, Mathematical modeling in optical science, SIAM Frontiers in Appl. Math, 2001.
DOI : 10.1137/1.9780898717594

G. Bao and D. C. Dobson, On the scattering by a biperiodic structure, Proc. Amer, pp.2715-2723, 2000.

G. Bao, H. Zhang, and J. Zou, Unique determination of periodic polyhedral structures by scattered electromagnetic fields, Transactions of the American Mathematical Society, vol.363, issue.9, pp.4527-4551, 2011.
DOI : 10.1090/S0002-9947-2011-05334-1

G. Bao and Z. Zhou, An inverse problem for scattering by a doubly periodic structure, Transactions of the American Mathematical Society, vol.350, issue.10, pp.4089-4103, 1998.
DOI : 10.1090/S0002-9947-98-02227-2

N. Bogdanskia, H. Schulza, M. Wissena, H. Scheera, J. Zajadaczb et al., 3d-hot embossing of undercut structures an approach to micro-zippers, Microelectronic Engineering, pp.73-74, 2004.

A. Bonnet-ben-dhia, L. Chesnel, and P. Ciarlet-jr, Optimality of tcoercivity for scalar interface problems between dielectrics and metamaterials, 2011.

A. Bonnet-ben-dhia, P. Ciarlet-jr, and C. M. Zwölf, Two- and three-field formulations for wave transmission between media with opposite sign dielectric constants, Journal of Computational and Applied Mathematics, vol.204, issue.2, pp.408-417, 2007.
DOI : 10.1016/j.cam.2006.01.046

URL : https://hal.archives-ouvertes.fr/hal-00876230

A. Bonnet-bendhia and F. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem, Mathematical Methods in the Applied Sciences, vol.12, issue.5, pp.305-338, 1994.
DOI : 10.1002/mma.1670170502

F. Cakoni and D. Colton, The linear sampling method for cracks, Inverse Problems, vol.19, issue.2, pp.279-295, 2003.
DOI : 10.1088/0266-5611/19/2/303

F. Cakoni, D. Colton, and H. Haddar, The linear sampling method for anisotropic media, Journal of Computational and Applied Mathematics, vol.146, issue.2, pp.285-299, 2002.
DOI : 10.1016/S0377-0427(02)00361-8

URL : https://hal.archives-ouvertes.fr/hal-00744175

S. N. Chandler-wilde and P. Monk, Existence, Uniqueness, and Variational Methods for Scattering by Unbounded Rough Surfaces, SIAM Journal on Mathematical Analysis, vol.37, issue.2, pp.598-618, 2005.
DOI : 10.1137/040615523

S. N. Chandler-wilde and B. Zhang, Scattering of Electromagnetic Waves by Rough Interfaces and Inhomogeneous Layers, SIAM Journal on Mathematical Analysis, vol.30, issue.3, pp.559-583, 1999.
DOI : 10.1137/S0036141097328932

D. Colton, J. Coyle, and P. Monk, Recent Developments in Inverse Acoustic Scattering Theory, SIAM Review, vol.42, issue.3, pp.396-414, 2000.
DOI : 10.1137/S0036144500367337

D. Colton, H. Haddar, and P. Monk, The Linear Sampling Method for Solving the Electromagnetic Inverse Scattering Problem, SIAM Journal on Scientific Computing, vol.24, issue.3, pp.719-731, 2002.
DOI : 10.1137/S1064827501390467

URL : https://hal.archives-ouvertes.fr/hal-00744171

D. Colton, H. Haddar, and M. Piana, The linear sampling method in inverse electromagnetic scattering theory, Inverse Problems, vol.19, issue.6, pp.105-137, 2003.
DOI : 10.1088/0266-5611/19/6/057

URL : https://hal.archives-ouvertes.fr/hal-00744163

D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, vol.12, issue.4, pp.383-393, 1996.
DOI : 10.1088/0266-5611/12/4/003

D. Colton, A. Kirsch, and P. Monk, The linear sampling method in inverse scattering theory, in Surveys on Solution Methods for Inverse Problems, pp.107-118, 2000.

D. Colton and P. Monk, A Linear Sampling Method for the Detection of Leukemia Using Microwaves, SIAM Journal on Applied Mathematics, vol.58, issue.3, pp.926-941, 1998.
DOI : 10.1137/S0036139996308005

D. L. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 1992.
DOI : 10.1007/978-1-4614-4942-3

M. Costabel, E. Darrigrand, and E. Koné, Volume and surface integral equations for electromagnetic scattering by a dielectric body, Journal of Computational and Applied Mathematics, vol.234, issue.6, pp.234-1817, 2010.
DOI : 10.1016/j.cam.2009.08.033

URL : https://hal.archives-ouvertes.fr/hal-00373279

M. Costabel, M. Dauge, and S. Nicaise, Corner Singularities and Analytic Regularity for Linear Elliptic Systems. Part I: Smooth domains
URL : https://hal.archives-ouvertes.fr/hal-00453934

D. Dobson and A. Friedman, The time-harmonic maxwell equations in a doubly periodic structure, Journal of Mathematical Analysis and Applications, vol.166, issue.2, pp.507-528, 1992.
DOI : 10.1016/0022-247X(92)90312-2

D. C. Dobson, A variational method for electromagnetic diffraction in biperiodic structures, ESAIM: Mathematical Modelling and Numerical Analysis, vol.28, issue.4, pp.419-439, 1994.
DOI : 10.1051/m2an/1994280404191

J. Elschner, R. Hinder, and G. Schmidt, Finite element solution of conical diffraction problems, Advances in Computational Mathematics, vol.16, issue.2/3, pp.139-156, 2002.
DOI : 10.1023/A:1014456026778

J. Elschner and G. Schmidt, Diffraction in periodic structures and optimal design of binary gratings. Part I: direct problems and gradient formulas, Mathematical Methods in the Applied Sciences, vol.3008, issue.14, pp.1297-1342, 1998.
DOI : 10.1002/(SICI)1099-1476(19980925)21:14<1297::AID-MMA997>3.0.CO;2-C

J. Elschner, G. Schmidt, and M. Yamamoto, An inverse problem in periodic diffractive optics: global uniqueness with a single wavenumber, Inverse Problems, vol.19, issue.3, pp.779-787, 2003.
DOI : 10.1088/0266-5611/19/3/318

J. Elschner and M. Yamamoto, Uniqueness results for an inverse periodic transmission problem, Inverse Problems, vol.20, issue.6, pp.1841-1852, 2004.
DOI : 10.1088/0266-5611/20/6/009

W. Ewe, H. Chu, and E. Li, Volume integral equation analysis of surface plasmon resonance of nanoparticles, Optics Express, vol.15, issue.26, pp.15-18200, 2007.
DOI : 10.1364/OE.15.018200

V. Girault and P. Raviart, Finite Element Methods for Navier-Stokes Equations, 1986.
DOI : 10.1007/978-3-642-61623-5

P. Grisvard, Singularities in Boundary Value Problems, 1992.

H. Groß and A. Rathsfeld, Mathematical aspects of scatterometry ? an optical metrology technique, in Intelligent solutions for complex problems ? Annual Research Report, Weierstrass Institute for Applied Analysis and Stochastics, 2007.

H. Haddar and A. Lechleiter, Electromagnetic wave scattering from rough penetrable layers, To appear in SIAM, J. Math. Anal, 2011.

F. Hettlich, Frechet derivatives in inverse obstacle scattering, Inverse Problems, vol.11, issue.2, pp.371-382, 1995.
DOI : 10.1088/0266-5611/11/2/007

F. Hettlich and W. , A Second Degree Method for Nonlinear Inverse Problems, SIAM Journal on Numerical Analysis, vol.37, issue.2, pp.587-620, 2000.
DOI : 10.1137/S0036142998341246

T. Hohage, On the numerical solution of a three-dimensional inverse medium scattering problem, Inverse Problems, vol.17, issue.6, pp.1743-1763, 2001.
DOI : 10.1088/0266-5611/17/6/314

G. Hu, F. Qu, and B. Zhang, A linear sampling method for inverse problems of diffraction gratings of mixed type, Mathematical Methods in the Applied Sciences, vol.41, issue.9, pp.1047-1066, 2012.
DOI : 10.1002/mma.2511

G. Hu and B. Zhang, The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure, Mathematical Methods in the Applied Sciences, vol.30, issue.5, pp.509-519, 2011.
DOI : 10.1002/mma.1375

M. Huber, J. Schöberl, A. Sinwel, and S. Zaglmayr, Simulation of Diffraction in Periodic Media with a Coupled Finite Element and Plane Wave Approach, SIAM Journal on Scientific Computing, vol.31, issue.2, pp.31-1500, 2008.
DOI : 10.1137/070705118

M. Ikehata, Reconstruction of an obstacle from the scattering amplitude at a fixed frequency, Inverse Problems, vol.14, issue.4, pp.949-954, 1998.
DOI : 10.1088/0266-5611/14/4/012

A. Kirsch, Diffraction by periodic structures, Proc. Lapland Conf. on Inverse Problems, pp.87-102, 1993.
DOI : 10.1007/3-540-57195-7_11

A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford Lecture Series in Mathematics and its Applications 36, 2008.
DOI : 10.1093/acprof:oso/9780199213535.001.0001

A. Kirsch and S. Ritter, A linear sampling method for inverse scattering from an open arc, Inverse Problems, vol.16, issue.1, pp.89-105, 2000.
DOI : 10.1088/0266-5611/16/1/308

J. Kottmann and O. Martin, Accurate solution of the volume integral equation for high-permittivity scatterers, IEEE Transactions on Antennas and Propagation, vol.48, issue.11, pp.1719-1726, 2000.
DOI : 10.1109/8.900229

R. Kress and W. , A quasi-Newton method in inverse obstacle scattering, Inverse Problems, vol.10, issue.5, pp.1145-1157, 1994.
DOI : 10.1088/0266-5611/10/5/011

A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Problems and Imaging, vol.3, issue.1, pp.123-138, 2009.
DOI : 10.3934/ipi.2009.3.123

URL : https://hal.archives-ouvertes.fr/hal-00782982

A. Lechleiter and D. L. Nguyen, Spectral volumetric integral equation methods for acoustic medium scattering in a 3D waveguide, IMA Journal of Numerical Analysis, vol.32, issue.3, 2011.
DOI : 10.1093/imanum/drr036

URL : https://hal.archives-ouvertes.fr/hal-00548844

W. Mclean, Strongly Elliptic Systems and Boundary Integral Operators, 2000.

A. Meier, T. Arens, S. N. Chandler-wilde, and A. Kirsch, A Nystr??m Method for a Class of Integral Equations on the Real Line with Applications to Scattering by Diffraction Gratings and Rough Surfaces, Journal of Integral Equations and Applications, vol.12, issue.3, pp.281-321, 2000.
DOI : 10.1216/jiea/1020282209

P. Monk, Finite Element Methods for Maxwell's Equations, 2003.
DOI : 10.1093/acprof:oso/9780198508885.001.0001

J. Nédélec and F. Starling, Integral Equation Methods in a Quasi-Periodic Diffraction Problem for the Time-Harmonic Maxwell???s Equations, SIAM Journal on Mathematical Analysis, vol.22, issue.6, pp.1679-1701, 1991.
DOI : 10.1137/0522104

L. Rayleigh, On the Dynamical Theory of Gratings, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.79, issue.532, pp.79-399, 1907.
DOI : 10.1098/rspa.1907.0051

M. Pinsky, N. Stanton, and P. Trapa, Fourier Series of Radial Functions in Several Variables, Journal of Functional Analysis, vol.116, issue.1, pp.111-132, 1993.
DOI : 10.1006/jfan.1993.1106

R. Potthast, A fast new method to solve inverse scattering problems, Inverse Problems, vol.12, issue.5, pp.731-742, 1996.
DOI : 10.1088/0266-5611/12/5/014

D. W. Prather, M. S. Mirotznik, and J. N. Mait, Boundary integral methods applied to the analysis of diffractive optical elements, Journal of the Optical Society of America A, vol.14, issue.1, pp.14-34, 1997.
DOI : 10.1364/JOSAA.14.000034

J. Rahola, Solution of Dense Systems of Linear Equations in the Discrete-Dipole Approximation, SIAM Journal on Scientific Computing, vol.17, issue.1, pp.78-89, 1996.
DOI : 10.1137/0917007

A. Rathsfeld, G. Schmidt, and B. Kleemann, On a fast integral equation method for diffraction gratings, Commun. Comput. Phys, vol.1, pp.984-1009, 2006.

F. Rellich, Darstellung der Eigenwerte von? u+? u=0 durch ein Randintegral, Mathematische Zeitschrift, vol.46, issue.1, pp.635-636, 1940.
DOI : 10.1007/BF01181459

J. Richmond, Scattering by a dielectric cylinder of arbitrary cross section shape, IEEE Transactions on Antennas and Propagation, vol.13, issue.3, pp.334-341, 1965.
DOI : 10.1109/TAP.1965.1138427

W. Rudin, Functional Analysis, 1991.

K. Sandfort, The factorization method for inverse scattering from periodic inhomogeneous media, 2010.

J. Saranen, On a inequality of Friedrichs., MATHEMATICA SCANDINAVICA, vol.51, pp.310-322, 1982.
DOI : 10.7146/math.scand.a-11983

J. Saranen and G. Vainikko, Periodic integral and pseudodifferential equations with numerical approximation, 2002.
DOI : 10.1007/978-3-662-04796-5

A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, Domain decomposition method for maxwells equations: Scattering of periodic structures, J. Comput . Physics, pp.226-477, 2007.

G. Schmidt, On the Diffraction by Biperiodic Anisotropic Structures, Applicable Analysis, vol.28, issue.1, pp.75-92, 2003.
DOI : 10.1016/0022-247X(92)90312-2

V. M. Shalaev, Optical negative-index metamaterials, Nature Photonics, vol.83, issue.1, pp.41-48, 2007.
DOI : 10.1038/nphoton.2006.49

L. Song, E. , and Q. H. Liu, A fast 2d volume integral-equation solver for scattering from inhomogeneous objects in layered media, Microwave and Optical Technology Letters, pp.47-128, 2005.

G. Vainikko, Fast Solvers of the Lippmann-Schwinger Equation, Direct and Inverse Problems of Mathematical Physics, p.423
DOI : 10.1007/978-1-4757-3214-6_25

C. Weber, A local compactness theorem for Maxwell's equations, Mathematical Methods in the Applied Sciences, vol.46, issue.3, pp.12-25, 1980.
DOI : 10.1002/mma.1670020103

Y. Wu and Y. Y. Lu, Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method, Journal of the Optical Society of America A, vol.26, issue.11, pp.26-2444, 2009.
DOI : 10.1364/JOSAA.26.002444

J. Yang and B. Zhang, An inverse transmission scattering problem for periodic media, Inverse Problems, vol.27, issue.12, p.22, 2011.
DOI : 10.1088/0266-5611/27/12/125010

J. Yang, B. Zhang, and R. Zhang, A sampling method for the inverse transmission problem for periodic media, Inverse Problems, vol.28, issue.3, p.17, 2012.
DOI : 10.1088/0266-5611/28/3/035004

P. Zwamborn, P. Van-den, and . Berg, The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems, Microwave Theory and Techniques, IEEE Transactions on, pp.40-1757, 1992.