%0 Journal Article %T Guided Waves by Electromagnetic Gratings and Non-Uniqueness Examples for the Diffraction Problem %+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS) %A Bonnet-Ben Dhia, Anne-Sophie %A Starling, Felipe %< avec comité de lecture %@ 0170-4214 %J Mathematical Methods in the Applied Sciences %I Wiley %V 17 %N 5 %P 305-338 %8 1994-04 %D 1994 %R 10.1002/mma.1670170502Journal articles %X We consider the two-dimensional scalar problem of the diffraction of a plane wave by an infinite grating of conducting bodies immersed in a periodical dielectric medium. A Fredholm-type formulation is derived and studied. The existence of a solution is proved and some uniqueness results are established. A detailed description of the guided modes of the grating is carried out. Finally, various non-uniqueness examples for the diffraction problem are exhibited. %G English %L hal-01010197 %U https://ensta-paris.hal.science/hal-01010197 %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-SACLAY %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ INRIA2