Guided waves by electromagnetic gratings and non‐uniqueness examples for the diffraction problem

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.