VARIATIONAL FORMULATION OF MAXWELL EQUATI ONS IN A DOUBLY-PERIODIC GRATING IN R3

In this Note we deal with Maxwell's equations in periodic structures. The considered media may contain perfect conductors and materials with non constant coefficients. We will only consider ''quasi-periodic'' e xcitations and solutions. Using the Dirichlet-Neumann operator, we set an equivalent problem in a truncated elementary cell. Then we write a variational formulation of this problem which is of saddle point type and follows from Fredholm's alternative. This allows the study of the existence of solutions and the eigenvalue problem.