Functional Analysis and Applications Seminar 

03/10/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Ana Moura Santos, Instituto Superior Técnico, U.T. Lisboa

Wave Diffraction by a Strip Grating: The two-straight line approach

The present work deals with the problem of wave diffraction by a periodic strip grating which occurs in several application areas, in particular, antenna and waveguide problems, in electrical engineering, and diffraction of sound waves by periodic screens, in acoustics. We give a rigorous formulation of boundary-value problems of wave diffraction by a periodic strip grating, in which the width of each strip can be different from the spacing between any two adjacent strips, and also, greatly simplify the study of the invertibility of the operator which is associated with the diffraction problem restricted to Dirichlet and Neumann boundary conditions when the period is equal to double the width of the strips. The equivalence of the operators that appear in the original formulation of the diffraction problems to a Toeplitz operator defined on a space of functions with a two-straight line domain allows us to give sufficiently simple formulas for the inverse of the operator when the period of the grating is equal to double the width of the strips. This is a joint work with Prof. Amélia Bastos e Prof. Ferreira dos Santos.