Resonant modes of a bottle-shaped cavity and their effects in the response of finite and infinite gratings

The resonant frequencies of a one-dimensional bottle-shaped cavity embedded in a ground plane are calculated using a modal approach for s and p polarizations. The same formalism is used to solve the problem of scattering from a surface with a finite number of cavities and from an infinite periodic grating. We show numerical results where the resonant behavior is evidenced as dips in the curve of intensity specularly reflected from a surface with one or several bottle-shaped grooves. The surface shape resonances of a single cavity are also shown to have a great influence on the efficiency distribution of the diffracted orders from infinite gratings made of bottle-shaped cavities. The excitation of even and odd modes is analyzed for both polarizations.