Resonant effects in compound diffraction gratings: Influence of the geometrical parameters of the surface

We explore and discuss the influence of the geometrical parameters of a compound diffraction grating on the generation of $\pi$ resonances, which appear when the surface is illuminated by a p-polarized plane wave. We consider a grating with rectangular grooves, and analyze the evolution of $\pi$ resonances when depth, width, distance between grooves, and period of the grating are varied. In particular, we performed a detailed study for a grating with five grooves per period, and found that there are certain values of the geometrical parameters that optimize the enhancement of the electromagnetic field inside the corrugations. For an increasing depth of the grating, the resonant frequency verges on the value that corresponds to a finite grating. We also show numerical examples of the amplitude and phase of the electromagnetic field, where the differences in the near field for resonant and nonresonant configurations become apparent.