The excitation of a surface plasmon polariton (SPP) wave on a metal-air interface by a diffraction grating under monochromatic normal illumination is investigated numerically. The influence of the different experimental parameters (grating thickness, period, and duty cycle) is discussed in detail for a semi-infinite metal and a thin film. Both engraved (grooves) and deposited (protrusions) gratings are considered. The most efficient coupling to the SPP is obtained for a groove grating which duty cycle is about 0.5. Furthermore a small grating depth of some tens of nanometers is sufficient to excite a SPP mode with a coupling efficiency higher than 16% in each direction. Implications for practical SPP experiments are discussed. (c) 2006 American Institute of Physics.