On metallic gratings with very narrow slits, the Fabry-Perot-like phenomenon has been found in the SP resonant
transmission: Transmission peaks appear periodically according to the increment of grating depth. We study the
phenomenon by setting constants of the structure to be at nanometer scale. The rigorous coupled-wave analysis method
(RCWA) has been used in this work. The grating structure we examined is composed of silver. Slits are filled with
dielectric. For silver, its plasma wavelength λp=110nm. We study the gratings with period of gratings d=3λp, the grating
depth h=2.5λp, width of slits is 0.22λp, and slits on the grating is filled with GaP which refraction index is 3.7. Under
this situation, there is no excited peak at the wavelength theory predicts. Next we have investigation on the transmission
of the SP resonant mode. Wavelength of normally incident TM-polarized plane wave equals period of gratings. It can be
seen from the zero-order SP resonant transmission versus the grating depths, that there is no Fabry-Perot-like
phenomenon upon the wavelength calculated from the theory, which appears evidently at greater geometry.
Transmission value falls quickly via grating depth increases. Fabry-Perot-like phenomenon is caused by energy
transmission in the slits, but nanometer scale slits will cut off the energy transmission in the slits. It's concluded that the
surface plasmons execute negative effect on transmission anomalies when the grating dimension is at nanometer scale.
It's useful for the fabrication of the sub-wavelength optical element.