Two types of double-sided nanostructure, one possessing a slit aperture with parallel grooves and the other possessing a circular aperture with concentric grooves, were fabricated to examine the similarities and differences of their diffraction behavior in one-dimensional (1-D) and two-dimensional (2-D) nanostructures. Based on the projection-slice theory, we conjecture that the surface plasmons in these two different nano-scale grooves possess similar modes. A localized surface plasmon (LSP) was used to examine the transmission characteristics induced by the apertures. The transmission characteristics of the slitted nanostructure and the circular nanostructure aperture were then measured. We coupled the transmission spectra measured from these two apertures with a 1-D parallel groove transmission curve simulated by a 1-D rigorous coupled wave analysis. Measured spectra results show reasonable agreement with the simulated data. We propose that the apparent blueshift observed in the peak frequency of a 2-D nanostructure is due to the difference in the shape of the aperture and the spot transmission characteristics of 1-D and 2-D systems as induced by a LSP.