The giant transmission of light through a metallic nano-slit surrounded by periodic grooves on the input surface is revisited theoretically. It is shown that the influence to the transmission comes from three parts: the groove-generated surface plasmon wave (SPW), the nano-slit-generated SPW and the incident wave. The groove-generated SPW is the main factor determining the local field distribution around the nano-slit opening, which is directly related to the transmission through the nano-slit. The nano-slit-generated SPW can be considered as a disturbance to the light distribution on the input surface. The influence of the incident wave can be strongly reduced when strong surface plasmon wave is generated on the input surface by many periods of deep grooves. Our study shows that the slit-to-groove distance for a maximal transmission through the nano-slit surrounded with periodic grooves can not be predicted by several previous theories, including the magnetic field phase theory of a recent work (Phys. Rev. Lett. 99, 043902, 2007). A clear physical explanation is given for the dependence of the transmission on the slit-to-groove distance.PACS numbers: 42.25. Bs, 42.25.Fx, 42.79.Ag, 73.20.Mf Transmission efficiency of an isolated nano-aperture in a metallic film is quite low [1,2]. However, by using periodic grooves around the aperture on the input surface, transmission efficiency could be greatly enhanced (see e.g.[3-6]). Such a phenomenon has been intensively studied [7][8][9] and can be applied in many potential applications [10,11].However, until now the physical mechanism of this phenomenon is still not fully explained. For example, one important issue is the dependence of the transmission on the distance between the nano-slit center and the nearest groove center, and this has been studied in Refs. [7] and [9] with inconsistent conclusions (both conclusions are not correct as one will see below in our study). In this letter, through an extensive study of the transmission (field) property for different slit-to-groove distances in various scenarios, we explain clearly the physical mechanism of extraordinary transmission through the nano-slit surrounded with periodic grooves. First we study the structure with groove depth H = 60 nm, width W g = 250 nm, period P = 720 nm and number N = 12.The distance between the slit center and the nearest groove center (slit-to-groove distance) is denoted by L and the width of the nano-slit is W s = 50 nm. In Fig. 2(a), we show transmission efficiency η as a function of L when t = 340 nm (thin solid curve; forming a non-resonant nano-slit) or t = 200 nm (thick solid curve; resonant). Since the transmission through the nano-slit is directly related to the local field distribution around the nano-slit opening, we fill the air nano-slit with the same metal (gold) and check the magnetic field amplitude |H y | at point (0, -10 nm) as a function of distance L [the dashed curve in Fig. 2(a)]. One sees that the dashed curve oscillates with the same features as the thin solid curve...