A theoretical revisit of giant transmission of light through a metallic nano-slit surrounded with periodic grooves

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.

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. 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][4][5][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, and also has similar features but with some mismatches compared with the thick solid curve (e.g., the positions of the two peaks in each period have some small shifts and the relative intensities of the two peaks do not match quite well). This is because the influence of the nano-slit can be considered as a disturbance to the light distribution on the input surface. Both the grooves and the nano-slit can generate SPWs on the input surface. However, the intensity of the groove-generated SPW on the input surface is much larger than that of the nano-slit-generated SPW. Furthermore, due to destructive interference in the slit cavity, a non-resonant nano-slit gives negligible influence [2] to the local field distribution (on the input surface) generated by the grooves [this explains the good matching between the thin solid curve and the dashed curve in Fig. 2 slit-to-groove distance L 0 in the first period, and its corresponding field distribution |H y | is shown in Fig. 3(a). In Now we come back to study the structure of Fig. 1 (called the whole-grating case hereafter). We redraw in Fig. 2 half-gratings; opened with the nano-slit) as shown in Fig.   3(b)-(e) for |H y | distributions at the above two peaks and two valleys. For a minimal transmission situation (corresponding to slit-to-groove distance L 2 ) shown in Fig. 3(c), the field distribution on the grating interface is the same as the field distribution on the grating interface for the half-grating case in Fig. 3(a) and an oscillation peak (but not large field intensity) is formed on the flat metal-air interface [also seen clearly in the middle square region of curve |H y | ~ x in shown in Fig. 3(e), the field distribution is very similar to that in Fig. 3(c), and the only difference is that there are three oscillations on the flat metal-air interface between the two half-gratings [a small one at the center and two large ones on the sides, seen from the enlarged insert for |H y | ~ x in Fig. 3(e)]. The small (or extremely small) amplitude at the center is the reason for the low transmission when L = L 2 (or L = L 4 ). For a maximum transmission situation (L = L 1 ) shown in Fig. 3(b), the field distribution on the grating interface is no longer the same as that for the half-grating case, instead, it is strongly confined at x = 0 (the opening position of the nano-slit) and an oscillation is formed between the nearest left and right grooves [see curve |H y | ~ x in the square region of Fig. 3(b), which is much stronger than that in Fig. 3(c)]. For the other maximum transmission situation (L = L 3 ) shown in Fig. 3(d), the field distribution on the grating interface is quite similar to that in Fig. 3 The authors of Ref. [9] proposed a magnetic field phase theory and argued that the maximal (or minimal) transmission through the nano-slit corresponds to constructive (or destructive) interference between the groove-generated SPW and the incident plane wave at the nano-slit center, which was realized by adjusting the slit-to-groove distance to L ≈ 0.5λ sp (or L ≈ λ sp ). According to their magnetic field phase theory, the maximal transmission should appear when L= 0.5λ sp + Kλ sp (K is an integer) and there should be only one maximal transmission per period (λ sp ) for the curve η ~ L, which conflicts with our results shown in Fig. 2(a) that there are two transmission peaks per period. Their mistake is that they predicted the optimal distance (L) of maximal transmission through a nano-slit surrounded with 33 pairs of grooves by using the excitation phase of the SPW of only one groove on one side of the nano-slit. In Fig. 2(b) we plot curve η ~ L when only one groove is milled on one side of the nano-slit (i.e., half-grating with N = 1) with the thin dashed curve. From this curve one sees only one oscillation peak per period, which is completely different from the thick solid curve (for the whole-grating case when N = 12). The theory in Ref. [9] is not reliable as one sees clearly in Fig. 2 for this special case. In addition, we plot in Fig. 2(b) curve η ~ L (thin solid) for the whole-grating case when N = 1.
Unlike the big difference between the thick solid curve (whole-grating) and the thick dashed curve (half-grating) in Next we check whether the directly incident plane wave plays a significant role in the transmission enhancement or suppression of light through the nano-slit (the authors of both Refs. [7] and [9] believe that the directly incident plane wave plays a significant role). We replace the plane wave with two separated point sources (actually line sources in a 3D space) located at (±11 μm, -10 nm). In Fig. 4, we show curves η n ~ L for four different sets of groove depth and width for this side-point-source case (thick curves) and compare with the incident plane wave case (thin curves).
When the groove depth is large (H = 60 nm), one can see in shapes, as shown in Fig. 4(d). This can be explained as follows. For the side-point-source case, there is little light illuminating directly on the nano-slit, hence curve η n ~ L is mainly determined by the groove-generated SPW. When a plane wave impinges directly onto the slit opening, it will interfere with the groove-generated SPW [note that all the magnetic fields are in the same direction (y-direction)]. For periodic grooves with a large depth, the intensity of the groove-generated SPW near the input surface is very strong, usually several times larger than the incident field. Thus the influence of the incident field to light distribution (on the input surface) generated by the grooves is negligible, and consequently the curves of η n ~ L for the side-point-source case and the plane wave incident case are quite similar.
However, for shallow grooves, the input surface can be approximated as a flat metallic surface and the groove-generated SPW is weak. After interfering at the slit opening with this weak SPW generated by the grooves, the incident plane wave changes quite much the shape of η n ~ L as compared with the incident wave from the two point sources.
In summary, through the above analysis we have shown the influence to transmission through the nano-slit surrounded with periodic grooves should come from three parts: the groove-generated SPW, the nano-slit-generated SPW, and the incident wave. We have also shown that several previous theories, including the magnetic field phase theory of Ref.
[9], can not be used to predict the slit-to-groove distance for a maximal transmission through the nano-slit. We have given a clear physical explanation for the dependence of transmission on the distance between the nano-slit and the nearest groove by studying and comparing various scenarios.