To characterize the optical properties of 3DCLHs, we measured the zero-order angle-resolved transmission for p-polarized waves (the electric field is on the incident plane). It should be pointed out that, in all the angle-resolved spectra shown in this paper, the curves are plotted with subsequent vertical offsets of 5% for each step increase of incident angle. Figure a shows the results where the electric field is pointing along with the cross-line of the 3DCLH as shown in the inset. Two transmission dips are in 546 and 634 nm at normal incidence, as indicated by red arrows; these two dips are composed of a large dip. There are two peaks which are at 570 and 1,028 nm. In order to understand this transmission, we simulated the transmission of the 3DCLHs arrays via finite-difference time-domain (FDTD) method [41
]. Because the domain size is about 10 μm, the cross-lines of 3DCLHs are oriented to different direction from Γ
in various domains with different lattice orientations. In simulation, we have to consider all these conditions. Here, we simulated various 3DCLHs arrays with their cross-lines oriented to different lattice directions, and made an average of these transmissions. The simulated transmission spectra of the 3DCLHs arrays with their cross-line parallel to Γ
directions are nearly the same except that there is a surface plasmon polariton peak at 490 nm for Γ
direction, as shown in Fig. . This means that the different orientations of the crescent-like holes arrays have the same optical transmission when the wavelength is larger than 550 nm. In other words, when the wavelength is larger than 550 nm, the transmission property of the array are mainly decided by 3DCLH rather than the periodic structure. The simulation results show that there are two dips at 554 and 668 nm, and two peaks at 600 and 952 nm as well. Overall, the simulation results match with experimental results well, except that there exists a deviation at peak position which may be caused by the structure used in simulation not being perfectly the same as the real structure (the rough surface is not considered here). We further inspect the electric field distribution at each dips and peaks, as shown in Fig. . It is found that, at the peak position of 962 nm, the electric field is concentrated on the outer surface of 3DCLH and strongly localized at the crescent tip, which enables the resonant field to be re-radiated into the PS film as transmitted wave. In a unit cell, the resonant mode is a dipole resonance, as indicated by the charge polarity. The strong localized field at the crescent tip is mainly caused by the crescent structure and rather than a periodic effect. At the dip position of 668 nm, the electric field is mainly trapped within the dimples covered with silver, and thus, most of which is reflected back into the air. Because the electric field is localized at the 3D crescent-like holes area, the peak at 962 nm and dip at 668 nm are caused by localized surface plasmon. This can also be found from the experimental angle-resolved transmission spectra of Fig. , where the transmission peak position at 1,028 nm and dip position at 634 nm do not change with the change of incident angle. While for the peak position at 600 nm and dip position at 554 nm will change their positions with the change of the incident angle, this can be found from their electric field distribution which is weakly localized at dip’s area, especially the area having silver. Their field distributions also indicate dipole resonance as well. This is caused by the combination of surface plasmon polariton and localized surface plasmon, the detailed mechanism becomes more complicated which requires further study.
Fig. 3 a The zero-order angle-resolved transmission spectra of the 3DCLHs array shown in Fig. a for the electric field of incident p-polarized waves being along the cross-line; the curves have been plotted with subsequent vertical offsets of 5%. The (more ...)
Figure a represents the angle-resolved zero-order transmission when the electric field of the incident p-polarized waves is perpendicular to the cross-line of 3DCLH. Because the unit cell of the 3DCLHs array has no mirror symmetry for positive and negative incident angles, we measured the angle-resolved spectra from −60° to 60° as shown in the inset. There exists a wide dip at 595 nm when the incident angle is 0°. The peak transmission at normal incidence at the wavelength of 1,336 nm is about 32.22% which is much higher than that in the case of electric field being along with the cross-line of 3DCLH. If the transmission is normalized with the fraction of holes’ area of 7.7%, the transmission can be over 4.18, which exhibits an extraordinary optical transmission phenomenon. It is surprising that this transmission peak does not shift with the change of incident angle. To understand the physics of this transmission, we also simulate the transmission through FDTD method. It is shown in Fig. , where the simulated transmission is an average of the transmissions of the 3DCLHs arrays when the cross-lines of 3DCLHs are oriented to Γ
, respectively. The transmission spectra of the 3DCLHs arrays with different orientations of the 3DCLH’s cross-line are shown in this figure. It is found that the transmission spectra of these two cases with different orientations of the cross-lines are nearly the same. This means that the orientation of the cross-line of the 3DCLH does not affect the transmission in the normal incidence. Comparing the simulating results with the experimental results, it is found that the shape of the transmission spectra agrees well with each other except that the position of the peak has slightly deviation where the simulating and experimental transmission peaks are at 1,442 and 1,336 nm, respectively. The deviation is caused by the simulation structure is not perfectly matching to the experimental one as mentioned before. For the wavelength shorter than 600 nm, it is not considered here because both SPP and LSP play roles in the transmission and makes it more complicated. Looking into the electric field distribution at the peak position shown in Fig. , it can be found that the electric field is strongly localized at the low arc of the 3DCLH, which indicates an asymmetric localized surface plasmon resonance. Such a resonance, it could show an angle insensitive coupling to incident light similar to the symmetric localized plasmon resonance [27
], this might be the reason why the peak is consistent with the change of the incident angle when the electric field of the incident beam is perpendicular to the cross-line of the 3DCLH. Therefore, we found a novel physical phenomenon of EOT whose peak position is determined by an asymmetric LSP rather than SPP. The peak position is nearly stable with the change of incident angles. It might be useful for the sub-wavelength integrated optics and optical sensors.
Fig. 5 a and b are the zero-order angle-resolved transmission spectra of the 3DCLHs array shown in Fig. a for the electric field being perpendicular to the cross-line of 3DCLH, a for p-polarized waves; b for s-polarized waves. In all spectra graphs, (more ...)
Because SPP can only exist efficiently in the p-polarized wave and does not exist in s-polarized waves [42
] to further exclude the SPP effect on the abnormal EOT, we also measured the zero-order transmission when the electric field of the incident s-polarized waves is perpendicular to the cross-line of the 3DCLH, as shown in Fig. . It is found that, even with the incident angle up to 60°, the transmission is still as high as 18.34%, and the peak position does not shift as well. Therefore, we could also obtain a conclusion that this EOT is induced by LSP rather than SPP.
To study this EOT in details, we fabricated various 3DCLHs arrays with different thicknesses of the silver film and various gaps. Figure shows the p-polarized angle-resolved transmission of the 3DCLHs array with 37 nm thickness of silver as shown in Fig. . The filling fraction of the crescent-like holes is 13.56%. For the electric field of the incident waves being perpendicular to the cross-line, there also exists an EOT peak (48.32%) at the wavelength of 1,228 nm which does not change with the incident angle, if it is normalized with the fraction of the holes’ area, the transmission can reach 3.56. It is found that, if the hole area is nearly the same, the peak position shifts to the short wavelength with the increase of the thickness of the silver; if the thicknesses of the silver are nearly the same, the peak position shifts to the long wavelength with the decrease of the gap, and the normalized transmission with the fraction of the hole area is also becoming larger with the decrease of the gap.
Fig. 6 The angle-resolved transmission spectra of the 3DCLHs array shown in Fig. b for the electric field of the incident p-polarized waves being vertical to the cross-line, where the black thin line is the transmission of a thin silver film with a (more ...)