Extraordinary optical transmission (EOT) of light passing through sub-wavelength holes array in a metallic film has been found in 1998 [1]. It has attracted lots of attention, because this effect can be used in sub-wavelength integrated optical circuits [2–7], biosensors [8], surface plasmon enhanced Raman scattering [9, 10]. Lots of efforts have been made on this field in order to understand the fundamental physical mechanism and design more efficient structures [11–26]. Nowadays, it is considered that EOT of the sub-wavelength holes array is caused by the coupling between the incident waves and the surface plasmon polariton (SPP) with the help of the periodic two-dimensional holes array [7, 11]. In addition to circular holes arrays, EOT phenomenon was also found in holes arrays with different shapes, such as elliptical, rectangular, and annular holes [12–18]. Later, it is found that the localized surface plasmon resonance (LSP) could also play a role in the EOT in the holes with rectangular or elliptical shapes together with the SPP. To specify the contribution of the LSP, arrays of holes with a nanoparticle in each hole are fabricated and measured [19–22], it is found that both the SPP and the LSP contribute to the optical transmission, and both the real and imaginary parts of the polarizability of the particles which induce LSP play important roles in the transmission suppression and enhancement [20]. Very recently, an array of holes with very acute angles was found to exhibit a strong EOT effect caused by the LSP [27], an array of three-dimensional holes was also found that it has strong EOT effect induced by the LSP [28]. The waveguide mode across each hole can also play an important role in the extraordinary transmission through Fabry–Perot resonance [14, 29]. Until now, there have been no reports about the extraordinary transmission in a non-planar asymmetric structure. Here, we developed a unique fabrication method and prepared periodic arrays of three-dimensional crescent-like holes (3DCLH) as shown in Fig. 1a, by colloidal lithography with shadow metal evaporation method. We report, to our knowledge, the first evidence of the extraordinary transmission induced by an asymmetric localized surface plasmon resonance in the arrays of 3DCLHs. This phenomenon can be useful for the coupling of the incident light to localized surface plasmon, e.g., for sensing applications. It is also valuable in the applications of sub-wavelength optoelectronic circuits.

To fabricate 3D crescent-like holes array, an inverted hemispherical colloidal lithography method [40] is adopted; the fabrication procedure plotted in Fig. 1a can be described as follows: First, a layer of sacrificial polyacrylic acid (PAA) film was spin-coated on a cleaned silicon wafer, and baked at a hotplate with 120 °C for 5 min—the thickness of the PAA is around 220 nm; then, a layer of 137 nm polystyrene (PS) film was spin-coated on the sacrificial layer, the baking temperature and time were 120 °C and 5 min respectively; after that, the surface was modified by oxygen etching. Secondly, a multilayer of silica spheres with a diameter of 264 nm was spin-coated on the PS film, then the sample was placed on the hotplate with a temperature of 115 °C for 7 min to make the bottom layer of silica spheres embed into the PS film with a depth of around 98 nm. Thirdly, the silica spheres were removed by hydrofluoric acid (HF) with a concentration of 2%, a layer of dimple array was formed on the PS film, and then the PAA film was dissolved in water, a floating patterned PS film was formed and transferred onto the quartz slide. Finally, a shadow evaporation method was employed to deposit a layer of silver on the patterned PS film, a 3D crescent-like holes array was formed. The schematic structure of fabricated sample is shown in the last step of Fig. 1a. On the top surface, it looks like a periodic array of holes. However, within a unit cell, part of dimple is also deposited with silver because the shadow evaporation method can deposit metal on the part of the dimple by varying the deposition angle α, as shown in Fig. 1a. In other words, how much area within the dimple is deposited with silver can be controlled by α. It looks like an array of crescent holes in top view; it is a three-dimensional structure. Here, it is named as a periodic array of three-dimensional crescent-like holes (3DCLH). The thicknesses of the silver at the top surface and the dimples are quite different since the metal evaporation angle varies at different parts within a unit cell. Figure 1b is the cross-sectional view of the unit cell by cutting along a line which passes through the center of the circle and is perpendicular to the cross-line. t is the thickness of the metal on the top of the PS film, θ is the metal evaporation angle, g is the gap width of the crescent-like hole, tf is the thickness of the thickest metal part where silver is deposited vertically. The interface between the PS top surface and metal layer is at z=0. The depth of the dimple before depositing metal layer is h. The diameter of the dimple is w.

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 3a 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−M to Γ−K 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−M and Γ−K directions are nearly the same except that there is a surface plasmon polariton peak at 490 nm for Γ−M direction, as shown in Fig. 3b. 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. 4a–d. 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. 3a, 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.