1. Introduction

Surface plasmons excited by periodic structures have been widely used in bio-sensing [1–4], nano-lasing [5–8], particle trapping [9,10] and signal processing [11]. Among various periodic nanostructures, ring as a basic element is the most intensively investigated one, which shows the diversity of optical properties through varying the size, numbers of rings and the distance between each other [12,13]. Fano resonance which is super sub- and sup-radiation modes excited from ring arrays by coupling SP modes with other modes has been realized [14–17]. In addition to theoretical analysis, fabrication of diverse of ring nanostructure has also been a significant problem as traditional nanofabrication technique is still constrained by fabrication efficiency and costs, such as focused ion beam lithography and electron beam lithography [18–20]. Fortunately, a recently developed low-cost and high-efficiency method, nanosphere lithography method, has shown prominent prospect for a certain type of nanostructures, which affords a flexible approach to produce versatile periodic structures through a layer of assembled sphere arrays, especially ring or concave arrays [18,21]. Moreover, non-concentric rings have been fabricated by this method. Recently, a great variety of patterns has been created by moire lithography method that is known as a modified nanosphere lithography method [22,23]. However, compared with two-dimensional thin ring slabs, rings with large height do not attract much attention due to fabrication difficulties.

The height variety in the third dimension affords more freedom to tailor optical properties [24,25]. For example, a single dielectric ring tube can support coaxial waveguide mode in height direction, as have been theoretically investigated in Ref [17]. Although rings slabs with varied diameter and arrangement were thoroughly understood, RTAs with height in hundred nanometers have not been experimentally and theoretically studied.

In this paper, large area close-packed RTAs were fabricated by NSL method and their optical properties were investigated. Using monolayer colloidal crystals (CCs) as a template and followed with reactive ion etching (RIE), RTAs have been created. Coupled cavity mode and surface plasmon polaritons excited by RTAs are analyzed by calculating the distribution of the electromagnetic field and charge density at resonance wavelength by FDTD. In addition, RTAs with varying silver film thicknesses and heights are theoretically and experimentally explored.

2. Experimental methods

2.1 Preparation of close-packed RTAs

Firstly, Polystyrene (PS) microsphere (Bangs laboratory, 10 wt%) aqueous solution diluted to concentration of 0.5 wt%, and then added with 0.002 vol% acidic catalyzed TEOS solution (TEOS solution: 0.1mol/L HCl: EtOH is 1: 1: 2, stirred for 1 hour before use) and dispersed by ultrasound for 5 min. Then a cleaned slide was inserted into the solution and fixed vertically. Microsphere diameter used in this experiment is 690 nm. The solution was placed inside an oven with temperature constant at 45°C ± 1°C (Zhicheng Instruments). As the solvent evaporated slowly, the monolayer PS microspheres were self-assembled on the surface of the glass slide, and the SiO₂ precursors are filled in the interstices between the microspheres in the form of gel. About 20 hours later, a monolayer composite PS microsphere arrays with a length of 2 cm are produced on the slide.

As depicted schematically in Fig. 1(a), the fabrication process consists of four steps. Firstly, the PS microspheres in the composite arrays were removed by high-temperature sintering or toluene and leaving a two-dimensional periodic hemispherical concave array, which consists of SiO₂ gel. Secondly, the above two-dimensional periodic hemispherical concave arrays were dry etched to form RTAs by reactive ion etching (RIE) (SF₆: O₂ = 50 sccm: 20 sccm, 150W). The key point to form RTAs is that the etching rate at the central of the concave edges is faster than other concave edges [18]. Consequently, as the etching time increasing, the different etching rates (A, B and C) at different locations in the hemispherical concave arrays result in the close-packed RTAs, as shown in Fig. 1(a). Followed by sputtering a layer of silver film on the structure, we obtained metal RTAs, as illustrated in Fig. 1(b) and 1(c) by SEM images. Here t represents etching processing time. Polyurethane (PU) dropped cast on the RTA and cured by UV light and then was peeled off to get freestanding cylindrical column arrays (CCAs) (see Appendix A, Fig. 6).

 

Fig. 1 (a) Schematic diagram of the fabrication processes to produce close-packed nanoring tube arrays (RTAs) and A, B, C represent different RIE etching rates, which results in the RTAs from concave array. (b) Top view SME image of close-packed RTAs. (c) SME image of close-packed nanoring tube arrays coated with Ag. Scale bar in images (b) and (c) are 1μm, respectively.

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2.2 Finite-difference time-domain simulation

In order to investigate the origin of optical properties of Ag close-packed RTAs, FDTD simulation was conducted to simulate electric field distribution at resonance wavelength. The dielectric ring height h was 440 nm, dielectric ring outer radius R and inner radius r were 345 nm and 245 nm respectively, the Ag film thickness d was 100 nm, and the wall of the dielectric ring in the cavity was coated with a 30 nm thick Ag film. A grid size of 5 nm in x-, y-, and z-direction was used to conduct the simulation.

3. Results and discussion

3.1 Optical properties of Ag close-packed RTAs

Large-area highly ordered Ag close-packed RTAs were produced by the nanosphere lithography (NSL) methods (Fig. 1(a)), and the simulated reflectance spectrum of the metal RTA structure presents multiple reflectance dips in the visible and near-infrared range, which are λ₁ = 425 nm, λ₂ = 614 nm and λ₃ = 780 nm, as shown in Fig. 2(a). According to the simulated electric field distributions and charge density distributions at both XOZ and XOY plane, the three resonance modes show different patterns, as presented in Fig. 2(b)-2(j). The λ₁ = 425 nm is attributed to surface plasmon polaritons Bloch wave (SPP-BW), which can be calculated from the theoretical SPP dispersion relation of two-dimensional hexagonal arrays [13,24,26]:

 

Fig. 2 FDTD simulated optical properties of Ag close-packed RTAs. (a) The simulated reflectance spectrum of close-packed RTAs. Calculated electric field and charge density distributions at the wavelengths of 425 nm, 614 nm, 780 nm. (b - d) the electric field distribution at XOZ plane. (e - g) the electric field distribution at XOY plane with Z = 380 nm. (h - j) charge density distributions calculated from the electric field distribution shown in (b - d). Length unit of X and Y axis in (a - g) are m and nm in (h - j).

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In the visible spectral region, another reflectance dip at λ₂ = 614 nm is due to the Wood’s anomaly (WA), confirmed by simulated electric field distribution pattern and the calculated value of 597.5 nm from WA calculation Eq. (2) [26], as shown in Fig. 2(c) and 2(i). Strong resonances characterized by large local enhanced electric field are excited at RTA edge along polarization direction.

Characterized by a broad reflectance dip at ~780 nm, a localized surface plasmon resonance in the cavity was excited. The electric field located mainly inside the Ag nanoring tube, which confirms that λ₃ originates from the cavity mode of the nanoring tube, as depicted in Fig. 2(d), 2(g) and 2(j). This mode is sensitive to materials inside the tube.

3.2 Reflectance spectra of Ag close-packed RTAs with varying height

According to Eqs. (1) and (2), SPP-BW and WA are tunable over a large spectral range by changing periodicity. To investigate the dependence of cavity mode on geometry size, reflectance spectra of the RTAs with varied height were simulated (Fig. 3(a)). As RTAs height increases, there is a red shift of the cavity mode at around 780 nm, whereas the locations of the (1, 0) Ag/Air reflectance peak and (1, 0) WA unchanged (Fig. 3(b)). Thus, the wavelength of the cavity mode is proportional to the height of RTAs, and it will couple to WA as height decrease to ~100 nm and emerge to one dip. Since the height of RTAs can be precisely adjusted by RIE etching time t, the dip can be tuned from ~640 nm to ~780 nm. Evolution of electric field distribution at cavity mode wavelength with increased height is given in Appendix B.2, Fig. 8. Due to the optimized self-assembly parameters, the wall thickness of the ring tube is mostly fixed at about 65 nm ± 10 nm in the experiments, and the wall thickness will slightly shift the cavity mode wavelength, similar to the height. Increase the wall thickness, the cavity mode will shift to a shorter wavelength (see Appendix B.3).

 

Fig. 3 (a) Simulated reflection spectra for the close-packed RTA with Ag film thickness d = 100 nm of varying height for h = 100 nm, 150 nm, 200 nm, 250 nm, and 440 nm. (b) Dependence of the plasmon resonance dip on the RTAs height h. Blue arrow denotes the Wood’s anomaly and the dotted line indicates the evolution of the cavity mode position versus height variation.

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3.3 Experimental results of RTAs with varied t and d

Reflectance spectra of Ag closed-packed RTAs with varying etching time t and silver film thicknesses d are experimentally measured, as shown in Fig. 4. As revealed in the previous paper [18], the etching time t and the density of silica gel determine the structure morphology. Insert figure in Fig. 4(a) clearly indicates the relationship between silver film thickness and the resonant wavelength. When etching time t = 3 min, the structure is still concave hole arrays because of insufficient etching time, and the reflection dip at wavelength of ~720 nm is a cavity mode. As a comparison, increasing t to 7 min when RTA is formed, a clear red-shift of the cavity-mode SPP as the thickness of Ag film increase (be equivalent to RTAs height increase) can be observed, which is in coincidence with the simulation results, as shown in Fig. 3(a).

 

Fig. 4 (a - d) Measured reflectance spectra of close-packed RTAs with a layer of varying Ag film thickness under etching time of t = 3, 7, 10, 16 min. (e) Measured angle-resolved reflectance spectra of Ag close-packed RTAs with t = 10 min, d = 175 nm for TM-polarized incident light. (f) Measured angle-resolved reflectance spectra of Ag close-packed RTAs with t = 10 min, d = 175 nm for TE-polarized incident light. The dotted line in (f) shows the broadened cavity mode as incident light angle increase.

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To investigate the different behavior of the cavity mode between t = 3 min and t = 7 min, we simulate the electric field distribution of the cavity mode at t = 3 min and find out that the electric field of this cavity mode are mostly located at the opening of the concave hole as Ag film thickness varies. Moreover, the maximum electric field is mainly located at the top and bottom edge of Ag film at the concave hole opening (see Appendix B.4.). Therefore, compared to the mode distribution shown in Fig. 2(d), we consider that the difference between t = 3 min and t = 7 min is mainly due to the modulation of the cavity. While the enhanced electric field is mainly located at the opening of the cavity and has less interact with the concave hole for t = 3 min, the cavity mode electric field is mainly located inside the ring tube and the cavity geometry change will affect the electric field distribution inside the cavity for t = 7 min. As etching time t further increase to 10 min and 16 min, the structure height is relatively low and tends to become ring arrays pattern, and thus, SPP-BW become the dominant effect in the reflectance spectra and the cavity resonance mode turns to weak and disappears finally (see Fig. 4(c) and 4(d)). The dips at about 550 nm correspond to the (1, 1) SPP mode at the Ag/SiO₂ turns up and do not shift as Ag film thickness increase.

Evolution of the reflectance spectrum of Ag close-packed RTAs with varied incident angle and polarization was also experimentally investigated. As incident angle increase, new modes were excited on metal RTAs, as presented in Fig. 4(e) and 4(f). The Ag close-packed RTAs is produced by t = 10 min and d = 175 nm. The cavity-mode at about 680 nm remains as the angle of incident light increase from 0° to 45° for both TE and TM polarization. Two new modes (mode 1 and mode 3) emerge as the angle increase from 0° to 60° for TM polarization, which is both attributed to the (1,0) SPP-BW at the Ag/Air interface and can be deduced from Eq. (1). In addition, the formation of mode 2 is due to the interaction of cavity mode SPP and propagating SPP modes. In comparison, a broadening of the cavity mode as incident angle increase can be observed for TE polarization, and no SPP-BW were excited in Fig. 4(f). It should be noted that the reflectance spectra are polarization independent under normal illumination (see Appendix B.5, Fig. 11).

3.4 Close-packed RTAs as a template

Furthermore, the RTAs were also used as templates to produce column arrays by nanoimprint method. Freestanding PU films patterned with non-close-packed CCAs are produced. The gap size between neighboring columns is determined by the wall thickness of the rings, as shown in Fig. 5(a). In addition, FDTD simulation of the CCAs reveals multiple dips in the reflectance spectrum.

 

Fig. 5 (a) SEM image of the non-close-packed CCAs. (b) Simulated reflection spectra for the Ag non-close-packed CCAs. The three dark circles in the image are three broken cylindrical columns formed at the peeling off process. (c - g) Simulated electric field distributions for the dips respectively. (h - l) charge density distribution calculated from the electric field distribution shown in (c - g). The dielectric column radius is 245 nm, the side wall of the dielectric column is coated with 30 nm Ag, the Ag film thickness is 100 nm, the cylindrical column height is 440 nm, and the periodicity is 690 nm.

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There are three dips in the visible bands and two dips in the near-infrared region under the linearly polarized normal incident light, as shown in Fig. 5(b). The dominant effect in the CCA is a gap plasmon mode, which forms at gaps between different neighboring columns, indicated as D4 and shown in Fig. 5(f) and 5(k). From electric field distribution and charge density distributions (Fig. 5(c)-5(e) and 5(h)-5(j)), D1-D3 are (1, 1) SPP-BW, (1, 0) WA at Ag/air interface, and SP at Ag/PU interface, respectively. Since CCA has multiple unique surface plasmon properties, it can be employed as SERS substrates and in solar cells.

4. Conclusion

In summary, we proposed a method to produce large-area ordered Ag close-packed RTAs and investigated the optical properties of RTAs theoretically and experimentally. Combined with nanosphere lithography method and nanoimprint lithography method, RTAs could support SPP-BW, WA and cavity modes at normal incidence, and these modes are largely dependent on the height of RTAs. WA and cavity modes are in dominant for high height RTAs while SPP-BW and WA dominate the optical characters of RTAs with a short height. In addition, the cavity mode shows less angle and polarization dependent in the range from 0° to 45°. Different modes with electric field enhancement in different position make the RTAs flexible candidate for bio-sensing and solar cells. High absorption of Ag RTAs over the visible and near IR range has been experimentally demonstrated. Moreover, we have obtained large-area ordered CCAs by using close-packed RTAs as templates, which also exhibit a strong gap plasmon effect and can be applied as SERS substrates.

Appendix A Fabrication process for non-close-packed CCAs

 

Fig. 6 Schematic diagram of the fabrication process of non-close-packed CCAs: (1) PU drop cast on RTAs, (2) ultra-violet (UV) curing and peel off from the RATs template, (3) coating silver film.

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Appendix B Additional optical properties of non-close-packed CCAs

B.1 Fabry-Perot interference induced reflection dip

There is a small reflection dip (call it λ₄ here) between λ₁ and λ₂ in Fig. 1(a) and Fig. 3(a) in the main text. To understand the extra dip, we simulate the electric field distribution of this dip (λ₄) and the reflection peak (λ₅) between λ₁ and λ₄, as shown in Fig. 7(c) and 7(d). Because SPP-BW mode dominates the dip λ₁ and there is a weak F-P like interference in the vertical direction of the tube, the dip λ_4, and the peak λ₅ are probably attributed to the superposition of the F-P like interference and the SPP-BW mode. And this can be further confirmed by comparing to reflectance spectra of concave arrays with t = 3 min where no F-P like interference are observed and there is only one reflectance dip at 425 nm, as shown in Fig. 10(a).

 

Fig. 7 (a) FDTD simulated optical properties of Ag close-packed RTAs. (b - g) Calculated the electric field and charge density distributions at the wavelengths of 425 nm, 452 nm, and 471 nm.

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B.2 Evolution of the electric field distribution with RTAs height increase

 

Fig. 8 (a) and (b) Simulated reflection spectra of the close-packed RTAs with Ag film thickness d = 100nm and with varying height for h = 50 nm, 150 nm, 300 nm, 350 nm, and 440 nm. (c - f) Calculated the electric fields corresponding to the wavelengths of the cavity mode for tube height of h = 50 nm, 150 nm, 300 nm, 350 nm, and 440 nm at XOZ plane.

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B.3 Wall thickness of RTA–fabrication and influence on the cavity mode

The wall thickness of the ring tube is largely determined by the density of silicate gel infiltrated in the gap, and this density is largely affected by the self-assembly conditions such as evaporation rate and evaporation temperature which also determine the order of the self-assembled array. Based on SEM images collected from experiments, we examined the wall thickness of the ring tubes. The result shows that in our experiments with the same fabrication parameters (optimized self-assembly parameters to obtain high order sphere arrays and etching parameters), the wall thickness of RTA is typical ~ 65 nm and varies in a range of about ± 10 nm, as shown in Fig. 9(a)-9(d).

The wall thickness of the ring tube will affect the location of the cavity mode since the cavity geometry change will shift the location of the cavity mode. As the wall thickness decrease, the cavity mode shifts to longer wavelength, and vice versa. Similar to the effect of height on the cavity mode wavelength, as shown in Fig. 9(e).

 

Fig. 9 (a - d) SEM images of RTA before metal deposition fabricated from the same optimized self-assembly and etching parameters. The wall thickness of the RTAs is about 65 ± 10 nm. Scale bar in (a - d) is 100 nm. (e) Simulated reflection spectra of the Ag close-packed RTAs with SiO₂ wall thickness varying from 60 nm to 110 nm.

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B.4 Electric field distribution of the cavity mode for varied Ag film thickness for t = 3 min

 

Fig. 10 (a) Reflectance spectra of RTAs with increased silver film thickness at t = 3 min. (b) the electric field distribution at wavelength of 759 nm with 100 nm thick silver film. (c) the electric field distribution at wavelength of 755 nm with 150 nm thick silver film.

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B.5 The hexagonal lattice utilized in this work is polarization insensitive for normal incident light

 

Fig. 11 (a) Simulated reflectance spectra of close-packed RTAs for TM- and TE-polarized incident light, h = 440 nm, d = 100 nm. (b) Experimentally measured reflectance spectra of close-packed RTAs for TM- and TE-polarized incident light, t = 10 min, d = 175 nm.

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Funding

National Natural Science Foundation of China (61605082, 61875089, 41875035, 11374161, 61405094); the Natural Science Foundation of Jiangsu Province (BK20160969); the Primary Research & Development Plan of Jiangsu Province (No.BE2016756); the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (16KJB510020); and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD); China Postdoctoral Science Foundation Funded Project (2017M611654); Postdoctoral Science Foundation of Jiangsu Province (1701074B); The Startup Foundation for Introducing Talent of NUIST (2015r040); Open Project of Jiangsu Key Laboratory of Meteorological Observation and Information Processing under Grant KDXS1506.

Acknowledgments

We would like to thank Prof. Yixian Ge for helpful discussion.

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