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We design and investigate a 2.5-dimensional multi-resonant plasmonic nanostructure, which is a multilevel plasmonic nanoterrace array for enhancing both the excitation and emission processes of an optical effect. The new structure supports multiple resonances, which spatially match with each other and can be tuned independently by changing its geometrical parameters. It allows simultaneous enhancement of the local electric fields at multiple wavelengths associated with various optical processes. Moreover, as a 2.5-dimensional structure, the fabrication of the plasmonic nanoterrace array is simple and fast, making it a promising design for various surface-enhanced spectroscopy applications.
© 2017 Optical Society of America
1. Introduction
Plasmonic nanostructures can function as a resonant optical antenna for enhancing weak light-matter interactions [1]. On resonances, they can trap the far-field propagating field E0 into nanoscale spots in the near-field regime with a large field enhancement g = |Eloc/E0| [2–4], and vice versa due to the reciprocity principle [5]. This unique property makes plasmonic nanostructures a powerful platform for enhancing both the excitation (by g(λex)2 = |Eloc(λex)/E0(λex)|2) and emission processes (by g(λem)2 = |Eloc(λem)/E0(λem)|2) of various optical effects. To date, numerous structures have been studied for different applications ranging from the linear processes, such as surface-enhanced Raman scattering [6, 7] and surface-enhanced fluorescence [8] to nonlinear optical effects, such as second-harmonic generation (SHG) [9, 10] four-wave mixing [11, 12], and optical Kerr effects [13, 14], to name a few. However, most of the applications are based on the large local field enhancement generated by the resonance mode at the excitation frequency [15], despite that the total enhancement gtotal = g(λex)2 · g(λem)2 is also dependent on g(λem). This severely limits the performance of the plasmonic substrates. Particularly, for nonlinear optical processes, the emission frequency is commonly far away from the excitation and it is impossible to enhance both the emission and excitation with the commonly used single-resonance plasmonic nanostructures.
To address this issue, multi-segment designs were proposed recently to create multiple resonant modes. For example, strong enhancement of SHG signals at well separated “hot spots” were demonstrated experimentally [16, 17]. Despite the successes, those structures focused on the enhancement at sparse “hot spots”, and the design of multi-resonant plasmonic substrates capable of generating a large average enhancement of a given optical process uniformly is still a challenging task since it requires simultaneous optimization for the local field enhancement at two different wavelengths of a dense array structure. In fact, even for the case of single wavelength, uniform high enhancement was not possible until the recent progresses in the design of periodic plasmonic nanostructures [18, 19].
To tackle the above challenges, in this paper, we propose a new type of vertically coupled multi-resonant plasmonic structure, tri-level plasmonic nano-terrace array (3L-PNTA). We numerically investigate the optical properties of the 3L-PNTA, including its resonance frequencies, local field enhancement, and spatial matching between different modes, with the goal of developing a new type of highly efficient multi-resonant nanostructures for enhancing both the excitation and emission processes of optical effects and moreover applying in various surface-enhanced spectroscopy applications.
2. Design principle of the tri-level plasmonic nano-terrace array (3L-PNTA)
As illustrated in Fig. 1, the 3L-PNTA structure can be treated as an extended vertical version of a laterally coupled multi-segment plasmonic nanoantenna, which is one of the most popular and also the most flexible designs of multi-resonant plasmonic nanoantennas.
Fig. 1 (a) Lateral thin-film-based multi-segment plasmonic nanoantenna. (b) Vertical thin-film-based multi-segment plasmonic nanoantenna. (c) Extended vertical version of a thin-film-based multi-segment plasmonic nanoantenna. (d) Sketch of the 3L-PNTA array structure.
In the case of a multi-segment antenna, light is highly confined and enhanced in the nanogaps thanks to the lateral couplings between neighboring segments. On the other hand, the strong lateral coupling makes the antenna sensitive to gap sizes [20, 21]. Expensive high accuracy nanopatterning techniques, such as electron beam lithography and focus-ion beam milling are therefore needed for the fabrication [22]. More importantly, this type of antennas have a large footprint, limiting the density of “hot spots” and consequently the average enhancement.
To circumvent the above issues, in this work, we convert the laterally coupled structure into a vertical coupling structure. It results in a small footprint, allowing us to arrange the structures into a dense array. Moreover, in the case of vertical design, the size of the nanogaps can be precisely controlled by simply using standard etching and deposition processes. The precision can reach a few nanometers (< 10 nm), which is difficult to achieve for lateral designs with normal patterning techniques, including the electron beam lithography and focus ion beam. To make it polarization independent, we further extend the structure from 3 segments to 9 segments as depicted in Fig. 1(c). After arranging such a 9-segment structure into a 2D array, the final design is obtained, as shown in Fig. 1(d).
The 3L-PNTA structure offers a variety of near-field coupling channels. It not only allows multiple resonances (Fig. 2(b)), but also brings a high density of the nanogaps (12 nanogaps per unit cell), which is crucial for creating large average enhancement.
Fig. 2 (a) Waterfall plot of the reflection spectra of 3L-PNTA structures (A = 300 nm, L1 increases from 80 nm to 220 nm). The two white dash lines represent the reflection spectra in the case of L1 = 120 nm and L1 = 180 nm. (b) The reflection spectra of the 3L-PNTA structures with L1 = 120 nm (red line) and L1 = 180 nm (blue line).
3. Modeling and simulation method
The optical properties of the 3L-PNTA structure was numerically studied using a commercial finite-difference time-domain (FDTD) solver (FDTD Solutions, Lumerical Solutions Inc.). Periodic boundaries were used in the X and Y directions and perfectly matched layers were used in the Z direction. The mesh was 2.5 nm × 2.5 nm × 2.5 nm. The structure was excited by a linear polarized (along the X axis) plane wave from the normal direction (along the Z direction) with the wavelength ranging from 500 nm to 2000 nm. The permittivity reported by Johnson and Christy was used for the Au nanotiles [23] and the permittivity of SiO2 substrate was set to 2.10 in the simulations.
The detailed geometry of the 3L-PNTA structure is depicted in Fig. 1(d). The structure is a 2D periodic array. In each unit cell, there are 9 Au nanotiles lying on three different levels of the terrace-like glass substrate with A representing the period of the structure in both X and Y directions and L1 and L2 controlling the sizes of the nanotiles. In the simulation, we kept the height of the terraces h = 70 nm and the thickness of the Au nanotiles t = 40 nm. For simplicity, we let A = L1 + L2 = 300 nm. This makes the 3L-PNTA a polarization independent structure.
4. Multiple resonant modes of 3L-PNTA
Figure 2(a) shows the reflection spectra of the structure with different L1 (from 80 nm to 220 nm, and L2 decreases from 220 nm to 80 nm correspondingly). There are four resonance modes in the map, namely mode 1, mode 2 + , mode 2- and mode 3.
The behaviors of resonance modes are different. Mode 1 appears at L1 = 80 nm and disappears after L1 = 150 nm. The resonance wavelength of mode 1 stays constant at 630 nm and is nearly independent to the size of the nanotiles. The resonance wavelengths of mode 2 and mode 3, however, show strong dependence on L1. When L1 increases, mode 2 shows redshift, while mode 3 shows blueshift. At L1 = 140 nm, the two modes approach to each other, and mode splitting is observed. This anti-crossing effect is a widely observed phenomenon in various plasmonic systems [24, 25], and it is caused by the couplings between two surface plasmon modes (i.e., mode 2 and mode 3). For convenience, we call the lower part (with shorter wavelength) and upper part (with longer wavelength) of mode 2 mode 2 + and mode 2-, respectively.
5. Resonant enhancement of light in nanogaps
Plasmon resonances can induce strong local field enhancement in the near-field regime, particularly in the nanogaps. To demonstrate it, we calculated the field intensity distribution at the peak wavelengths of the four resonance modes of the 3L-PNTA structure, and Fig. 3 shows the enhancement maps at the two key cross-sections of the 3L-PNTA structure (mode 1, mode 2 + and mode 3 for the case of L1 = 120 nm, mode 2- for the case of L1 = 180 nm). For mode 2 and mode 3, the light intensity is enhanced by 2 orders of magnitude in the nanogaps between the nanotiles at the top and middle levels. In the case of mode 1, the enhancement is slightly lower than the case of mode 2 and mode 3. For all the modes, the enhancement in the nanogap between the nanotiles at the bottom and middle levels can also be observed in the figures, but it is slightly lower than the enhancement in the gaps between the two top levels.
Fig. 3 Field intensity distributions (on a logarithmic scale) at the peak wavelengths of the four modes of the 3L-PNTA structure in two cross-sectional views respectively. The scale bar represents 100 nm.
The large field enhancement is caused by the coupling between the plasmonic nanotiles. In order to elaborate this point, we calculated the corresponding local charge density distributions of the four modes (Fig. 4). In the case of mode 2 and mode 3, charges are strongly localized in the gap areas between the nanotiles at the top and middle levels. The strongly confined charges cause the large local field enhancement. Compared with mode 2 and mode 3, the charge density of mode 1 is several times smaller, and this explains why the field enhancement is smaller than the cases of mode 2 and mode 3. Meanwhile, the charge density in the bottom level is slightly smaller than that in the gaps between the two top levels. This is also in agreement with the field enhancement in Fig. 3.
Fig. 4 Charge distributions at the peak wavelengths of the four modes of the 3L-PNTA structure in two cross-sectional views respectively. The scale bar represents 100 nm.
6. Independent tuning of the resonance modes
One of the major advantages of the 3L-PNTA structure is that mode 2 and mode 3 can be independently tuned by adjusting L1 and L2 respectively. As a result, we can engineer the resonances for enhancing any given optical processes. To prove this point, we calculated the reflection spectra of 3L-PNTAs with L1 and L2 changing from 80 nm to 220 nm, retrieved the resonance wavelengths of mode 1, mode 2 + , mode 2- and mode 3, and plotted the resonance wavelength as a function of L1 and L2 (Fig. 5).
Fig. 5 (a)-(d) are the resonance wavelengths of the four resonance modes as the function of L1 and L2.
As shown in the result, the behaviors of the modes are considerably different. Mode 1 is nearly independent to the size of nanotiles, and only exhibits minute shifts (< 100 nm) when L1 and L2 increase from 80 nm to 220 nm. This result is consistent with Fig. 2(a).
On the contrary, mode 2 and mode 3 show strong dependence on L1 and L2, respectively. In the case of mode 2 + and mode 2-, the resonance wavelength, λ2, is linearly related with L1. When L1 is changed from 80 nm to 220 nm and L2 is fixed, the resonance wavelengths will change by >300 nm. However, when L1 is fixed and L2 is changed from 80 nm to 220 nm, the resonance wavelengths only show small variation (< 60 nm). Similarly, the resonance wavelength of mode 3, λ3, shows strong linear dependence on L2, while it is nearly independent to L1. For clarity, we summarized the relations between resonance wavelengths and geometrical parameters (i.e., L1 and L2) in Table 1.
Table 1. The dependence of resonance wavelengths of mode 2 and mode 3 on L1 and L2.
7. Spatial matching between resonant modes
To enhance both the excitation and emission processes simultaneously, it is essential to have the two corresponding resonance modes (i.e., mode 2 + and mode 3) spatially matched [16]. In other words, the resonance modes at the excitation and radiation wavelengths should spatially overlap with each other. For the 3L-PNTA structure, the electric fields are always confined in the nanogaps between the Au nanotiles at the top and middle levels at both mode 2 + and mode 3 due to the strong vertical couplings, as shown in Fig. 6. The spatial overlap of the field enhancement makes the 3L-PNTA an excellent platform for enhancing both the excitation and emission processes of a given optical effect.
Fig. 6 (a)-(b) Field intensity distribution (on a logarithmic scale) of mode 2 + and mode 3. (c) Total enhancement at both mode 2 + and mode 3 (on a logarithmic scale). The scale bar represents 100 nm.
To demonstrate the mode matching between the mode 2 + and mode 3, we calculated the total enhancement (|Eloc(λex)/E0(λex)|2 · |Eloc(λem)/E0(λem)|2). As shown in Fig. 6(c), the total enhancement reaches 104, two more orders of magnitude than the case of the enhancement factor at a single resonance (Fig. 6(a) and 6(b)).
8. Creating “hot spots” using plasmonic nanodots
The field enhancement can be further improved by inserting Au nanoparticles (NPs) in the nanogaps between the plasmonic nanotiles. The NP-decorated 3L-PNTA structure can enhance the light in a cascade fashion. First, light is trapped by the nanogaps and enhanced by a factor of gNG. Then, the traped light is enhanced again by a factor of gNP. The total enhancement becomes gNG · gNP, which can be significantly higher than the case without NPs [26, 27].
To demonstrate this effect, we added a single 10 nm Au NP in the gap (Fig. 7(a)), and calculated the optical properties of the new structure. With the Au NP, the resonance wavelengths of the four modes stay constant (Fig. 7(b)). Meanwhile, dramatic improvement of the local field enhancement is observed in the nanometer “hot gap” created by the additional NP (Fig. 7(d)-7(g)). In the “hot spots”, compared with the case without Au NPs, the field can be improved by 15 times, 10 times, 4 times and 2.5times for mode 1, mode 2 + , mode 2- and mode 3 respectively.
Fig. 7 (a) A unit cell of the 3L-PNTA structure with an additional Au nanoparticle. (b) The reflection spectra with (square marker line) and without (solid line) an additional Au nanoparticle when L1 = 120 nm (red) and L1 = 180 nm (blue). (c) 3D schematic view of the 3L-PNTA structure showing the cross-section in X -Z plane. (d)-(g) Field intensity distribution (on a logarithmic scale) at the peak wavelengths of the four modes of the 3L-PNTA structure with an additional Au nanoparticle. The scale bar represents 100 nm.
Figure 7(a) shows the case of a single NP. In practice, for each nanogap, tens of NPs can be inserted, leading to a large number of “hot spots”. This will in turn boost the average enhancement significantly [28].
It is worth noting that the 3L-PNTA is a 2.5D structure, which can be fabricated easily using the electron-beam lithography, focused ion beam, thermal probe lithography technique [29], and nanoimprint [19]. Indeed, because of the advantage in fabrication, the two-level vertical couple structures have been widely used today for different applications, including surface-enhanced spectroscopy [19, 28], index sensing [30] and high resolution display [31]. On the other hand, the fabrication of conventional 3D structures is often extremely difficult and expensive [32]. This property makes the 3L-PNTA structure a practically attractive design for enhancing various optical effects.
9. Summary
In this paper, we designed and numerically studied a new type of multi-resonant plasmonic nanostructure, the 3L-PNTA, which is a 2.5D structure consisting of an array of vertically coupled plasmonic nanotiles on dielectric nanoterrace substrate. The results show that the 3L-PNTA supports multiple resonances, which can be independently tuned by changing different geometrical parameters. On the resonances, local light intensity can be enhanced by more than two orders of magnitude in the nanogaps between the plasmonic nanotiles due to the strong vertical couplings. Moreover, the enhanced fields associated with different resonant modes are spatially overlapped, allowing the 3L-PNTA to enhance optical processes at both excitation and emission wavelengths, simultaneously. In addition to the optical properties, as a 2.5D structure, the 3L-PNTA can be fabricated easily using conventional fabrication techniques, such as focus ion beam, thermal nanoprobe etching, and nanoimprint techniques, and does not need complex layer-by-layer fabrication technique commonly needed by 3D nanostructures. This makes the 3L-PNTA a perfect multi-resonant plasmonic nanostructure for enhancing various optical processes.
Funding
National Key R and D Program of China (No. 2016YFA0201104); National Basic Research Program of China (No. 2015CB659400); National Natural Science Foundation of China (No. 11374152, 11574142, and 11621091); the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.
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