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Abstract
The intrinsic fluorescence of biomolecules such as proteins and nucleic acids lies in the ultraviolet (UV) range of the spectrum. UV plasmonic nano-structures have been shown to enhance the fluorescence quantum yield and reduce the lifetimes of various biomolecules. Fluorescence enhancement is contributed to by both excitation rate and emission rate enhancement. Since biomolecules are prone to photon-degradation in the UV range, excitation rate enhancement should be minimized, while radiative rate enhancement should be maximized. Although numerous nano-structures have been proposed both numerically and experimentally to enhance the fluorescence of native biomolecules, very few studies have achieved more than 10x radiative rate enhancement. Here we report systematic studies of fluorescence enhancement by equilateral bowtie nano-antennas (BNA) made of aluminum (Al) or magnesium (Mg) in the ultraviolet region. We modeled the emission rate enhancement using the excitation and emission peak wavelength of tryptophan. The quantum yield of tryptophan is also taken into account. Our results show that with the optimal geometry, Al BNA with oxide yields an excitation enhancement of 21× at the excitation wavelength of tryptophan (270nm), a radiative enhancement of 37×, a quantum yield enhancement of 5×, and a net fluorescence count rate enhancement of 64× at the emission wavelength of tryptophan (340nm). Mg BNA with oxide sustains the highest Purcell factor enhancement, 14×. The effect of the native oxide layer on both metals is investigated. The studies reported here are meaningful in the design of better UV plasmonic nano-structures for label-free sensing of biomolecules.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultraviolet (UV) plasmonics has drawn increasing attention in recent years due to its applications in label-free biomolecule and organic waste sensing, high contrast cell imaging, etc [1–5]. The challenges of detecting the native fluorescence of biomolecules are their small extinction cross-section and quantum yield [6,7]. Therefore, significant fluorescence enhancement needs to be achieved in order to realize label-free sensing of biomolecules. Plasmonic nano-structures can enhance both the excitation and emission rate of the native fluorescence of biomolecules. Since large excitation rate can potentially degrade biomolecules, it is desirable to enhance the fluorescence yield by maximizing the radiative rate enhancement. The fluorescence yield is the total number of photons collected from a molecule before it photo bleaches and is proportional to its radiative rate [8]. Numerous nano-structures have shown large excitation rate enhancements (100$\times$) [9–13]; however, very few studies have focused on the radiative rate enhancement. McArthur and Papoff have numerically predicted larger than 200x radiative rate enhancement by placing an Al nanoparticle on top of an Al thin film with 5 nm gap size [14]. However, the gap enhanced fluorescence is highly lossy, resulting in quantum yield reduction of about 5-10$\times$, which is not desirable for fluorescence enhancement. In addition, the proposed geometry is hard to fabricate with controlled gap size, and loading molecules to such a small gap is another challenge.
Here we present our numerical studies on the native fluorescence enhancement by Al and Mg equilateral bowtie nano-antennas (BNA). A BNA is composed of two triangles with tips facing each other. Due to its high localized field enhancement, bowtie antennas have been used for many applications such as biosensing, particle trapping, high harmonic generation, Surface Enhanced Raman Scattering [15–18]. In the literature, most of the reported BNAs are made of gold or silver thus are proper for applications in the visible or IR range. There are a handful of numerical studies on electric field enhancement by Al BNAs. Wang et al. designed an Al BNA array with metal-insulator-metal configuration and achieved 20$\times$ excitation enhancement in the UV range but did not consider emission enhancement [19]. He et al. studied the near field enhancement by semiconductor BNAs and have reported 20$\times$ excitation enhancement for a gap size of 5nm and 40$\times$ for a gap size of 1nm, which is hard to achieve in practice [20]. Forestiere et al. studied net enhancement of an ideal dipole (quantum yield as 1) by Al dipole and bowtie antennas and reported 100x fluorescence count rate enhancement for a gap size 10nm [21]. However, most intrinsic fluorescence of molecules has very small quantum yield and does not obey ideal dipole approximation.
In our studies, we use tryptophan as the model molecule and consider its intrinsic quantum yield as 0.08 [22]. The excitation and emission rate enhancement factor were calculated at the absorption and emission peak of tryptophan in aqueous solution [23]. In terms of plasmonic materials, we choose Al and Mg due to their large localized surface plasmon (LSP) figure of merit in the UV range [24]. In this report, we numerically studied the rate enhancement by an equilateral BNA made of Al or Mg and show 37$\times$ radiative rate enhancement and 64$\times$ net enhancement with a 20 nm gap size.
2. Fluorescence model
Decay rate engineering of fluorescence is briefly described in this section [25,26]. Net enhancement (NE) is the number of photons emitted per excitation cycle by a molecule adjacent to a plasmonic nanostructure, divided by the photons emitted by a molecule in free space. NE is expressed as
where $f_I$ is the excitation enhancement and $f_{\kappa }$ is change in collection efficiency (which we assume to be 1). where $E^2$ is the electric field in the vicinity of the BNA and $E^2_{0}$ is the electric field of the incident wave. $f_{rad}$ is the ratio of the radiative rate in the presence of metallic structure ($k'_{rad}$) and without the structure ($k_{rad}$). $P_{rad}'$ is the radiated power of dipole within the BNA. $P_{rad}$ is the radiated power of the dipole in free space [27].3. Simulation model
The geometry analyzed in the simulations is shown in Fig. 1. Figure 1(a) depicts the top view of the BNA with a 4nm oxide layer on the surface. Figure 1(b) shows the cross-section view of the BNA, placed on top of a quartz substrate and immersed in 1-octanol solution. The refractive index of 1-octanol is 1.45. 1-octanol is used to prevent degradation of Mg film in ambient environment [24]. The optical constant of Al, Mg, and the corresponding oxide layer are taken from Palik handbook data [29]. The bowtie is composed of two equilateral triangles facing each other, the gap between the bowtie is 20 nm for no-oxide layer and 12 nm for oxide layer since the oxide layer extends into the gap region. Each apex in the triangle has a radius of curvature (r) of 5nm. This vertex radius of curvature is different from the radius (R), defined from the centroid of the triangle to the vertex. The height of the bowtie is 100 nm. The apex angle is fixed at 60 degrees.
Fig. 1. (a) Top view of the bowtie antenna used in the simulation. The radius (R) is defined from the centroid of the triangle to the vertex. The radius of curvature (r) of each apex in the triangle is also defined. (b) Cross-section view of the bowtie antenna.
Full wave three-dimensional electromagnetic simulations are performed using Lumerical FDTD Solutions. Detailed simulation configuration can be found in [24]. The mesh size is 2$\times$2$\times$2 nm$^3$. In order to calculate the excitation enhancement, a plane wave with unit amplitude (1 V/m) normally excites the BNA from the bottom, polarized along the long axis of the nano-antenna. Average excitation enhancement is calculated by integrating the total electric field intensity within a field monitor at the BNA gap. The length and width of the field monitor is the same as the gap of the bowtie and the height of the field monitor is 10nm. The center of the field monitor moves from 5nm to 95 nm above the quartz substrate, with step size 10 nm. For the emission calculations, an electric dipole with unit amplitude (1 V/m) is positioned at the center of the gap region. The height of the dipole moves from 5nm to 95 nm above the quartz substrate, with step size 10 nm. The radiative enhancement can be calculated by dividing the radiative emission in the presence of the nanoaperture ($k_{rad}'$) to the radiative emission in the absence of the nanoaperture ($k_{rad}$) . The lifetime change of the ideal dipole $\zeta$ [30] is calculated by dividing the spontaneous emission from the dipole within the nanoaperture ($k'_{rad} + k'_{nr} + k_{nr}$) to the dipole emission in the absence of the nanoaperture ($k_{rad} + k_{nr}$); the predicted lifetime change of a real molecule is then obtained from $\zeta$ by using the molecule’s native QY as a correction factor (see Eqn. 4) [31,32], which takes into account non-radiative losses. For the simulation, tryptophan is used as the model fluorophore. The absorption maximum for tryptophan is near a wavelength of 270nm and the emission maximum is near 340nm. The quantum yield of tryptophan is taken as 0.08 since only half of the light emitted is collected through the bottom interface.
4. Results
In the following figures, we discuss the BNA excitation and emission enhancement results. Figure 2 represents the excitation rate enhancement for the Al and Mg BNAs. Panels (a) and (b) correspond to Al BNAs without and with oxide, respectively; and panels (c) and (d) correspond to Mg without and with oxide, respectively. R is varied from 20 to 60 nm in 10 nm steps; the different traces in each panel correspond to cases corresponding to different values of R. Increasing the radius R of the bowtie will red-shift the resonance peak and increase the peak intensity. In the wavelength range considered here 250 to 600 nm, Al BNAs only exhibit one major peak, which correspond to the dipole resonances. For Al BNAs, it is observed that the oxidization layer slightly increases the excitation enhancement peak while red shifting the peak by about 10-20 nm. This is caused by a reduction in the gap size due to the oxidization layer.
Fig. 2. (a) Excitation enhancements at 5 nm above the substrate versus the excitation wavelength for Al BNA without oxide, (b) Excitation enhancements at 5 nm above the substrate versus the excitation wavelength for Al BNA with oxide, (c) Excitation enhancements at 5 nm above the substrate versus the excitation wavelength for Mg BNA without oxide. (d) Excitation enhancements at 5 nm above the substrate versus the excitation wavelength for Mg BNA with oxide.
The excitation enhancements for Mg BNAs show two to three peaks for each of the different radii. The lower energy peaks red-shift with increasing R as it is characteristic of dipole resonances. The higher energy peaks, on the other hand, stem from out-of-plane modes within the nano-gap and are independent of R. We have observed a similar out-of-plane mode in Mg hole-arrays [33]. In comparison with Al BNAs, the Mg BNAs dipole resonance peak red-shifts about 50 nm for the same geometry of BNAs. Although the peak intensity for Mg BNAs is larger than that for Al BNAs of the same dimension, the peak red-shifts to the visible range ($>$400 nm).
Figure 3 represents the excitation rate enhancement versus the position of the field monitor for the Al and Mg BNAs at 270 nm. There are two excitation enhancement peaks for Al BNAs. One peak occurs at 95 nm above the quartz substrate, which is at the metal and 1-octanol interface. Another excitation enhancement peak occurs at 40 to 60 nm above the substrate. The oxidization layer lowered the excitation enhancement peak at the metal and 1-octanol interface. Increasing the radius R of the bowtie will reduce the excitation enhancement. The maximum excitation enhancement for Mg BNAs occurs not at the metal-dielectric interface, but near the center of the gap. The oxidization layer slightly lowered the excitation enhancement peak. The different behavior for Al and Mg BNAs can be explained by different resonance modes at 270 nm, as discussed in the previous paragraph.
Fig. 3. (a) Excitation enhancements at 270 nm excitation wavelength versus the height above the substrate for Al BNA without oxide, (b) Excitation enhancements at 270 nm excitation wavelength versus the height above the substrate for Al BNA with oxide, (c) Excitation enhancements at 270 nm excitation wavelength versus the height above the substrate for Mg BNA without oxide. (d) Excitation enhancements at 270 nm excitation wavelength versus the height above the substrate for Mg BNA with oxide.
The emission peak of tryptophan is near 340nm. For radiative rate calculation, we place an ideal dipole at 340 nm at the center of the BNA gap with height 5nm to 95 nm above the substrate, in 10 nm step. The far field monitor is at the side of the source to collect light emitting back into the direction of the excitation source, reflecting what would be used in a fluorescent microscope setup. In the following figures, we discuss the BNA radiative enhancement, Purcell factor, quantum yield, and the net enhancement results.
Figure 4 represents the radiative enhancement versus emission wavelength at dipole position 5 nm above the substrate for Al and Mg BNAs. The radiative enhancement for Al BNAs resembles that of excitation enhancement. Increasing R will cause the peak of radiative rate enhancement to red-shift. The peak intensity also increases with R except for the smallest R (20 nm). The presence of an oxidization layer red-shifts the emission peak by 10-20 nm. Similar to excitation enhancement, the radiative enhancement increases by about 10-20% with the addition of an oxidization layer. With an oxidization layer, at 340 nm, an Al bowtie with radius 20 nm gives rise to the highest radiative rate enhancement 37$\times$ at 340 nm. The oxidization layer also red-shifts the radiative enhancement peak (by about 20 nm) for Mg BNAs. Furthermore, an out-of-plane mode is observed at around 340 nm. This out-of-plane mode is more prominent in Mg BNAs with an oxidization layer. We can take advantages of this out-of-plane mode for UV fluorescence enhancement. By harnessing this, we observe a 37$\times$ radiative enhancement at 340 nm by a Mg BNA with an oxidization layer with 20 nm radius.
Fig. 4. (a) Radiative enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Al BNA without oxide, (b) Radiative enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Al BNA with oxide, (c) Radiative enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Mg BNA without oxide. (d) Radiative enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Mg BNA with oxide.
Figure 5 represents the radiative rate enhancement versus the position of the dipole for the Al and Mg BNAs at 340 nm. The maximum radiative rate enhancement for Al BNAs occurs at the metal-dielectric interface as well as near the center of the gap except for Al BNAs with an oxidization layer with R 20 nm. The oxidization layer slightly increases the peak radiative enhancement for Al BNAs. For Mg BNAs, the oxidization layer significantly increases the radiative rate enhancement, with maximum radiative rate enhancement similar to that of Al BNAs.
Fig. 5. (a) Radiative enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Al BNA without oxide, (b) Radiative enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Al BNA with oxide, (c) Radiative enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Mg BNA without oxide, (d)Radiative enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Mg BNA with oxide.
Figure 6 represents the Purcell factor enhancement for tryptophan (QY=0.08) of Al and Mg BNAs by placing a power monitor enclosing the dipole, which can capture all power emitted by the dipole. Purcell factor is the change of total decay rate, which includes radiative and non-radiative rate. Figure 6 represents the Purcell factor enhancement versus emission wavelength at dipole position 5 nm above the substrate for Al and Mg BNAs. The Purcell factor enhancement peak for Al BNAs red-shifts with increasing R. The oxidization layer red-shifts the peak of Purcell factor enhancement and increases the peak intensity. For Mg BNAs, there are three prominent peaks. For Mg BNAs without an oxidization layer, there are two stationary peaks at 280 nm and 350 nm and a peak in the visible range that red-shifts with increasing R. The addition of an oxidization layer red-shifts the stationary peaks to 310 and 400 nm, and increases the amplitude of peaks.
Fig. 6. (a) Purcell factor enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Al BNA without oxide, (b) Purcell factor enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Al BNA with oxide, (c) Purcell factor enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Mg BNA without oxide, (d)Purcell factor enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Mg BNA with oxide.
Figure 7 represents the Purcell factor enhancement versus the position of the dipole for Al and Mg BNAs at 340 nm. The maximum Purcell factor enhancement for Al BNAs occurs at the metal-dielectric interface as well as near the center of the gap. The oxidization layer slightly increases the peak Purcell factor enhancement for Al BNAs. For Mg BNAs, the Purcell enhancement shows two peaks near 30 and 70 nm above the substrate. The oxidization layer significantly increases the peak Purcell factor enhancement for Mg BNAs. A Mg BNA with an oxidization layer sustains the largest Purcell factor enhancement 14$\times$ at R 20 nm.
Fig. 7. (a) Purcell factor enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Al BNA without oxide, (b) Purcell factor enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Al BNA with oxide, (c) Purcell factor enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Mg BNA without oxide, (d)Purcell factor enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Mg BNA with oxide.
Figure 8 shows the quantum yield (QY) enhancement versus emission wavelength at dipole position 5 nm above the substrate for Al and Mg BNAs with and without an oxidization layer. For both Al and Mg BNAs, QY enhancement presents multiple peaks. The peak position red-shifts with increasing R. The effect of an oxidization layer is very small on the QY enhancement.
Fig. 8. (a) QY enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Al BNA without oxide, (b) QY enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Al BNA with oxide, (c) QY enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Mg BNA without oxide, (d)QY enhancements at dipole position 5 nm above the substrate versus the emission wavelength for Mg BNA with oxide.
Figure 9 represents the QY enhancement versus the position of the dipole for Al and Mg BNAs at 340 nm. At 340 nm, the highest QY enhancement is 5$\times$ for Al with an oxidization layer, 3$\times$ for Mg with an oxidization layer. The formation of a native oxidization layer on Mg BNAs helps to increase the QY due to the enhanced radiative rate. With 5$\times$ enhancement of QY, the QY of tryptophan is 0.4 instead of 0.08, the intrinsic QY. This enhanced QY can facilitate label-free biosensing.
Fig. 9. (a) QY enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Al BNA without oxide, (b) QY enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Al BNA with oxide, (c) QY enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Mg BNA without oxide, (d)QY enhancements at 340 nm emission wavelength versus the height of the dipole above the substrate for Mg BNA with oxide.
In order to calculate the net enhancement factor (NE) by BNAs, the excitation rate at 270 nm needs to be multiplied by the quantum yield enhancement at 340 nm (see Eqn. 1). The calculated net enhancement factor is shown in Fig. 10. The maximum NE for Al BNAs occurs at the metal and1-octanol interface and 20-30 nm above the substrate. An Al BNA with an oxidization layer has the largest NE 64$\times$ at R 20 nm. The maximum NE for Mg BNAs occurs at 15 nm above the substrate. A Mg BNA with an oxidization layer has the largest NE 29$\times$ at R 20 nm. Our results suggest that Al is a better material choice since Al BNAs sustain higher excitation, radiative, QY, and NE and smaller Purcell factor enhancement, in comparison with Mg.
Fig. 10. (a) NE vs the positions of the dipole emitter for Al BNA without oxide, (b)NE vs the positions of the dipole emitter for Al BNA with oxide, (c) NE vs the positions of the dipole emitter for Mg BNA without oxide, (d) NE vs the positions of the dipole emitter for Mg BNA with oxide.
5. Conclusion
We studied the fluorescence enhancement of tryptophan using Al and Mg BNAs through numerical modeling. We studied the effect of the surface oxide layer on the excitation and emission rate enhancement. In comparison with Al, Mg BNAs have comparable radiative rate enhancement but higher Purcell factor enhancement, thus smaller NE. The highest excitation rate enhancement is 21$\times$ by a 20 nm Al BNA with an oxidization layer. The highest radiative rate enhancement is 37$\times$ achieved by a 20 nm Al BNA with an oxidization layer. The highest NE is 64$\times$ by a 20 nm Al BNA with an oxidization layer. The highest Purcell factor enhancement is 14$\times$ by a 20 m Mg BNA with an oxidization layer.
Acknowledgments
The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged.
Disclosures
The authors declare no conflicts of interest.
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