1. Introduction

Owing to the unrivaled advantages in selectively labeling the target species such as proteins, cells and chemical ingredients, fluorescence (e.g. quantum dot, dyes etc.) based sensing and imaging techniques play crucial roles in a wide range of applications such as DNA/RNA sequencing [1,2], medical toxin detection [3,4], and environmental pollution measurement [5], among the others [6,7]. Driven by these emergent applications, the detection and tracking of target species at a single molecular level is extremely vital, thereby challenging the capability of routinely used fluorescence assay.

To fully reveal the insight of the biological activities and chemical reactions, two obstacles are commonly faced in the fluorescence single molecule detection. First, the fluorescence intensity needs to be high enough so that the target species can be visualized at a very low concentration. However, the original optical signal from the fluorophore is very weak, and an appropriate enhancement technique needs to be adopted. Second, the polarization information of fluorophores generally needs to be obtained correctly in order to extract the corresponding photophysical parameters of the bio-chemical system [8–12]. For instance, the orientation of the carbocyanine dye on a biological membrane is able to reflect the abnormal feature of the membrane [13]. Nevertheless, the polarization information of the fluorophore depends not only on the intrinsic properties of the emitter, but also could be modified by the external environment, hence is difficult to be obtained precisely at the far field.

Coupling a noble-metal nanoantenna to a fluorophore leads to a strong fluorescence intensity enhancement [14], offering a viable solution for the single molecule detection. The mechanism can be briefly explained in two aspects [15]. First, the surface plasmon resonance of the metal nanoantenna is able to confine the incident optical radiation into a small sub-wavelength hotspot, creating a strong localized field enhancement that is orders of magnitudes higher than that in the free space [16]. Such a strong field enhancement can significantly boost the excitation rate of the fluorescence emitter. Second, after excitation, the emitter subsequently releases a photon which can in turn couple to the resonance of the nanoantenna [17]. The presence of nanoantenna manipulates the local optical density of states (LDOS) in the proximity of the fluorophore, potentially resulting in an enhanced radiative decay rate and quantum yield [18]. Combining both the excitation and emission processes, previous studies have shown that coupling fluorophores with plasmonic nanoantennas could improve the fluorescence emission characteristics at multi-dimensional levels [19–22].

Besides these promising features, the nanoantenna is commonly designed to enhance the fluorescence intensity for a particular emitter orientation, albeit the fluorophore is generally randomly oriented in reality [23,24]. The resultant fluorescence intensity, which is statistically averaged over all emitter orientations, is always lower than the expected value of the design. Other than that, the nanoantenna would alter the directivity of the fluorescence emission [25–27], resulting in a radiation pattern that is different from that of an isolate fluorophore. The original polarization information of the emitter could be lost at the far field, thereby compromising its applicability in certain fields that is highly polarization dependent, for instance, measuring the structural dynamics of biomolecules [28,29]. To achieve the same enhancement extent for randomly oriented fluorophores while preserving its orientation information, a delicate nanoantenna design is needed.

Highly-symmetrical nanoantennas (e.g. ring resonator [30–33], cross nanoantenna [34–37], bull’s eye structure [38,39] etc.), could potentially resolve the problems due to their highly symmetrical geometries. The nanoantenna couples to the emitters equally over all its orientations, which could, in principle, excite any arbitrarily oriented fluorophore while preserving its angular polarization at the far field. However, the previous works only preliminarily studied the electromagnetic field enhancement properties of the highly symmetrical nanoantenna, without thoroughly investigating the complex fluorescence enhancement process, which needs to account the excitation rate, the radiative/non-radiative decay rate, the quantum yield and the fluorescence enhancement factor [40]. The design principle of the highly-symmetrical nanoantenna as well as its advantages against other low-symmetrical counterparts still remains obscure.

In this theoretical work, we systematically investigate the fluorescence enhancement capability as well as the orientation preservation capability for an arbitrary oriented fluorophore using a highly-symmetrical cross-nanoantenna. First, for better guiding the experiment, the geometrical parameters of nanoantenna are rigorously designed to match the plasmonic resonance and the excitation wavelength of emitter, maximizing the fluorescence excitation rate. Next, under the weak coupling framework, the nanoantenna enhanced fluorescence excitation rate, radiative/non-radiative decay rate, quantum yield and the ultimate fluorescence enhancement factor are carefully studied for random emitter orientations. Finally, the 3D far field radiation pattern and the associated defocused imaging pattern [41] are employed to explore the angular polarization properties of the emitter. For the comparison purpose, an ordinary dimer configuration is used as a reference throughout the paper. Other issues such as substrate effect are also briefly discussed.

2. Methods

2.1 Nanoantenna enhanced fluorescence

Under weak coupling assumption (e.g. the donor and acceptor are distinguishable and there is no energy back transfer between them) [42], the fluorescence emitter can be approximated as an oscillating dipole, and the excitation and emission process can be treated independently since there is no coherence between them. The fluorescence enhancement factor (${\eta }_{em}/{\eta }_{em}^0$) can be neatly expressed as the product of the excitation rate ${\gamma }_{exc}/{\gamma }_{exc}^0$and quantum yield $q/q^0$ [43]

2.2 Defocused imaging calculation

To access the orientation information of the emitter, the far field radiation pattern needs to be examined. Albeit possible, the complete 3D far field radiation pattern is difficult to be obtained in the experiment. The defocused imaging technique [41,44] transforms the complex 3D far field pattern into a simple 2D imaging plane, without losing the accuracy of the angular polarization. It provides a better visualized effect, and can be directly observed from a conventional CCD camera. Briefly, the defocused imaging can be obtained by first decomposing the total far field radiation of the emitter in the objective space into the p-polarized (in-plane) and s-polarized (out-of-plane) components $E_p$ and $E_s$ respectively, followed by mapping them into the defocused imaging space via the well-known Abbe’s relation. The resultant field distribution in the image plane is shown in Eq. (3).

2.3 Finite-element method

Finite-element method using COMSOL Multiphysics is adopted for the numerical calculation of coupled fluorophore-nanoantenna system. For the excitation process, the model is based on the example Scatter on Substrate provided by COMSOL [45], which computes the absorption and scattering cross sections of a nanostructure by incorporating the substrate effect inside. For the emission process, an electric point dipole source is adopted to represent the fluorescence emitter. Table 1 below lists the simulation parameters we used in this paper.

Table 1. Simulation parameters of coupled fluorophore-nanoantenna system

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Although the linear polarized plane wave is commonly used as the pumping source, in this work, a circular polarized light $E=E_0[\cos (wt-kz)e_x+\sin (wt-kz)e_y]$ is deliberately chosen for two reasons: (1) the electric field of the circular polarized light rotates steadily with time, which is more appropriate to excite a randomly oriented fluorophore; and (2) the electric field of the circular polarized light can always be decomposed into the x- and y-components, each component can be exploited to excite part of the cross-nanoantenna, thereby maximizing the advantages of the highly-symmetrical structure. The resultant plasmonic resonance characteristics of the nanoantenna, including its spectral position and the electric field enhancement, can be obtained straightforwardly by examining the extinction spectral response and the near field distribution, from which the excitation rate ${\gamma }_{exc}$ can be calculated.

To evaluate the emission characteristic of the fluorescence emitter, the dipole source is routinely set at the middle gap of the nanoantenna [17]. The radiative decay rate and non-radiative decay rate in Eq. (2) can be equivalently represented with the respective power quantities as ${\gamma }_r/{\gamma }_r^0=P_r/P_0$ and ${\gamma }_{abs}/{\gamma }_r^0=P_{abs}/P_0$. Here $P_0$ is the radiation power of the isolated dipole, $P_{\text{r}}$ is the scattering power integrated over the surface enclosing the nanostructures, and$P_{\text{abs}}$ is the ohmic loss integrated over the volume of the nanoantenna [46].

3. Results

3.1 Spectra analysis of the cross-nanoantenna

The plasmonic resonance strongly depends on the morphology of the nanostructure. The spectral position of the resonance can be tuned to match the excitation wavelength of the fluorescence emitter, maximizing the excitation rate. As a starting point, a systematic analysis is carried out to understand the plasmonic feature of the cross-nanoantenna.

3.1.1 Schematic of the cross-nanoantenna

The schematic of the cross-nanoantenna is shown in Fig. 1(a), and the dimer-nanoantenna with the same dimensional parameters is depicted in Fig. 1(b) as a reference. Each component of nanoantenna can be characterized by the length of the cuspidal head (H), the length (L) and the width (W) of the rectangle body, and the gap distance (G) between the two opposite constituents. The cuspidal head enables the gap distance G to be adjusted at a greater extent so that the adjacent components can get close enough to produce a sufficiently large electrical field enhancement. The incident circular polarized light illuminates along the z-axis from the top of the structure. The fluorophore is located at the middle of the gap, whose orientation is described by the deviation angle Φ with respect to the x-axis as shown in Fig. 1(c) and 1(d).

 

Fig. 1 Schematics of (a) Au cross-nanoantenna & (b) Au dimer-nanoantenna on a Hikari glass substrate. The fluorescence emitter is located at the middle of the gap, and is oriented at an angle Φ with respect to the x-axis. The incident circular polarized light illuminates along the z-axis from the top of the structure. The plan view of the (c) cross-nanoantenna (d) dimer nanoantenna,

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To mimic the empirical condition, Hikari glass with a refractive index 1.4 is considered as the substrate [47]. Without losing the generality, Alexa Flour 680 (the excitation wavelength λ_exc = 680 nm, the emission wavelength λ_emi = 700 nm, and the intrinsic quantum yield q⁰ = 0.3 [48]) is selected as the fluorophore. This kind of emitter is routinely applied in many applications such as the super-resolution microscopy, antibody labeling for direct detection, annexin V-conjugates for apoptosis imaging, among the others [49–51]. To match the excitation wavelength at 680 nm, Au is the preferred material than Ag since it is able to generate strong plasmonic resonance at longer wavelength [52,53]. Other plasmonic materials and fluorophores can also be adopted as long as the same design principle holds. Note that in nanoantenna-enhanced fluorescence theory, the property of the emitter has commonly been simplified into the excitation wavelength and the emission wavelength [43], while the complete spectra with band features are not omitted here.

3.1.2 Matching the plasmonic resonance with the excitation wavelength of the fluorophore

Upon circular polarized light illumination, the extinction cross-sections over the visible and near infrared regime are plotted in the left panel of Fig. 2, with respect to: (a) the gap distance G, (b) the length L, (c) the width W, and (d) the cuspidal head H of the nanoantenna, respectively. The corresponding field-distribution patterns at the resonance peaks of the spectra are illustrated in the right panel. Obviously with the shrinking of G, the near field coupling effect between the adjacent components becomes stronger, and the plasmonic resonance of the individual arm interacts with the adjacent component to form a hybrid plasmonic mode [54,55]. This mode hybridization shifts the resonance peak to longer wavelength, and the electromagnetic field enhancement increases rapidly in the gap. Next, the increment on the length L and width W both enhance the electromagnetic field in the gap region. However, the increment on L results in a red shift on the resonance peak, whereas the increment on W causes a spectral blue shift. Lastly, the increment on H not only lengthen the whole components, but also sharpen the heads, which again creates a red shift on the resonance peak and an even greater enhancement on the electromagnetic field than just increasing L.

 

Fig. 2 Extinction cross-sections with respect to the main geometrical parameters of the cross-nanoantenna: (a) the gap distance G, (b) the length L, (c) the width W, and (d) the cuspidal head H. The spectral response is shown in the left panel while the corresponding field distribution is illustrated in the right panel. By controlling these parameters, the plasmonic resonance of the nanoantenna can be tuned to match the excitation wavelength of the fluorescence emitter, providing a large field enhancement in the gap region to maximize the excitation rate.

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The above analysis clearly indicates that the resonance characteristic of the cross-nanoantenna can be flexibly tuned by controlling various geometrical parameters, which can be used to match the excitation wavelengths of any types of emitters, greatly expanding the application scope. In particular, changing the gap distance G appears to be the most effective way in tailoring both the resonance peak position as well as the field enhancement. Followed by the cuspidal head H, it also has decent effects in modifying the plasmon resonance properties. The length L and the width W, albeit can still be used to control the resonance position, have less effect in manipulating the electromagnetic field inside the gap.

A set of parameters are rigorously selected as L = 50 nm, W = 40 nm, G = 30 nm, and H = 30 nm to match the excitation wavelength of Alexa Fluor 680 at λ_exc = 680 nm. The gap distance G is selected at a moderate value of 30 nm for two reasons: (1) a moderate gap size effectively balances the excitation rate and the quantum yield. A smaller gap can create a larger electromagnetic field enhancement but also accompanied by a higher nonradiative dissipation, which would cause severe quenching phenomenon and is detrimental for fluorescence enhancement applications [56]. (2) The proximity effect of the electron beam generally prohibits a small gap size. A moderate gap size can be experimentally realized via the modern electron beam lithography with a reasonable good quality.

3.2 Fluorescence enhancement for arbitrary emitter orientation

With the designed geometrical parameters, the fluorescence enhancement performance of the nanoantenna can be characterized by analyzing the excitation rate, radiative/non-radiative decay rate, quantum yield and the ultimate enhancement factor.

3.2.1 Enhanced excitation rate for arbitrary emitter orientation

To confirm that the plasmonic resonance of the nanoantenna yields the strongest electromagnetic field, the spectral response of the field intensity at the middle of the gap for both cross-nanoantenna and dimer-nanoantenna are depicted in Fig. 3. It is obvious that the maximum field intensities occur exactly at 680 nm, which is consistent with the designed plasmonic peak in Fig. 2. The separated x- and y-components of the field intensities are shown in Fig. 3(a). It is found that a circular polarized light can strongly excite both the x- and y- components equally for the cross-nanoantenna, benefiting from its highly symmetrical geometry, whereas for the dimer counterpart, only x-polarization can be primarily excited.

 

Fig. 3 (a) Separated x- and y-components at the gap center for both cross-nanoantenna and dimer nanoantenna Cross nanoantenna can generate large field enhancements equally along both x- and y-directions, whereas the dimer configuration can only produce field enhancement along x-direction. (b) The excitation rate enhancement with respect to the fluorophore emitter’s orientation angle Φ. Highly symmetrical cross-nanoantenna can yield higher excitation rate over arbitrary emitter orientation, which is superior than the dimer counterpart.

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Figure 3(c) illustrates the excitation rate ${\gamma }_{exc}$ with respect to the various emitter orientations Φ, which can be expressed as ${\gamma }_{exc}=|p\cdot E{|}^2=|\left|p\right|cos\Phi \cdot E_x+\left|p\right|\sin \Phi \cdot E_y{|}^2$. For the cross-nanoantenna, the excitation rate can be approximated as ${\gamma }_{exc}=\left|p{|}^2\right|E_x{|}^2(1+2\sin \Phi \cos \Phi )$, since it can enhance the electromagnetic fields equally along both x- and y-directions. After normalizing with the input field, we obtain a stable enhancement value as ${\gamma }_{exc}/{\gamma }_{exc}^0=|E_x{|}^2/|E_0{|}^2\approx 74$, regardless of the orientation of the emitter. In contrast, the excitation rate for the dimer structure becomes ${\gamma }_{exc}=\left|p{|}^2\right|E_x{|}^2\cos {\Phi }^2$ because only the x-component electric field can be primarily excited. The normalized enhancement value now is${\gamma }_{exc}/{\gamma }_{exc}^0=(|E_x{|}^2/|E_0{|}^2)\cdot [\cos {\Phi }^2/(1+2\cos \Phi \sin \Phi )]$, which only produces a maximum excitation rate ~78 at Φ = 0° and decays rapidly as Φ increases. This result clearly proves that a highly symmetrical cross-nanoantenna can yield higher excitation rate over any arbitrary orientation of the emitter, which is superior to its dimer counterpart.

3.2.2 Enhanced quantum yield for arbitrary emitter orientation

After the excitation, the Alexa Fluor 680 emitter subsequently releases photons at λ_em = 700 nm. Figure 4(a) presents the radiative decay rate ${\gamma }_r$ and the non-radiative decay rate ${\gamma }_{nr}$ of the cross- and dimer-nanoantenna, respectively, as a function of the emitter orientation. It is clear that both ${\gamma }_r$ and ${\gamma }_{nr}$ for the cross-nanoantenna remains stationary over all the emitter orientations, indicating the capability of the cross configuration to strongly interact with any arbitrary oriented emitter. Qualitatively, any emitter orientation can be decomposed into an x-oriented dipole $p_x=p\cdot \cos \Phi$ and y-oriented dipole$p_y=p\cdot \sin \Phi$. Each dipole component can always couple to one pair of arms of the cross-nanoantenna, thereby yielding ${\gamma }_r$ and ${\gamma }_{nr}$ that are less dependent on the emitter orientation. On the contrary, the dimer configuration consists of only one pair of arms, which can only selectively couple to the x-oriented dipole $p_x$. Therefore, the ${\gamma }_r$ and ${\gamma }_{nr}$ gradually diminish as Φ increases.

 

Fig. 4 Comparison of (a) radiative rate ${\gamma }_r$ and non-radiative rate ${\gamma }_{nr}$ and (b) quantum yield q between the cross nanoantenna and dimer nanoantenna with respect to the emitter orientation. The quantum yields of the cross structure is generally much stronger than those of the dimer counterpart, showing the advantage of the high-symmetrical structure.

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Using Eq. (2), Fig. 4(b) calculates the enhancements of quantum yields, taking into account the competition between the radiative and non-radiative decay rates. Consistent with the radiative/non-radiative decay rate results, the quantum yields of cross structure remains relatively unchanged for all the emitter orientations, and it is generally much stronger than those of the dimer counterpart, which again illustrates the advantage of the highly-symmetrical structure.

3.2.3 Fluorescence enhancement factor for arbitrary emitter orientation

The ultimate fluorescence enhancement factor can be obtained straightforwardly via multiplying the excitation rate (see Fig. 3) and quantum yield (see Fig. 4), according to Eq. (1). Figure 5 shows that the highly symmetrical cross nanoantenna generates a constant fluorescence enhancement factor for a randomly oriented fluorophore, owing to its capability to produce both stable excitation rate and quantum yield. On the other hand, the dimer configuration can only generate a maximal enhancement value at Φ = 0°, because it selectively enhances the x-component of the electric field and selectively couples to the x-oriented emitter. The fluorescence enhancement factor diminishes rapidly as Φ increases. When the emitter aligns completely orthogonal to the dimer axis (Φ = 90°), the fluorescence enhancement factor vanishes completely. To give a quantitative evaluation, we define an average fluorescence enhancement value as$<{\eta }_{em}/{\eta }_{em}^0>={\displaystyle \int ({\eta }_{em}/{\eta }_{em}^0\text{)d}\Phi }/{\displaystyle \int \text{d}}\Phi$, which shows that the average fluorescence enhancement factor of the cross nanoantenna (~117) is approximately 2.4 times that of the dimer nanoantenna (~49).

 

Fig. 5 Ultimate fluorescence enhancement factor for the cross- and dimer-nanoantenna under circular polarized incidence for arbitrary emitter orientations. The cross structure can provide lager and stable fluorescence enhancement factor than the dimer configuration.

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3.3 Preservation of emitter’s orientation at the far field

Besides the enhanced fluorescence intensity, the cross-nanoantenna also functions to preserve the polarization of the emitter at the far field. Figure 6 shows the 3D far field pattern obtained for three scenarios: (a) an isolated dipole, (b) a dipole coupled with the cross nanoantenna, and (c) a dipole coupled with the dimer nanoantenna, respectively, with 0°, 45°, 90° oriented emitters. Using Eq. (3), the corresponding defocused imaging patterns are also illustrated to offer a better visualization. For an isolated dipole on the substrate, its far field pattern as well as the defocused imaging rotates accordingly as Φ increases (see Fig. 6(a)). Concerning about the emitter couple to the cross nanoantenna in the center of the gap, the high symmetrical feature of cross helps to preserve the original polarization of the emitter, result in a similar 3D far field pattern and the defocused imaging comparing with those of the isolated dipole (see Fig. 6(b)). On top of that, the far field intensity is significantly enhanced regardless of the emitter orientation, which is consistent with the fluorescence enhancement results in Fig. 5. On the contrary, the radiation pattern from the dimer configuration cannot rotate properly with respect to the orientation of the emitter, but only reflects the main feature at Φ = 0° where the emitter aligns parallel to the dimer axis (see Fig. 6(c)). In addition, the intensity of the far field is gradually reduced as Φ increases since the coupling strength between the emitter and the dimer-nanoantenna becomes weaker. Especially for Φ = 90°, where the emitter aligned completely orthogonal to the dimer axis, the antenna has little effect on the radiation pattern of the emitter and it behaves like an isolated dipole.

 

Fig. 6 3D far field radiation pattern and 2D defocused imaging for (a) an isolated dipole on the substrate, (b) a dipole coupled with the cross nanoantenna and (c) a dipole coupled with the dimer nanoantenna, respectively, with 0°, 45°, 90° oriented emitters. Highly-symmetrical cross-nanoantenna can preserve the original orientation of the emitter while enhancing its intensity, whereas dimer configuration only reflects the main feature at Φ = 0° where the emitter aligns parallel to the dimer axis.

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4. Discussion

4.1 Spatial displacement of the emitter

Although it is a common practice to assume that the emitter is placed at the center of the gap [35,36], the exact location of the emitter is generally unknown in the real experiment. Figure 7 calculates the excitation rates ${\gamma }_{exc}$, quantum yields $q$ and the fluorescence enhancement factors ${\eta }_{em}$ when the emitter deviates from the center of the gap with various distances $(\Delta x,\Delta y)$. The results clearly show that the largest fluorescence enhancement occurs at the center of the gap, indicating the best balance between the excitation rate and the quantum yield. Some position (e.g. $\Delta x$ = 7.5 nm, $\Delta y$ = 7.5 nm) at the gap between the two perpendicular arms), might have stronger excitation rate (see Fig. 7(a)) due to larger field enhancement yielded from a smaller gap distance (≈21.2 nm, smaller than the common gap distance G = 30 nm), but it suffers from the lower quantum yield (see Fig. 7(b)), which compromises the ultimate fluorescence enhancement ${\eta }_{em}$ (see Fig. 7(c)). In addition, the displacement of the emitter breaks the symmetrical condition, and renders the fluorescence enhancement factor no longer orientation intensive. However, the average fluorescence enhancements $<{\eta }_{em}/{\eta }_{em}^0>$ are 92 for the position ($\Delta x$ = 5 nm, $\Delta y$ = 0 nm), 75 for the position ($\Delta x$ = 10 nm, $\Delta y$ = 0 nm), and 108 for the position ($\Delta x$ = 7.5 nm, $\Delta y$ = 7.5 nm) respectively, still outperform that of the dimer structure (~49).

 

Fig. 7 (a) Excitation rate, (b) quantum yield and (c) fluorescence enhancement factor for various displacement distance of the emitter. The largest fluorescence enhancement occurs at the center of the gap, indicating the best balance between the excitation rate and the quantum yield. The average fluorescence enhancements of the cross structure still outperform that of the dimer structure, regardless of its position.

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Furthermore, Fig. 8 studies the 3D far field patterns as well as the associated defocused imaging for various displacement distances of the emitter. Comparing with the situation where the emitter is at the center of the gap (Fig. 8(a)), the main features of the 3D far field and the defocused imaging still rotate properly with respect to the emitter orientation regardless of the deviation distance, and the polarization information could be correctly retrieved. Nevertheless, the displacement of the emitter would modify the intensity distribution of the imaging, resulting in an unsymmetrical imaging pattern. For instance, when the emitter moves to the right with ($\Delta x$ = 5 nm, $\Delta y$ = 0 nm) (see Fig. 8(b)), the right part of the imaging is slightly brighter than the left part, which is more obvious at a larger deviation ($\Delta x$ = 10 nm, $\Delta y$ = 0 nm) (see Fig. 8(c)). Similarly, when the emitter is close to the upper right quadrant ($\Delta x$ = 7.5 nm, $\Delta y$ = 7.5 nm) (see Fig. 8(d)), the upper right part of image is slightly brighter. This systematic change in intensity distribution of the image in turn might be helpful to estimate the displacement position of the emitter. Figure 6 and Fig. 8 clearly proves the unique capability of a highly-symmetrical cross-nanoantenna to preserve the orientation of the emitter in the far field while enhancing its intensity, even if it is displaced from the center, which is robust against the conventional dimer counterpart.

 

Fig. 8 Schematic of emitter position, 3D far field pattern and 2D defocused imaging for (a) dipole at the center of the gap with zero deviation ($\Delta x$ = 0 nm, $\Delta y$ = 0 nm), (b) dipole deviates along the x-axis to the right with ($\Delta x$ = 5 nm, $\Delta y$ = 0 nm), (c) dipole deviates along the x-axis to the right with ($\Delta x$ = 10 nm, $\Delta y$ = 0 nm), (d) the dipole deviates to the first quadrant with ($\Delta x$ = 7.5 nm, $\Delta y$ = 7.5 nm). The displacement mainly changes the intensity distribution of the image, but has little on the shape of the pattern. The main features of the 3D far field and the defocused imaging still rotate properly with respect to the emitter orientation, and the polarization information is still preserved in general.

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4.2 Substrate effect

Thus far, all the results are based on the assumption that the structure is fabricated on a Hikari glass substrate with a refractive index ~1.4. Previous studies have shown that the substrate could also modify the plasmonic resonances of the nanostructures [57,58]. Here we briefly discuss the influence of the substrate. As shown in Fig. 9(a), with the increment of the refractive index of the substrate, the plasmonic resonance redshifts to longer wavelength with diminished resonance amplitude. Consequently for the cross nanoantenna, the excitation rate ${\gamma }_{exc}$, quantum yield q and fluorescence enhancement factor ${\eta }_{em}/{\eta }_{em}^0$ keep decreasing as the refractive index of the substrate increases, as shown in Fig. 9(b). These results are consistent with the previous reports that a high refractive index substrate could destroy the plasmonic resonance due to the imaging charge generated in the substrate. Therefore, a low refractive index substrate is preferred to obtain a large fluorescence enhancement factor.

 

Fig. 9 Influence of substrate’s refractive index (n_sub) on (a) Extinction cross-section and (b) fluorescence enhancement performance (excitation rate, quantum yield and fluorescence enhancement factor). A low refractive index substrate is better to obtain a large fluorescence enhancement factor. (c) 3D far-field patterns and the corresponding defocused imaging as a function of the refractive index of the substrate. The substrate could change the directivity and the intensity of the radiation pattern, but has little effect on the orientation of the emitter at the far field.

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Figure 9(c) presents the evolution of the 3D far-field patterns as well as the associated defocused imaging as the refractive index of the substrate increases. It is clear that the substrate could change the directivity and the intensity of the radiation pattern, since a high index substrate could convert the evanescent wave of the dipolar emitter into the propagating wave. Nevertheless, the orientation information is still preserved at the far field owing to the presence of the cross nanoantenna. The substrate will not disturb the orientation of the emitter. Nevertheless, the orientation information can still be retrieved from the respective defocused imaging owing to the presence of the cross nanoantenna.

4.3 Others

In this paper, the plasmonic resonance of the nanoantenna matches the excitation wavelength of the emitter to generate a larger electric field enhancement so as to produce a large excitation rate. Shifting the plasmonic resonance to the emission wavelength might result in two consequences: 1) the excitation rate decreases because the plasmonic resonance moves away from the excitation wavelength; 2) the quantum yield would also decrease since the dipole emission now coincides with the plasmonic resonance, where the non-radiative decay rate is the highest. Figure 10 clearly proves this point by matching the plasmonic resonance with the excitation wavelength and the emission wavelength respectively. The excitation rate decreases by 17.8%, while the quantum yield decreases by 15.8% when the plasmonic resonances match the emission wavelength. Ultimately, the fluorescence enhancement factor dropped by 32.5%.

 

Fig. 10 (a) Matching the plasmonic resonance λ_res with the excitation wavelengthλ_exc at 680 nm and the emission wavelengthλ_emi at 700 nm respectively. (b) Excitation rate, (c) quantum yield and (d) ultimate fluorescence enhancement of the two situations. The excitation rate decreases by 17.8%, while the quantum yield decreases by 15.8% when the plasmonic resonances match the emission wavelength. Ultimately, the fluorescence enhancement factor dropped by 32.5%.

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In principle, other highly-symmetrical nanoantennas (e.g. ring resonator) should function similarly to the cross structure. Nevertheless, the cross nanoantenna is deliberately chosen for the fluorescence enhancement applications in consideration of three aspects: (1) the cross nanoantenna is made of four adjustable components whose geometries can be characterized by the length, width, cuspidal head and gap distance, which offers more freedom to tune the plasmonic resonance to match the excitation wavelength of the emitter. (2) The cross configuration can easily generate a strong electromagnetic field enhancement by controlling the gap distance, which is generally stronger than that of a ring resonator. Such a large field enhancement directly benefits the fluorescence excitation rate. (3) Compared with the ring shape structure, the cross structure uses less metal material, naturally suppressing the non-radiative decay channel and creating a high quantum yield.

5. Conclusion

A theoretical study has been carried out to illustrate the robustness of a highly symmetrical cross nanoantenna in enhancing the fluorescence emission intensity of an arbitrarily oriented emitter, while preserving its orientation information at the far field. Due to the highly symmetrical geometry, the cross structure is able to generate a stable excitation rate and quantum yield regardless of the emitter orientation. In contrast, the dimer configuration can only strongly excite the electromagnetic field along the dimer axis, and selectively couple to the emitter when it aligns parallel to the dimer axis. Its performance degrades rapidly when the emitter aligns orthogonal to the dimer axis. As a result, the cross configuration can yield a consistent fluorescence enhancement factor ~117 for any arbitrarily oriented fluorophore, which is 2.4 times that from a dimer counterpart. On top of that, the 3D far field pattern and the associated defocused imaging results have shown that only the cross structure is able to preserve the original orientation information of an arbitrarily oriented emitter at the far field, which is unachievable with the conventional dimer nanoantenna. Our results have proven that a highly-symmetrical cross nanoantenna outperforms the conventional dimer configuration for the practical fluorescence enhancement application, where the emitter is generally randomly oriented.