Dielectric-loading approach for extra electric field enhancement and spatially transferring plasmonic hot-spots

Let us start by considering the simplest conventional plasmonic nanoantenna—a single spherical Au nanoparticle (AuNP) of radius R embedded in a homogeneous medium (e.g. air, n = 1.0), as shown in the inset in figure 1(a). In this case, the radius of the AuNPs could be optimized to maximize the field enhancement for a given incident wavelength. Figure 1(a) shows the field enhancement factors calculated at the surface point P corresponding to the incident electric field direction as functions of the radius R and the incident wavelength λ, in which the calculations are performed using the three-dimensional finite element-method software COMSOL Multiphysics and the permittivity of Au is taken from the experimental data [29]. By plotting a vertical line in figure 1(a), which corresponds to a chosen wavelength, the optimal radius for the maximum field enhancement could be directly obtained at this particular wavelength. For example, for a typical incident wavelength of λ =633 nm, when the radius of the AuNP is optimized to R = 74 nm, the field enhancement in the AuNPs could reach the maximum value of ∼27, as indicated by the point I in the dashed line in figure 1(a).

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To engineer the spatial position of the hot-spots, a dielectric-loading strategy that involves conformally coating plasmonic nanoantennas with a thin layer of high refractive index dielectrics (relative to the surrounding medium) is proposed. It is noted that high refractive index dielectric coating would increase the effective refractive index of the surrounding medium and induce a red-shift in the localized surface plasmon resonances (LSPRs) of the dielectric-loaded plasmonic nanoantennas [30]. Therefore, the conventional plasmonic nanoantennas need to be scaled down before dielectric coating to possibly counteract the red-shift effect. In that case, the dielectric-loaded and conventional plasmonic nanoantennas can both be optimized to resonate at the same wavelength to achieve a fair comparison.

According to this strategy, dielectric-loaded AuNPs are constructed by firstly reducing the size of the AuNP from its original optimal size R = 74 nm to, for example, r = 50 nm, and consequently coating a thin dielectric layer (inset in figure 1(b)). Since the electric fields distributed outside of the dielectric-loaded AuNPs could be sensed by the external matters, in the following discussions we mainly focus on the external field enhancement at the dielectric surface. When the radius of the core AuNP is fixed to r = 50 nm, two degrees of freedom, including the shell refractive index and shell thickness, could be optimized to maximize the external field enhancement at the given incident wavelength of λ = 633 nm. Figure 1(b) shows the electric field enhancement factors calculated at λ = 633 nm at the dielectric surface point Q corresponding to the incident electric field direction in the dielectric-loaded AuNPs with a fixed r = 50 nm as functions of shell thickness (t) and shell refractive index (n). Contour lines with a value of 27, which represents the maximum field enhancement factor achieved in the conventional AuNPs (point I in figure 1(a)), are also plotted as red solid lines in figure 1(b). It is seen from figure 1(b) that as the shell refractive index and the shell thickness locate within the range enclosed by the contour lines, the dielectric-loaded AuNPs could produce larger external field enhancement than the conventional AuNPs. For example, for a shell refractive index of n = 2.7 (which is represented by a vertical dashed line in figure 1(b)), when the shell thickness is optimized to t = 16 nm, the external field enhancement at λ = 633 nm in the dielectric-loaded AuNPs can reach the maximum value of ∼86, as indicated by the point II in figure 1(b).

The electric field distributions calculated at λ =633 nm for the optimal conventional AuNP (R = 74 nm, corresponding to the point I in figure 1(a)) and the optimal dielectric-loaded AuNP (r = 50 nm, n = 2.7, t = 16 nm, corresponding to the point II in figure 1(b)) are shown in figures 1(c) and (d), respectively. As expected, for the conventional AuNP the strongest fields of the resonant hot-spots locate at the metal surface of the AuNP (figure 1(c)). After coating the AuNP with a thin dielectric layer, the resonant hot-spots are found to mostly distribute at the most outside surface of the dielectric-loaded AuNP (figure 1(d)), which directly validates that the dielectric-loading approach allows the strongest field of the hot-spots to be transferred from the metal surface to the dielectric surface.

Furthermore, the field enhancement factors extracted along the central section lines in the two optimal nanoantennas are plotted in figures 1(e) and (f), respectively. Associated with the excitation of the LSPR, electric fields are found to be enhanced at x = R = 74 nm in the conventional AuNP (as indicated by a blue vertical line in figure 1(e), which represents the Au-air interface) and x = r = 50 nm in the dielectric-loaded AuNP (as indicated by a blue vertical line in figure 1(f), which represents the Au-shell interface). It should be noted that compared to the conventional AuNPs, there is an additional interface between the high refractive index shell and the low refractive index surrounding medium (shell-air interface) in the dielectric-loaded ones. Due to the continuity boundary condition of the normal component of the electric displacement vector at the interface between two different materials [31], electric fields that decay away from the metal surface are expected to be abruptly enhanced at the shell-air interface in the dielectric-loaded AuNPs. As indicated by a red vertical line in figure 1(f), electric fields at x = r + t = 66 nm (corresponding to the dielectric surface of the dielectric-loaded AuNP) are indeed enhanced with a factor of ∼86, which exceeds the maximum field enhancement factor of ∼27 achieved in the optimal conventional AuNP. Therefore, in addition to the ability to spatially transfer the hot-spots from the metal surface to the dielectric surface, the dielectric-loading approach could also provide an extra enhancement in the local electric fields.

In practice, the dielectric materials that are suitable for acting as the shells of the dielectric-loaded plasmonic nanoantennas should be considered. Fortunately, dielectrics such as silica (SiO₂, n ≈ 1.46) [25–28], alumina (Al₂O₃, n ≈ 1.8) [32], zirconium dioxide (ZrO₂, n ≈ 2.1) [33], zinc sulfide (ZnS, n ≈ 2.2) [34], cerium oxide (CeO₂, n ≈ 2.3) [35] and titanium dioxide (TiO₂, n ≈ 2.7–2.8) [36] have been reported to be able to form a conformal shell around the noble metal NPs with a tunable shell thickness. Also, it is noted that in the above demonstration, to construct the dielectric-loaded plasmonic nanoantennas, the radius of the AuNP is, to some degree, reduced arbitrarily from R = 74 nm to r = 50 nm. Actually, the coating dielectric materials, i.e. the shell refractive index, could be firstly selected, and then the radius of the core AuNP and the shell thickness are simultaneously varied to maximize the external field enhancement in the dielectric-loaded AuNPs for a given incident wavelength

Figure 2(a) shows the electric field enhancement factors calculated at λ = 633 nm at the surface point Q in the TiO₂-loaded AuNPs (with a fixed shell refractive index of n = 2.7) as functions of core radius (r) and the shell thickness (t). As indicated by the marked point III in figure 2(a), when the core radius and the shell thickness are optimized to r = 36 nm and t = 17 nm, the TiO₂-loaded AuNPs could produce the external field enhancement factor as high as ∼112 at λ = 633 nm, which is 4 times larger than the maximum achievable field enhancement factor of ∼27 in the optimal conventional AuNP (point I in figure 1(a)). For direct comparison, the external field enhancement factors at λ = 633 nm in the SiO₂-loaded AuNPs (with a fixed shell refractive index of n = 1.46) are also plotted in figure 2(b) as functions of r and t. The external field enhancement in the SiO₂-loaded AuNPs is found to monotonically decrease with increasing the shell thickness. As indicated by the marked point IV in figure 2(b), the external field enhancement reaches the maximum value of ∼27 at r = 74 nm and t = 0 nm, which is identical to the optimal case of the conventional AuNPs (point I in figure 1(a)). This reveals that due to the low shell refractive index, the SiO₂-loaded AuNPs are unable to provide higher external field enhancement than the optimal conventional AuNP. Therefore, the shell refractive index plays a key role in the dielectric loading approach. The maximum achievable external field enhancement factors at λ =633 nm in the dielectric-loaded AuNPs with different shell refractive indices (i.e. different coating dielectrics) are summarized in figure 2(c). Provided that the shell refractive index is larger than n = 1.7, the dielectric-loaded AuNPs could always outperform the optimized conventional Au NP in terms of field enhancement. It is also found that the dielectric-loaded AuNPs with higher shell refractive index can produce larger external field enhancement. Therefore, the TiO₂ (n = 2.7) is chosen as dielectric shell materials in the following discussions.

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In the above demonstrations, the incident wavelength is fixed to λ =633 nm. The proposed dielectric-loading approach could also work for other incident wavelengths. Figures 3(a) and (b) show the external field enhancement in the TiO₂-loaded AuNPs with different core radii and shell thicknesses calculated at λ = 590 nm and λ = 690 nm, respectively. For these two incident wavelengths, the radius of the conventional AuNPs could be varied to maximize the field enhancement. It could be found from figure 1(a) that when the radius is optimized to R = 67 nm for λ = 590 nm and R = 82 nm for λ = 690 nm, the field enhancement in the conventional AuNPs could reach the maximum values of ∼33 and ∼23. As indicated by the marked points V and VI in figures 3(a) and (b), when the geometry parameters are optimized to (r = 30 nm, t = 10.7 nm) for λ = 590 nm and (r = 42 nm, t = 25 nm) for λ = 690 nm, the TiO₂-loaded AuNPs could produce the external field enhancement factors of ∼150 and ∼79, which are 3–4 times larger than the maximum field enhancements achieved in the optimal conventional AuNPs at the respective wavelengths. The electric field distributions calculated for the TiO₂-loaded AuNPs with optimal parameters (corresponding to the points V and VI in figures 3(a) and (b)) at λ = 590 nm and λ = 690 nm further present that the resonant electric fields are mostly distributed outside the dielectric-loaded AuNPs (figures 3(c) and (d)), which again validate the ability of the dielectric-loading approach to spatially transfer the hot spots to the dielectric surfaces.

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As a demonstration application, in what follows we show that compared to the conventional plasmonic nanoantennas the dielectric-loaded ones are able to provide an extra fluorescence enhancement. Here, we consider a single emitter (e.g. Nile blue dye molecule) interacting with the conventional and dielectric-loaded AuNPs, respectively. For weak excitation, the excitation and emission processes of an emitter could be treated independently because there is no coherence between the two processes [23]. To simulate the excitation process, the antennas are irradiated by a plane wave. Since the excitation rate of the molecule is proportional to the intensity of the local excitation field, its enhancement factor can then be written as

$$\begin{equation}{f_{exc}} \equiv {\gamma _{exc}}/\gamma _{exc}^0 = {\left| {{{\bf{n}}_p}.{\bf{E}}} \right|^2}/{\left| {{{\bf{n}}_p}.{{\bf{E}}_0}} \right|^2}\end{equation} \tag{ 1 }$$

where n _p is a unit vector pointing in direction of the molecule, E and E₀ are the electric field with and without the antenna at the location of the molecule, respectively [23]. To simulate the emission process, the excited molecule is approximated as a classical dipole source. In the presence of the antenna, the normalized quantum yield of the molecule is given by

$$\begin{equation}{f_q} \equiv q/{q^0} = \frac{{{f_{rad}}/{q^0}}}{{{f_{rad}} + {f_{nrad}} + (1 - {q^0})/{q^0}}}\end{equation} \tag{ 2 }$$

where q⁰ is the free-space intrinsic quantum yield of the molecule, and ${f_{rad}} \equiv {\gamma _{rad}}/\gamma _{rad}^0$ and ${f_{nrad}} \equiv {\gamma _{nrad}}/\gamma _{rad}^0$ are the normalized radiative and non-radiative decay rates, respectively [37–39]. The normalized energy-transfer rates in equation (2) could also be written as ${f_{rad}} \equiv {P_{rad}}/{P_0}$ and ${f_{nrad}} \equiv {P_{nrad}}/{P_0}$ with P_rad being the power radiated into the far field by the dipole in the presence of the antenna, P_nrad being the power dissipated in the metal part of the antenna due to ohmic loss, and P₀ being the power radiated by the same dipole in the absence of the antenna [40]. The normalized fluorescence rate is then obtained from the product of the normalized excitation rate and quantum yield, i.e. ${f_{em}} = {\gamma _{em}}/\gamma _{em}^0 = {f_{exc}}\,\,{f_q}$.

For a single molecule placed near the conventional AuNPs (inset in figure 4(a)), its fluorescence enhancement is calculated and plotted in figure 4(a) as functions of the radius R and the molecule-Au separation distance g. In the calculations, the orientation of the molecule, the polarization of the excitation plane wave and the dipole source are along the axis connecting molecule and AuNP center. The wavelengths of the excitation plane wave and the dipole source are set to λ_exc = 633 nm and λ_em = 663 nm, which correspond to the peak absorption and emission of Nile blue molecules, respectively, such that the Stokes shift is empirically taken into account. The molecule is assumed to have unity intrinsic quantum yield q⁰ = 1. As indicated by the point I in figure 4(a), when the molecule-Au separation distance and the radius of the conventional AuNP are optimized to g = 11 nm and R = 78 nm, the fluorescence enhancement could reach the maximum value of ∼11. The detailed energy-transfer rates f_exc, f_q and f_em of the molecule coupled to the conventional AuNP with a radius R = 78 nm for different molecule-Au separation distances are present in figure 4(b). It is found that with decreasing the molecule-Au separation distance, the excitation rate f_exc increases due to the enhanced electric fields (blue curve in figure 4(b)), while the quantum yield f_q decreases due to the increased non-radiative decay rate (dissipation in the metal) (green curve in figure 4(b)). As a result, the fluorescence enhancement f_em can reach the maximum value when the balance between f_exc and f_q is achieved at an optimal molecule-Au separation distance g = 11 nm (red curve in figure 4(b)). Clearly, at this optimal separation distance g = 11 nm the excitation rate just reaches f_exc ≈ 14, which is smaller than the maximum achievable rate of f_exc ≈ 27 at g = 0 nm (corresponding to the Au surface), and thus revealing that the non-zero optimal emitter-metal separation distance prevents the emitter from fully utilizing the resonant hot-spot in the conventional plasmonic nanoantennas.

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In the case of the dielectric-loaded AuNPs, the molecule is directly placed on the outer dielectric surface, as schematically shown in the inset in figure 4(c). The fluorescence enhancement factors of the single molecule coupled to the SiO₂-loaded AuNPs (with a fixed shell refractive index of n = 1.46) and the TiO₂-loaded AuNPs (with a fixed shell refractive index of n = 2.7) are plotted in figures 4(c) and (e), respectively, as functions of the core radius r and the coating thickness t. For the SiO₂-loaded AuNPs, when the geometrical parameters are optimized to r = 68 nm and t = 17 nm, the fluorescence intensity can reach a maximum enhancement factor of ∼19 (the point II in figure 4(c)). In particular, the maximum fluorescence enhancement achieved in the TiO₂-loaded AuNPs with optimal geometrical parameters of r = 42 nm and t = 17 nm is found to reach a factor as high as ∼57 (the point III in figure 4(e)), which is increased by about 5.2 times compared to the optimal case of the conventional AuNP, and thus validating that the dielectric-loading approach is able to further increase the maximum achievable fluorescence intensity.

To understand the origin of the extra fluorescence enhancement, the detailed energy-transfer rates of the molecule coupled to the SiO₂-loaded AuNPs with a fixed core radius of r = 68 nm (corresponding to the point II in figure 4(c)) and the TiO₂-loaded AuNPs with fixed r = 42 nm (corresponding to the point III in figure 4(e)) are plotted in figures 4(d) and (f), respectively, as a function of the coating thickness. The excitation rate and quantum yield in the SiO₂-loaded AuNPs (green and blue curves in figure 4(d)) are found to basically follow the same trend as those in the conventional AuNPs (green and blue curves in figure 4(b)). At the optimal SiO₂ coating thickness of t = 17 nm, the balance between f_exc and f_q is achieved. Compared to the optimal case of the conventional AuNPs, where the optimal molecule-Au separation distance is g = 11 nm, the 17 nm-thick SiO₂ shell provides a relatively larger molecule-Au separation distance. The normalized quantum yield of f_q ≈ 0.84 achieved in the optimal case of the SiO₂-loaded AuNPs with n = 1.46 and r = 68 nm (the intersection point of the vertical dashed line and green curve in figure 4(d)) is thus larger than f_q ≈ 0.79 achieved in the optimal case of the conventional AuNPs (the intersection point of the vertical dashed line and green curve in figure 4(b)). On the other hand, although the SiO₂-loaded AuNPs could not outperform the conventional AuNPs in the maximum achievable field enhancement, the external field enhancement on the outer surface of the SiO₂-loaded AuNPs could exceed the field enhancement achieved at a distance away from the conventional AuNPs. The excitation rate of the molecule in the SiO₂-loaded AuNPs could reach f_exc ≈ 22.1 at t = 17 nm (the intersection point of the vertical dashed line and blue curve in figure 4(d)), which is larger than f_exc ≈ 14 achieved in the conventional AuNPs at g = 11 nm (the intersection point of the vertical dashed line and blue curve in figure 4(b)). Compared to the optimal conventional AuNPs, both the excitation rate and the quantum yield are slightly improved in the optimal SiO₂-loaded AuNPs, and thus the maximum fluorescence enhancement is correspondingly increased from a factor of ∼11 to ∼19.

For the TiO₂-loaded AuNPs, the resonant hot spots could be transferred to the dielectric surface and the maximum field intensity could gain an extra enhancement, as demonstrated in figure 2(a). The molecule coupled to the TiO₂-loaded AuNPs is thus expected to sense more intense excitation fields than that in the conventional and SiO₂-loaded AuNPs. Unlike the cases of the conventional and SiO₂-loaded AuNPs, where the excitation rate enhancement increases monotonically with decreasing the molecule-Au distance (blue curve in figures 4(b) and (d)), the TiO₂-loaded AuNPs exhibit a peak in the excitation rate enhancement spectrum (blue curve in figure 4(f)). When the coating thickness of the TiO₂-loaded AuNPs with n = 2.7 and r = 42 nm is tuned to t = 17 nm, the excitation rate enhancement could reach a maximum value as high as f_exc ≈ 102.8 (the intersection point of the vertical dashed line and blue curve in figure 4(f)). Compared to the optimal conventional AuNP, the optimal TiO₂-loaded AuNP improves the excitation rate by a factor of ∼7, and compared to the optimal SiO₂-loaded AuNP, the improvement is almost a factor of ∼5. It is noted that more energy could be transferred from a dipole to the adjacent dielectrics with higher refractive index [41] and also to the nearby metal nanoparticles with smaller size [23]. For this reason, the non-radiative decay rate in the optimal TiO₂-loaded AuNP with a relatively higher shell refractive index of n = 2.7 and smaller core radius of r = 42 nm is expected to be higher than that in the optimal SiO₂-loaded AuNP with relatively smaller n = 1.46 and larger r = 68 nm. The normalized quantum yield in the optimal TiO₂-loaded AuNP is found to be f_q ≈ 0.56 at t = 17 nm (the intersection point of the vertical dashed line and green curve in figure 4(f)), which is indeed smaller than f_q ≈ 0.84 achieved in the optimal SiO₂-loaded AuNP at t = 17 nm (the intersection point of the vertical dashed line and green curve in figure 4(d)). In spite of the relatively low normalized quantum yield, the resultant fluorescence enhancement in the optimal TiO₂-loaded AuNP could reach a maximum value of ∼57, which is improved by a factor of ∼5.2 compared to the optimal conventional AuNP and by a factor of ∼3 compared to the optimal SiO₂-loaded AuNP. This reveals that the excitation rate enhancement, which is attributed to the ability of the dielectric-loaded AuNPs to spatially transfer the hot spots and further enhance their intensities, could play a dominant role in the fluorescence enhancement, and thus verifying the importance of the hot-spots engineering provided by the dielectric loading approach.

The extra fluorescence enhancement factors, defined as the ratio of the maximum achievable fluorescence enhancement in the dielectric-loaded AuNPs with different shell materials (i.e. different coating refractive indices) to that in the conventional AuNPs, are also calculated by simultaneously optimizing the core radius r and the coating thickness t, and summarized in figure 5. As demonstrated in figure 2(c), the external field enhancement achieved in the dielectric-loaded AuNPs increase monotonically with increasing the coating refractive index, which imposes positive effect on the fluorescence enhancement by increasing the excitation efficiency. Therefore, the extra fluorescence enhancement is found to initially increase with increasing the coating refractive index (figure 5). On the other hand, the optimal core radius is smaller and the corresponding optimal coating thickness is thinner for the dielectric-loaded AuNPs with higher coating refractive index, which could accelerate the non-radiative decay rate [23] and thus impose an adverse effect on the fluorescence enhancement by lowering the quantum yields. As the coating refractive index is increased to n = 2.6, the balance is achieved between the increased excitation rate and the decreased quantum yields, and the extra fluorescence enhancement reaches the highest factor of ∼5.3 in the dielectric-loaded AuNPs with optimal core radius of r = 42 nm and coating thickness of t = 18 nm (figure 5). With further increasing the coating refractive index, the adverse effect of lowering the quantum yields would prevail, and the extra fluorescence enhancement achieved in the dielectric-loaded AuNPs begins to decrease. Nevertheless, within the calculated coating refractive index range from n = 1.2 to 3.0, the dielectric-loaded AuNPs could always be optimized to outperform the conventional AuNPs in the fluorescence enhancement.

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In the above discussions, a single Nile blue molecule with the peak absorption and emission wavelengths being λ_exc = 633 nm and λ_em = 663 nm is chosen. Here, we also present the fluorescence enhancement results for another type of dye molecule, crystal violet, coupled with the conventional and TiO₂-loaded AuNPs. The peak absorption and emission wavelengths of the crystal violet molecules are λ_exc = 590 nm and λ_em = 640 nm, respectively. The intrinsic quantum yield is assumed to be q⁰ = 0.001. For the single crystal violet molecule coupled with the conventional AuNPs, when the geometrical parameters are optimized to R = 72 nm and g = 3 nm, the fluorescence enhancement could reach the maximum value of ∼481 (point I in figure 6(a)). The detailed energy-transfer rates are also calculated for the conventional AuNPs with R = 72 nm and shown in figure 6(b) as a function of the molecule-Au separation distance g. It is seen that at the optimal molecule-Au separation distance g = 3 nm, in addition to the excitation rate enhancement of f_exc ≈ 26.3, the normalized quantum yield is also significantly enhanced and reaches a factor as high as f_q ≈ 18.3 (the intersection point of the vertical dashed line and green curve in figure 6(b)), due to the low intrinsic quantum yield of the crystal violet molecule. As a result of both enhancement in the excitation rate and normalized quantum yield, when coupled to the conventional AuNPs, the crystal violet molecules could gain higher fluorescence enhancement than the Nile blue molecules with higher intrinsic quantum yield (figure 6(b) vs figure 4(b)), which is consistent with previously reported results that fluorescence enhancement depends on the intrinsic quantum yield of the molecule and higher enhancement can be achieved for lower q⁰ [12, 38–40].

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Figure 6(c) shows the fluorescence enhancement factors of the single crystal violet molecule coupled to the TiO₂-loaded AuNPs with different core radii r and the coating thicknesses t. As indicated by the marked point II, the maximum fluorescence enhancement is achieved at r = 38 nm and t = 11.5 nm. By further plotting the energy transfer rates for the TiO₂-loaded AuNPs with fixed core radius of r = 38 nm as a function of the coating thickness, the excitation rate enhancement is found to reach a peak value of f_exc ≈ 135 at the optimal coating thickness of t = 11.5 nm (the intersection point of the vertical dashed line and blue curve in figure 6(d)), and meanwhile the normalized quantum yield reaches an enhancement factor of f_q ≈ 12 (the intersection point of the vertical dashed line and green curve in figure 6(d)). Although the normalized quantum yield enhancement in the optimal TiO₂-loaded AuNP is slightly smaller than that in the optimal conventional AuNP, the excitation rate in the former case is greatly enhanced (figure 6(d) vs figure 6(b)). Therefore, the fluorescence enhancement achieved in the optimal TiO₂-loaded AuNP could reach a maximum value as high as ∼1472. Compared to the optimal case of the conventional AuNPs, the optimal TiO₂-loaded AuNP improves the fluorescence enhancement by a factor of ∼3, which demonstrates that the dielectric-loading approach could also be applied to provide an extra enhancement in the fluorescence of the molecules with different transition bands and intrinsic quantum yields.