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Abstract
Plasmonic tip nanofocusing has widely been applied in tip-enhanced Raman spectroscopy, optical trapping, nonlinear optics, and super-resolution imaging due to its capability of high local field enhancement. In this work, a substrate with a circular nanocavity is proposed to enhance the nanofocusing and optical trapping characteristics of the plasmonic tip. Under axial illumination of a tightly focused radial polarized beam, the circular nanohole etched on a metallic substrate can form a nanocavity to induce an interference effect and further enhance the electric field intensity. When a plasmonic tip is placed closely above such a substrate, the electric field intensity of the gap-plasmon mode can further be improved, which is 10 folds stronger than that of the conventional gap-plasmon mode. Further analysis reveals that the enhanced gap-plasmon mode can significantly strengthen the optical force exerted on a nanoparticle and stably trap a 4-nm-diameter dielectric nanoparticle. Our proposed method can improve the performance of tip-enhanced spectroscopy, plasmonic tweezers and extend their applications. We anticipate that our methods allow simultaneously manipulating and characterizing single nanoparticles in-situ.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nanofocusing can compress electromagnetic fields into nanoscale volume, which is one of the main subjects in optical physics and technologies over the past decade [1]. The most commonly used way for achieving nanofocusing is based on converting light into surface plasmons (SPs) by utilizing plasmonic nanostructures including tapered metallic tips [2], sharp metal wedges [3], stripes [4], V-grooves [5] etc. Due to the capability of high field localization and enhancement, plasmonic nanofocusing can extremely strengthen nanoscale light-matter interactions and has widely been exploited in plasmon-enhanced spectroscopy (including tip-enhanced Raman spectroscopy (TERS)) [6,7], optical tweezing [8], and amplification of optical nonlinearities [9,10]. TERS is one of the most interesting techniques of nanoscale analysis, which can provide label-free chemical information with nanometer spatial resolution and corresponding topological imaging [11–14].
Sharp plasmonic tips are generally adopted in TERS systems since they can be readily integrated with scanning probe microscopes. When a laser light with appropriate polarization is focused onto the apex of the plasmonic tip, a nanofocusing field can be effectively formed in the vicinity of the tip apex [15]. So far, various works, including tip designs, excitation laser mode, and illumination geometry configuration, have been proposed to furtherly enhance the intensity of the tip nanofocusing field [15]. A tip with nano-grating near the tip apex can tune the resonance wavelength and improve the field enhancement factor simultaneously [16–18]. Focused radially polarized beam (RPB) excitation can improve TERS signal than that of linearly polarized beam excitation [19,20]. Meanwhile, a gap-plasmon mode originated from the coupling between the tip and metallic substrate can exert prominent effects on the performance of the nanofocusing field and TERS application, where the gap-plasmon mode offers a higher enhancement in a smaller mode volume [21–23]. It’s worth noting that a virtual SPs probe can be excited on a thin and flat metallic film by a tightly focused RPB [24,25]. As a counterpart of the real probe, the virtual probe is a standing wave generated by constructive interference of SPs waves. In the electric field of the virtual probe, the longitudinal field component is dominant, which is more suitable to excite the gap-plasmon mode between the substrate and tip apex [26,27]. It has been demonstrated that a gap-plasmon hybridization between a virtual probe and a metallic tip leads to greater field enhancement and higher resolution in TERS imaging [28]. Nonetheless, further enhancement of the gap-plasmon mode between a virtual probe and a metallic tip is still an attractive research direction, which can expand the scope of its application.
In this work, we propose to use a circular nanohole in a flat gold film to improve the electric field enhancement characteristic of the gap-plasmon mode residing in a plasmonic tip and a virtual SPs probe. Firstly, a circular nanohole etched on a metallic substrate can form a nanocavity to induce an interference effect. Thus, the intensity of the virtual SPs probe can be effectively enhanced and the mode volume can be compressed. When the real tip is closely placed above such a gold film, the electric field intensity of the gap-plasmon mode can further be improved, which is 10 folds stronger than that of the conventional gap-plasmon mode. Meanwhile, we investigate the influence of the lateral distance between the center of nanohole and tip axis on the electric field enhancement. By this feat, our results indicate that such a gap-plasmon mode can also increase the optical force so that can stably trap 4-nm-diameter dielectric particles. We envision that the proposed method can improve the performance of TERS, plasmonic tweezer, and their applications, and will allow trapping a single nanoparticle for in-situ spectral characterization.
2. Methods
Figure 1(a) depicts our considered model, which consists of a gold plasmonic tip and a gold substrate with a circular nanohole. An RPB with the wavelength of 632.8 nm is tightly focused via an oil-immersion objective with NA=1.4, whose maximum incident angle on the gold film satisfying the requirements of SPs excitation (Fig. S1). Then, the focused RPB is axially illuminating at the tip apex. The gap between the objective lens and the glass substrate is filled with index-matching oil (n=1.515). A gold rounded-tip cone with a cone angle α = 25° terminated by a hemisphere with curvature radius r = 5 nm is placed above the substrate by a gap size g. The thickness of the gold substrate is 45 nm, which is the optimum thickness to effectively excite SPs (Fig. S1). A circular nanohole etched on the gold substrate forms a nanocavity, which is defined by radius R and depth h.
Fig. 1. Sketch map of the tip nanofocusing axially excited via a tightly focused radially polarized beam (RPB). The upper right inset is the enlargement of the tip with geometric parameters. The lower left inset shows the intensity distribution of the RPB, where the arrows indicate the electric field vectors of the beam.
To derive the improvement effect of the circular nanocavity on the field enhancement, the 3D finite difference time domain (FDTD Solutions, Lumerical/Ansys Inc., Canada) method is adopted for simulation. The permittivity of Au is taken from the experimental data of Johnson and Christy [29]. The tightly focused RPB is calculated by MATLAB codes based on the vector diffraction theory and then imported into the FDTD software [30]. The perfectly matched layer (PML) is used as an absorption boundary to avoid unphysical reflections around structures. In addition, the PML is placed along the upper cone surface to reduce the reflection of SPPs from the upper tip cone boundary [31]. Due to the rotational symmetry of the structure and the excitation source, the symmetry boundary is utilized to save the simulation time. To ensure a good tradeoff between accuracy, computational resources and time, we employ non-uniform grid sizes for all calculations. More simulation details are shown in the Supplement 1 S2 section. Rigorous convergence testing is performed for PML, the size of mesh regions, and minimum mesh sizes. Parameters are thought to converge when subsequent refinements produce relative changes in the values of field intensity and optical force of 5% [31]. The electric field intensity enhancement factor is defined as EF=|Eloc|2/|E0|2, where |Eloc|2 is the localized electric field intensity located 2 nm above the substrate, and |E0|2 is the incoming electric field intensity of the focused RPB.
The time-averaged optical force produced by the tip nanofocusing field is obtained by Maxwell stress tensor (MST) [32]
3. Results and discussions
3.1 Generation of virtual SPs probe
We first consider the generation of the virtual SPs probe in the nanocavity and the enhancement of the nanocavity to the electric field intensity of the virtual probe. As depicted in Fig. 2(a), the radius and depth of the circular nanohole are R and h, respectively. In Figs. 2(b) and 2(c), a typical virtual probe field pattern excited on a flat gold substrate without a nanocavity are shown at the xz plane and the xy plane 5 nm above the gold-air interface, respectively. From the transverse field profile, the full width at half maximum (FWHM) size of the focus spot is about 222 nm (∼0.35 λ0). A circular nanohole etched on the gold metallic substrate will affect the EF. Figure 2(d) illustrates the relationship between EF and the radius of the nanohole R when the depth h varies from 5 nm to 45 nm. Note that when h=45 nm, EF is slightly smaller than that of the typical virtual probe due to the absence of the gold-air interface in the center to support the existence of SPs wave (Fig. S4(a)). In this case, EF is dependent on the transmittance of incident light through the nanohole and increases with the size of the nanocavity [33]. Remarkably, in the case of h=35 nm, EF exhibits a significant interference effect, because the sidewall of the nanohole can be regarded as a reflector to reflect SPs wave so that the nanohole forms a nanocavity. As seen, there are two maxima EF at R=160 nm and 270 nm. These peaks arise from constructive interferences caused by the nanocavity (Fig. S4(b)). Figures 2(e) and 2(f) indicate the EF distributions of the enhanced virtual SPs probe at the xz plane and the xy plane (R=270 nm, h=35 nm). Compared with the typical virtual probe, the enhanced virtual SPs probe is much tighter and stronger, whose EF is improved by 10 folds, and the FWHM is compressed to about 124 nm (∼0.196 λ0). Under the conditions of h=5, 15, and 25 nm, there is no obvious interference phenomenon in spite of slight EF improvement (Fig. S4(c)-(d)).
Fig. 2. (a) Schematic of a circular nanohole in a thin gold film on a glass substrate. Intensity enhancement factor (EF) maps at (b) the xz plane and (c) xy plane of the typical virtual SP probe on a flat Au surface. (d) EF with different radius and depths of the circular nanohole. EF maps at (e) the xz plane and (f) xy plane of the enhanced virtual SP probe excited on a gold substrate with a nanohole (R=270 nm, h=35 nm). The white solid lines in (c) and (f) indicate the EF profile along the x-axis.
When the center of the circular nanohole and the incoming RPB are aligned, the system is rotationally symmetric. The broken symmetry of the system will affect the interference effect and thus affect EF. Consequently, the EF is analysed as the center of the nanohole moves away from the optical axis, as shown in Fig. 3(a) (R=270 nm, h=35 nm). It is clear that EF decreases as the distance Δx increases. Figure 3(b) depicts the corresponding EF distributions under Δx=50, 100, and 150 nm in the xz plane and the xy plane. As the center of the nanohole moves away from the optical axis (white dashed line), there is a side lobe located near the virtual SPs probe and the EF of the side lobe is gradually increasing. Due to the deviation of the center of the nanohole from the optical axis, the SPs waves reflected by the sidewall of the nanohole propagate different lengths, which leads to the generation of the side lobe. The side lobe can be ignored when its EF is less than half of that of the virtual SPs probe. Under this condition, the effective alignment error between the center of the nanohole and the optical axis is 100 nm, which can provide more freedom for experiments.
Fig. 3. (a) EF as a function of the distance between the circular nanohole center and optical axis Δx. (b) EF distributions in the xz plane and xy plane of the Virtual SP probe excited on a substrate with a nanohole when Δx=50 nm, 100 nm, and 150 nm (R=270 nm, h=35 nm). The white dashed lines in (b) is the optical axis, and the white solid line indicates the EF profile along the x-axis. The scale is same as the Fig. 2.
3.2 Generation of the gap-plasmon mode
Compared with the virtual SPs probe, the gap-plasmon mode generated between the virtual SPs probe and the plasmonic tip can lead to a hot spot with greater field enhancement and smaller size. Figure 4(a) depicts the schematic diagram of the generation of the gap-plasmon mode, which consists of two nanocavities, one is a transverse nanocavity formed by the nanohole in the gold substrate and the other is a longitudinal nanocavity formed by the virtual SPs probe and plasmonic tip. To show the enhancement of the transverse nanocavity to the gap-plasmon mode, a flat gold substrate was first selected and calculated. Figures 4(b) and 4(c), respectively, display the EF maps at the xz plane and xy plane 2 nm above the gold substrate. It is clearly seen that a strong hot spot is excited on the tip apex. Noticeably, the FWHM of this hot spot can be squeezed down to 8.5 nm, as shown in Fig. 4(c). Owing to the effect of the interference caused by the transverse nanocavity, when the tip is near the virtual SPs probe, an additional enhancement can be achieved. Figure 4(d) shows the EF varies with the radius of the nanohole R. A clear maximum EF is observed at R=160 nm, which is one order of magnitude higher than that without the circular nanocavity. Under the case of R=160 nm, the corresponding EF distributions at the xz plane and xy plane are shown in Figs. 4(e) and 4(f). It is found that, compared with Figs. 4(b) and 4(c), the existence of the nanohole only enhances the EF without decreasing the volume of the gap-plasmon mode. The calculated results explicitly demonstrate that the nanohole with the appropriate size in the substrate will better the gap-plasmon mode performance.
Fig. 4. (a) Schematic of a longitudinal nanocavity composed of a gold tip and a thin gold film with a circular nanocavity. Here the gap size g is 5 nm, and the depth of the nanohole h is 35 nm. EF distributions at the xz plane (b) and xy plane (c) of the gap-plasmon mode excited on a smooth gold substrate without nanohole.(d) EF of the gap-plasmon as a function of the radius of the nanohole. EF distributions at the xz plane (e) and xy plane (f) of the gap-mode excited on a smooth gold substrate with nanohole (R=160 nm). The xy plane is 2 nm above the gold substrate in (c) and (f) and the white solid line indicates the EF profile along the x-axis.
As analysed above, the broken symmetry of the system will affect EF. Keeping the tip axis aligned with the optical axis, EF decreases as the center of the nanohole moves away from the optical axis (R=160 nm), as shown in Fig. 5(a). At Δx=±50 nm, the EF of the gap-plasmon mode excited on the substrate with the nanocavity is still 5 folds than that of the substrate without the nanocavity (black solid line in Fig. 4(a)). Thus, the effective alignment error between the center of the nanohole and the optical axis is 50 nm, which is enough for nanometer measurements and application. Figure 5(b) shows the EF distributions at Δx=20, 40, and 60 nm in the xz plane and the xy plane. Furthermore, although the EF decreases as |Δx| increases, the electromagnetic field is still confined on the tip apex and the size of the hot spot remains unchanged.
Fig. 5. (a) EF as a function of the distance between circular nanohole center and tip axis Δx. (b) Electric field intensity distributions in the xz plane and xy plane of the SPP virtual probe excited on a substrate with a nanohole when Δx=20 nm, 40 nm, and 60 nm. The white solid line indicate the EF profile along the x-axis. The scale is same as the Fig. 4.
3.3 Optical trapping force exerted on a nanoparticle
Due to the momentum exchange between the interaction of light and matter, nanoparticles placed in a light field will suffer from optical forces [34–36]. In particular, the magnitude of the optical force is closely correlated to the optical properties of particles and the electromagnetic field distribution around them. Since the electric field of the gap-plasmon mode is highly localized at the tip apex, the ability to bring targets into the hot spot zone is important for in-situ plasmon-enhanced spectroscopy. In the following, we show that the enhanced gap-plasmon mode can provide sufficient optical force to capture a 4-nm-diameter dielectric nanoparticle. Figure 6(a) schematically shows the plasmonic tip tweezer. In addition, the nanoparticle is considered to be placed in water (nb = 1.33). Here, the optimal design of circular nanohole in water is used (h=35 nm, R=140 nm, Fig. S5). The gap size between the tip apex and the gold substrate is set as g=6 nm. A 4-nm-diameter dielectric nanoparticle is placed underneath the tip apex at d=1 nm. Without loss of generality, the refractive index of the nanoparticle is set to n=2, an intermediate value between the typical refractive index of biological species and quantum dots [37]. The power density of the incoming RPB is set as a constant of 100 mW/μm2.
Fig. 6. (a) Schematic diagram of a plasmonic tip nanotweezer for nanoparticle trapping. (b)-(d) x, y, and z component of the optical forces in the xy plane exerted on the nanoparticle placed 1 nm above the nanohole substrate. (e) Electric field intensity distribution in the xy plane when the nanoparticle is located at x=4 nm, the white line indicates the nanoparticle. Comparisons of the optical force induced by the gap-plasmon mode generated by the substrate with and without the nanohole (f)-(g).
By raster moving the nanoparticle around in the xy plane, we calculate the transverse and vertical forces. Figures 6(b) and 6(c), respectively, present the x and y components of the optical force acting on the nanoparticle. From the distributions of Fx and Fy, the force shows different signs on two sides of the field center (x = y=0 position), where the nanofocusing field reaches its maximum intensity (Fig. 6(e)). Owing to the rotational symmetry of the nanofocusing field, the transverse force radially points to the center. Figure 6(d) shows the vertical optical force (Fz), which has direction along the positive z-axis and a magnitude almost 3 times larger than that of the transverse force. Due to the synthetic actions of the transverse and vertical forces, the balance position is under the tip apex, implying the nanoparticle can be trapped and pushed to a target position by the tip. By comparing the Fx along the x-axis (white dashed line in Fig. 6(b)) under the condition of the gold substrate with and without nanohole, the magnitude of the maximum transverse force is increased by nearly 17 folds with the aid of the nanohole, as shown in Fig. 6(f). Similarly, Fig. 6(g) displays the comparison of Fz along the x-axis (white dashed line in Fig. 6(d)) under the case of the substrate with and without nanohole, it is clearly indicated that the magnitude of maximum Fz is enhanced more than 10 times by the nanohole. Consequently, the presence of the nanohole in the gold substrate can enhance the EF of the gap-plasmon mode as well as increase the optical force exerted on a nanoparticle in the gap.
Trapping potential well is a criterion to characterize the stability of the trap. According to Eq. (3), we calculate the distribution of trapping potential well resulting from the transverse force in Figs. 6(b) and 6(c), as shown in Fig. 7(a). It is found that a quasi- harmonic potential with a depth of 17.5 kBT is generated when there exists a nanocavity in the substrate, where kB is the Boltzmann constant and T is the temperature (T=300 K). The Boltzmann term kBT describes the random thermal energy due to the Brownian motion of particles. In principle, a potential well with |U|>1 kBT is sufficient to suppress the Brownian thermal motion of the particle to trap the particle [38]. Figure 7(b) is the potential well generated under the condition of the substrate without the nanohole. The 3D results clearly show that the two potential wells are Gaussian shape and consistent with the distribution of nanofocusing field in Figs. 4(f) and 4(c). To compare the potential wells quantitatively, distribution curves of the potential wells along the x-axis (dashed line labelled in Figs. 7(a) and 7(b)) are plotted in Fig. 7(c). It shows that the potential depths for both cases are higher than 1, indicating that the enhanced gap-plasmon mode can be used for the stable trap of a nanoparticle. Notably, with the presence of the nanohole, the potential depth falls from 1.5 to 17.5 kBT accompanied by the potential width increasing from 3 to 13 nm. It signifies that a more stable trap is achievable after processing the substrate.
Fig. 7. Transverse optical trapping potential on a 4-nm-diameter dielectric particle placed 1 nm above the substrate with (a) and without (b) the nanohole. (c) Its corresponding cross-section along the x-axis (the white dashed line in (a) and (b)).
4. Conclusions
In summary, we have theoretically studied and analyzed the electric field improvement effect of the circular nanohole in a flat gold film on the virtual SPs probe and the gap-plasmon mode residing in real-virtual probes. The results show that with the aid of the circular nanocavity, the intensity of the virtual probe can be effectively enhanced and mode volume can be compressed due to the interference effect. When the real plasmonic tip is closely placed above such a gold film, the electric intensity of the gap-plasmon mode can be further improved, which is 10 folds stronger compared with that of the traditional forms. Meanwhile, we investigate the influence of the lateral distance between the center of nanohole and tip axis on the electric field enhancement. By using the MST method, we show the feasibility of stably trapping 4-nm-diameter dielectric particles with this enhanced gap-plasmon mode. The potential depth becomes more than 10 folds higher and the potential width increases more than 4 times with the circular nanocavity in the substrate. We anticipate that the proposed method can be a tool to trap a single nanoparticle for in-situ plasmon-enhanced spectral characterization.
Funding
Financial supports from the Guangdong Major Project of Basic and Applied Basic Research(2020B0301030009); National Natural Science Foundation of China (11974282, 12104316, 61805157, 91950207); Natural Science Foundation of Guangdong Province (2016A030312010); Leading Talents of Guangdong Province Program (00201505); Shenzhen Peacock Plan (KQTD20170330110444030).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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