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Abstract
Tip-enhanced Raman spectroscopy (TERS) is a promising label-free super-resolving imaging technique, and the electric field gradient of nanofocusing plays a role in TERS performance. In this paper, we theoretically investigated the enhancement and manipulation of the electric field gradient in a bottom-illumination TERS configuration through a tightly focused perfect radially polarized beam (PRPB). Improvement and manipulation in electric field enhancement and field gradient of the gap-plasmon mode between a plasmonic tip and a virtual surface plasmons (SPs) probe are achieved by adjusting the ring radius of the incident PRPB. Our results demonstrate that the method of optimizing the ring radius of PRPB is to make the illumination angle of incident light as close to the surface plasmon resonance (SPR) excitation angle as possible. Under the excitation of optimal parameters, more than 10 folds improvement of field enhancement and 3 times of field gradient of the gap-plasmon mode is realized compared with that of the conventional focused RPB. By this feat, our results indicate that such a method can further enhance the gradient Raman mode in TERS. We envision that the proposed method, to achieve the dynamic manipulation and enhancement of the nanofocusing field and field gradient, can be more broadly used to control light-matter interactions and extend the reach of tip-enhanced spectroscopy.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recently, tip-enhanced Raman spectroscopy (TERS) has attracted extensive attention due to its capability of high spatial resolution in nanometer scale and high detection sensitivity even at single-molecule level [1–8]. As a powerful imaging technology, TERS has been widely used in sample research from organic monolayer to 2D materials [9], catalytic chemical reactions [10], biological applications, etc. [11]. A plasmonic tip in TERS serves as a topography scanner and an optical antenna to confine the incident light near the tip apex and boost the Raman signal, simultaneously [12–14].
An acquired TERS spectrum depends on various aspects of enhanced plasmonic nanofocusing field and sample properties [15,16]. The plasmonic nanofocusing field on a sample has profound effects on its Raman spectrum, leading to differences between far-field Raman spectroscopy and TERS, such as tensorial Raman scattering [17], infrared active vibration [18], and Stark-shifted vibration resonances [19]. In this respect, the vector components of the nanofocusing field and its strong electric field gradient are well worth considering [5,20].
Prior theoretical analyses and experimental observations show that a strong electric field gradient at the nanoscale makes it possible to visualize Raman forbidden transitions of molecules [21–24]. In order to explore the vibrational modes of molecules, it is very necessary to control the near-field gradient in the TERS configuration. The common method to manipulate the field gradient is to control the gap distance between the tip and a molecule on the substrate because the intensity of the nanofocusing field depends on the gap distance [25]. In order to study light-matter interactions in a static plasmonic cavity, the tip-to-sample distance should be maintained. Recently, a method to modulate and shape the incident wavefront controlled by adaptive optics algorithms was introduced to a TERS configuration to enhance the field gradient dynamically [26]. In addition, there still lack efficient methods to control the gradient of nanofocusing field at the tip to develop the TERS platform.
In this work, we investigate the enhancement and manipulation of the electric field gradient in a bottom-illumination TERS configuration through a tightly focused perfect radially polarized beam (PRPB). By adjusting the ring radius of the incident PRPB, the electric field can be enhanced and the field gradient can be manipulated for the gap-mode nanofocusing field between the plasmonic tip and substrate. Compared with the traditional focused radially polarized beam (RPB) excitation, the optimal PRPB excitation results in a 10-fold increase in the field enhancement and a 3-fold increase in the field gradient for the gap-plasmon mode. By this feat, our results indicate that this method can further enhance the gradient Raman mode in TERS. Our theoretical results provide a precise and feasible method for realizing the dynamic field gradient manipulation and electric field enhancement for the nanofocusing field, which can be widely used to control light-matter interactions and expand the application range of tip-enhanced spectroscopy.
2. Methods
Figure 1(a) shows a schematic diagram of the model for a bottom-illumination TERS configuration, assigned with a rounded-tip cone with a cone angle φ = 25° terminated by a hemisphere with a radius of r = 10 nm. The distance between the tip apex and the substrate is kept at g = 1 nm. An RPB or PRPB with a wavelength of 632.8 nm is tightly focused by an oil-immersion objective lens with NA = 1.4. The gap between the objective lens and the substrate is filled with index-matching oil (n = 1.515).
Fig. 1. (a) Schematic of tip nanofocusing with axial excitation by a tightly focused radially polarized beam (RPB). The upper right inset is the enlargement of the tip with geometric parameters. (b)-(d) Distributions and focus states of the input RPB (α=0, β=θmax), PRPB (0<α<β & 0.5θmax≤β≤θmax), and PRPB with low-NA focusing (0<α<β≤0.5θmax), where the black arrows indicate the polarization directions, α, and β are the innermost and outermost illumination angle, respectively.
Here, we used the 3D finite difference time domain (FDTD) software (FDTD Solutions, Lumerical/Ansys Inc., Canada) to calculate the electric field and its gradient in the aforementioned TERS configuration. The permittivity of Au is taken from the experimental data of Johnson and Christy [27]. The simulation area is 8000 × 8000 × 6000 nm3, which is large enough for all simulations. In order to avoid the unphysical reflections around structures, the perfectly matching layer (PML) is used as an absorption boundary. In addition, the PML is placed along the upper cone surface of the plasmonic tip to reduce the reflection of surface plasmons (SPs) from the upper boundary [28]. Because of the rotational symmetry of the structure and excitation, the symmetric boundary is utilized to save simulation time. Non-uniform mesh sizes are employed for all calculations to ensure a good balance between calculation accuracy, computational resources, and time. The minimum grid size of 0.25 nm is set in the region containing the tip apex. Rigorous convergence testing is performed for PML, the size of mesh regions, and minimum mesh sizes [28]. The amplitude of the RPB or PRPB is 1.0 V/m. Therefore, the electric field enhancement factor can be defined as M2 = |Eloc|2, where |Eloc| is the localized electric field amplitude located 0.5 nm underneath the tip apex.
The beams of perfect optical vortices (POVs) can confine all incident energy into a sharp bright ring, the radius of which is independent of the topological charge and can be adjusted as needed [29–34]. The idea of PRPB follows the concept of a POV beam, but with zero topological charges and radial polarization. The PRPB can be efficiently generated by two coaxial axicons or a spatial light modulator in an experiment with a tunable radius. By tuning the sharp ring radius to fit the excitation angle of surface plasmon resonance (SPR), the PRPB has been used to improve the gap-mode surface-enhanced Raman spectroscopy (SERS) sensitivity and plasmonic trapping stiffness [35,36]. The incident electric field of an RPB can be written in the pupil plane as [37]
3. Results and discussion
3.1 Enhancement to virtual SPs probe
Firstly, we considered the electric field enhancement for a virtual SPs probe excited on a metallic film by a tightly focused PRPB. As a counterpart of a real probe, the virtual probe is a standing wave generated by constructive interference of SPs waves [38]. Figure 2(a) depicts the schematic diagram of the SPs excitation process by focusing PRPB on an air-Au-SiO2 interfacial system. The excitation angle of SPR can be calculated by using Fresnel formula [39]. As shown in Fig. 2(b), the reflectance curve at the wavelength of 632.8 nm presents a sharp dip at 0.75θmax, which is the resonance angle to couple the energy of incident light to SPs at the gold-air interface.
Fig. 2. (a) Schematic of the virtual SPs probe excited by a focusing RPB. (b) The calculated reflectance of a three-layer system illuminating from the glass side.
For the sake of simplicity, we define α=m×θmax (0 ≤ m < 1) and β=n×θmax (0 < n≤1), with m = 0 and n = 1 for RPB and m > 0 and n < 1 for PRPB cases. Thus, the inner and outer radius of the ring of a PRPB can be adjusted by m and n, respectively. Figure 3(a) illustrates the relationship between M2 and m and n. It is obvious that when m < 0.75 and n> 0.75, M2 is greater than 1. And the closer m and n to 0.75, the larger M2 is. This is when the range of illumination angle of the incident light is smaller and covers the SPR angle [0.75θmax, Fig. 2(b)], the more energy of the incident light is coupled to SPs. Thus, it can be concluded that the optimal ring radius of the PRPB is to just cover the SPR angle and the optimum parameters in this work is m = 0.7 and n = 0.8. We calculate the electric field distributions of the virtual SPs probe under different PRPB excitation. In Figs. 3(b) and 3(c), a virtual SPs probe field pattern excited by RPB are displayed on the xz plane and the xy plane 5 nm above the gold-air interface, respectively. Compared with the Figs. 3(b) and 3(d)–3(f), the electric field distribution of virtual probe excited by PRPB is similar to that of RPB because the SPR angle is constant, but the excitation efficiency of the SPs is greatly improved. In the case of PRPB (m = 0.7, n = 0.8) excitation, M2 is improved by more than 6 folds compared with RPB excitation.
Fig. 3. (a) M2 of virtual SPs probe with different PRPB excitation. M2 maps at (b) xz plane and xy plane of the virtual SPs probe excited by RPB (m = 0, n = 1). The xy plane is 5 nm above the gold substrate in (c). M2 maps at xz plane of the virtual SPs excited by (d) PRPB (m = 0.7, n = 1), (e) PRPB (m = 0, n = 0.8) and (f) PRPB (m = 0.7, n = 0.8). m and n represent the adjustment parameters to the ring radius of a PRPB.
3.2 Enhancement to gap-plasmon mode
Subsequently, we calculated the gap-plasmon mode generated between the virtual SPs probe and the plasmonic tip. Figure 4(a) depicts the schematic diagram of the generation of the gap-plasmon excited by PRPB. Figure 4(b) shows the M2 varies with the ring radius of the PRPB, which has the same trend as the curves in Fig. 3(b). Similar to the excitation of the virtual SPs probe, the optimal parameters of PRPB for enhancing the gap-plasmon mode are m = 0.7 and n = 0.8. Under the case of RPB excitation, the corresponding M2 and polarization distributions of the gap-plasmon mode in the xz plane and xy plane are shown in Figs. 4(c) and 4(d), respectively. To better understand the influence of the PRPB on the gap-plasmon mode and as a comparison, Figs. 4(e) and 4(f) display the field and polarization distributions of the gap-plasmon mode excited by an optimized PRPB. It is clearly seen that the PRPB excitation only enhances the field intensity without changing the mode volume and polarization of the gap-plasmon mode. Remarkably, compared with the RPB excitation, M2 is increased by more than 10 folds. The field distribution of the gap-plasmon mode is inhomogeneous on the nanoscale, and the polarization direction of the gap-plasmon mode is longitudinal (along the tip). The simulation results indicate that the PRPB with the suitable ring size will manipulate and improve the performance of gap-plasmon mode.
Fig. 4. (a) Schematic of the gap-plasmon mode generated between the virtual SPs probe and the plasmonic tip. (b) M2 of the gap-plasmon mode with different PRPB excitation. M2 and polarization maps at (c) xz plane and (d) xy plane of the gap-plasmon mode excited by RPB (m = 0, n = 1). M2 and polarization maps at (e) xz plane and (f) xy plane of the gap-plasmon mode excited by PRPB (m = 0.7, n = 0.8), where the white arrows indicate the polarization directions. The xy plane is 0.5 nm above the gold substrate in (c) and (f).
3.3 Enhancement to the electric field gradient
The induced dipole moment of a molecule placed in a non-uniform electromagnetic field is given by [21,40]
Significantly, Eq. (4) depends on the field enhancement properties of the TERS configuration and the molecular polarizability, respectively.
It is known from the previous studies, for a small nanogap between the tip and the substrate, the field distribution is almost uniform in the vertical direction (z-direction), thus the origin of the gradient Raman modes in TERS is attributed to the existence of in-plane (xy plane) electric field gradient (∇Mxy) below the tip [22,41]. To quantify the influence of the PRPB on the electric field gradient of the gap-plasmon mode, the quantitative relationship between the maximum∇Mxy and the ring size of PRPB is calculated and shown in Fig. 5(a). It is clearly seen that the variation trend of the electric field gradient ∇Mxy with PRPB is the same as that of the electric field intensity [Fig. 4(a)]. This is because the size of the gap-plasmon mode does not change with the incident light [Figs. 4(c)–4(f)], thus ∇Mxy is only dependent on the value of M. Figures 5(b) and 5(c) depict the corresponding ∇Mxy distributions under the case of RPB and optimal PRPB excitation, respectively. The maximum ∇Mxy is off-center and forms a ring shape, and the spatial distribution is unchanged with PRPB.
Fig. 5. (a) The relationship between the electric field gradient (∇Mxy) of the gap-plasmon mode and the PRPB. In-plane electric field gradient distribution of the gap-plasmon mode excited by RPB (b) and PRPB (c). The xy plane is 0.5 nm above the gold substrate in (b) and (c). Note that the unit of electric field amplitude is V/m, and the unit of the electric field gradient is V/m/au, where au is the atomic unit.
To quantitatively compare the electric field gradient, distribution curves of ∇Mxy along the x-axis (white dashed line labeled in Figs. 5(a) and 5(b)) are plotted in Fig. 6(a). We define R as the distance from the center of the xy-plane. As can be seen the full width at half maximum (FWHM) of ∇Mxy is located within the area of 0.78 nm < R < 4.77 nm for all cases [dashed line Fig. 6(a)]. Changing the incident light does not cause the change of the FWHM of ∇Mxy, which depends on the radius of the tip apex and the distance between the tip and substrate [24]. Notably, with the optimization of the incident light, the maximum ∇Mxy increases from 0.41 to 1.38, which is increased by more than 3 folds. This means that a stronger electric field gradient can be obtained by using the optimal PRPB and the maximum electric field gradient of gap-plasmon mode can be controlled by the ring radius of the PRPB. Figure 6(b) shows the ratio between ∇Mxy and M along the x-axis, which could stand for the intensity ratio of gradient Raman modes to dipole Raman modes in TERS [24]. ∇Mxy/M shows a ring shape region for the spatial distribution, which means that the molecules located in such regions have the maximum opportunity to simultaneously show the dipole Raman mode and gradient Raman mode in TERS. Since M and ∇Mxy increase in the same amount, and the spatial distribution of M and∇Mxy is unchanged with the change of PRPB, therefore∇Mxy/M does not change with PRPB, as shown in Fig. 6(b).
Fig. 6. (a) ∇Mxy cross-section along the x-axis (the white dashed line in Figs. 5(b) and 5(c)). (b) ∇Mxy/M cross-section along the x-axis.
4. Conclusion
In conclusion, we have theoretically investigated the enhancement and manipulation of the electric field gradient in a bottom-illumination TERS configuration through a tightly focused PRPB. Improvement and manipulation in electric field enhancement and field gradient of the gap-plasmon mode between a plasmonic tip and a virtual SPs probe are achieved by adjusting the ring radius of the incident PRPB. Our results demonstrate that the method of optimizing the ring radius of PRPB is to make the angle of incident light as close as possible to the SPR excitation angle. Under the excitation of optimal parameters, compared with that of the conventional focused RPB, more than 10 folds improvement of field enhancement and 3 times of field gradient of the gap-plasmon mode is realized. Our results indicate that such a method can further enhance the gradient Raman mode in TERS. We envision that the proposed method to achieve the dynamic manipulation and enhancement of the nanofocusing field and field gradient can be more broadly used to control light-matter interactions and expand the reach of tip-enhanced spectroscopy.
Funding
Guangdong Major Project of Basic and Applied Basic Research (2020B0301030009); National Natural Science Foundation of China (11974282, 12104316, 61805157, 91950207); Leading Talents of Guangdong Province Program (00201505); Natural Science Foundation of Guangdong Province (2016A030312010); Shenzhen Peacock Plan (KQTD20170330110444030); China Postdoctoral Science Foundation (2021M702271).
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 may be obtained from the authors upon reasonable request.
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