1. Introduction

The Raman spectroscopy detection technology shows the benefits of simplicity, label-free detection and high specificity [1–5], and is easy to be combined with a variety of optical microscopic systems to form Raman imaging systems [6–10]. With the development of nanophotonics, more and more high-resolution Raman imaging technologies have been proposed and studied, in which tip-enhanced Raman scattering (TERS) is the most representative one. The TERS technology not only has sub-nanometer resolution [11,12], but also can detect the morphology and spectral information of molecular samples. Currently, TERS technology has become a powerful tool for nanotechnology and nanoscience research, and has shown great applications in chemistry [13], materials [14–17], life science [18, 19] and other fields [20–22].

Many previous research works have demonstrated that metallic substrates have an important impact on the performance of TERS [23–24]. Metallic substrates can be used to generate a high-intensity SPP field, and form the gap-plasmon mode in the gap region between the metallic tip and the substrate [25–28], resulting in both high spatial resolution and strong enhancement of Raman signals. It is known that in an inverted TERS configuration [6,29] with focused incident light from the bottom, there are two different field enhancement modes depending on the thickness of the metal film. When the thickness is less than the penetration depth of light in the metal (∼20 nm or less) [30], most of the incident light can pass through the metal film, and form an optical focus to enhance the local electric field in the gap region between the tip and the metal substrate. In contrast, when the thickness is larger than the penetration depth (more than 30 nm), most incident light is reflected by the metal film, and only a fraction of incident light matching the SPP excitation angle can form an SPP focus to enhance the local field in the gap structure. For example, in our previous research works [25–28], a metal film with thickness of 45 nm (larger than the penetration depth) is often used to excite a sharp SPP focus (also called SPP virtual probe) on the surface of metal film through an objective lens with a high numerical aperture (NA). Therefore, both the optical focus and the SPP focus can contribute to the enhancement of local field in the gap structure of the TERS system, however, the different performances and interaction of the two focuses remain to be studied for optimizing the TERS system. In addition, besides the local field enhancement in the gap region for Raman signal excitation, the radiative mechanism for Raman scattering from the sample molecules in the gap region to the far field, i.e., the Purcell is also very important and needs further examinations.

Previously [25], we presented an inverted TERS system with a Raman enhancement mechanism enabled by a focused gap-plasmon mode. Compared to top or side illuminations, the inverted TERS system allows for the use of high-NA objective lens, resulting in ultra-small optical focus and the ability to form the high-intensity SPP virtual probe on metallic substrate, which could couple with the metallic tip of atomic force microscopy (AFM) for further enhancement of Raman signals [6,25]. To further understand the whole process of Raman enhancement of the TERS system, in this paper, we theoretically analyze the enhancement effects of Raman excitation and scattering of the gap structure in TERS system, including the local field enhancement generated by optical/SPP focus and the outward scattering enhancement of molecular samples. We compare the enhancement effects of optical focus and that of the SPP focus while varying the metal substrate thickness, and then the maximum local electric field enhancement in the gap structure occurs when the metal substrate is about 30 nm thick, resulting from the joint action of the two focuses. It is also found that in this process, a SPP Electromagnetically Induced Transparency (EIT)-like phenomenon [31] appears in the gap structure due to the interaction of the two enhancement modes from the two focuses. Subsequently, we investigate the outward scattering enhancement of molecular samples in the gap structure, and obtain the influence of Purcell effect of the gap with different structural parameters. By combining the local field enhancement and sample scattering enhancement in the gap structure, a whole enhancement mechanism of TERS is discussed and quantitatively evaluated. The final Raman gain coefficient of the TERS system is obtained as high as ${10^{11}}$. Finally, we study the directivity of Purcell effect in this process and indicate its influence on Raman signal collection efficiency in practical experiments. This work reveals the properties and enhancement mechanisms in the Raman excitation and scattering processes of TERS, and contributes to the design of exciting light field and the optimization of Raman radiation collection, thus has importance for the design and optimization of TERS system.

The remainder of the paper is organized as follows. In Section 2, we first study the different performances of the optical focus and the SPP focus in the inverted TERS system in Subsection 2.1, and analyze the local field enhancement of gap-plasmon mode between total focused field and metal tip in Subsection 2.2. The comprehensive enhancement process and the Purcell effect of the TERS system are studied in Subsection 2.3. Meanwhile, we also analyze the far-field Raman signal detection in Subsection 2.4. Finally, our conclusions are summarized in Section 3.

2. Results and discussion

2.1 Optical/SPP focus enhanced electric field on metal surface

In our TERS system, the structure for SPP excitation is schematically shown in Fig. 1(a). The background is air (${n_0}$=1), the others from top to bottom are silver film, glass substrate (${n_g}$=1.5), and a high-NA objective (NA = 1.49). Through the high-NA objective, the incident light beam produces a wide range of convergent angles, which includes the angle ${\theta _{SPP}} \approx 44^\circ $ for SPP excitation on the silver film surface. Here the silver was chosen because its dielectric constant supports stronger SPP resonance than other common-used metals in the range around the selected wavelength $\lambda $=532 nm of incident light [32–33]. In our previous experimental work [25], the measured enhancement in the TERS system is much lower than that in theory, due to the fact that only a small part of incident light focused by the high-NA objective can match the SPP excitation angle, leading to a low-efficiency excitation of SPP. In order to enhance the SPP excitation efficiency, here we change the incident light from a common radially polarized beam to a perfect radially polarized beam (PRPB) [34], which can confine all incident energy into a narrow bright ring (shown in the upper right inset of Fig. 1 (a)) that perfectly match the SPP excitation angle, and thus the SPP excitation efficiency can be greatly enhanced [34].

 

Fig. 1. (a) Schematic of the structure for SPP excitation. The optical focus of the penetrating beam is located above the silver film, and the SPP focus is formed at the center on the silver film. The upper right inset is the intensity shape of the incident PRPB source. (b) SPP focus intensity (black) and optical focus intensity (red) as a function of thickness of silver film in the case of (a) obtained by FDTD. (All results are normalized according to the incident light intensity.) (c) the electric-field intensity distributions on the top surface of $h$=5 nm silver film in (b). (d) the electric-field intensity distributions on the top surface of $h$=35 nm silver film in (b). (e) Schematic of the structure for SPP excitation that the SPP focus and optical focus overlap in z-direction. (f) Total focusing intensity at the center on the silver film as a function of silver film thickness in the case of (e). (g)-(h) are the electric-field intensity distributions on the silver film for thickness h of 20 nm and 45 nm, respectively (the two figures use the same colorbar for comparison).

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The high-NA objective lens can generate both optical focus and SPP focus simultaneously in the structure. To distinguish the different performances of SPP focus and optical focus, we separate the two focuses in z-direction by placing the silver film close to the objective lens and below the optical focus of the light penetrating through the silver film, as shown in Fig. 1(a). Therefore, SPP is firstly excited in an annular profile on the top surface of the silver film by the incident PRPB, and then propagates inwards and finally forms the SPP focus at the center on the silver surface. Since the SPP focus and optical focus are separated in z-direction, it is convenient for us to study the roles of the two focuses respectively.

To obtain the SPP/optical focusing field, we choose the 3-dimentional finite-difference time-domain (3D-FDTD) simulation method (Lumerical FDTD Solutions). The incident light source in the simulation is set as the PRPB [34] with wavelength $\lambda $=532 nm. The dielectric constant of silver was chosen from the built-in Johnson and Christy data. The FDTD simulation region is 15µm × 15µm × 6.5µm and perfectly matched layer (PML) is used in all boundaries. In order to ensure the simulation accuracy, a gradient mesh with minimum grad size of 0.5 nm is adopted. In addition, all FDTD-simulated results of electric field are normalized according to the incident light to clearly show the field enhancement.

Based on the FDTD method, we first consider the influence of the thickness h of the silver film [35] on the field enhancement, as shown in Fig. 1(b). The detection position for SPP is 2 nm above the silver surface. Since the vertical electric component E_z dominates the focal field in TERS structure [36], we mainly focus on the enhancement of E_z component. In Fig. 1(b), it can be found that the intensity of optical focus (red curve) above the silver film decreases when the thickness h increases, due to the fact that thicker silver film reduces the energy of penetrating light. In contrast, in Fig. 1(b) the SPP focal intensity (black curve) first increases and then decreases with the increasing thickness h, resulting in a peak at about h = 35 nm. This result can be divided into two cases and explained. In the first case that the thickness h is smaller than the penetration depth of light in the silver film, a large part of incident PRPB can pass through the silver film and result in a bright ring in the electric-field distributions on the silver film (as shown in Fig. 1(c)). At the same time, the excitation of SPP is limited by the small amount of free electrons in the very thin silver film, and thus the SPP focus intensity increases with the thickness h until reaches the peak at about h = 35 nm. In the second case that the thickness h exceeds 35 nm, the incident light hardly penetrates through the silver film and thus the bright ring disappears, leaving only the SPP focus at the center (as shown in Fig. 1(d)). The intensity of the SPP focusing field begins to decline with h > 35 nm, due to the rapid increase of the loss in the thicker silver film in SPP excitation process.

We further explore the influence of the interaction between the optical/SPP focus on the field enhancement. As shown in Fig. 1(e), the silver film is moved upward to make the SPP focus and optical focus overlap in z-direction, and therefore both the optical focus and SPP focus can contribute to the field enhancement together on the silver surface. According to the results in Fig. 1(f), the peak of field enhancement shifts from the thickness $h$ = 35 nm (Fig. 1(b)) to $h$ = 20 nm, due to the influence of the optical focus on the total enhancement. In addition, the peak value in Fig. 1(f) is increased by about 4 times than that in Fig. 1(b), indicating that the cooperation of the optical focus and SPP focus provides stronger enhancement effect than that from each focus. It is noted that even without SPP focus (thickness $h = 0$), the optical focus intensity in Fig. 1(f) is also larger than that in Fig. 1(b), because the evanescent wave on the glass surface can form an evanescent-wave focus in the case of Fig. 1(e) but cannot in the case of Fig. 1(a) due to the short propagating distance of the evanescent wave on the glass surface. Two examples of the corresponding focal field distributions on the silver surface with thickness $h$=20 nm and $h$=45 nm are shown in Fig. 1(g) and Fig. 1(h), respectively, both presenting a single stronger focus due to the overlap of optical and SPP focus. These results prove that by choosing an appropriate thickness of metal film (e.g. $h$=20 nm in Fig. 1(e)), the ratio of optical/SPP focus can be modulated to optimize the enhancement of surface electromagnetic field for TERS applications.

2.2 Analysis of gap-plasmon mode between surface focal field and metal tip

Based on the above-studied surface-field enhancement due to the cooperation of the optical focus and SPP focus (Fig. 1(e)), we add a silver probe above the center of silver film surface to form the tip-film gap structure used in TERS system (as shown in Fig. 2(a)), and investigate the field enhancement in the gap region where the Raman samples are located. It is well-known that the silver probe can form the localized surface plasmon (LSP) mode on the tip [36], which could be further enhanced in our structure by the total focus on the metal surface (Fig. 1(f)). Since the vertical E_z component dominates the focal field on the silver film, it can be coupled with the metal tip to excite stronger electric dipole oscillation in z-direction and enhance the LSP mode (as shown in Fig. 2(b)), and such effect is influenced by the silver film thickness h that determines the intensity of focal field (Fig. 1(f)). In addition, as the silver film thickness h increases, there is enough free charge in the silver film to form a mirror electric field coupled with the actual metal probe [37] (as schematically shown in Fig. 2(c)), which also enhances the electric field intensity in the gap region. Based on the above analysis, these enhancement effects (including the SPP/optical focus and the Gap mirror electric field) are all dependent on the silver film thickness h, so the thickness h plays an important role in the field enhancement in the gap region.

 

Fig. 2. (a) Schematic of gap-plasmon mode between focal field and metal tip. (b) Schematic of excited LSP and electric dipole oscillation at the tip. (c) Schematic of mirror electric field coupling formed by tip and thick silver film. (d) The maximum electric field intensity and contrast in the gap as a function of silver film thickness. (e) Electric field component E_z real part (red solid), imaginary part (red dashed) and intensity value (black) in the gap with different incident light wavelengths. (f)-(h) Distribution of E_z intensity in the gap region when the silver film thickness is (f) $h$ = 0 nm, (g) $h$ = 25 nm, and (f) $h$ = 30 nm.

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The FDTD results of electric-field enhancement in the gap region with different film thicknesses h are shown in Fig. 2(d). The detection position is 1 nm away from the tip. The structural parameters of the silver probe are chosen as: tip-cone angle of 10°, tip diameter $d$ = 40 nm, and the vertical gap size of 5 nm (Fig. 2(c)). In Fig. 2(d), the variation trend of Contrast (defined as the ratio of maximum electromagnetic field intensity on the silver film surface with/without probe) [38] is similar to that of maximum electric field intensity in the gap. The electric field intensity first increases with the film thickness in the range of $h$ < 20 nm, but then a concave region between two peaks at h = 20 and 30 nm appears, which indicates that the gap structure in this range forms a SPP EIT-like system. This SPP EIT-like effect results from the coupling of the radiative mode and the dark mode [39]. In particular, the LSP is excited with a strong free electron cluster oscillation on the surface of the metal tip, so the tip can be approximately regarded as an electric dipole (i.e., a radiative atom providing radiative mode [39]) in the quasi-stationary state. While the SPP/optical focus excited on the silver film surface constitutes the dark mode in the SPP EIT-like system, which is analogy of the metastable energy level [31]. In the concave range (about $h$=20-30 nm), due to the coupling between the above-mentioned radiative mode (Tip) and dark mode (SPP), the electric field in the gap presents an EIT-like effect of optical transparency, leading to a concave curve rather than an enhancement peak. When the value of thickness h is away from this region, the condition for the coupling of radiative and dark modes no longer exists, and thus the SPP EIT-like system is destroyed, resulting in the two enhancement peaks at h = 20 and 30 nm (Fig. 2(d)) corresponding to the local field enhancement peak around h = 20 nm (Fig. 1(f)). In the range of h > 30 nm, it can be found that the field intensity in the gap decreases due to the stronger reflection and absorption of thicker silver film. However, the Contrast value shows a peak around $h$= 50 nm (Fig. 2(d)), because at such film thickness the proportion of SPP field in the total focal field dominates, which is more suitable for exciting vertical electric dipole oscillation on the tip than the penetrating light, leading to the Contrast peak value between with/without probe cases.

In order to further verify the EIT-like effect in the gap structure, we choose the silver film thickness of $h$ = 30 nm and simulate the maximum electric field intensity in the gap region in a wavelength range around $\lambda $=532 nm, as shown in Fig. 2(e). In the intensity spectrum of E_z (black curve), a concave shape between two peaks around the wavelength $\lambda $=520 nm can be observed, which is consistent with the typical spectral characteristics of SPP EIT-like system [31]. In Fig. 2(e), we also show the real and imaginary parts of E_z, where a flip split appears in the middle region especially in the imaginary part, also similar to the previous reports on EIT effect [31].

Figures 2(f)–2(h) show the electric-field distribution in the gap region under several representative film thicknesses. When the silver film does not exist (h = 0 in Fig. 2(f)), only the LSP (radiative mode) on the tip surface is excited by the optical focus, there is no radiation-dark mode coupling and thus the electric field in the gap region is not well enhanced. In Figs. 2(g) and 2(h), due to the excitation of SPP with the silver film, there is field enhancement on both the upper tip and the bottom silver film surface, and the radiative mode and dark mode of electric field can be coupled and form the SPP EIT-like system at $h$ = 25 nm in Fig. 2(g). Since in the EIT condition the gap structure can be considered as an effective optical transparent medium, so the field enhancement effect is much weaker than that in Fig. 2(h), corresponding to the concave curve in Fig. 2(d). These results indicate that due to the SPP EIT-like effect in the gap structure, the thickness of metal film should be carefully optimized to get the maximum enhancement of the local electric field in the gap structure for TERS applications.

2.3 Scattering enhancement and Purcell effect in TERS

In many previous researches on TERS, the Enhancement Factor ($EF$) is generally used as a quantitative evaluation for Raman enhancement, which is expressed as [40–41]

The complete Raman scattering enhancement process includes not only the enhancement of the local electromagnetic field in the gap structure, but also the enhancement in the outward scattering from the sample in the gap affected by the Purcell effect of the gap structure [44]. Therefore, the scattering enhancement effect of sample molecules in gap structure should also be investigated, and combined with the local field enhancement to achieve a total quantitative evaluation of the whole process of Raman scattering enhancement.

Based on the symmetry properties of the dyadic Green’ s function, a more accurate definition of average TERS enhancement factor can be obtained as [45]

According to Eq. (3), once the two factors (Purcell factor ${F_P}$ and Local field intensity enhancement factor ${L_I}$) are obtained, a more comprehensive and complete evaluation of the Raman enhancement effect of the gap structure can be given. The local field intensity enhancement factor ${L_I}$ can be obtained from the gap-field enhancement results in Section 2.2, where the data of field intensity in Fig. 2(d) and the SPP focal area in Figs. 2(f)–2(h) can be used to calculate the factor ${L_I}$ by using the method in [38], and the corresponding result is shown in Fig. 4(b). Next, we study the outward scattering enhancement of molecular samples in the gap structure to obtain the Purcell factor ${F_P}$.

The FDTD simulation structure for Purcell factor is schematically shown in Fig. 3(a). According to previous researches [46,47], here an electric dipole is placed in the middle of the gap to represent the molecular samples, and the Raman scattering from the molecular samples is approximated as the scattering from the dipole. Since the E_z component dominates the electric field in the gap, here the dipole is designed with the vertical vibration direction. According to the optimized enhancement results in Section 2.2, the structural parameters are chosen as: silver film thickness $h$=30 nm, gap = 5 nm, and tip diameter $d$ = 40 nm. To obtain the Purcell factor under this condition (${F_p} = P/{P_0}$, where P is the Poynting vector integral around the dipole in the gap and ${P_0}$ is the Poynting vector integral in free space [48]), in FDTD we detect the Poynting vector integral around the dipole at different wavelength, and compare the result with the Poynting vector integral in the free space around the same dipole. It is noted that the Purcell factor ${F_P}$ is a result of energy normalization, so we do not need to consider the local field enhancement in the gap structure studied in the previous Section, but only consider the process of dipole scattering from the gap.

 

Fig. 3. (a) Schematic diagram of scattering from a dipole in the gap of TERS system. (b) Purcell factor with different dipole heights H as a function of wavelength, the tip diameter $d = 40nm$. (c) Purcell factor with different tip diameters (6∼40 nm, corresponding to different color curves) as a function of wavelength. (d) The Purcell factor ${F_p}$ as a function of silver film thicknesses, the tip diameter $d = 40nm$, and the dipole heights $H = 2.5nm$, the wavelength of dipole $\lambda $=532 nm.

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Figure 3(b) show the results of the Purcell effect ${F_p}$ with different height H between the dipole and the silver film surface (as shown in Fig. 3(a)). It can be found that the dipole in the middle of the gap (H = 2.5 nm) has the lowest Purcell factor, that is, the closer dipole to the both edges of the gap structure results in higher Purcell factor ${F_p}$. These results of Purcell factor are due to the fact that the electric field excited by the dipole close to the tip (H = 4 nm) is the strongest, the field excited by the dipole close to the silver film (H = 1 nm) is lower, and the dipole in the middle (H = 2.5 nm) excites the lowest field. From the above results, it can be determined that the scattering enhancement of the sample mainly depends on the sample position in the gap structure of the TERS. When the scattering sample is closer to the tip or the metal substrate, stronger SPP field can be excited on the surface of tip or metal substrate, thus enhancing the Purcell effect in the gap structure. In addition, the results in Fig. 3(b) show that the Purcell effect is higher for the dipole close to the tip (H = 4 nm) than that close to the metal substrate (H = 1 nm), because the sharp tip of metal probe could produce much higher charge density and stronger plasmonic field on the tip than that on the metal substrate. These results indicate that in TERS or SERS experiments, it would be better to add an additional layer on the metal substrate to make the sample close to the tip, thereby enhancing the Raman scattering.

Since the tip structure has an effect on both the structural quality factor Q [49] and the mode volume, we study the variations of Purcell factor under different diameter of tip, as shown in Fig. 3(c). As the tip becomes sharper (diameter d decreases), the Purcell factor ${F_p}$ increases rapidly (although it fluctuates with wavelength, the smaller d leads to higher ${F_p}$ overall), and shows approximate periodic peaks in the spectrum, which is approximated as Rabi period and consistent with the previous reported effect of strong quantum interaction between dipole and gap structures [50].

In order to form a systematic study corresponding to the results in Fig. 2(d), we calculate the Purcell factor with different thickness of silver film substrates in Fig. 3(d) by using the same parameters as in Fig. 2(d). A peak of Purcell factor appears at about the thickness $h$=5 nm, because the very thin silver film and transparent substrate form a composite layer [47], which affects the structure quality factor Q. When $h$ > 20 nm, the Purcell effect is almost unchanged, because the thickness of silver film exceeds the penetration depth of light and no longer affects the quality factor Q of gap structure.

Based on the combination of the above-studied local field enhancement and the sample scattering from the gap, we can present a comprehensive enhancement process of TERS. As schematically shown in Fig. 4(a), Raman scattering enhancement in gap structure consists of three steps. First, the incident laser generates the enhanced SPP/optical focusing field on metal surface, and secondly the focusing field interacts with the metal probe to produce local field enhancement (gap-plasmon mode). Finally, due to the Purcell effect in gap structure, the scattering of Raman molecules produces another gain effect. Combining the three steps, the total TERS enhancement factor $EF$ can be calculated according to the Eq. (3) with the local field enhancement factor ${L_I}$ and the Purcell factor ${F_P}$, as shown in Fig. 4(b). The result of local field enhancement factor ${L_I}$ is calculated from the data in Fig. 2(d) and using the method as [38], and the result of Purcell factor ${F_P}$ at different silver film thicknesses is from the data in Fig. 3(d). It can be found that the total enhancement factor $EF$ in Fig. 4(b) can achieve the magnitude of 10¹¹, and its variation trend is similar to that of the field enhancement factor ${L_I}$ as well as the result in Fig. 2(d), indicating that the contribution from the local electromagnetic field in the gap structure to enhancement is larger than that from the Purcell effect of sample in the gap. It is noted that the result of $EF$ can be further increased by optimizing parameters such as the tip diameter according to the results in Fig. 3 for higher Raman enhancement.

 

Fig. 4. (a) Schematic diagram of whole enhancement process of TERS. (b) The total Enhancement Factor $EF$ (blue curve) of TERS, the local field enhancement factor ${L_I}$ (black curve). All parameters are as in Fig. 2(d) and the dipole height is $H$ = 2.5 nm.

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2.4 Directivity of far-field radiation in TERS

Generally, the far-field detection of Raman signals in experiment is achieved by using the objective lens with certain collection angles. Since the Purcell effect has not only a high enhancement factor but also a strong directivity for scattering light [51], which greatly affects the detection of Raman signals. Therefore, it is important to study the directivity of far-field scattering of the TERS system for better collection of Raman signals.

In Fig. 5(a), we consider collecting Raman scattering signals through an objective lens at the top with a maximum collection angle $\alpha $. To quantify the Raman collection performance, a scattering signal enhancement factor is defined as ${f_{far}} = {P_{r,cf}}/{P_{0,cf}}$, where ${P_{r,cf}}$ and ${P_{0,cf}}$ are the radiation energy entering the far field at (0∼ $\alpha $) angle range from the dipole in the gap structure and in free space, respectively. As shown in Fig. 5(b), ${f_{far}}$ increases as the collection angle $\alpha $ of the objective lens increases, but its maximum value of ∼120 is quite smaller than the Purcell effect results in Fig. 3, due to the fact that most energy radiated from the dipole is absorbed by the gap structure and only a small part of scattering light can enter the far field and be collected at certain angles. This result also explains why in experiment the detected Raman enhancement factor (e.g., about ∼1157 in [25]) is often much weaker than the maximum theoretical enhancement factor (e.g., about ∼10¹¹ in Fig. 4(b)).

 

Fig. 5. (a) Schematic diagram of far-field scattering signal collection structure (the tip diameter $d = 40nm$, dipole height is $H$ = 2.5 nm.) (b) Radiation enhancement factor as a function of collection angles of objective lens with the condition of different tip diameters (6∼40 nm, corresponding to different color curves). (c) Far-field distribution of scattered light intensity in polar coordinate when the tip diameter is $d$ = 10 nm. (d) The normalized result of Far-field scattering light intensity at different scattering angles with different tip diameters (6∼40 nm).

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We further study the detailed far-field distribution of the scattering light at different scattering angles, as shown in Fig. 5(d). It is found that the far-field radiation mainly has two peaks around 35° and 65°, respectively, which fit the slope of corresponding curves in Fig. 5(b). The highest signal collection result appears at the condition of tip diameter $d$ = 10 nm, and the corresponding far-field scattering intensity distribution is presented in Fig. 5(c), where two bright ring regions appear at about 35° and 65°, well agreeing with the two peaks in Fig. 5(d). This angle-dependent result is actually an effect of equal inclination interference of the scattering light from two sides of the silver film, so the scattering peak could appear alternately in the top and bottom sides of the gap structure at different angles. These results indicate that the collection of Raman signals can be optimized by choosing appropriate numerical aperture and position of the objective lens.

3. Conclusion

In this work, we systematically study the Raman enhancement mechanism in the TERS system based on the coupling of SPP/optical focus and metal probe. Two enhancement processes, including the local field enhancement excited by incident light and the outward scattering enhancement of molecular sample in the gap, have been separately studied with different structure parameters and finally combined to evaluate the overall Raman enhancement of the gap structure system. Our results reveal that several parameters have strong effects on the final Raman enhancement performance.

First, in Subsection 2.1, we study the different performances of the optical focus and the SPP focus in the inverted TERS system, and analyze the local field enhancement of gap-plasmon mode between total focused field and metal tip in Subsection 2.2. It is found that the thickness of metal film can be controlled to affect the intensity of both optical/SPP focus and the ratio between them, as well as the EIT-like effect of the gap-plasmon mode and the local field enhancement in the gap structure. The results show that the 30nm-thick silver film has the maximum local field intensity, while the thicker silver film maintains a higher contrast. Thus, the thickness of metal film can be modulated to optimize the enhancement of electromagnetic field in the gap structure for TERS applications.

Next, since the complete TERS process includes not only the field enhancement in the gap structure studied in Subsections 2.1 and 2.2, but also the enhancement in the outward scattering from the sample in the gap affected by the Purcell effect, hence the Purcell effect of the TERS system is studied in Subsections 2.3. It is found that the tip structure and the position of Raman molecular samples both have effects on the Purcell effect. When the molecule is closer to the silver film or the tip, the electric field and Purcell effect is higher, and the enhancement effect close to the silver tip is much higher than that close to the silver film. As the tip becomes sharper, the Purcell factor ${F_p}$ increases rapidly, and shows approximate periodic peaks in the spectrum. These results are important for TERS experiment to optimize the position of Raman molecules in the gap and the shape of tip used in experiment.

Finally, since the far-field collection angle of the objective lens is also important to the final performance of TERS system, in Subsection 2.4 we investigate the directivity of scattering light in TERS system. The far-field radiation mainly shows two peaks around 35° and 65°, which proves that the Purcell effect has not only a high enhancement factor but also a strong directivity for scattering light in the TERS system. According to this result, when collecting the far-field Raman signals in TERS experiment, a proper NA and position of objective lens should be selected depending on the scattering peaks around 35° and 65°. This work could not only deepen the understanding of different enhancement mechanisms in TERS technology, but also contribute to the design and optimization of TERS experimental systems.