1. INTRODUCTION

Surface-enhanced Raman scattering (SERS) is an important application of surface plasmon polaritons (SPPs) and has great potential for biological sensing ^[1,2]. Recently, increasing interest has been focused on the near-infrared (NIR) region, where blood and tissue are mostly transparent and light can penetrate tissues deeply, giving a chance for SERS to be utilized in vivo ^[3,4]. Due to the effect of “hot spots,” structures composed of nanoscale noble metal particles provide strong Raman signals when molecules are absorbed at or near the surface of nanoparticles. Structures composed of unordered metallic nanoparticles ^{[57" target="_self" style="display: inline;">–7]} have been studied and provide high SERS enhancement factors up to 1014. With the development of micro–nano processing technology, metallic nanostructures such as nanodisks ^[8], nanorings ^[9], and nanorods ^[10] are proposed to achieve more stable and reproducible SERS substrates. Recent studies have proved that it is an effective way to achieve a high local electric field and tune the plasmon resonances by putting metallic nanostructures on metal films ^[11,12]. For example, Kim and Cheng found high optical field enhancements at the edges of the nanostructures originating from coupling of localized surface plasmon resonance (LSPR) and gap SPPs. They predicted such SERS enhancement factors of up to 1011 for equilateral triangular nanostructures ^[11]. Lévêque and Martin have reported that setting gold nanosquares on a gold film can modify the plasmon resonance wavelength from 600 to 900 nm by changing the dielectric spacer thickness ^[12].

It is well accepted that the SERS enhancement is proportional to the product of the local electric intensities both at the frequency of exciting light and at the Stokes frequency of scattered light ^[13]. Based on this theory, periodic nanostructures upon metallic film separated by a dielectric layer are introduced to provide double-resonance substrates for selective Raman signal enhancements ^[14,15]. For such structures, SPPs supported by the grating strongly couple with the localized surface plasmons of gold nanodisks, resulting in double resonances.

In this paper, we convert the single disk array into a pair disk array ^[16] and change the surrounding material from air to water, which provides a promising substrate for SERS detection in biological media. According to the analysis of Hao and Schatz ^[7], the SERS enhancement factors in dimer structures are a factor of 10 larger than those in monomers. Besides, the water environment also provides a minor refractive index contrast between water and glass substrates compared with the air environment, which enables lager field enhancements. We optimize the coupling efficiency between surface plasmon resonance (SPR) and LSPR by tuning the thickness of the dielectric spacer. By tuning the interval of the gold nanoparticle pair, we realize the modulation of the LSPR wavelength and provide higher electric field intensity than that in the single disk case.

2. SIMULATION MODELS

The structure under investigation includes an array of gold disk pairs upon gold film separated by a silica spacer. The schematic of the structure is shown in Fig. 1. The finite-element method is used to calculate the near field of the structure. The normally incident light is polarized along the x direction. The diameter and the thickness of the disk are set as 130 and 30 nm to get a LSPR mode in the NIR region that can couple with the SPR mode excited by the dimer grating. The thickness of the gold film is 150 nm, large enough to prevent LSPR coupling with the bottom side of the film. The dielectric permittivity of gold is taken from Johnson and Christy’s experimental data ^[17]. The refractive index of silica is set to a constant value of 1.45 with the neglect of frequency change ^[18]. The near field of the gold nanoparticle pairs is calculated for different structure parameters.

Fig. 1. Schematic of double-resonance gold dimer array substrate.

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The enhancement factor of SERS ^[19,20] can be expressed as where Eloc(exc) and Einc(exc) are the local electric field and incident electric field of the exciting wavelength, respectively. Eloc(Raman) and Einc(Raman) represent the local and the incident electric fields at the Raman scattered wavelength. According to this equation, we take a product of the near-field intensity enhancements at LSPR and SPR wavelengths to qualitatively estimate the GSERS.

To excite the SPR mode of the gold film, an external wavevector should be supplied by the grating ^[21], which can be expressed as where G=2π/Px is the reciprocal grating vector of the structure with x-direction grating constant Px, (i, j) denotes the grating diffraction order, k∥ is the wavevector component of incident light along the surface, and n is the refractive index of water. Under normal incidence we have k∥=0; the first-order SPP mode occurs when the wavevector satisfies the equation kspp=G/n. Here we fix the period of the x direction as 550 nm, which makes the wavelength of the SPP mode almost constant by ignoring slight wavelength variations caused by other geometrical parameter changes. This special characteristic provides a reasonable usage at the excited wavelength of SERS. Besides, the sharper Q factor of the SPP and the broader Q factor of LSPR also exhibit a rational property in the application of the SERS substrate.

3. SIMULATION RESULTS AND DISCUSSION

Before optimizing the dimer grating structure, we simulate four structures, as shown in Fig. 2(c), to compare the electric intensity enhancement factors. The grating constants Px and Py are set to 550 and 500 nm, respectively. The gold nanodisk is 30 nm high and 130 nm in diameter, and the interval of the dimer is 15 nm.

Fig. 2. (a) Simulated electric field intensity enhancement factors of the dimer grating (green solid line), the single disk grating (black square line), a single dimer (red circle line), and a single disk (blue triangle line) upon gold film separated by a layer of silica spacer. (b) Ez amplitude at position 2 for the gold dimer array case. (c) Schematics of the four structures simulated.

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As shown in Fig. 2(a), the structures with the dimer grating and the single disk grating exhibit two resonant modes, corresponding to the LSPR mode and the SPR mode, respectively. Besides, the electric field intensity in the dimer grating is larger than that in the other three structures, which is caused by the interaction of the disks of the dimer and the Fano resonance resulting from the coupling between the SPR mode and the LSPR mode. The amplitude of Ez of the SPR on the gold film at position 2 is shown in Fig. 2(b), which behaves similarly with the near-field enhancement factor.

The two resonant modes in the dimer array case, respectively, correspond to the SPR [Fig. 3(a)] and LSPR [Fig. 3(b)] as the thickness of the silica spacer is 45 nm and the separation of the dimer is 15 nm. Figure 3(a) exhibits an obvious grating-like electric field distribution, while Fig. 3(b) shows that the electric field is mainly confined in the gap of the disk pair. As we know, the SPR mode is mainly determined by the array period and exhibits a global electric field distribution with interference strikes on the surface of the whole structure. The LSPR mode of the dimer has the feature of high field enhancement, which is mainly localized between the disks. So the electric field distribution shown in Fig. 3(a) is related to the SPR mode, and that in Fig. 3(b) corresponds to the LSPR mode. Besides, the highly confined electric field in the gap means that this structure possesses good spatial selection.

Fig. 3. (a) Intensity (|E|2) distribution on the half-height surface of the gold disk with hSiO2=45nm at 785 nm (SPR) with maximum intensity 2042. (b) 950 nm (LSPR) with maximum intensity 7066 corresponding to the two resonant modes of the dimer grating case in Fig. 2(a), respectively.

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Figure 4(a) shows the influence of the silica spacer thickness. Keeping the other parameters unchanged when the silica spacer thickness increases, the LSPR presents an obvious blue shift due to the weaker coupling between the gold nanoparticle pairs and its image in the gold film. A slight wavelength change of the SPR mode is observed due to the increase of the effective refractive index above the gold film.

Fig. 4. (a) Simulated electric field spectrum for the structure with Px=550nm, Py=500nm, and d=60nm at different thicknesses of the silica spacer. (b) Holistic enhancement GSERS via the change of the thickness of the silica spacer.

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In order to obtain an optimal thickness of the silica spacer, we investigate how GSERS changes with the thickness of the dielectric layer based on Eq. (1). An asymptotically stable enhancement via the increase of the silica spacer thickness is obtained, as shown in Fig. 3(b), which helps us to determine 45 nm as the optimal thickness of the silica spacer.

To study the LSP resonance quality of this double-resonant substrate, the effective mode volume normalized to (λ/2)3, Veff, the quality factor Q, and the ratio of these two values Q/Veff are calculated, as shown in Table 1. The effective mode volume Veff is calculated based on theories discussed in Refs. ^[22,23]. The quality factor Q is calculated by fitting the simulated spectral to Lorentzian functions to estimate the full width half-maximum of the resonance ^[24]. As the interparticle distance increases, both the Veff and the Q factor become larger for the weaker interaction between the disks of the dimer. Besides, we also calculate these parameters with a single dimer with the gap of 15 nm and a single disk separated from gold film by a 45 nm thick layer of silica spacer, which are listed in the last two rows of Table 1. We find that the gold dimer grating structures have a larger Q/Veff compared to the single dimer and the single disk with the gold film and silica spacer unchanged, which represents a higher enhancement gain in SERS. Therefore, the structure with the gold dimer array is more suitable for the SERS substrate than that without an array.

To modulate the LSPR mode, methods by changing the grating constant, the diameter and thickness of the disks, and the thickness of the spacer have been proposed and analyzed in the last few years. Here, we provide an additional method to modulate the LSPR mode by varying the gap of the dimer. Figure 5 presents the simulated electric field intensity enhancement factor around the Au-nanodisk-pairs–silica–Au-film structures with the gap changed from 15 to 45 nm. The grating constant, the silica spacer, and the parameters of the disk are unchanged. As the gap increases, the LSPR mode shows a significant blue shift as the interaction of the disks becomes weaker, while the SPR mode corresponding to the incident frequency is almost unchanged. The LSPR’s blue shift with the increase of the interparticle separation was demonstrated experimentally by Jain et al. ^[25,26]. When two disks are close to each other, they form dipole–dipole coupling. The LSPR mode of the dimer corresponds to the bonding mode ^[27]. With the increase of the separation distance in dimers, the coupling of the two particles becomes weaker and the LSPR mode moves toward the dipole mode of individual disks. This property provides an additional method for the wavelength modulation along different electric field enhancements for SERS detection.

Fig. 5. Electric field spectrum with Px=550nm, Py=500nm, and hSiO2=45nm at different interparticle separations: 15 nm (black line), 30 nm (red dot-dotted dash line), and 45 nm (blue dotted–dashed line).

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4. CONCLUSIONS

In conclusion, we propose a SERS substrate with extremely high field enhancements between the dimer at both excitation and Stokes frequencies. Compared to the single disk structure, the dimer grating structure possesses not only higher excitation efficiency of SPPs at the shorter wavelength resonance, but also a higher Q factor and a relatively smaller mode volume resulting from the dimer gap. Furthermore, the SPR and the LSPR form a Fano resonance that provides higher SERS enhancement. Such a dimer structure can also be designed to have three or even more resonant modes by introducing multilayers into disks, which can specifically enhance more Stokes frequencies of target molecules besides the excitation frequency to improve recognition.

5 ACKNOWLEDGMENT

Acknowledgment. This work is supported by the National Science Foundations of China (Grant No. 11274062) and the Program of Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 14KJB510016).