1. Introduction

The collective oscillation of the electrons within noble metal nanostructures enables the resonant excitation of light at a particular wavelength, which is called localized surface plasmon resonance (LSPR). At the resonant wavelength, enhanced local electric fields (E fields) occur at the surface of metal nanostructures. These enhanced E fields contribute to the major part of the surface enhanced Raman scattering (SERS) intensity [1–3]. The resonant wavelengths depend strongly on the topological shapes of the metal nanostructures and their surrounding environments [4–12]. Usually, the metal nanostructures are put on the dielectric substrates [4–10]. The plasmonic properties of the metal nanostructures on the metal base layers have not been widely investigated.

Recently, aligned silver nanorod arrays have been prepared to obtain large SERS enhancements for biological or chemical detections [13–16]. For this SERS substrate, a base layer of silver film is first deposited onto the glass slides, and then silver nanorod arrays are deposited on the top of the silver film by the oblique angle deposition (OAD) method. Driskell et al. compared the SERS intensity from the rod-film substrate with that from the rod array on bare glass slides [15]. The results show that the absolute Raman intensity of trans-1,2-bis(4-pyridyl)ethane (BPE) from the rod-film substrate is three orders of magnitude stronger than that from the nanorod array without film. Although Zhou et al. found that the SERS intensity from the rod-film substrate increases linearly with the base layer reflectivity, the origin of the larger SERS intensity is not clearly known [17]. Because the enhanced E fields contribute to the major part of SERS intensity, there could be stronger E fields around the nanorods in the rod-film substrates than those around the individual nanorods.

When E fields interact with the metal film covered by a dielectric medium, the surface plasmon polariton (SPP) waves are excited and then propagate along the surface of the metal film [18]. For the rod-film nanostructure, the SPP waves could launch to the nanorod and subsequently to the top of the nanorod [19]. Do the SPP waves propagating along the nanorod contribute to the much enhanced E fields around the nanorods?

To prove the existence of the much enhanced E fields around the nanorods in the rod-film nanostructures and study the origin of these E fields, the E field distributions of the rod-film nanostructures are calculated by the finite difference time domain (FDTD) method and compared with those of the individual nanorods. The results show that the E fields around the nanorods in the rod-film nanostructures are much larger than those around the individual nanorods. These E fields are not mainly due to the SPP waves propagating along the nanorod but the superposition of the E fields of the incident wave and the reflection wave. In addition, we investigate how the height and the radius of the nanorod as well as the thickness of the base layer affect the E fields around the nanorod in the rod-film nanostructure. These results are of great relevance to design SERS substrates to obtain larger SERS intensities.

2. Simulation and method

FDTD method is a popular computational electrodynamics modeling technique [20]. In this paper, we perform the FDTD method (Remcom XFDTD) to calculate the E field distributions of the rod-film nanostructures and the individual nanorods.

Figure 1 illustrates the geometry of the rod-film nanostructure and the polarization configuration of the incident plane wave used in the calculations. For the rod-film nanostructure, the nanorod locates at the center of the rectangular film. The length (along x-axis) and the width (along y-axis) of the film are fixed at 4000 nm and 800 nm, respectively. The thickness (along z-axis) of the film is defined as t. The nanorod has a height of H and a radius of r. To compare the E fields around the nanorods in the rod-film nanostructures with those around the individual nanorods, the E field distributions of individual nanorods are also calculated. In all the calculations, plane waves are incident along –z direction with a horizontal polarization (along x-axis) as shown in Fig. 1. The wavelength of the excitation is fixed at λ = 785 nm. The cell size used in FDTD calculations is 5 nm. The permittivity of silver is given by the modified Debye model [21].

 

Fig. 1 Schematics for the incident direction and the rod-film nanostructure.

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3. Results and discussion

Figure 2(a) illustrates the E field distribution of the nanorod with a height of 600 nm and a radius of 40 nm. Light is incident along the long axis with a polarization perpendicular to the long axis. As shown in Fig. 2(a), Enhanced E fields occur around the lateral surface of the nanorod. These E fields are due to the transverse mode electron oscillations in the nanorod [5]. Figure 2(b) illustrates the E field distribution of the rod-film nanostructure for x-z plane at y = 0. For the rod-film nanostructure, the thickness of the base layer t is 80 nm and the nanorod has the same parameters as those in Fig. 2(a). As shown in Fig. 2(b), the E fields occur at the lateral surface and congregate to the top and 1/3 of the way from the bottom of the nanorod. The magnitude of the E fields of the rod-film nanostructure is much larger than that of the E fields of the individual nanorod. Therefore, the rod-film nanostructures, when used as SERS substrates, are more capable of capturing and detecting small amount of molecules.

 

Fig. 2 (Color online) E field distributions of individual nanorod and rod-film nanostructure: (a) E ² of the individual nanorod, (b) E ² of the rod-film nanostructure, (c) E _z ² of the rod-film nanostructure, and (d) E _x ² of the rod-film nanostructure.

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In the rod-film nanostructures, when SPP waves propagate along the nanorod, the major part of the E fields would occur in z-axis direction. Therefore, we plot the E field distributions of E _z and E _x components. As shown in Fig. 2(c), the E fields of E _z component congregate to the top of the nanorod. Therefore, only the enhanced E fields at the top of the nanorod are due to the SPP waves propagating along the nanorod. As shown in Fig. 2(d), the E fields of E _x component has a similar distribution and magnitude as those in Fig. 2(b). The much enhanced E fields appear around the top and 1/3 of the way from the bottom of the nanorod. Therefore, the much enhance E fields in Fig. 2(b) are not a result of the SPP waves propagating along the nanorod. When light is incident along the individual nanorod with the polarization perpendicular to the long axis (transverse mode excitation), strong E fields occur around the lateral surface of the nanorod [5]. Therefore, the much enhanced E fields in Fig. 2(b) are due to the transverse mode electron oscillations in the nanorod. In order to clearly illustrate the E field distributions along the nanorods, the averages of E ², < E ²>, around the nanorods are calculated. Figure 3 illustrates the E field distributions along the nanorod as a function of z. z denotes the distance to the bottom of nanorod. Then z = H denotes the top of the nanorod. As shown in Fig. 3, for the individual nanorod, E fields almost evenly distribute around the lateral surface except at the two ends. For the rod-film nanostructure, the maximums of the E fields appear around z = 187 nm and z = 600 nm. Although the E fields do not evenly distribute along the nanorod, the rod-film nanostructure has more hot spots than does the individual nanorod.

 

Fig. 3 (Color online) E field distributions (E ²) along the individual nanorod and the nanorod in the rod-film nanostructure.

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When plane wave is incident to the base layer, it would be reflected to the z > 0 region (as shown in Fig. 1) where the intensity of the superposition of the E fields of the incident wave and the reflection wave is determined by the phase difference between them. There are two contributions to this phase difference. The reflection wave must pass twice through the distance 2z before reaching the position of z. This additional path contributes to the phase difference between the incident wave and the reflection wave. Another contribution to the phase difference is a sudden change in phase of π that occurs when a wave is reflected at the top surface of the film. At the incident wavelength λ = 785 nm, the reflectivity is close to 100% [17]. If we suppose a total reflection here, the superposition of the E fields, E _sum, at the position of z can be written as $E_{sum}=[1+\cos (\pi +4\pi z/\lambda )]E{}_0=\gamma E_0$,where E ₀ is the magnitude of the incident field and $\gamma =1+\cos (\pi +4\pi z/\lambda )$. The maximums of E _sum occur at

In the following study, we investigate how the structural parameters of the rod-film nanostructures affect the E fields around the nanorod. We first investigate the effect of the thickness t of the base layer by varying t from t = 10 nm to t = 120 nm with fixed H = 600 nm and r = 40 nm. Figure 4 shows the E field distributions along the nanorods with t = 10, 30, 50, 70, 90, and 110 nm, respectively. For different t, they have similar trends and magnitudes as those of t = 80 nm, especially when t is larger than 30 nm. Since the much enhanced E fields around the nanorod are mainly due to the superposition of the E fields of the incident wave and the reflection wave reflected from the top surface and the increase of the thickness does not affect the reflectivity, the increase of t does not affect the E field distributions dramatically. However, for smaller t, the decrease of t would decrease the reflection E fields dramatically, which results in the visible change around z = 187 nm of t = 10 nm case in Fig. 4.

 

Fig. 4 (Color online) E field distributions (E ²) along the nanorods in the rod-film nanostructures with different film thickness t.

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In order to investigate how the radius r of the nanorod affects the E fields around the nanorod, r is increased from r = 25 nm to r = 80 nm with fixed t = 80 nm and H = 600 nm. Figure 5 shows the E fields along the nanorods with r = 30, 40, 50, 60, and 70 nm, respectively. For different r, the maximum E fields also occur at the positions around z = 187 nm and z = 600 nm. However, the magnitude of the maximum E fields increase with the increasing r. We performed FDTD calculations of the extinction spectra of individual nanorods with H = 600 nm. The results show that when r increases from 30 nm to 70 nm, the transverse dipole mode plasmon peak red shift from 417 nm to 562 nm, which is approaching the incident wavelength in this paper and thereby results in the increasing E fields in Fig. 5.

 

Fig. 5 (Color online) E field distributions (E ²) along the nanorods in the rod-film nanostructures with different nanorod radius r.

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In order to investigate how the height H affects the E fields around the nanorod, H is increased from H = 100 nm to H = 1200 nm with fixed t = 80 nm and r = 40 nm. Figure 6 shows the E field distributions along the nanorods different H. When H = 100 nm and H = 200 nm, the maximum E fields appear at the top of the nanorod. When H is larger than 300 nm, the locations of maximum E fields do not change with the increase of H, which occur around z = 187, 581, and 977 nm, respectively. The height difference between adjacent locations of maximum E fields is around 395 nm which is close to λ/2. The characteristics of the locations of maximum E fields satisfy Eq. (1). Therefore, the height dependent E field distribution consistent with our previous conclusion that the much enhanced E fields around the nanorod are due to the superposition of the E fields of the incident wave and the reflection wave. In Ref [15], the SERS intensity from the Ag nanorod-film substrate depends strongly on the height of the nanorods. Being relative to substrates with short nanorods, the SERS intensity increases dramatically with the increase of nanorod height. After the SERS intensity reaches its maximum, a further increase in nanorod height leads to a dramatic decrease in SERS intensity. The height dependent E field distributions in Fig. 6 would give some hints for explaining the height dependent SERS in Ref [15].

 

Fig. 6 (Color online) E field distributions (E ²) along the nanorods in the rod-film nanostructures with different nanorod height H.

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4. Conclusions

In this paper, the optical properties of the rod-film nanostructures are calculated by the FDTD method to prove that the much enhanced E fields around the nanorod do exist and study the origin of the much enhanced E fields. The results show that the E fields around the nanorod in the rod-film nanostructures are much enhanced compared with those around the individual nanorod. The enhanced E fields are not mainly due to the SPP waves propagating along the nanorod but the superposition of the E fields of the incident wave and the reflection wave which works as the excitation for the transverse mode electron oscillations in the nanorod. The E field distributions around the nanorod do not depend obviously on the thickness of the base layer. However, they depend strongly on the structural parameters of the nanorod. These results would be much helpful for designing SERS substrates to obtain larger SERS intensities.