Plasmon focusing in short gold sphere nanochains for surface-enhanced Raman scattering Pascal Delange,1,2 Ya-Lun Ho,1 and Jean-Jacques Delaunay1,* 1
Department of Mechanical Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan 2
Physics Department, Ecole Polytechnique ParisTech, Palaiseau Cedex 91128, France *Corresponding author: [email protected]‐tokyo.ac.jp
Received 6 September 2013; revised 18 November 2013; accepted 26 November 2013; posted 26 November 2013 (Doc. ID 197287); published 17 December 2013
Power-flow focusing in metal nanostructures is attracting growing attention to design efficient and tunable substrates for surface-enhanced Raman spectroscopy (SERS), and to propose a more reliable alternative to random surfaces for single-molecule sensing. In this paper, finite-difference time-domain simulations were used to explore the near-field amplification features of short chains of gold (Au) nanospheres. Short chains of gold spheres were found to induce stronger field enhancements than infinite chains due to a more efficient trapping and focusing of the incident energy. In addition, interaction with a suitably tuned SiO2 ∕Au double-layer substrate was demonstrated to widen the resonance’s bandwidth, meeting another practical need for SERS. © 2013 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (250.5403) Plasmonics; (290.5850) Scattering, particles; (350.4990) Particles; (240.6695) Surface-enhanced Raman scattering; (050.4865) Optical vortices. http://dx.doi.org/10.1364/AO.52.008809
1. Introduction
Surface-enhanced Raman scattering (SERS) was discovered in 1977, when two groups measured Raman signals millions of times stronger than expected on previously chemically roughened silver electrodes [1,2]. Since then, SERS has developed into a major technique in biosensing. The potential signal enhancement compared to classical Raman scattering is such that on chemically roughened noble metal substrates (e.g., gold and silver), single molecule detection has been reported, corresponding to signals enhanced up to the order of 1010 times [3–5]. A part of this enhancement has a chemical origin, due to the change in the electronic environment of the molecules attached to the substrate [6]. However, most of the enhancement was proven to originate from the strongly enhanced field radiated by localized surface plasmon polaritons (LSPP), and to be roughly proportional to the square of the normalized incident 1559-128X/13/368809-08$15.00/0 © 2013 Optical Society of America
and Stokes-shifted electric fields [7]. Enhancements high enough for single molecule detection have typically been observed in random systems, but those lack control of the hot spots’ locations, density, and excitation wavelength. Single-molecule sensing has thus been difficult to reproduce. In order to obtain a better control on the enhanced wavelengths, self-assembled aggregates of chemically synthesized noble metal colloids of several forms have been widely used, among them are spheres [8], triangles [9], and nanorods [10]. More control of the SERS enhancement’s spatial localization was made possible by techniques such as electron-beam lithography, which enables one to accurately define the particles’ position and shape with an error of less than a few nanometers [11,12]. Pairs of nanoparticles with a small gap are known to produce a strong field enhancement within the gap, so that the nanoparticle dimer has become one of the most studied systems for SERS. The nanoparticle structures can be fabricated using a bottom-up technique (bowtie [13], triangles [14], and disks [15]) and a top-down technique (spheres [16]). However, gaps 20 December 2013 / Vol. 52, No. 36 / APPLIED OPTICS
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as small as a few nanometers are difficult to fabricate even with state-of-the-art electron-beam lithography equipment, and it has been shown that quantum tunneling through the gap eventually limits the amplification in the very narrow gap limit [17]. In order to reach enhancements strong enough for singlemolecule detection, geometries such as an array of particles deposited next to each other may not be sufficient. This limitation calls for more complex structures sustaining further optical energy concentration into well-defined hot spots. One of the limits of a SERS substrate formed by single spheres periodically aligned on an array seems to be its “excessive” symmetry, because in this geometry no point is particular enough to host a very high electric field. While this allows for a high spatially averaged field enhancement, it can be desirable to obtain higher enhancements in some specific but tunable points of the structure. Recently, several designs have been proposed to solve this limit. The new designs rely on tailored long- and short-range energy transfer between nanoparticles. They include cascade amplification in aggregates of nanospheres with different sizes [18,19], quasi-periodic arrays [20], and surface plasmon lenses [21]. Furthermore, several studies emphasized the role played by the substrate in coupling adjacent nanoparticles and carrying the optical power flow, whether for SERS substrates or in plasmon waveguides [22,23]. In the following, we present a family of SERS substrates whose field enhancement was studied theoretically with the aim of using plasmon hybridization between gold nanospheres and their substrate to achieve efficient subwavelength power flow focusing. Taking an array of infinite gold nanospheres chains as a reference, we consider a geometry where the translation symmetry was reduced by isolating short chains of nanospheres. This geometry is shown to allow strong energy focusing within the central gaps. A significantly increased bandwidth of the resonance is also demonstrated for carefully tailored substrates. 2. Simulation Method and Field Enhancement
Simulation results of the field enhancement of a periodic array whose unit cell contains a chain of five aligned Au nanospheres (gold nanochains) are reported. A schematic of the studied structure is given in Fig. 1 together with a description of the relevant geometrical parameters. The spheres are of radius r 50 nm, except in Fig. 4 where we look into the dependency of the response on the sphere radius. In the general case, the periodicities in the x and y directions are p 760 nm and w 600 nm, respectively. Only in Fig. 4, where larger spheres (up to r 90 nm) were considered, the periodicity p was increased to 1 μm to allow for the spheres to fit into one unit cell. The gap in the x direction between two adjacent spheres within the unit cell is g 10 nm. With those dimensions, the array is effectively 8810
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Fig. 1. (a) Side and (b) top views of the studied structure having aligned Au spheres on an Au∕SiO2 double-layer with respective thicknesses dSiO2 and dAu . The gap g between the spheres is fixed to 10 nm, the sphere radius r is 50 nm, and the periods in the x and y directions are, respectively, p 760 nm and w 600 nm, unless stated otherwise. The structure is illuminated at normal incidence with a plane wave of wavelength λ having its electric field polarized along the x direction.
formed of isolated groups of five aligned spheres, separated from the nearest groups by a larger gap of 220 nm in the x direction and of 500 nm in the y direction. The effect of the nanochain substrate (SiO2 , Au, SiO2 ∕Au double-layer) is investigated. The SiO2 and Au layers have respective thicknesses dSiO2 and dAu and when included, the Au layer’s thickness dAu is 50 nm. The incident light is a normally incident plane wave of wavelength λ having its electric field polarized along the x direction, parallel to the aligned spheres. The simulations were done using the finitedifference time-domain technique (FullWAVE, Rsoft Design Group, Ossining, USA). The Au permittivity is the one measured by Johnson and Christy [24], and the SiO2 permittivity is that measured by Malitson [25]. Periodic boundary conditions are applied in the x and y directions, and perfectly matched layer boundary conditions are applied on the top and the bottom of the simulated domain. The grid size is equal to 2.5 nm. Accordingly, the time step τ is set to 4.8 × 10−18 s, corresponding to 1.44 nm in cT units to ensure convergence. The total calculation time T is equal to 213 τ. While random nanosphere aggregates have been widely used to obtain SERS [8], we study and optimize a family of structures whose resonance wavelengths can be tuned and field enhancement factors are larger than in random geometries. Short (five spheres) and separated chains of Au nanospheres are used instead of an infinite chain. In
this configuration, one given nanochain gathers the energy incoming on a larger surface, leading to a significantly higher enhancement maximum at the resonance. In what follows, we show which parameters govern this configuration’s efficiency. In relationship with this, we also show how the substrate design (material and thickness) influences a given nanostructure’s behavior. Metallic nanospheres illuminated by light with the adequate frequency show resonant modes, also called localized plasmon modes, which are described by analytic Mie theory [26,27]. The strength and resonance frequency of these modes can be modified by the shape, size, and surroundings of the spheres [28]. Using the configuration described in Fig. 1, we studied the role of the different geometrical parameters in order to optimize the field enhancement in the so called “hot spots,” located in the gap between adjacent spheres. Figure 2(a) shows the electric field enhancement in the vertical plane [defined in Fig. 1(a)] at the resonance wavelength λres 750 nm for the Au nanospheres deposited on a SiO2 substrate. The resonance wavelength for five aligned spheres is significantly redshifted compared to the case of a single sphere in vacuum (λres ≈ 550 nm), as a result of their plasmons’ hybridization [29,30]. The induced electric field distribution around each sphere corresponds to a dipolar mode with its dipolar moment in the x direction, as expected from the x polarization of the incoming electric field. However, the field induced by the sphere plasmons remains localized very closely around the spheres (with a range less
Fig. 2. Vertical cross sections of the jExj2 (left) and jEzj2 (right) amplitude distributions in the steady state for the Au spheres on (a) the dielectric substrate, (b) the gold mirror, and (c) the Au∕SiO2 double-layer. The distributions are shown in log scale for the resonance wavelengths [(a) λ 750 nm, (b) λ 700 nm, and (c) λ 710 nm]. The maximum values of jEj2 found in the sphere gaps of (a), (b), and (c) are 900, 4875, and 5025, respectively. The electric field amplitude is normalized to the electric field amplitude of the incoming wave.
than 50 nm). The locally highest amplification obtained is jEj2 900 in this case. With only a SiO2 substrate, however, much of the incident field flows through the surface and is essentially lost for sensing purposes. In order to trap the energy more effectively within the nanochain and obtain stronger field enhancements, we add a 50 nm thick Au layer below the Au spheres. The plasmon coupling between the spheres and the Au layer changes the resonance wavelength λres to 710 nm [29,31,32]. As seen in Fig. 2(b), the electric field enhancement all around the nanospheres and especially within the gaps is considerably stronger than for the configuration of the spheres on SiO2 , reaching up to jEj2 4875 at the resonance. In this configuration, a relatively strong electric field enters the spheres and the Au layer near the contact points. jEj within the gold spheres reaches up to three times the incident wave’s amplitude, that is, four times more than without the Au mirror. Figure 2(b) shows that if deposited over an Au layer, the Au spheres scatter the field in the z direction with a characteristic decay length greater than 200 nm and in the x direction with a characteristic decay length greater than 100 nm. In comparison, the scattered field goes to zero within a few tens of nanometers over a SiO2 substrate. This long range vertical field is thought to be created by dipolar images excited on the Au layer. However, this strong field within the metal causes Ohmic dissipation. Furthermore, the field near the Au layer’s surface is much more localized around the contact points and points to suboptimal energy transfer along the nanochain’s axis. There is a need to design the substrate to make the nanochain more efficient in transporting the energy from the outside toward the center along the contact line. With this aim in mind, we have added a 50 nm SiO2 layer between the spheres and the mirror. In doing so, a different plasmonic structure was formed since the spheres and the gold layer are no longer coupled by direct contact. However, the nanochain and the Au layer do not become independent as plasmon hybridization is still possible at a distance. Figure 2(c) shows how this transforms the nearby electric field distribution, especially in the gold layer’s vicinity. In this configuration, the plasmons at the Au layer’s surface are not localized around the contact points with the spheres, but are instead spread evenly over the whole contact line. This indeed turns out in a more efficient energy trapping around the spheres, as we demonstrate in the following. The electric field enhancement is slightly superior, reaching up to jEj2 5025, and the resonance wavelength is not changed at λres 710 nm. The surface plasmons on both sides of the gold layer partly couple. Independent far-field simulations using the rigorous coupled-wave analysis algorithm confirm that a little more light is thus transmitted through the mirror, especially in the short wavelength domain λ < 650 nm as evidenced in Fig. 3. However, the small leak is compensated by the reduced dissipation in 20 December 2013 / Vol. 52, No. 36 / APPLIED OPTICS
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Fig. 3. Reflected, absorbed, and transmitted light by the fivesphere chains on a double-layer structure with dSiO2 50 nm. The local maximum in the reflection curve at λ 710 nm coincides with the field enhancement’s resonance wavelength. More light is transmitted in the short-wavelength domain than through a plain gold layer (50 nm) or in the configuration without the SiO2 layer. An almost perfect extinction occurs at λ 770 nm.
the metal, and by a more advantageous spectral behavior. 3. Choice of the Particles’ Size and Array Periodicities
While the usage of nanochains and infinite chains leads to different field enhancement properties, our simulations (not shown here) showed that increasing the period p in the x direction led to very little change in the plasmonic behavior as long as the gap between two adjacent nanochains remains large compared to the spheres’ diameter. Keeping a distance greater than 200 nm between the latter gave satisfying results. In order to look at the effect of changing the radius of the spheres, p was increased to 1 μm in order to allow for more or larger spheres to fit into one unit-cell. For this value of 1 μm and in the case of 50 nm radius spheres, the behavior was verified to be similar to that of the reference configuration (p 760 nm). The sphere radius was found to dramatically influence the spectral behavior and the resonance amplitude. Figure 4 represents the optical amplification jEj2 as a function of wavelength for a sphere radius increasing from 25 to 90 nm, in the case of five Au spheres directly on an Au layer. By increasing the spheres’ radius, the resonance wavelength increases from 600 to 1050 nm while the field enhancement increases from 300 to 6000. This is to be compared with the much slower rate at which the resonance redshifts for a single sphere [33] and again highlights the importance of the plasmon hybridization in the nanochain. Comparing the resonance curves for the 75 and 90 nm radius gives an insight into the importance of keeping successive nanochains separated, as mentioned before. Indeed, while the resonance height steadily increases as r goes from 20 to 75 nm, it decreases instead in the case r 90 nm 8812
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Fig. 4. Electric field amplification jEj2 in the sphere gap as a function of wavelength for different sphere radii (25, 35, 50, 75, and 90 nm). For this simulation, the period p along x was increased to 1 μm to allow for larger spheres to fit into one unit-cell. The general trend is that the resonance amplitude increases with the sphere radius. However, in the case of the 90 nm radius spheres, the amplification instead decreases compared to the 75 nm radius spheres as the spheres fill the whole unit cell. The resonance wavelength steadily increases with the sphere’s radius.
where this separation goes down to 60 nm, which is small compared to the diameter. The clear dependence of the spectral behavior on the sphere radius, when combined with accurate control of the synthesized nanospheres, enables the design of the nanochains, whose resonance is tuned to the available excitation laser wavelengths for sensing with SERS. Practically, one may want to use large spheres to obtain the highest possible enhancement, while keeping the resonance wavelength near the laser wavelength. Another parameter that has to be controlled precisely to attain high field amplification is the gap between two adjacent spheres. The gap width g is here taken everywhere to be equal to 10 nm, but the electric field amplitude jEj was shown to decrease a little faster than 1∕g (over the explored range of gap widths, from 10 to 50 nm, the fitting to a power law shows a dependency as g−1.3 ). For those relatively large gaps (more than a few nm), classical electrodynamics give a good description as quantum effects in the gap, such as electron tunneling, can be neglected [17]. 4. Discussion of Power-Flow Trapping in Gold Nanochains
We now go back to the reference layout described in Fig. 1 with five spheres per nanochain, p 760 nm, r 50 nm, and g 10 nm. In what follows, we develop on why this configuration made of short chains, along with the choice of the substrate, is more favorable for SERS sensing than an infinite chain of Au spheres. Compared to the latter, nanochains achieve higher amplification with a larger bandwidth. Last, we propose an explanation for this behavior.
As mentioned before, adding a SiO2 layer between the spheres and the Au layer fundamentally transforms the geometry and the plasmonic behavior. Indeed, Fig. 5(a) shows that the field enhancement with no SiO2 layer is very different from the limit case of dSiO2 0 nm. For a thin dielectric layer (10 nm), the field enhancement is actually weaker
Fig. 5. (a) Electric field enhancement jEj2 in the sphere gap at λ 710 nm (inset for λ 600 nm) as a function of the dielectric thickness dSiO2 . When the spheres are separated from the mirror, the behavior becomes significantly different from the situation where the spheres are directly on the mirror. While the amplification is weaker with a very thin dielectric layer, it reaches a maximum for dSiO2 ≈ 50 nm. A 170 nm layer leads to a perfect extinction. jEj2 in the sphere gap as a function of the wavelength λ is shown for an array of five-sphere chains and an infinite chain deposited on (b) the gold mirror and (c) the SiO2 ∕Au double-layer. On the gold mirror, the nanochains blueshift the resonance and make the resonance stronger and sharper near λres. On the SiO2 ∕Au doublelayer, the nanochains significantly enhance the electric field in a large bandwidth.
than when the spheres directly touch the Au layer. But as the SiO2 layer gets thicker, the field amplification increases and reaches a maximum for dSiO2 around 30–50 nm, stronger than in the configuration where this layer is absent. If the layer gets even thicker, the amplification decreases and reaches a near-perfect extinction around dSiO2 170 nm. Further increase in the layer thickness results in an increase in the enhancement. At the resonance wavelength λres 710 nm, the second maximum does not reach values nearly as high as the first maximum. It should be noted, however, that for other wavelengths apart from the resonance this second maximum amplitude is actually higher to that of the first one. This point is illustrated for λ 600 nm in the inset of Fig. 5(a). This result is explained by the twofold effect of the mirror. On one hand, the Au layer leads to a short-range plasmon hybridization with the nanospheres that transform the whole plasmonic behavior. On the other hand, whatever the distance, the Au layer also reflects the incident wave which can lead to interference in the spheres’ plane. Those interferences are here revealed by the fact that in Fig. 5(a) and for similar curves realized for different wavelengths, the additional dielectric thickness between the maximum and the extinction amounts to a phase difference almost equal to π. While Fig. 5(a) only compares the maximal amplifications attained at the resonance wavelength, if the system is to be used for SERS, the variations of the said enhancement around its maximum value matter as well. Indeed, in a simple model the SERS amplification is proportional to the squared electric field amplifications at both the incident and the Raman-shifted wavelengths. As reported by Van Duyne et al. [34,35], the SERS enhancement is greater when both the excitation and Raman-shifted wavelengths are near the plasmon resonance, which typically happens when the plasmon resonance is between these two wavelengths. While the Raman shifts can be very small in terms of wavelength at visible wavelength excitation, they may reach values as large as 100 nm when the excitation wavelength is in the red or near-infrared domain. Furthermore, the choice of the excitation wavelength is usually limited to readily available fixed wavelength laser sources, so that a large excitation bandwidth may be convenient. The most important benefit of adding a thin dielectric layer between the spheres and the mirror is to enlarge the bandwidth. It also emphasizes the need of isolating the nanochains. Figure 5(b) compares jEj2 as a function of the wavelength for the nanochains and the infinite chain, without a dielectric layer. Figure 5(c) shows the configuration with a 50 nm thick SiO2 layer. In the case of a simple gold mirror substrate, isolating short sphere chains does not change the resonance curve’s shape much far from λres , but blueshifts it by 40 nm and makes it higher and sharper near the top. The increase in the maximal enhancement jEmax j2 amounts to 20 December 2013 / Vol. 52, No. 36 / APPLIED OPTICS
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25%. Furthermore, comparing the nanochains and the infinite chain with a dielectric layer shows a radical transformation of the resonance curve, as seen in Fig. 5(c). The presence of a SiO2 spacing layer plays a complex role, increasing the field enhancement for the nanochains, but decreasing it for an infinite chain. The comparison of the curves shown in Figs. 5(b) and 5(c), respectively, illustrates the real benefit of using the SiO2 layer. While the highest point of the resonance is not affected, having the same wavelength λres 710 nm, the field amplification remains high after reaching its maximum (over 90% of the peak value) over a much larger wavelength region: 75 nm in width instead of 20 nm for the direct mirror contact configuration. However, the drawback for these changes, as compared with the infinite chain, is that the field enhancement becomes more localized in some specific sphere gaps. This means that the spatially averaged enhancement will not necessarily be increased, as the infinite chain has more equivalent hot spots than multiple nanochains. We have thus observed important changes in the plasmonic properties of isolated nanochains of gold spheres placed on an Au∕SiO2 double-layer. In the following, we will propose an explanation for those changes, based on the power flow around the Au spheres. For single metallic nanospheres, optical vortices appear on both sides of the sphere [36,37]. Those vortices help to redirect the incident light from a larger area toward the sphere and trap the electromagnetic energy around it. The power flow exhibits a complex pattern with multiple singular points, whose nature and positions vary greatly with the excitation wavelength. In particular, the vortices change their direction as the wavelength passes the resonance, pointing outward for shorter wavelengths, and inward for longer wavelengths. The efficiency of noble metal nanoparticles in several optical phenomena (enhanced scattering and extinction, LSPR) is directly linked to this property, which accounts for the increased cross section as well as the energy trapping. In the configuration we studied, the same kind of power-flow singularities account for the strong energy trapping between the spheres. For the nanochain geometry, however, the energy flows around the whole chain and not only single spheres. For spheres aligned on a dielectric substrate, while the coupling between the localized plasmons is shown by the resonance redshift, the power flow is similar to a juxtaposition of those obtained for single spheres. This is different when the gold spheres are deposited on the Au layer. Indeed, the energy flows from the outside to the inside of the nanochain along the sphere/mirror contact line, as shown in Figs. 6(a) and 6(d). The incident light thus enters the structure through the gaps and on the sides and is concentrated exactly where it will achieve high amplification, i.e., in the spheres and the central gaps. This kind of substrate-enhanced energy 8814
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transfer in chains of particles has been reported before in the case of plasmon waveguides [22,23,38]. The collective resonance of the gold spheres is responsible for the energy trapping around the spheres and especially within the gaps. This power flow shows why such a difference exists between the present nanochain configuration and an infinite sphere alignment. Here, every unit-cell is designed as to absorb and focus as much incoming energy as possible toward the center. In contrast with this, an infinite line is missing an “entry point.” Furthermore, an infinite line does not possess a well-defined center (every sphere being an inversion center), while in the present case the energy is concentrated toward the center of the nanochain, the field amplification being significantly higher in the central gaps than in the border ones. Another weaker mode usually exists where the opposite happens, but the two resonances are separated by hundreds of nanometers and hardly overlap. When a 50 nm thick SiO2 layer is added [Figs. 6(b) and 6(e)], the power flow at the resonance shows two clear optical vortices around the second and fourth
Fig. 6. Poynting vector in the vertical (left) and the horizontal (right) planes passing through the spheres’ centers. Parts (a) and (d) represent the spheres directly on the gold mirror, (b) and (e) represent the situation with a 50 nm thick dielectric layer, and (c) and (f) the situation with a 170 nm thick dielectric layer (λ 710 nm). For the two first cases, which achieve high field amplification, the vertical view shows how the energy flow is focused from the sides toward the spheres and the gaps. The horizontal view also shows how the energy is focused toward the spheres, from the whole unit-cell surface. With the presence of a 50 nm dielectric layer, we see in (b) that optical vortices and saddle points effectively trap the incoming energy in the vicinity of the nanochains. When the dielectric thickness further increases to 170 nm (corresponding to the extinction wavelength), two additional vortices are formed in the dielectric, thus redirecting the energy flow outward of the spheres as seen in (c).
spheres. As the energy flows in one direction around the sphere, a second optical vortex in the opposite direction appears within the sphere, following the conservation of topological charge [39]. Furthermore, the energy flow within the dielectric layer is strong, the mirror’s surface plasmons being efficient at transporting energy. A small fraction of the incoming energy is transmitted to the other side of the mirror, secondary surface modes being excited on the backside. However, as the log scale figure shows, most of the energy is trapped and flows around the side spheres. This is made visible by the presence of three saddle points just over the spheres which separate the energy flowing out of the gap, one part being reflected and the other redirected to flow around the spheres. The effect of the number of spheres for the SiO2 ∕Au double layer is investigated in Fig. 7. It is found that improved electric field enhancement
is realized for all the short nanochains, the case of the infinite chain giving the smallest electric field enhancement. The maximum field enhancement wavelength is redshifted as the number of spheres increases, going to a maximum corresponding to the infinite chain. This is in agreement with numerical calculations done using the hybridization method by Nordlander et al. [30] generalized with an increasing number of spheres. When the dielectric layer is 170 nm thick [Figs. 6(c) and 6(f)], however, the field amplitude in the sphere gaps goes to zero. In terms of the Poynting vector field, two optical vortices (one on each side) appear within the SiO2 layer. The optical vortices inverse the energy flow direction: while the energy still flows inward near the Au mirror, it flows outward next to the spheres. The power flow in the horizontal plane containing the middle of the spheres is also completely different from the two other cases. Both figures show how the spheres “repel” the power flow instead of attracting it. The energy flows out of the spheres and not toward them, and the overall amplitude is strongly reduced. As a consequence, the structure with a 170 nm thick SiO2 layer realizes the exact opposite of the energy trapping of the 50 nm dielectric structure. 5. Conclusion
We investigated the field-enhancement properties of a family of nanostructures for use as a SERS substrate with a finite-difference time-domain technique. The studied nanostructures consisted of a periodic array whose elementary cell contains a short chain of Au spheres over a SiO2 and Au layers, and a SiO2 ∕Au double-layer. We studied what parameters lead to a high field enhancement within the sphere gaps. We showed that larger spheres generally lead to a higher field enhancement, but that keeping an open space between two adjacent sphere nanochains is important for the structure’s efficiency, as in the limit of an infinite chain efficiency is reduced. Next, simulation shows that rather than placing the gold spheres directly on an Au mirror, inserting a dielectric layer between the spheres and the mirror leads to a stronger enhancement over a larger wavelength region. Finally, we showed how the Poynting vector field clearly reveals light trapping by the nanochains on the SiO2 ∕Au double-layer, accounting for the efficient field enhancement as compared to random substrates in general, or even Au sphere nanochains over a simple Au mirror. References Fig. 7. Effect of the number of spheres in the nanochains on (a) the electric field amplification jEj2 and (b)–(g) the Poynting vector in the horizontal planes passing through the spheres’ centers. Part (g) corresponds to the infinite chain. The results are shown for the case of the SiO2 ∕Au double-layer with a 50 nm thick dielectric layer.
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20. A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. D. Negro, “Deterministic aperiodic arrays of metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17, 3741–3753 (2009). 21. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5, 1399–1402 (2005). 22. G. Lévêque and R. Quidant, “Channeling light along a chain of near-field coupled gold nanoparticles near a metallic film,” Opt. Express 16, 22029–22038 (2008). 23. F. Zhou, Y. Liu, and Z.-Y. Li, “Surface-plasmon-polaritonassisted dipole-dipole interaction near metal surfaces,” Opt. Lett. 36, 1969–1971 (2011). 24. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). 25. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1208 (1965). 26. C. F. Bohren and D. R. Huffman, “Absorption and scattering by a sphere,” in Absorption and Scattering of Light by Small Particles (Wiley-VCH Verlag GmbH, 2007), pp. 82–129. 27. M. Quinten and U. Kreibig, “Absorption and elastic scattering of light by particle aggregates,” Appl. Opt. 32, 6173–6182 (1993). 28. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003). 29. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). 30. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004). 31. T. Takemori, M. Inoue, and K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987). 32. P. Nordlander and E. Prodan, “Plasmon hybridization in nanoparticles near metallic surfaces,” Nano Lett. 4, 2209– 2213 (2004). 33. Y. Q. He, S. P. Liu, L. Kong, and Z. F. Liu, “A study on the sizes and concentrations of gold nanoparticles by spectra of absorption, resonance Rayleigh scattering and resonance non-linear scattering,” Spectrochim. Acta, Part A 61, 2861–2866 (2005). 34. C. L. Haynes and R. P. Van Duyne, “Plasmon-sampled surfaceenhanced Raman excitation spectroscopy,” J. Phys. Chem. B 107, 7426–7433 (2003). 35. A. D. McFarland, M. A. Young, J. A. Dieringer, and R. P. Van Duyne, “Wavelength-scanned surface-enhanced Raman excitation spectroscopy,” J. Phys. Chem. B 109, 11279–11285 (2005). 36. Z. B. Wang, B. S. Luk’yanchuk, M. H. Hong, Y. Lin, and T. C. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B 70, 035418 (2004). 37. S. V. Boriskina and B. M. Reinhard, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale 4, 76–90 (2012). 38. J.-W. Dong and Z.-L. Deng, “Direct eigenmode analysis of plasmonic modes in metal nanoparticle chain with layered medium,” Opt. Lett. 38, 2244–2246 (2013). 39. H. F. Schouten, T. D. Visser, and D. Lenstra, “Optical vortices near sub-wavelength structures,” J. Opt. B 6, S404–S409 (2004).
Department of Mechanical Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan 2
Physics Department, Ecole Polytechnique ParisTech, Palaiseau Cedex 91128, France *Corresponding author: [email protected]‐tokyo.ac.jp
Received 6 September 2013; revised 18 November 2013; accepted 26 November 2013; posted 26 November 2013 (Doc. ID 197287); published 17 December 2013
Power-flow focusing in metal nanostructures is attracting growing attention to design efficient and tunable substrates for surface-enhanced Raman spectroscopy (SERS), and to propose a more reliable alternative to random surfaces for single-molecule sensing. In this paper, finite-difference time-domain simulations were used to explore the near-field amplification features of short chains of gold (Au) nanospheres. Short chains of gold spheres were found to induce stronger field enhancements than infinite chains due to a more efficient trapping and focusing of the incident energy. In addition, interaction with a suitably tuned SiO2 ∕Au double-layer substrate was demonstrated to widen the resonance’s bandwidth, meeting another practical need for SERS. © 2013 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (250.5403) Plasmonics; (290.5850) Scattering, particles; (350.4990) Particles; (240.6695) Surface-enhanced Raman scattering; (050.4865) Optical vortices. http://dx.doi.org/10.1364/AO.52.008809
1. Introduction
Surface-enhanced Raman scattering (SERS) was discovered in 1977, when two groups measured Raman signals millions of times stronger than expected on previously chemically roughened silver electrodes [1,2]. Since then, SERS has developed into a major technique in biosensing. The potential signal enhancement compared to classical Raman scattering is such that on chemically roughened noble metal substrates (e.g., gold and silver), single molecule detection has been reported, corresponding to signals enhanced up to the order of 1010 times [3–5]. A part of this enhancement has a chemical origin, due to the change in the electronic environment of the molecules attached to the substrate [6]. However, most of the enhancement was proven to originate from the strongly enhanced field radiated by localized surface plasmon polaritons (LSPP), and to be roughly proportional to the square of the normalized incident 1559-128X/13/368809-08$15.00/0 © 2013 Optical Society of America
and Stokes-shifted electric fields [7]. Enhancements high enough for single molecule detection have typically been observed in random systems, but those lack control of the hot spots’ locations, density, and excitation wavelength. Single-molecule sensing has thus been difficult to reproduce. In order to obtain a better control on the enhanced wavelengths, self-assembled aggregates of chemically synthesized noble metal colloids of several forms have been widely used, among them are spheres [8], triangles [9], and nanorods [10]. More control of the SERS enhancement’s spatial localization was made possible by techniques such as electron-beam lithography, which enables one to accurately define the particles’ position and shape with an error of less than a few nanometers [11,12]. Pairs of nanoparticles with a small gap are known to produce a strong field enhancement within the gap, so that the nanoparticle dimer has become one of the most studied systems for SERS. The nanoparticle structures can be fabricated using a bottom-up technique (bowtie [13], triangles [14], and disks [15]) and a top-down technique (spheres [16]). However, gaps 20 December 2013 / Vol. 52, No. 36 / APPLIED OPTICS
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as small as a few nanometers are difficult to fabricate even with state-of-the-art electron-beam lithography equipment, and it has been shown that quantum tunneling through the gap eventually limits the amplification in the very narrow gap limit [17]. In order to reach enhancements strong enough for singlemolecule detection, geometries such as an array of particles deposited next to each other may not be sufficient. This limitation calls for more complex structures sustaining further optical energy concentration into well-defined hot spots. One of the limits of a SERS substrate formed by single spheres periodically aligned on an array seems to be its “excessive” symmetry, because in this geometry no point is particular enough to host a very high electric field. While this allows for a high spatially averaged field enhancement, it can be desirable to obtain higher enhancements in some specific but tunable points of the structure. Recently, several designs have been proposed to solve this limit. The new designs rely on tailored long- and short-range energy transfer between nanoparticles. They include cascade amplification in aggregates of nanospheres with different sizes [18,19], quasi-periodic arrays [20], and surface plasmon lenses [21]. Furthermore, several studies emphasized the role played by the substrate in coupling adjacent nanoparticles and carrying the optical power flow, whether for SERS substrates or in plasmon waveguides [22,23]. In the following, we present a family of SERS substrates whose field enhancement was studied theoretically with the aim of using plasmon hybridization between gold nanospheres and their substrate to achieve efficient subwavelength power flow focusing. Taking an array of infinite gold nanospheres chains as a reference, we consider a geometry where the translation symmetry was reduced by isolating short chains of nanospheres. This geometry is shown to allow strong energy focusing within the central gaps. A significantly increased bandwidth of the resonance is also demonstrated for carefully tailored substrates. 2. Simulation Method and Field Enhancement
Simulation results of the field enhancement of a periodic array whose unit cell contains a chain of five aligned Au nanospheres (gold nanochains) are reported. A schematic of the studied structure is given in Fig. 1 together with a description of the relevant geometrical parameters. The spheres are of radius r 50 nm, except in Fig. 4 where we look into the dependency of the response on the sphere radius. In the general case, the periodicities in the x and y directions are p 760 nm and w 600 nm, respectively. Only in Fig. 4, where larger spheres (up to r 90 nm) were considered, the periodicity p was increased to 1 μm to allow for the spheres to fit into one unit cell. The gap in the x direction between two adjacent spheres within the unit cell is g 10 nm. With those dimensions, the array is effectively 8810
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Fig. 1. (a) Side and (b) top views of the studied structure having aligned Au spheres on an Au∕SiO2 double-layer with respective thicknesses dSiO2 and dAu . The gap g between the spheres is fixed to 10 nm, the sphere radius r is 50 nm, and the periods in the x and y directions are, respectively, p 760 nm and w 600 nm, unless stated otherwise. The structure is illuminated at normal incidence with a plane wave of wavelength λ having its electric field polarized along the x direction.
formed of isolated groups of five aligned spheres, separated from the nearest groups by a larger gap of 220 nm in the x direction and of 500 nm in the y direction. The effect of the nanochain substrate (SiO2 , Au, SiO2 ∕Au double-layer) is investigated. The SiO2 and Au layers have respective thicknesses dSiO2 and dAu and when included, the Au layer’s thickness dAu is 50 nm. The incident light is a normally incident plane wave of wavelength λ having its electric field polarized along the x direction, parallel to the aligned spheres. The simulations were done using the finitedifference time-domain technique (FullWAVE, Rsoft Design Group, Ossining, USA). The Au permittivity is the one measured by Johnson and Christy [24], and the SiO2 permittivity is that measured by Malitson [25]. Periodic boundary conditions are applied in the x and y directions, and perfectly matched layer boundary conditions are applied on the top and the bottom of the simulated domain. The grid size is equal to 2.5 nm. Accordingly, the time step τ is set to 4.8 × 10−18 s, corresponding to 1.44 nm in cT units to ensure convergence. The total calculation time T is equal to 213 τ. While random nanosphere aggregates have been widely used to obtain SERS [8], we study and optimize a family of structures whose resonance wavelengths can be tuned and field enhancement factors are larger than in random geometries. Short (five spheres) and separated chains of Au nanospheres are used instead of an infinite chain. In
this configuration, one given nanochain gathers the energy incoming on a larger surface, leading to a significantly higher enhancement maximum at the resonance. In what follows, we show which parameters govern this configuration’s efficiency. In relationship with this, we also show how the substrate design (material and thickness) influences a given nanostructure’s behavior. Metallic nanospheres illuminated by light with the adequate frequency show resonant modes, also called localized plasmon modes, which are described by analytic Mie theory [26,27]. The strength and resonance frequency of these modes can be modified by the shape, size, and surroundings of the spheres [28]. Using the configuration described in Fig. 1, we studied the role of the different geometrical parameters in order to optimize the field enhancement in the so called “hot spots,” located in the gap between adjacent spheres. Figure 2(a) shows the electric field enhancement in the vertical plane [defined in Fig. 1(a)] at the resonance wavelength λres 750 nm for the Au nanospheres deposited on a SiO2 substrate. The resonance wavelength for five aligned spheres is significantly redshifted compared to the case of a single sphere in vacuum (λres ≈ 550 nm), as a result of their plasmons’ hybridization [29,30]. The induced electric field distribution around each sphere corresponds to a dipolar mode with its dipolar moment in the x direction, as expected from the x polarization of the incoming electric field. However, the field induced by the sphere plasmons remains localized very closely around the spheres (with a range less
Fig. 2. Vertical cross sections of the jExj2 (left) and jEzj2 (right) amplitude distributions in the steady state for the Au spheres on (a) the dielectric substrate, (b) the gold mirror, and (c) the Au∕SiO2 double-layer. The distributions are shown in log scale for the resonance wavelengths [(a) λ 750 nm, (b) λ 700 nm, and (c) λ 710 nm]. The maximum values of jEj2 found in the sphere gaps of (a), (b), and (c) are 900, 4875, and 5025, respectively. The electric field amplitude is normalized to the electric field amplitude of the incoming wave.
than 50 nm). The locally highest amplification obtained is jEj2 900 in this case. With only a SiO2 substrate, however, much of the incident field flows through the surface and is essentially lost for sensing purposes. In order to trap the energy more effectively within the nanochain and obtain stronger field enhancements, we add a 50 nm thick Au layer below the Au spheres. The plasmon coupling between the spheres and the Au layer changes the resonance wavelength λres to 710 nm [29,31,32]. As seen in Fig. 2(b), the electric field enhancement all around the nanospheres and especially within the gaps is considerably stronger than for the configuration of the spheres on SiO2 , reaching up to jEj2 4875 at the resonance. In this configuration, a relatively strong electric field enters the spheres and the Au layer near the contact points. jEj within the gold spheres reaches up to three times the incident wave’s amplitude, that is, four times more than without the Au mirror. Figure 2(b) shows that if deposited over an Au layer, the Au spheres scatter the field in the z direction with a characteristic decay length greater than 200 nm and in the x direction with a characteristic decay length greater than 100 nm. In comparison, the scattered field goes to zero within a few tens of nanometers over a SiO2 substrate. This long range vertical field is thought to be created by dipolar images excited on the Au layer. However, this strong field within the metal causes Ohmic dissipation. Furthermore, the field near the Au layer’s surface is much more localized around the contact points and points to suboptimal energy transfer along the nanochain’s axis. There is a need to design the substrate to make the nanochain more efficient in transporting the energy from the outside toward the center along the contact line. With this aim in mind, we have added a 50 nm SiO2 layer between the spheres and the mirror. In doing so, a different plasmonic structure was formed since the spheres and the gold layer are no longer coupled by direct contact. However, the nanochain and the Au layer do not become independent as plasmon hybridization is still possible at a distance. Figure 2(c) shows how this transforms the nearby electric field distribution, especially in the gold layer’s vicinity. In this configuration, the plasmons at the Au layer’s surface are not localized around the contact points with the spheres, but are instead spread evenly over the whole contact line. This indeed turns out in a more efficient energy trapping around the spheres, as we demonstrate in the following. The electric field enhancement is slightly superior, reaching up to jEj2 5025, and the resonance wavelength is not changed at λres 710 nm. The surface plasmons on both sides of the gold layer partly couple. Independent far-field simulations using the rigorous coupled-wave analysis algorithm confirm that a little more light is thus transmitted through the mirror, especially in the short wavelength domain λ < 650 nm as evidenced in Fig. 3. However, the small leak is compensated by the reduced dissipation in 20 December 2013 / Vol. 52, No. 36 / APPLIED OPTICS
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Fig. 3. Reflected, absorbed, and transmitted light by the fivesphere chains on a double-layer structure with dSiO2 50 nm. The local maximum in the reflection curve at λ 710 nm coincides with the field enhancement’s resonance wavelength. More light is transmitted in the short-wavelength domain than through a plain gold layer (50 nm) or in the configuration without the SiO2 layer. An almost perfect extinction occurs at λ 770 nm.
the metal, and by a more advantageous spectral behavior. 3. Choice of the Particles’ Size and Array Periodicities
While the usage of nanochains and infinite chains leads to different field enhancement properties, our simulations (not shown here) showed that increasing the period p in the x direction led to very little change in the plasmonic behavior as long as the gap between two adjacent nanochains remains large compared to the spheres’ diameter. Keeping a distance greater than 200 nm between the latter gave satisfying results. In order to look at the effect of changing the radius of the spheres, p was increased to 1 μm in order to allow for more or larger spheres to fit into one unit-cell. For this value of 1 μm and in the case of 50 nm radius spheres, the behavior was verified to be similar to that of the reference configuration (p 760 nm). The sphere radius was found to dramatically influence the spectral behavior and the resonance amplitude. Figure 4 represents the optical amplification jEj2 as a function of wavelength for a sphere radius increasing from 25 to 90 nm, in the case of five Au spheres directly on an Au layer. By increasing the spheres’ radius, the resonance wavelength increases from 600 to 1050 nm while the field enhancement increases from 300 to 6000. This is to be compared with the much slower rate at which the resonance redshifts for a single sphere [33] and again highlights the importance of the plasmon hybridization in the nanochain. Comparing the resonance curves for the 75 and 90 nm radius gives an insight into the importance of keeping successive nanochains separated, as mentioned before. Indeed, while the resonance height steadily increases as r goes from 20 to 75 nm, it decreases instead in the case r 90 nm 8812
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Fig. 4. Electric field amplification jEj2 in the sphere gap as a function of wavelength for different sphere radii (25, 35, 50, 75, and 90 nm). For this simulation, the period p along x was increased to 1 μm to allow for larger spheres to fit into one unit-cell. The general trend is that the resonance amplitude increases with the sphere radius. However, in the case of the 90 nm radius spheres, the amplification instead decreases compared to the 75 nm radius spheres as the spheres fill the whole unit cell. The resonance wavelength steadily increases with the sphere’s radius.
where this separation goes down to 60 nm, which is small compared to the diameter. The clear dependence of the spectral behavior on the sphere radius, when combined with accurate control of the synthesized nanospheres, enables the design of the nanochains, whose resonance is tuned to the available excitation laser wavelengths for sensing with SERS. Practically, one may want to use large spheres to obtain the highest possible enhancement, while keeping the resonance wavelength near the laser wavelength. Another parameter that has to be controlled precisely to attain high field amplification is the gap between two adjacent spheres. The gap width g is here taken everywhere to be equal to 10 nm, but the electric field amplitude jEj was shown to decrease a little faster than 1∕g (over the explored range of gap widths, from 10 to 50 nm, the fitting to a power law shows a dependency as g−1.3 ). For those relatively large gaps (more than a few nm), classical electrodynamics give a good description as quantum effects in the gap, such as electron tunneling, can be neglected [17]. 4. Discussion of Power-Flow Trapping in Gold Nanochains
We now go back to the reference layout described in Fig. 1 with five spheres per nanochain, p 760 nm, r 50 nm, and g 10 nm. In what follows, we develop on why this configuration made of short chains, along with the choice of the substrate, is more favorable for SERS sensing than an infinite chain of Au spheres. Compared to the latter, nanochains achieve higher amplification with a larger bandwidth. Last, we propose an explanation for this behavior.
As mentioned before, adding a SiO2 layer between the spheres and the Au layer fundamentally transforms the geometry and the plasmonic behavior. Indeed, Fig. 5(a) shows that the field enhancement with no SiO2 layer is very different from the limit case of dSiO2 0 nm. For a thin dielectric layer (10 nm), the field enhancement is actually weaker
Fig. 5. (a) Electric field enhancement jEj2 in the sphere gap at λ 710 nm (inset for λ 600 nm) as a function of the dielectric thickness dSiO2 . When the spheres are separated from the mirror, the behavior becomes significantly different from the situation where the spheres are directly on the mirror. While the amplification is weaker with a very thin dielectric layer, it reaches a maximum for dSiO2 ≈ 50 nm. A 170 nm layer leads to a perfect extinction. jEj2 in the sphere gap as a function of the wavelength λ is shown for an array of five-sphere chains and an infinite chain deposited on (b) the gold mirror and (c) the SiO2 ∕Au double-layer. On the gold mirror, the nanochains blueshift the resonance and make the resonance stronger and sharper near λres. On the SiO2 ∕Au doublelayer, the nanochains significantly enhance the electric field in a large bandwidth.
than when the spheres directly touch the Au layer. But as the SiO2 layer gets thicker, the field amplification increases and reaches a maximum for dSiO2 around 30–50 nm, stronger than in the configuration where this layer is absent. If the layer gets even thicker, the amplification decreases and reaches a near-perfect extinction around dSiO2 170 nm. Further increase in the layer thickness results in an increase in the enhancement. At the resonance wavelength λres 710 nm, the second maximum does not reach values nearly as high as the first maximum. It should be noted, however, that for other wavelengths apart from the resonance this second maximum amplitude is actually higher to that of the first one. This point is illustrated for λ 600 nm in the inset of Fig. 5(a). This result is explained by the twofold effect of the mirror. On one hand, the Au layer leads to a short-range plasmon hybridization with the nanospheres that transform the whole plasmonic behavior. On the other hand, whatever the distance, the Au layer also reflects the incident wave which can lead to interference in the spheres’ plane. Those interferences are here revealed by the fact that in Fig. 5(a) and for similar curves realized for different wavelengths, the additional dielectric thickness between the maximum and the extinction amounts to a phase difference almost equal to π. While Fig. 5(a) only compares the maximal amplifications attained at the resonance wavelength, if the system is to be used for SERS, the variations of the said enhancement around its maximum value matter as well. Indeed, in a simple model the SERS amplification is proportional to the squared electric field amplifications at both the incident and the Raman-shifted wavelengths. As reported by Van Duyne et al. [34,35], the SERS enhancement is greater when both the excitation and Raman-shifted wavelengths are near the plasmon resonance, which typically happens when the plasmon resonance is between these two wavelengths. While the Raman shifts can be very small in terms of wavelength at visible wavelength excitation, they may reach values as large as 100 nm when the excitation wavelength is in the red or near-infrared domain. Furthermore, the choice of the excitation wavelength is usually limited to readily available fixed wavelength laser sources, so that a large excitation bandwidth may be convenient. The most important benefit of adding a thin dielectric layer between the spheres and the mirror is to enlarge the bandwidth. It also emphasizes the need of isolating the nanochains. Figure 5(b) compares jEj2 as a function of the wavelength for the nanochains and the infinite chain, without a dielectric layer. Figure 5(c) shows the configuration with a 50 nm thick SiO2 layer. In the case of a simple gold mirror substrate, isolating short sphere chains does not change the resonance curve’s shape much far from λres , but blueshifts it by 40 nm and makes it higher and sharper near the top. The increase in the maximal enhancement jEmax j2 amounts to 20 December 2013 / Vol. 52, No. 36 / APPLIED OPTICS
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25%. Furthermore, comparing the nanochains and the infinite chain with a dielectric layer shows a radical transformation of the resonance curve, as seen in Fig. 5(c). The presence of a SiO2 spacing layer plays a complex role, increasing the field enhancement for the nanochains, but decreasing it for an infinite chain. The comparison of the curves shown in Figs. 5(b) and 5(c), respectively, illustrates the real benefit of using the SiO2 layer. While the highest point of the resonance is not affected, having the same wavelength λres 710 nm, the field amplification remains high after reaching its maximum (over 90% of the peak value) over a much larger wavelength region: 75 nm in width instead of 20 nm for the direct mirror contact configuration. However, the drawback for these changes, as compared with the infinite chain, is that the field enhancement becomes more localized in some specific sphere gaps. This means that the spatially averaged enhancement will not necessarily be increased, as the infinite chain has more equivalent hot spots than multiple nanochains. We have thus observed important changes in the plasmonic properties of isolated nanochains of gold spheres placed on an Au∕SiO2 double-layer. In the following, we will propose an explanation for those changes, based on the power flow around the Au spheres. For single metallic nanospheres, optical vortices appear on both sides of the sphere [36,37]. Those vortices help to redirect the incident light from a larger area toward the sphere and trap the electromagnetic energy around it. The power flow exhibits a complex pattern with multiple singular points, whose nature and positions vary greatly with the excitation wavelength. In particular, the vortices change their direction as the wavelength passes the resonance, pointing outward for shorter wavelengths, and inward for longer wavelengths. The efficiency of noble metal nanoparticles in several optical phenomena (enhanced scattering and extinction, LSPR) is directly linked to this property, which accounts for the increased cross section as well as the energy trapping. In the configuration we studied, the same kind of power-flow singularities account for the strong energy trapping between the spheres. For the nanochain geometry, however, the energy flows around the whole chain and not only single spheres. For spheres aligned on a dielectric substrate, while the coupling between the localized plasmons is shown by the resonance redshift, the power flow is similar to a juxtaposition of those obtained for single spheres. This is different when the gold spheres are deposited on the Au layer. Indeed, the energy flows from the outside to the inside of the nanochain along the sphere/mirror contact line, as shown in Figs. 6(a) and 6(d). The incident light thus enters the structure through the gaps and on the sides and is concentrated exactly where it will achieve high amplification, i.e., in the spheres and the central gaps. This kind of substrate-enhanced energy 8814
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transfer in chains of particles has been reported before in the case of plasmon waveguides [22,23,38]. The collective resonance of the gold spheres is responsible for the energy trapping around the spheres and especially within the gaps. This power flow shows why such a difference exists between the present nanochain configuration and an infinite sphere alignment. Here, every unit-cell is designed as to absorb and focus as much incoming energy as possible toward the center. In contrast with this, an infinite line is missing an “entry point.” Furthermore, an infinite line does not possess a well-defined center (every sphere being an inversion center), while in the present case the energy is concentrated toward the center of the nanochain, the field amplification being significantly higher in the central gaps than in the border ones. Another weaker mode usually exists where the opposite happens, but the two resonances are separated by hundreds of nanometers and hardly overlap. When a 50 nm thick SiO2 layer is added [Figs. 6(b) and 6(e)], the power flow at the resonance shows two clear optical vortices around the second and fourth
Fig. 6. Poynting vector in the vertical (left) and the horizontal (right) planes passing through the spheres’ centers. Parts (a) and (d) represent the spheres directly on the gold mirror, (b) and (e) represent the situation with a 50 nm thick dielectric layer, and (c) and (f) the situation with a 170 nm thick dielectric layer (λ 710 nm). For the two first cases, which achieve high field amplification, the vertical view shows how the energy flow is focused from the sides toward the spheres and the gaps. The horizontal view also shows how the energy is focused toward the spheres, from the whole unit-cell surface. With the presence of a 50 nm dielectric layer, we see in (b) that optical vortices and saddle points effectively trap the incoming energy in the vicinity of the nanochains. When the dielectric thickness further increases to 170 nm (corresponding to the extinction wavelength), two additional vortices are formed in the dielectric, thus redirecting the energy flow outward of the spheres as seen in (c).
spheres. As the energy flows in one direction around the sphere, a second optical vortex in the opposite direction appears within the sphere, following the conservation of topological charge [39]. Furthermore, the energy flow within the dielectric layer is strong, the mirror’s surface plasmons being efficient at transporting energy. A small fraction of the incoming energy is transmitted to the other side of the mirror, secondary surface modes being excited on the backside. However, as the log scale figure shows, most of the energy is trapped and flows around the side spheres. This is made visible by the presence of three saddle points just over the spheres which separate the energy flowing out of the gap, one part being reflected and the other redirected to flow around the spheres. The effect of the number of spheres for the SiO2 ∕Au double layer is investigated in Fig. 7. It is found that improved electric field enhancement
is realized for all the short nanochains, the case of the infinite chain giving the smallest electric field enhancement. The maximum field enhancement wavelength is redshifted as the number of spheres increases, going to a maximum corresponding to the infinite chain. This is in agreement with numerical calculations done using the hybridization method by Nordlander et al. [30] generalized with an increasing number of spheres. When the dielectric layer is 170 nm thick [Figs. 6(c) and 6(f)], however, the field amplitude in the sphere gaps goes to zero. In terms of the Poynting vector field, two optical vortices (one on each side) appear within the SiO2 layer. The optical vortices inverse the energy flow direction: while the energy still flows inward near the Au mirror, it flows outward next to the spheres. The power flow in the horizontal plane containing the middle of the spheres is also completely different from the two other cases. Both figures show how the spheres “repel” the power flow instead of attracting it. The energy flows out of the spheres and not toward them, and the overall amplitude is strongly reduced. As a consequence, the structure with a 170 nm thick SiO2 layer realizes the exact opposite of the energy trapping of the 50 nm dielectric structure. 5. Conclusion
We investigated the field-enhancement properties of a family of nanostructures for use as a SERS substrate with a finite-difference time-domain technique. The studied nanostructures consisted of a periodic array whose elementary cell contains a short chain of Au spheres over a SiO2 and Au layers, and a SiO2 ∕Au double-layer. We studied what parameters lead to a high field enhancement within the sphere gaps. We showed that larger spheres generally lead to a higher field enhancement, but that keeping an open space between two adjacent sphere nanochains is important for the structure’s efficiency, as in the limit of an infinite chain efficiency is reduced. Next, simulation shows that rather than placing the gold spheres directly on an Au mirror, inserting a dielectric layer between the spheres and the mirror leads to a stronger enhancement over a larger wavelength region. Finally, we showed how the Poynting vector field clearly reveals light trapping by the nanochains on the SiO2 ∕Au double-layer, accounting for the efficient field enhancement as compared to random substrates in general, or even Au sphere nanochains over a simple Au mirror. References Fig. 7. Effect of the number of spheres in the nanochains on (a) the electric field amplification jEj2 and (b)–(g) the Poynting vector in the horizontal planes passing through the spheres’ centers. Part (g) corresponds to the infinite chain. The results are shown for the case of the SiO2 ∕Au double-layer with a 50 nm thick dielectric layer.
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