A novel surface-enhanced Raman scattering (SERS) excitation source based on focusing of surface plasmons around the center hole of a metal disk for cascaded enhancement is put forward and studied theoretically. The device offers intense SERS excitation with quasi-uniformity and horizontal polarization over a comparatively large hole through the combination of electromagnetic field focusing and hole plasmon resonance. As revealed by finite-difference time-domain (FDTD) method, the intensity spectra and the characteristics of the near field for the wavelength range of 650-1000nm exhibit a number of enhancement modes. Electric field intensity of the optimal mode enhances the SERS signal inside the hole by over four orders. An analytical model was also developed to gain precise interpretation on FDTD results. Our model also reveals the possibility of achieving eight orders of enhancement by optimizing the scale of the disk. In addition to generation of highly optimized hot spots, the large active hole also offers potential applications in fluorescence enhancement and nonlinear spectroscopy.
© 2009 OSA
Surface plasmon polaritons (SPPs) are electromagnetic waves that propagate along the surface of a noble metal via fluctuations in electron density . In the last decade, SPPs effects gained widespread attention for their potential application in photonic devices, sensing [2,3], surface-enhanced fluorescence [4,5], and Surface-Enhanced Raman Scattering (SERS) [6,7]. The SPP excited on metal nanostructures has been shown to generate enhanced electromagnetic (EM) field. It is generally accepted that SPP or localized surface plasmons (LSP) are primarily responsible for SERS, which is proportional to the fourth power of the local EM field . The pioneer achievement in SERS is the Single Molecule SERS (SMSERS) which in some cases allows for vibrational spectroscopy down to the single molecule detection limit [9,10]. Although SMSERS is an exciting detection technology, it can be achieved only in several kinds of molecules  with the assistance of either surface-enhanced resonance Raman scattering (SERRS) or cascade enhancement effects . In order to achieve SMSERS more readily in simple arrangements, one need to further increase the EM enhancement factor to a sufficient level. To boost EM SERS enhancement, many efforts have been directed at the development of novel SERS substrates. The use of dimmer gaps, including the closely spaced metal nanoparticles [13,14], the bowtie structure , are commonly believed to offer sizeable EM SERS enhancement.
In addition, it has been reported that the cascade effect plays an important role in achieving extremely large enhancement factor  especially for SMSERS. Recently, experimental results revealed that the combined hole-nanoparticle system provides an enhancement factor even higher than that obtained through conventional metal-nanoparticle aggregation . To a certain extent, this can be seen as supporting evidence for the cascaded enhancement effect. Here we demonstrate that by integrating a plasmonic lens  and a hole, thus forming a hollow metal disk, the EM energies of SPPs can be focused to produce an excitation source. The width of this excitation source is about , and it can lead to an additional increase of EM SERS enhancement by more than four orders of magnitude from the linear cascade effect. The optimal enhancement mode is mainly attributed to two effects, namely focusing electromagnetic (FEM) enhancement and hole plasmon resonance (HPR) enhancement [18,19]. FDTD and analytical results are presented to demonstrate its performance. The analytical model also reveals that the SERS enhancement factor can be as high as eight orders if we further optimize the geometry of the hollow disk. Compared to the cases of focusing using plasmonic lens  or SPPs excited by radial polarization , which may produce hot spots directly, the spatial excitation source reported herein is more suitable for generating the hole-nanoparticle system for further incorporation of nanostructures to provide cascaded enhancement because of its uniform field distribution and horizontal polarization. The central hole region readily provides a very convenient area for incorporation of additional nano-structures for further applications that take advantage of the uniformly distributed high EM field intensity produced by the condensed SPP energy.
2. Geometry and the FDTD setting
The structure of the hollow metal disk is shown in Fig. 1 .
A hollow gold disk is fabricated on the surface of a silicon substrate. The refractive index of silica is 1.51. The circular hole at the center of the gold disk has a diameter of , which is optimally selected for the best coupling efficiency at the vicinity of 800nm , namely the middle of the 650-1000nm region. The hollow metal disk is illuminated by a normal incident light from air, with polarization along the Z axis and unity amplitude. We use FDTD method to simulate the EM response of our device. In our simulation experiments, the dielectric function of gold is described by the Debye equation,22]. In the 650-1000nm wavelength region, the experimental data reported by Johnson and Christy  fit quite well with Eq. (1). The parameters with values , , s, S/m obtained from this fitting procedure can be used directly for incorporating dispersive characteristic of the material used here. In the simulation, we calculate the EM spectral response of a certain point in the metal structure by two steps. First, the object is illuminated with a modulated Gaussian pulse that contains the wavelength range of interest. From this step, we obtain a damping oscillation curve that traces the time-evolution of the near field amplitude for the interest point. This curve is the superposition of many components induced by various incident lights of different frequencies (i.e. wavelengths) in time domain. To obtain the EM spectral response in frequency domain, in second step, we perform Fourier transform to the time domain result, and take the weight of each frequency in the pulse into consideration. The final plot reveals the EM spectral response with the different wavelengths for the interest point. This approach enables us to find the exact EM intensity peak for the interest point. Further calculation of the specific near-field amplitude at those peak wavelengths again reveals that this approach leads to an error less than 5%. Input parameters including which mesh size (10nm), stimulation dimension ( rectangular boxes), number of Perfectly Matched Layers (8 layers) and convergence degree () are chosen carefully to ensure that simulation results are of acceptable accuracy. To test the validity of our simulations, we have reproduced reported results obtained from a plasmonic lens , which has a structure similar to our hollow metal disk.
3. Simulation results and discussion
Using the approach described in Section 2, intensity distribution and spectral properties of the proposed device are obtained.
Figure 2 shows the intensity spectra of the steady amplitudes of at the center of the hole for various disk sizes. A series of sharp peaks are present in the plots because of the formation of different enhancement modes. Because smaller hollow disk will support SPP with lower near-field optical intensity (this issue will be addressed in later sessions), the interference between directly transmitted light through the gold film and the SPP in the hollow disk will play a major role as compared to the interference between SPPs . This situation leads to the detuning of the interference wave from the SPPs, and some of the enhancement modes will disappear gradually with decreasing disk size as shown in Fig. 2 (b). At the optimal enhancement mode of peak wavelength 793.3nm, the FDTD result of the near field distribution nearby the hole is shown in Fig. 3 (a) (b) (c). Figure 3 (a) (b) (c) indicate that the total electric field of the excitation source is mainly composed by , which indicates that the origin of the high field region is primarily coming from the direct interplay of plasmonic positive and negative charges around the hole. Because of the mirror symmetry distribution of the plasmonic charge along the Z axis, approaches zero in the whole space, and approaches zero in the center of the hole. The excitation source in the hole is relatively larger with a horizontal polarized uniform field, which is different from the case of focal point generated by a plasmonic lens  or the SPP excited by radial polarization  with the vertical near-field as the main component. Furthermore, the decay of the electric field inside the hole for hollow disk is shown in Fig. 3 (d), which shows remarkably uniform distribution and thus indicating an important attribute for a range of potential applications such as SERS, biosensing, non-linearity studies etc [25,26]. The uniform polarized field long Z axis, especially in the central region, can be attributed to the focused circular distribution of the charge.
When SERS active clusters are placed inside the hole, negligible perturbation of the focusing effect and its linear response can be assumed if the total diameter of the clusters is much smaller than that of the hole. We found that for the hole, the condition for linear response is that the attached particle or cluster is less than 60nm. In Fig. 3 (e) (f) (g), we present an example of maintaining the linear response from the quasi-uniform focusing source even after the incorporation of a gold nanoparticle with diameter 50nm. To ensure that our simulation is of acceptable accuracy, we use the subgridding algorithm with a Yee cell size of so that the unit cells are much smaller than the naonoparticle feature sizes. For a hollow gold disk with and at the optimal enhancement wavelength about , the maximum electric field amplitudes of the isolated gold nanoparticle on the silica substrate, and the combined source-nanoparticle system, and , are 3.64 and 14.80 respectively. The electric field amplitude of the isolated excitation source at the central point of the hole is 4.18. The linear amplification is fulfilled with reasonable agreement. Because of linear amplification, optimal enhancement mode occurring at 793.3nm, as shown in Fig. 3 (a) (b) (c), results in an electric field enhancement factor of about 16.4, which corresponds to an additional SERS enhancement factor of . At 830nm, a wavelength commonly used by semiconductor lasers, one can still obtain an additional SERS enhancement factor in the order of .
One origin of the enhancement modes is the HPR enhancement effect. As schematically illustrated in Fig. 4 (a) , steady-state near field patterns show that the energy of the excited SPP is mainly located in the silica substrate, which indicates that the enhancement mode is mainly due to HPR generated from the SPP in the substrate. We have found from various examples that the skin depth of light will increase the effective size of the hole . The skin depth is at first not clear from the illustration of component because it is overlapped with the first order interference fringe encircling the hole. However, the component can reveal the skin depth as shown in Fig. 4 (b). We found an empirical formula that the HPR occurs when half wavelength of the incident light equals to the effective diameter of the hole, , where is the skin depth, and r is the radius of the hole, the numerical factor 0.83 has the same origin as described in Ref .
To interpret the fringe patterns around the hole at the enhancement mode (i.e. under the HPR condition) will not only lead to better understanding of the near-field distribution, but also provides information on the role of FEM in the over enhancement process. As the case in plasmonic lens , the edge of the hollow metal disk can be considered as a line of SPP point sources. At the interface between semi-infinite planar gold surface and dielectric material, the wavelength of the SPP varies with different exciting wavelengths according to the dispersion curve of the gold film expressed as  , where is the SPP wavelength, is the wavelength of the incident light in vacuum, and , are the permittivities of the medium and gold, respectively. In the case of the metal film, for the Fano modes (i.e. the symmetric leaky and the antisymmetric bound mode), 50nm thickness is about the cutoff of the symmetric bound mode, which means both surfaces of the gold film can support SPP modes . The SPPs excited from both the inner and the outer edge interfering with each other create a series of convergent interference fringes. During resonance, the disk contains 2N interference fringes. For , N varies from 15 to 23 as is labelled in Fig. 2 (a). In our FDTD result, the electric field profile of the component gives the information of the space charge distribution and the SPP wavelength. For instance, in Fig. 4 (a), for incident light with wavelength , the upper and lower fringe periods are 262.5nm and 410.9nm respectively, which coincide with half of the SPP wavelength and at the interfaces of the gold film with the silica substrate and with air. Figure 4 (c) shows the interference pattern inside the silica substrate at a distance of 10nm from the gold-silica interface.
Due to polarization effects, only those portions of the circle where a polarization component of the incident electric field is perpendicular to the circle edge will excite SPPs. The flow directions of the SPPs are normal to the circular edge. Assuming that the hole in the upper interface is centered at the origin, and the Z-polarized incident light comes from the air at normal angle, the amplitude of the electric field at a point P in the hollow disk is the sum of the electric fields from two counterparts of the disk rim and the rim of the hole28], but with important remodeling to represent the more complex situation as presented here, the amplitude of each E in Eq. (2) takes the form ofFig. 5 , R is the radius of the disk, r is the radius of the inner hole and , which appears in , is the angle from the positive Z axis to account for the polarization of the incident light. The electric field of a plasmon point source is quantified by . The fitting parameter C is the coupling efficiency of the incident light to SPP via diffraction from the corner of the circumference edge, and it also involves the weight generated from changing a sum to an integral in the numerical calculation. The radius R of the disk is employed in the first term to account for the density of the SPP source which is proportional to the circle circumference. The last two terms are used to described the field distribution of the SPP, and the SPP characteristic parameters, and , are the decay length and the penetration depth respectively. Here the = 30nm , and the calculated values for SPP in Au film are obtained from the literature , and the values varies from ~ to ~ as a function of wavelength. When the SPP source and the point of interest P are separated by the vertical axis (i.e. the straight dash line in Fig. 5), the model reported in Ref . will run into trouble due to scattering of SPPs by the central hole. In view of the similarity between the plane SPP and the plane wave in their 2D propagation characteristics, the use of the Huygens’s principle [30,31] to describe the superposition of the electric field is physically acceptable.
As shown in Fig. 5 (b), in the spirit of the Huygens’s principle, a circular wavefront will form from superposition of the circular wavelets emerging from the edge. The wavefront will maintain its circular shape in the system because of the shape-matching characteristic of the center hole but a phase shift will be added to. The incident light induced phase difference π between both and is also taken into consideration. The inset in Fig. 5 (c) illustrates the integral interval βof the SPPs emerging from the edge of the hole. Figure 6 shows the FDTD result along the Z axis with the calculated intensity from Eq. (2). Compared to FDTD results, our analytical model has produced a small phase shift ranging from 0.06π to 0.22π, which can be expected in real physical situations due to the fact that opposite charges are induced on opposite rims of the hole during resonance under HPR conditions, while the size of the hole is just larger than half of the SPP wavelength.
Owing to the low reflection coefficient of the SPP , we have neglected multiple reflections from the edge. This may introduce slight deviations between the FDTD and analytical results near the disk edge. The coupling between SPP1 and SPP2 also results in some deviations. However, the two aforementioned deviations are not significant near the hole, where the intensity calculated from the analytical model matches very well with the FDTD one. Both models confirm that expected result that the peak size is approximately proportional to the intensity of the focusing induced field in the hole. Therefore, for the disk with various diameters, at the enhancement mode, the electric field induced from FEM in the hole can be derived from Eq. (3). It is proportional to , where is the circle circumference of the disk, and quantifies the propagation loss of SPP. The electric field in the center of the hole can be expressed as, where A is a complicated function of different incident light, which will play the role as a fitting parameter when fitting to the FDTD result, and the constant B is the intrinsic electric field contributed by the HPR of the hole and the transmitted field of the incident light. Although Bis still unevaluated, one can obtain a plot which can predict the values of the electric field for different diameters by fitting the derivative of E(i.e. the slope of the curve) to the slope of initial section of the curve given by the FDTD calculation. Figure 6 (d) shows the final results of the optimal enhancement modes for different diameters with the hole diameter .
It is found that the FEM enhancement will be boosted by increasing the circumferences of the disk, while an optimal size also exists due to the attenuating effect resulted propagating loss, which occurs as a competitive process. FEM enhancement creates an extraordinary intensity of electric field much higher than that in single nanometer hole in gold film which only supports the HPR enhancement [33,34]. The maximum enhancement factor ~160 occurs when the diameter equals to. This value is reasonable in view of the decay length can reach to at about. This robust enhancement corresponds to eight orders additional SERS enhancement on the premise of linear response of the attached SERS-active site. Note that the linear response area (about 60nm as above stated) is already suitable for containing SRES-active sites such as single-nanoparticle , aggregated nanoscale metal nonoparticles, clusters of metal nanocrystals , and especially the metal dimmer. As a rule the SERS-active site must have a strong plasmon resonance. The dimmer of the metal nonosphere or nanoshell will be a good candidate because their local surface plasmon resonance (LSPR) is tunable around the optimal enhancement wavelength 793nm [36–38]. Even though the hypothesis of linear response becomes somewhat weakly satisfied when the inner attachment exceeds a certain size or LSPR has taken place, considerable enhancement of the SERS signal still should be expected from the optimized excitation source. Further experimental and theoretical studies are necessary to explore this point. Moreover, if one further optimizes the design to incorporate the substrate effect  or grating structure around the disk , performance of the device will become tunable to serve a range of application requirements.
In conclusion, we have theoretically studied the generation of excitation source via focusing of surface plasmons in a hollow metal disk. The peaks in the intensity spectra of the total electric field and the uniformity of the near-field spatial distribution indicate that the hollow metal disk can act as a field source for cascade enhancement of SERS which may offer an additional enhancement by a factor of 104. On the premise of linear response coming from the attached SERS-active sites, the optimal enhancement mode is mainly attributed to focusing electromagnetic (FEM) enhancement and hole plasmon resonance (HPR) enhancement. Analytical model gives an explicit picture of the two physical mechanisms and reveals that the enhancement can be increased to eight orders by optimizing the scale of the disk. Most importantly, with the advent of nanofabricating technology, the feature size required by this excitation source will be well suited for the incorporation of particle aggregates or even tailor-made nanostructures to create highly optimized SERS hot spots. It is anticipated that the proposed hollow plasmonic disk design may lead to high performance SERS devices, especially for the SMSERS. Given its simple fabrication requirements, one can readily use the device in a two-dimensional format for high-throughout SERS micro-array applications as well as a range of other potential applications such as surface-enhanced spectroscopy, fluorescence enhancement, nonlinear spectroscopy, and other plasmonic resonance based biosensors.
The authors would like to acknowledge the financial support from an RGC Central Allocation Grant (HKUST 2/07C), which provides a research studentship (H. X. Zhang) for this project, and a RGC CRF Grant (CUHK 411208), which funds the arrayed biosensing initiatives of this project.
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