The behavior of the electromagnetic field interaction with gold nanotriangles organized in bow-tie arrays is investigated. A side-by-side comparison between the measured absorbance of the array and the modelled integrated electric field resonances confined around the gold structures is presented and discussed to explain the spectral shift between both parameters. Finite difference time domain calculations and Raman measurements of gold triangles of different sizes and periodicity are systematically performed. Numerical calculations show that the spectral maximum of the electric field varies in distinct areas over the metallic structures.
© 2014 Optical Society of America
Plasmonic structures have shown a large potential for a variety of applications in optics and spectroscopy [1, 2]. The frequency of the surface plasmon is dependent on all opto-geometric parameters associated with the structure, including the shape, size, refractive index of the structure and the surrounding environment . One of the advantages of using surface plasmons is the ability to generate an intense electromagnetic field confined at the interface formed by a metal and its dielectric surrounding. This localized surface plasmon resonance (LSPR) directly influence the optical properties of the surrounding material such as its absorption and non-linear response [4, 5]. For surface-enhanced Raman spectroscopy (SERS) experiments , the field enhancement originating from the LSPR can significantly increase the Raman signal from the molecules located in the vicinity of the metallic nanostructure. Noticeably, McFarland et al. show that the maximum SERS signal is observed when the EM enhancement is not coincident with the laser excitation wavelength . This implies that the maximum of the electric field induced by the irradiation does not occur at the same frequency as the experimentally determined absorption maximum of the nanostructure. It is therefore necessary to know the electric field intensity spectrum. In order to find the latter, a spectroscopic technique measuring the absorbance of a given structure is often used; this is not necessarily accurate since spectral shifts (usually a red shift) between absorbance and electric field may be observed. This red shift of the near-field peak energies with respect to the absorption has been investigated phenomenologically . Recently, J. Zuloaga et al. showed that the magnitude of this shift depends directly on the total damping of the system, whether it is intrinsic damping within the metal of the nanoparticle or radiative damping of the localized plasmon . In the present study, we investigate this spectral shift using several approaches including side-by-side comparison of the experimental absorbance spectrum and calculated electric field intensity spectrum as well as SERS measurements for a series of gold nanotriangles organized in arrays of bow-tie assemblies.
2. Results and discussion
An array of nanotriangles organized in bow-tie assemblies was made on a glass coverslip substrate by electron-beam lithography using the same procedure described in our previous work . The final device results in metallic nanotriangles arranged in bow-ties assemblies all directed along the same axis as shown in Fig. 1(a). Arrays of bowtie assemblies were made, with a length of triangle side L between 80 and 140 nm, a gap G between the opposed triangles of 0–150 nm, periodicities in the range of 400-2000 nm and 200-2000 nm for Px and Py respectively, and thicknesses of 3 and 25 nm for titanium and gold, respectively. Typical curvature radius of the individual triangle apices varied between 12 to 35 nm. This variation of geometrical parameters allows one to tune the wavelength of the LSPR between 600 to 800 nm. An optical setup was designed to measure absorption spectra over a circular area of 60 micron diameter. Briefly, an optical fiber connected to a halogen lamp illuminates the top of the sample through a polarizer and a collimating objective. The transmitted light was collected via an objective (x20, 0.5 N.A.), dispersed by a 600 gr/mm grating and detected by a CCD camera. The intensity of the transmitted light through each sample has been divided by the intensity of the source and each spectrum was normalized. The absorption of these metallic arrays was measured and compared to Finite Difference Time Domain (FDTD) modeling . FDTD, which rigorously solves Maxwell’s equations, is a method that calculates the electromagnetic field versus time and position, yielding the optical properties of the plasmonic structures. We modeled the gold nanotriangles arrays on a glass substrate using the SEM images obtained from the structures in order to keep the shapes as close as possible to those obtained experimentally. The values of optical indices for gold and titanium, were fitted on the visible spectrum in the 400-900 spectral range . Our simulation zone presents periodic conditions in the x and y directions and an infinite array of structures is considered. Along the Z direction, boundary conditions are perfectly matched layer (PML) which absorb all waves moving towards the exterior of the simulation zone (up and down) without reintroducing reflection. Air is the surrounding medium with a permittivity of 1. The light source is a plane wave polarized along x-axis or y-axis. After convergence test, the space-mesh size depends on the triangle size with a maximum size of 1 nm at the gold interface. The criterion of convergence is reached when the energy in the volume of the simulation zone drops down to 10−5 multiplied by the injected energy. Absorbance is specifically calculated here and compared directly to our experimental measurements. Figure 1(a) shows normalized absorbance measurements of structures composed of triangles with L = 140 nm, G = 100 nm and Px = 500 nm and Py = 200 nm. Two polarizations were used: along the X-axis or the Y-axis. Measurements are compared to the FDTD calculations and a good correlation is observed. The modeled field is always shifted towards smaller wavelength and the quadrupolar resonance is underestimated compared to the dipolar resonance (leading to a low calculated normalized absorbance between 500 – 700 nm). Several calculations were made with distinct sizes, gaps and periods in order to validate our optical model and a good agreement between calculated and experimental absorbance was obtained. Two resonances are generally observed in the absorbance spectra. At 𝜆 = 580 nm, the maps of the polarized electric field enhancements in logarithmic scale [Figs. 1(b)-1(c)] show that the enhancements are located along each side of the triangles, corresponding to the quadrupolar resonance.
Resonances at 𝜆 = 750 nm and 𝜆 = 800 nm corresponds to the dipolar contributions; the intensity maps in Figs. 1(d) and 1(e) shows that the normalized electric field resonances are located close to the corners, in agreement with previous work . The logarithms of the magnitude of the electric field enhancement at the dipolar resonance (1.3 for x-polarized and 1.6 for y-polarized) are larger than those obtained for the quadrupolar resonance (0.8 for x-polarized and 0.9 for y-polarized). The smaller gap between triangles along the y-axis (60 nm) compared to 100 nm along the x-axis leads to a larger increase when the polarization is along the y-axis. It appears that the dipolar resonance can be shifted in the range 𝜆 = 650 – 800 nm by changing the L parameter in the range of 80 – 140 nm. This range is adequate for an excitation with a 785 nm laser. Increasing the gap size G, leads to a decrease of the resonance wavelength up to 30 nm. For SERS measurements, the gold arrays are functionalized with a thiolated molecule. The length of these molecules is typically small (i.e. 1-2 nm) and can interact solely with the electric field confined in an area close to the gold nanoparticles. The electric field intensity was integrated in a volume delineated by a triangular monitor superimposed on a gold triangle using a monitor larger than the gold triangle (equal to the length of the particle plus 10 to 50 nm along the x and y axis, and equal to the thickness of the particle plus 10 to 50 along the z axis).
Figure 2(a) shows that the behavior of the electric field intensity is independent of the volume of the investigated zones. It is noteworthy that the electric field enhancement spectra and the absorbance spectra do not match exactly. The maximum of the electric field is obtained for a wavelength that is red-shifted compared to the maximum of absorbance. This factor is of importance in order to optimize SERS substrate and the sole use of the absorption spectra can be misleading. The spectral position of the maximum electric field intensity depends on its location within the simulated zone. In order to investigate this aspect, we have performed a series of calculations to determine the wavelength at which the maximum of the electric field intensity occurs for every mesh point. Figure 2(b) exhibits the map of the intensities for the same triangles discussed in the previous paragraph. The variation of this wavelength as a function of the position within the structure is clearly depicted in the color coded map in Fig. 2(b). For an input polarization along the x direction, two resonances clearly appear at 610 nm (along the Y-axis) and 720 nm (along the X-axis) corresponding to the quadrupolar and dipolar resonances, respectively. In Figs. 1(b) and 1(d), we can note the same behaviour even if the length of the particles is different: quadrupolar resonance is localized along the Y-axis while dipolar resonance is along the X-axis. The quadrupolar resonance is not usually along the Y-axis, but in the case of small periods (Px and Py), a coupling between the adjacent structures is possible. Therefore, the quadrupolar resonance leads to an electric field higher than the dipolar resonance for some specific positions. Using the simple case of a metallic nanosphere in air, a spectral shift between absorption and integrated electric field is also obtained [8, 9]. Such ideal structure allows one to understand the difference between absorption and scattering of the plasmonic structures originating from the complex part of the polarizability. The scattering cross-section, the absorption cross section of a metallic nanoparticle and the polarizability α are defined by Eq. (1).14]. The phase shift between the scattered and the transmitted fields lead to the appearance of destructive interferences, which reduce the electric near-field intensity when the absorption, and thus the imaginary part of the polarizability, is large [Figs. 3(a)-3(b)]. It is noteworthy that the complex polarizability also depends on the optical indices of the probe molecule adsorbed at the surface of the metallic nanoparticle. Therefore, if the molecule located over the plasmonic platform absorbs light (i.e. a non-null extinction coefficient), the polarizability and then the spectral shift between absorption and electric field enhancement should increase as shown in Fig. 3(c) when k varies from 0.01 to 0.2 keeping n = 1.0.
SERS spectra were measured on gold triangles functionalized with 4-nitrothiophenol (4-NTP). 1.5 mg of 4-NTP was dissolved in 10 mL of 100% ethanol. Each sample was placed in the solution during 24 hours, washed in ethanol and dried with nitrogen just prior to optical measurements. A 785 nm laser was focused with an intensity of 1 mW on the sample using a x100, N.A. 0.9 objective. The acquisition time was 10 s per spectrum. For every pattern, 5 measurements were done at several locations. The background was approximated with a polynomial law and subtracted. Figure 4(a) shows the Raman signal obtained on 4 different lengths, L: 80, 100, 120 and 140 nm, with G = 100 nm and a polarization along the X-axis. In order to keep a filling factor (FF) close for each pattern, we adopted the period: Px = Py = 400 nm for L = 80, 100 nm and Px = Py = 500 nm for L = 120, 140 nm, leading to FF of 4%, 5.5%, 5% and 6% for L = 80, 100, 120 and 140 nm, respectively. The FF corresponds to the percentage of the surface covered by gold. The Raman spectra of 4-NTP are consistent with literature . The main spectral features observed in Fig. 4(a) at 1077, 1107, 1333 and 1571 cm−1 (noted 1-4 on Fig. 4(a)) are assigned to ν7a coupled with C-S stretching, νϕ-N, νsNO2 and ν8a, respectively. Upon irradiation, the peaks at 1138 cm−1, 1388 cm−1 and 1430 cm−1 (noted 5-7 on Fig. 4(a)) correspond to C-N symmetric stretching, R-N = N-R stretching and C-H in-plane bending modes, respectively, and can be assigned to the formation of 4,4′-dimercaptoazobenzene (DMAB) possibly generated by plasmon mediated catalytical reaction . Nevertheless, irradiation time and the laser intensity were always the same for each structure. It is noteworthy that 4,4′-DMAB is more easily observable in the case of a pattern with triangle of 120 nm of side length although 4-NTP peaks are still more intense. However, Fig. 4(b) shows absorbance measured on identical patterns of nanotriangles. The excitation at 785 nm and the spectral Raman range up to 900 nm that corresponds to ~1700 cm−1 are indicated. Based on this figure, the triangle with a size of 140 nm should lead to a better SERS activity because its absorbance is higher above 785 nm. Nevertheless, the calculation of the electric field intensity around the gold nanotriangles [Fig. 4(c)] predicts a higher intensity in the range of characterization (785 – 905 nm) for triangle with L = 120 nm. The strongest SERS enhancement occurs under conditions where the incident and Raman scattered photons are both strongly enhanced . For L = 120 nm, the maximum of the integrated electric field intensity is centered in the range of Raman characterization, which allows to fill this criterion, unlike for L = 140 nm. This correlates the observations on the Raman spectra: L = 120 nm lead to a better SERS platform at an excitation wavelength of 785 nm, showing again the gap between absorbance and electric field intensity.
In this work, we have showed experimentally that a spectral shift between the maximum of absorbance and the maximum of the electric field intensity was generally observed in anisotropic metallic structures. The FDTD method can be used to predict the electric field enhancement spectrum which should be used primarily to select plasmon resonance with respect to a given excitation wavelength. This spectral shift can be due to destructive interferences between the scattered and the transmitted field.
The authors wish to gratefully acknowledge the Nanofabrication Facility at The University of Western Ontario. This research was funded by the Sciences and Engineering Research Council of Canada Discovery Grant and by the Canada Research Chairs program.
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