Identification of Multipolar Surface Plasmon Resonances in Triangular

Jun 11, 2009 - The DDA method was first introduced by Purcell and Pennypacker(38) and then, developed by Draine and Flatau.(36) The approximation ...
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J. Phys. Chem. C 2009, 113, 11597–11604

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Identification of Multipolar Surface Plasmon Resonances in Triangular Silver Nanoprisms with Very High Aspect Ratios Using the DDA Method† Peng Yang, Herve´ Portale`s, and Marie-Paule Pileni* UniVersite´ Pierre et Marie Curie, UMR 7070, LM2N, 4 Place Jussieu, 75005 Paris, France, and CNRS, UMR 7070, LM2N, 4 Place Jussieu, 75005 Paris, France ReceiVed: February 11, 2009; ReVised Manuscript ReceiVed: April 24, 2009

The extinction spectra of 5-nm thick, triangular silver nanoprisms are calculated using the discrete dipole approximation (DDA) method. The calculations are proved to accurately converged by satisfying the usual criteria related to the applicability of the DDA. The ultrathin thickness of the nanoprisms considered here has the advantage of making it possible to largely tune their aspect ratio (AR) from 5 to 40, and simultaneously limit all their dimensions below the wavelength of the incident light. For nanoprisms with AR g 15, several intense bands are observed. These bands correspond to the well-known, in-plane, dipolar surface plasmon resonance (SPR) and several multipolar modes emerging at higher energies. Because of the high AR of the nanoprisms considered in this work, the multipolar SPR are particularly well observed, thus making it possible to examine them in detail. The calculated extinction spectrum shows a clear dependence on the edge length, the thickness, the aspect ratio and the volume of the nanoprism. The evolution of the extinction spectrum when simulating the presence of a substrate is also investigated as well as that induced by changing the size of the truncation in snipped nanoprisms. The qualitative agreement of the presented simulations with previous experimental observations made by other groups confirms the ability of the DDA method to predict the optical properties of such ultrathin triangular nanoprisms. 1. Introduction The special optical behavior of metal nanocrystals results from the interaction of their free conduction electrons with the incident light.1 The surface plasmon resonance (SPR), which is shown by the emergence of an intense band in the extinction spectrum, arises when the oscillating electric field of the incident light resonantly couples with the conduction electrons making them collectively oscillate at the same frequency. The SPR spectra of noble metal nanocrystals have been demonstrated to markedly depend on the structural characteristics of the nanocrystals such as their size and shape,2 as well as their external dielectric environment.3 Detailed information on how all of these parameters can influence the optical properties of nanocrystals is crucial in order to use the surface plasmon resonance (SPR) of these nanocrystals for various applications such as those developed in optics,4-6 surface enhanced Raman spectroscopy (SERS),7,8 biosensor,9 and medical diagnostics.10-14 Several groups have developed new syntheses to produce triangular nanoparticles, also called nanodisks or nanoprisms, with various truncations and aspect ratios.8,9,15-22 They showed that the SPR spectra of these nanoparticles are highly sensitive to all the aforementioned parameters.9,15-17 Most of these experimental data were supported by simulations based on the discrete dipole approximation (DDA) method in order to assign the various bands observed in the SPR spectrum, as it has been already reported for silver and gold nanoprisms.4,15,23-26 Among all of these bands, the most intense corresponds to the in-plane dipole resonance. The extreme refractive index sensitivity of its energy was recently pointed out as the highest yet measured for nanoprisms.15 The other bands, which are assigned to higher †

Part of the “Hiroshi Masuhara Festschrift”. * To whom correspondence should be addressed. E-mail: pileni@ sri.jussieu.fr.

multipolar resonances, exhibit much weaker intensity and suffered of quite poor investigation until recent past. From all the previously reported experiments, it can be stressed that the proper observation and identification of the multipolar SPRs of triangular nanoprisms often remain difficult or uncertain because of the low intensity and partial superimposition of the corresponding bands. Some way to go beyond such a limitation consists therefore in looking for nanoprisms with very high aspect ratios. In a previous work,25 the Schatz’s group reported theoretical studies on the optical properties of gold triangular prisms with various edge lengths and widths and a maximum aspect ratio of 40. Multipolar excitations were assigned to different in-plane plasmon modes up to the third order of a multipole expansion through the corresponding vector polarization plots. In another theoretical work,24 Y. He and G. Shi have graphically assigned the SPRs of thin silver nanoprisms. In spite of the previous studies, it is worth to note the current lack of results dealing both with the synthesis of ultrathin triangular prisms of few nanometers in height and the study of their optical properties to provide a complete description and better knowledge of the multipole plasmon modes. As mentioned above, the synthesis of triangular particles with aspect ratios as high as 40 or more is a difficult task to achieve but this has been very recently carried out in our laboratory.27,28 These silver nanoprisms are obtained by using multiply twinned silver nanocrystals with 5 nm in size as former constituents. Briefly, the nanocrystals are first deposited on highly oriented pyrolitic graphite (HOPG) where they spontaneously selforganize in such a way to form assemblies consisting of well ordered mono- and multilayers. After mild annealing of the sample under atmospheric pressure at 50 °C and the subsequent nanocrystals coalescence, very thin triangular silver nanoprisms are formed in coexistence on the substrate with thicker crystalline coalesced nanocrystals of various shapes. Figure 1 is a

10.1021/jp901248e CCC: $40.75  2009 American Chemical Society Published on Web 06/11/2009

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Figure 1. TEM image showing silver triangular nanocrystals and other well-crystallized particles with different sizes and shapes. All of them are formed by mild annealing of 5 nm silver nanocrystals self-organized on HOPG. Inset: TEM image of one triangular silver nanocrystal with very high aspect ratio. The scale bar stands also for the inset.

transmission electron microscopy (TEM) image showing a mixture of both kinds of the obtained particles together with some not coalesced primitive 5 nm particles that are randomly distributed on the substrate. As deduced from TEM analysis, both triangular prisms and large faceted particles exhibit quite large size and shape dispersions. Most of the nanoprisms appears with homogeneous contrast and slight darkness (inset of Figure 1), which indicates they are very flat and thin single domain crystals. Obviously, the selective formation of prisms with precisely defined structural parameters, i.e. with controlled size, AR or truncation, is not yet achieved by using this route and still remains a challenging issue. The coexistence of so many different particle sizes and shapes in the same sample prevents from properly studying the optical response of these particles by extinction spectrophotometry. Apart from the inconvenient mentioned above, the synthesis protocol has nevertheless some interesting advantage. Indeed, using dynamic force microscopy (DFM), the nanoprisms height was estimated to not exceed only 5 nm.29 To our knowledge, such formed nanoprisms exhibit probably the thinnest height that has never been reported in the literature until now. Because of the absence of experimental results, all information about the optical properties of nanoprisms with geometry comparable to that of the produced ones, is therefore not only a guide for our work but also motivate future efforts toward monodisperse syntheses or size-selective separation of these thin nanoprisms. Using the DDA method to predict the optical features of very flat and thin nanoprisms and to identify their various SPRs is therefore important in order to enable their future comparison with experimental measurements when the control of their geometry will be achieved. Here, we assign the multipolar excitation peaks of ultrathin triangular silver nanoprisms with high aspect ratios (5 e AR e 40) via the DDA method. We combine a very low thickness (5 nm) with edge lengths ranging from 25 to 200 nm. This makes it possible to correctly distinguish the bands corresponding to the in-plane quadrupolar (l ) 2) and higher multipolar (l ) 3) modes, in addition to the dominant dipole resonance. Also, we report on the dependence of the multipolar excitations on the nanoprism geometry. 2. Computational Approach for the Simulations: Discrete-Dipole Approximation Several numerical techniques are now available to calculate the optical properties of nanocrystals with different shapes by solving the electromagnetic scattering problem, such as the

Figure 2. Schematic representation of a nanoprism with triangular faces oriented perpendicularly to the x-axis direction. The edge length and the thickness of the nanoprism are denoted L and e, respectively.

boundary element method (BEM),30,31 the discrete-dipole approximation (DDA), the finite-difference time-domain method (FDTD)32 and the finite element method (FEM).33 Note that the three former methods have been compared for modeling the optical properties of gold nanoparticles.34 Among all these techniques, the DDA, which is also known as the coupled dipole approximation, is a widely used, flexible and powerful method for computing scattering and absorption by targets of arbitrary geometry.35-37 In this paper, the versatility of the DDA method is exploded to largely tune the aspect ratio of silver triangular nanoprisms by choosing both their size and geometrical parameters in order to facilitate the study of their multipolar plasmon resonances. 2.1. Target Geometry. The DDA method was first introduced by Purcell and Pennypacker38 and then, developed by Draine and Flatau.36 The approximation involved in this method consists in representing the simulated object, which is the socalled target, by a finite array of polarizable points. Each of these points acquires a dipole moment in response to both the incident electric field and the fields created by all the other dipoles in the target. The target built to mimic a large triangular crystalline nanoprism is shown in Figure 2. This is a nanoprism whose triangular faces are oriented perpendicularly to the wave vector of the incident electromagnetic radiation. The latter is considered here to propagate along the x-axis direction and to be linearly polarized with its electric field being oriented along the y- or z-axis direction. It was checked by testing that the rotation of the target in the (yz) plane just changes the plasmon band intensity while the plasmon frequency remains unchanged in the extinction spectrum. In order to avoid long computing times we keep the same geometric incidence configuration for all our calculations. The dielectric function of the silver nanoprisms was taken to be the bulk experimental value, as published in Palik’s handbook39 since the nanoprisms under investigation in this work are large enough (with edge lengths of several tens of nanometers) to neglect the size dependence of their dielectric function. In addition, the silver triangular nanoprisms are simulated in vacuum with the refractive index of the surrounding medium fixed at unity. The typical dimensions of the nanoprisms range from 50 to 200 nm in edge length and from 5 to 7 nm in thickness. The aspect ratio, AR, which

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Figure 3. (A) Representation of the DDA targets designed to simulate four silver triangular nanoprisms with the same AR ) 5 (25:5) for which different interdipole distances, d, and number of dipoles, N, are used, i.e., d ) 1 nm (N ) 1360), 0.75 nm (N ) 3507), 0.5 nm (N ) 10 830), and 0.25 nm (N ) 86580). (B) Comparison of the extinction spectra calculated for a (25:5) silver nanoprism as modeled by using the different targets previously described. (C) Evolution of the extinction spectrum calculated for silver nanoprisms with different sizes but all with the same aspect ratio (AR ) 5). Here, the nanoprism size is varied either by changing the d parameter and keeping N constant (solid curves) or, inversely, by keeping d constant and assigning N (dashed curves) to 86 580, 292 260, and 692 760 dipoles for the (100:20), (150:30), and (200:40) nanoprisms.

is defined as the ratio of the edge length (L) to the thickness (e) of the nanoprism, therefore ranges from 5 to 40. 2.2. Applicability of the DDA to the Simulation of Ultrathin Nanoprisms. In the literature, there are various examples26,24,25 for which interdipole distance spacings such as 1 or 2 nm were found to accurately represent the optical properties of gold and silver nanoprisms with dimensions similar to those presented in this work. Here, several values of interdipole spacings ranging from 0.25 to 4 nm were employed to test the convergence of the DDA calculations when considering such ultrathin triangular nanoprisms. Figure 3A shows representations of the DDA target designed to simulate triangular silver nanoprisms with the same AR ) 5 (25:5) and different interdipole distances, i.e., d ) 1.0 nm, 0.75 nm, 0.5 and 0.25 nm. The total number of dipoles that are required to build these targets are 1360, 3507, 10830 and 86580, respectively. As obviously expected and clearly illustrated by these representations, the thinner the meshing of the dipole grid, the better the design of the target. To examine how the changes in the interdipole distance and number of dipoles can affect our DDA simulations, the extinction spectra calculated for the different targets presented above are compared in Figure 3B. Here, one can easily note that the spectrum obtained by using an interdipole distance of d ) 1.0 nm exhibits an unusual profile, which looks significantly different from the others with the appearance of several ripples in the intense dipolar plasmon band. The evolution of the extinction spectrum, with varying the meshing of the dipole grid, that is shown in Figure 3B, illustrates that, for a nanoprism with AR ) 5 (25:5), a maximum value of d ) 0.5 nm is required as interdipole distance in order to get reasonably converged calculations. Equivalently, the use of at least 10800 dipoles is therefore needed in this case to ensure the validity of the simulations. Moreover, when looking

at Figure 3A, one can also expect that using an interdipole spacing larger than 0.5 nm to mesh the dipole grid can induce significant variations in the design of the target compared to the perfect triangular nanoprismatic shape. Indeed, when the interdipole spacing is set at d ) 1.0 nm, it is worth noting that only five layers of dipoles are stacked along the thickness of the (25:5) nanoprism. Furthermore, such a crude meshing of the dipole grid favors the formation of sharp tips, as seen in Figure 3A for the target generated by using d ) 1.0 nm. As a result of both the imperfect design of the nanoprism and the sharpness of its tip, spurious effects are likely to affect the calculations and artifacts can therefore emerge in the simulated extinction spectrum. A pertinent pathway to go further in this analysis logically consists now in discerning the respective influence of the two parameters involved in the meshing of the dipole grid on the convergence of the calculations, i.e., the total number of dipoles, N, and the interdipole distance, d. For this, the evolution of the extinction spectrum calculated for silver nanoprisms with different sizes is presented in Figure 3C. All the nanoprisms considered here, were modeled by keeping, whatever the size, the aspect ratio at 5. In order to correctly estimate how the variation of the d and N parameters can independently affect the result of the DDA simulations, the nanoprism size was varied through two different procedures. On the one hand, the interdipole spacing was changed (0.5 nm e d e 4 nm) while keeping the total number of dipoles constant (N ) 10830) and on the other hand, d was fixed at 1 nm while setting N to different values between 10830 and 692760 dipoles. From the comparison of the spectra plotted in Figure 3C, it appears that both of the two proposed protocols enable us to observe the same general effect on the extinction spectrum, that is the significant red shift of the dipolar plasmon band on increasing

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Figure 4. Extinction spectrum of a silver nanoprism with AR ) 20 (100:5) calculated for the incoming light being x-polarized (dashed line), y-polarized (dotted line), and z-polarized (solid line). The inset shows a magnification of the spectrum for the x-polarized (green curve, dashed line) incoming light in the range of 3.2-4.1 eV.

the nanoprism size. Nevertheless, when comparing, for the largest sizes, the profile and amplitude of the spectra, one concludes that the results obtained by carrying out the calculations following the second procedure are converged. At variance, the spectra calculated by considering the nanoprisms as modeled according to the first procedure exhibit profiles with small ripples comparable to those which are observed in Figure 3B in the spectrum calculated for d ) 0.75 nm. All of the observations described above make it possible to expect our calculations to accurately converge, with the requirement of using a meshing that is fine enough to well design the target shape. For most of the nanoprisms under investigation in this work, fixing the interdipole spacing at d ) 0.5 nm is likely to satisfy this condition since this value actually does not exceed a tenth of the thickness of the thinnest nanoprisms. Another criterion that still needs to be satisfied, before to ensuring, the applicability

Yang et al. of the DDA method,40 is that the interdipole spacing must be small compared to the wavelength in vacuo, λ. This second criterion is usually expressed as |m|kd < 0.5, where m is the complex refractive index of silver, and k ≡ 2π/λ, the magnitude of the wave vector. The maximum value of |m|kd remains less than 0.05 for all of our calculations, thus providing the guarantee for their validity. Finally, note also that the DDA simulations reported in this work require a large computational effort. For instance, the calculations carried out by using an IBM BladeCenter JS21 server for simulating the (200:5) nanoprism with d ) 0.5 nm (N ) 692 820 dipoles) necessitate around 70 days of computing time. Thus, it appears rather unfruitful to adjust the meshing to values smaller than 0.5 nm when doing the balance between the extent of the additional effort to be invested and the limited gain to be expected in the accuracy of our results. 3. Results and Discussion 3.1. Polarization Dependence of the Extinction Spectrum. The extinction spectra plotted in Figure 4 were calculated for a silver nanoprism with AR ) 20 (100:5), with the incoming light being successively polarized in the three Cartesian directions. The two spectra calculated for the electric field of the incident wave oriented, respectively, along the y and z directions, i.e., for in-plane polarization of light, appear very similar in profile. Both of these spectra exhibit three bands centered at 1.5, 2.3, and 2.6 eV, respectively. From the examination of the polarization vectors for each resonance, one can then identify the corresponding excitation modes. Figure 5A shows the polarization vectors determined at 1.5-eV energy, i.e., at the maximum of the most intense extinction band (Figure 4). As clearly revealed by the schematic representation in Figure 5B, the SPR mode emerging at this energy corresponds to the dipolar resonance (l ) 1 mode) associated with in-plane polarization. When looking now at the main directions of the polarization vectors obtained at 2.3 eV (Figure 5C,D), the corresponding

Figure 5. Polarization vectors for a silver triangular nanoprism with AR ) 20 (100:5). The incoming light propagates along the x direction with its electric field E0 being oriented along the z direction as in the schematic description of the target in Figure 1. The polarization vectors are plotted for (A) a dipolar resonance (l ) 1 mode) at 1.5 eV, (C) a quadrupolar resonance (l ) 2 mode) at 2.3 eV and (E) the l ) 3 resonance mode at 2.6 eV. In each polarization plot, the symbols - and + are inserted to indicate the resulting polarity. For clarity, the schematics (B), (D), and (F) display the main directions of the polarization vectors as derived from the plots (A), (C), and (E), respectively.

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Figure 6. Evolution of the bands centered at ∼3.5 and 3.8 eV for x polarization: (A) when the nanoprism thickness is varied from 5 to 9 nm for the edge length fixed at L ) 50 nm and (B) when the edge length is varied from 50 to 200 nm for a fixed nanoprism thickness of e ) 5 nm.

band in the extinction spectrum can be accurately ascribed to the in-plane quadrupolar mode (l ) 2). Similarly, Figure 5E,F makes possible assigning the small band centered at 2.6 eV to a higher in-plane multipolar resonance (l ) 3). When the light electric field, b E0, is oriented along the x direction (out-of-plane polarization), two other bands with much lower amplitudes are observed at higher energies (∼3.5 and 3.8 eV), while all the previous bands are no longer seen in the spectrum (see green curve in Figure 4). These latter bands exhibit a slight dependence on the variation of the nanoprism thickness with a small shift toward lower energy for increasing e from 5 to 9 nm (Figure 6A). Conversely, as seen in Figure 6B, a very small blue shift is found on the increasing of the nanoprism edge length at a fixed thickness. This last result clearly indicates that the two resonances at higher energy are “out-of-plane” and explains therefore why they are visible only when the light is x polarized. Since the vector plots are more difficult to visualize and interpret for x polarization due to the short dimension of the nanoprism along this direction, in the following we will focus on the other bands observed for inplane polarization. All the simulations presented below are performed with the electric field of the incident wave oriented along the y or z direction. 3.2. Dependence on the Nanoprism Dimensions. At this stage, we can ask what is the dependence of the SPR spectrum on the nanoprism aspect ratio when keeping the volume of the nanoprism constant. Figure 7A shows the extinction spectra calculated for nanoprisms having different AR but the same volume. In increasing order of edge length, the used AR were 5 (100:20), 9.6 (125:13), 16.7 (150:9), and 40 (200:5), respectively. These ratios are such that the effective radius, i.e., the radius of the sphere having a volume equivalent to that of the triangular nanoprism, was fixed at around 27 nm for all of them. We note a significant evolution of the spectra plotted in Figure 7A with all of the SPR bands being shifted toward lower energies when the AR is increased. For a nanoprism with AR ) 5 (100:20), we observe two bands. In parallel, for a nanoprism

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Figure 7. Extinction spectra of triangular silver nanoprisms calculated for in-plane polarization in the following cases: (A) Nanoprisms with different aspect ratios but the same volume; (B) Nanoprisms with different aspect ratios but the same thickness (e ) 5 nm); Inset, dependence of the SPR energy on the edge length for the l ) 1-3 modes. In (A) and (B), the spectra have been vertically shifted for clarity.

with AR g 9.6 (125:13), three bands are observed. The bands at high energy, corresponding to multipolar SPR, are well resolved. Also, from data obtained previously, the lower energy band is due to the in-plane quadrupolar SPR (l ) 2 mode) whereas that at higher energy corresponds to the higher multipolar SPR (l ) 3 mode). The condition for observing the in-plane quadrupolar band in the spectrum seems therefore to be more sensitive to the nanoprism AR than its volume. Actually, this band is observed only for large values of AR. The increase in the band amplitude with AR at constant volume can obviously be explained by the fact that the triangular face area also increases. Note that, as expected, the in-plane dipolar resonance is shifted toward lower energies by increasing the aspect ratio.41 The spectra of triangular nanoprisms simulated for different edge lengths ranging from L ) 25 to 200 nm by steps of 25 nm are shown in Figure 7B with a constant thickness (e ) 5 nm). As expected, the in-plane dipolar SPR band (l ) 1 mode) moves toward lower energies on increasing the edge length. Note that for AR g 30, the dipolar SPR band moves out of the energy range under consideration in the present calculations. For the multipolar modes, the in-plane quadrupolar (l ) 2 mode) and in-plane higher multipolar (l ) 3 mode) SPR bands are also observed to shift toward lower energies when the edge length increases. For AR < 10, only the l ) 3 mode is observed. Then, on increasing the nanoprism AR, the band associated with the in-plane quadrupolar SPR (l ) 2 mode) is observed for AR g 15. Furthermore, for higher values of the AR, the inplane quadrupolar SPR band strengthens and “competes” in amplitude with the in-plane higher multipolar SPR band. Finally, for ARs as large as 40, the amplitude of the in-plane quadrupolar SPR band dominates the higher multipolar one (l ) 3 mode). Also it is evident that the energy difference between the various SPR bands does not vary by changing the AR (Figure 7B inset).

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Figure 8. Calculated extinction spectra of silver nanoprisms having an original AR of 20 (100:5) and truncated with different snips. From bottom to top, the TR value increases up to 0.2 by steps of 0.05. For all these spectra, in-plane polarization of the incident light is used. The inset shows the profile of a truncated nanoprism.

3.3. Effect of Truncation. From data obtained for rather thick silver42,15,43 and copper nanodisks,44 we know that the SPR spectrum is drastically affected by snipping. For very thin and rather large silver nanoprisms, this statement still remains an open question. The degree of truncation, TR, is defined as a/L, where a is the length of the snip (inset of Figure 8). In order to avoid a large variation in AR resulting from the truncation of a nanoprism, the extinction spectra were calculated with the TR not exceeding 0.2. The Figure 8 inset shows a front view of a snipped nanoprism. Before truncation (a ) 0), a nanoprism with AR ) 20 (100:5) is considered. From this nanoprism used as the original shape, different truncated nanoprisms were then investigated for various TR values up to 0.2, incremented by steps of 0.05, which correspond to the snips: a ) 5, 10, 15, and 20 nm, respectively. Note that the snipping slightly changes the AR. Figure 8 shows that the SPR bands shift toward higher energies when the TR increases. As previously described, in addition to the intense dipole resonance, two low intensity SPR bands are observed in the extinction spectrum for TR e 0.15: the quadrupolar in-plane resonance (l ) 2 mode) and the higher order in-plane resonance (l ) 3 mode). From the evolution of the spectra shown in Figure 8, one can expect the strength of the quadrupolar in-plane resonance to be nearly insensitive to the change in truncation whereas that of the l ) 3 mode progressively decreases until it disappears at TR ) 0.2. In order to confirm this assignation, the polarization vectors of a (100:5) nanoprism are determined for TR ) 0.1 at SPR energies of 2.5 and 2.7 eV. The polarization vectors are plotted in Figure 9, panels A and B, from which one can observe four and six distinct poles, respectively. This makes it possible to accurately assign the SPR bands centered at 2.5 and 2.7 eV to the quadrupolar in-plane resonance and the multipolar l ) 3 mode, respectively. Equivalently, when considering the same nanoprism as before with the largest truncation (TR ) 0.2) and the corresponding polarization vectors as plotted in Figure 9C, it appears that the unique low-intensity SPR band centered at 2.5 eV can be attributed to the in-plane quadrupolar resonance (l ) 2 mode). 3.4. Influence of a Dielectric Substrate. The dielectric environment may influence the optical properties of silver nanoprisms.3 For this reason, it seems pertinent to take into account the presence of a substrate in order to simulate the optical response of a system not only consisting of free nanoprisms but also, more realistically, of nanoprisms deposited on a solid base. As described in reference,3 the substrate is represented in the DDA target by a thin cylindrical slabs with

Figure 9. Plots showing the polarization vectors for a snipped silver triangular nanoprism with two different snips. The first two plots correspond to a nanoprism with a snip of a ) 10 nm for (A) a quadrupolar resonance (l ) 2 mode) at ∼2.5 eV, and (B) the l ) 3 resonance mode at 2.7 eV. Plot (C) shows the polarization vectors for the quadrupolar resonance (l ) 2 mode) of a nanoprism with a snip of a ) 20 nm, which is excited at 2.5 eV.

a diameter twice the nanoprism edge length and with a thickness equal to that of the triangular nanoprism. Such a dimensioning of the substrate has been shown to be the best compromise between the minimum size of the target to be designed to ensure the convergence of the calculations and the limitation inherent to the large computational endeavor that is required for larger sizes.3 Figure 10A shows a schematic view of the target used to investigate the influence of the substrate on the extinction spectrum of the (50:5) silver triangular nanoprism. From the previous arguments, the substrate is represented by a 100-nm diameter, 5-nm thick cylindrical slab. In addition, the incident

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J. Phys. Chem. C, Vol. 113, No. 27, 2009 11603 polarization of the incident electric field, the volume and the aspect ratio of the nanoprisms as well as their truncation. By changing the light polarization, bands originating from in-plane and out-of-plane plasmon modes can be identified in the spectrum. All the observed plasmon resonances dramatically shift toward lower energies on increasing the volume and/or the aspect ratio. Also, the aspect ratio and truncation are demonstrated to play a key role in determining the strength of the multipolar SPR. This theoretical study typically illustrates how DDA can guide design of nanostructures with unique optical properties when the experiment itself is fraught with practical difficulties. From the DDA simulations presented in this work, one can expect that such a high sensitivity of the optical properties of triangular nanoprisms with high aspect ratios to their shape and size characteristics should open interesting opportunities in using similarly shaped silver nanocrystals for practical applications.

Figure 10. (A) Schematic representation of the target designed to simulate an AR ) 10 (50:5) triangular silver nanoprism on MgO substrate whose diameter and thickness are 100 and 5 nm, respectively. The incident beam propagates along the x axis with its electric field b E0 parallel to the triangular face of the nanoprism (in-plane polarization); (B) Extinction spectrum calculated for the same nanoprism as described in (A) with (solid line) and without a (dashed line) substrate.

plane wave is considered to propagate along the prism axis (positive x direction) and the polarization vector b E0 is therefore oriented in the (yz) plane. Here, the material, chosen as substrate, is a dielectric crystal commonly employed for optical measurements, i.e., MgO. The dielectric function used to describe the substrate is that published in Palik’s handbook for bulk magnesium oxide.39 The extinction spectra of a silver nanoprism with and without a substrate are compared in Figure 10B. Obviously, the SPR bands are observed to significantly shift toward a lower energy on taking into account the substrate (in comparison to a free nanoprism) and their amplitude dramatically decreases. Such a red shift is qualitatively in agreement with the effect of the substrate index of refraction on the SPR wavelength that has been reported for DDA simulations of truncated tetrahedral particles on a mica slab.3 The decrease in the SPR energy is due to the increase in the “averaged” refractive index of the surrounding environment induced by the presence of the substrate in the close vicinity of the nanoprism relative to the case of a nanoprism in vacuum. At this point, this substrate effect still needs more investigation to be quantified via further calculations and comparison with experimental measurements. 4. Conclusion The surface plasmon resonance spectrum of silver triangular nanoprisms with high aspect ratios is studied by using the DDA method. The applicability of this numerical approach to our study is established. The calculated spectrum exhibits several bands corresponding to extinction of light due to the l ) 1-3 excitation modes. A significant dependence of the extinction spectrum is clearly revealed on the

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