Optical Responses of Gold Nanoparticles Undergoing a Change to

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Optical Responses of Gold Nanoparticles Undergoing a Change to Cluster Aggregates and Laser Beam Characteristics Effect M. Nikbakht and M. H. Mahdieh* Department of Physics, Iran University of Science and Technology, Narmak, Tehran, Iran ABSTRACT: The local field enhancement for fractal aggregate targets consisting of clusters of gold nanoparticles (NPs) placed over a metallic substrate is studied numerically. The field enhancement occurs when such targets are irradiated by polarized laser beam. Using the dipole-dipole approximation (DDA) and considering Fresnel relations, the spatial field distribution over the sample was calculated. The effects of the incident beam characteristics such as polarization, wavelength, and incident angle on the collective responses of cluster aggregates were investigated. The effect of target morphology characteristics was also studied. Numerical calculations indicate that, because of target morphological anisotropy and boundary conditions, there is an optimum value for cluster size which maximizes the averaged local field enhancement for the p-polarized incident beam.

’ INTRODUCTION The study of optical properties of metallic nanostructures has been interesting for its wide range of applications in nonlinear optics, electronics, photochemistry, biophysics, and light-matter interaction.1,2 Early research shows that plasmon resonance in these structures provides intense local fields responsible for the electromagnetic contribution to surface-enhanced Raman scattering (SERS). Many of the recent studies in SERS were performed in metal aggregates generated by the chemical reduction process,3 radiolytic techniques,4 and the laser ablation process.5,6 The gravitational deposition of these colloidal metals on a flat surface generally results in the formation of disorder structures.7-9 It has been shown that the localization of dynamical excitation in disordered structures, especially in fractals, plays an important rule in many physical processes. In particular, strong localization of the normal modes (collective surface plasmons) leads to strong fluctuation of local fields.10 These fluctuations are especially strong in clusters with self-similar or self-affine morphology.11-15 The prediction of individual normal modes' presence in the near-field spectra of self-affine fractal surfaces was first confirmed experimentally by Markel et al.14 Local fields in such samples are shown to be very inhomogeneous and consist of strongly localized sharp peaks which are called “hot spots”. In the “hot spots”, local fields exceed applied fields by several orders of magnitudes, resulting in giant enhancements of the optical nonlinearities.15,16 In the case of isolated metal nanoparticles (NPs), the plasmon resonance frequency and electromagnetic field configuration depend on their sizes, shape, and metal dielectric function.8,17-19 Aggregation of NPs into fractal cluster results in large field enhancements in the spectral range associated with collective dipolar resonances. In ensembles of interacting clusters, the interparticle r 2011 American Chemical Society

electromagnetic coupling influences the plasmon peak position and the local-field enhancement. The optical properties of noble metal NPs (silver, gold) exhibit prominent differences in comparison with their bulk responses.2 It has become increasingly evident that collective electron oscillations can be excited in noble metal NPs, especially across the whole visible region. This fact makes noble metal NPs, especially gold, a well-situated candidate for biological use due to their low chemical reactivity while strongly interacting with light.17 Several experimentally realizable geometries such as metal particle chains,20-25 metallic nanoplanets,19,26 nanorings,27 nanorods,8,28-30 nanoshells,31,32 nanoholes,33-35 and NP trimer36 have been used for creating plasmon resonances whose optical properties can be controlled by adjustment of the structure characteristics. Each of these nanostructured geometries comprises individual optical properties such as plasmon resonant frequency, spatial distribution of the local fields across the structure surface, and controlling propagation, polarization, and intensity of scattered light. An important topic in the field of plasmonics is the effect of symmetry breaking. Several studies have been devoted in this aspect recently. For nanostructures such as a nanoshell or concentric ring/disk cavity, the symmetry breaking was induced by displacement of the dielectric core with respect to the metallic shell,35 while in NP aggregates asymmetry could be induced by anisotropic arrangement of NPs. Shegai et al. studied the interaction of light with single molecule.36 On the basis of symmetry breaking, they showed that asymmetric nanocrystal Received: September 16, 2010 Revised: December 17, 2010 Published: January 11, 2011 1561

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aggregates like silver nanocrystal trimer could be used to tune the polarization and intensity of scattered light from molecule-aggregate. As a result, they found overall 10 anisotropic nanocrystal arrangements with complex wavelength-dependent behavior. Fractal aggregates are among those structures in which symmetry, if existing at all, is hidden. The growth of fractal aggregates under nonequilibrium conditions could be considered within the framework of a cluster-cluster aggregation (CCA) process. Such a process involves the aggregation of clusters by allowing the NPs (and subclusters) to diffuse and stick to the growing structures. In most applications, the maximum local field enhancement factor G(x,y) = EE*local/ EE*inc, with Einc being the amplitude of the incident field, can be achieved by optimizing the macroscopic parameters of both electromagnetic waves associated with the laser beam and the aggregate characteristics. By simply changing the excitation angle caused by changing the incident light angle from perpendicular to grazing, the response of the nanostructure would alter. As an example, Chan et al.33 (and Lei et al.34) have studied the dependence of surface plasmon polaritons (SPP) lifetime on the wavelength and the structure geometry. Through reflectivity measurements of p-polarized incident beam from two-dimensional uniform Ag (Au) hole arrays, they demonstrated that SPP play a significant role in SERS and holes geometry affect SPP. Due to the increasing importance of ultrafast lasers, theoretical and experimental studies on the interactions between high-peakpower subpicosecond laser pulses and medium have received more attentions during the past few years.37 Nanostructure surfaces are especially promising as highly absorbing targets for ultrafast laser-matter interaction. The strong fluctuations of the local electric field across such targets results in the corresponding enhancement of nonlinear effects. Efficient hot electron production even with moderate laser intensity has already attracted studies in use of porous targets for the efficient generation of KR.38,39 Recently theoretical and numerical studies of laserdriven femtosecond KR sources aimed to optimize emission from thin coating targets.40 A particular attention in these fields of study is to control and optimize the KR emission from femtosecond laser plasma by adjusting the target characteristics and/or angle of incidence appropriately.39-41 The aim of the present letter is to investigate the local field enhancement of ensembles of gold clusters placed over a gold substrate, by considering a full-interaction electromagnetic approach. The influence of the cluster size on the field enhancements and the spectral profile is discussed for both s and p polarization of the incident laser beam. It will be shown that local field enhancement is strongly correlated to cluster size.

ments. The idea used for cluster formation is a modified model based on the classic CCA model.42 In this modified model we assumed that initially 500 gold NPs are placed randomly in a 4000
4000 nm2 square lattice with periodic boundary conditions. The NPs and clusters were selected randomly, and an attempt was made to move them randomly in one of the four equally probable directions of a square lattice. It was also assumed that the diffusion probability (for cluster movement) is inversely proportional to the cluster size (mass). When two clusters collide they stick together, forming a larger cluster which then can move and make more collisions. It must be noted that after each step cluster sizes (number of NPs in cluster) were averaged over the aggregate and characterized as ÆSæ. The modified model can be used to simulate cluster aggregates of subclusters with approximately the same size. Despite its simplicity, this geometry is well-suited to restoring the geometry of nanoaggregates produced in the experiment.7,9,43 The incident wavelength and NP radius are fixed at λ = 800 nm and R = 10 nm, respectively. In this condition, attached particles (embedded in clusters) strongly interact through nearfield coupling, while far-apart clusters interact through far-field coupling.2 The enhancement of the electric field is due to electromagnetic interactions between NPs (embedded in clusters) in the presence of the substrate. Through these interactions, each NP experiences a field that is the sum of the incident plane-wave and the scattering from other NPs as well as the reflected wave from substrate. To study the optical properties of our system, the dipole-dipole approximation44,45,50 (DDA) is used to model NP electromagnetic interaction, and the dispersive dielectric response of the sample was modeled as described in ref 46. For a spherical particle, it can be assumed that only the dipole surfaceplasmon resonance contributes to the enhancement process. With this assumption, it is possible to consider each NP as an elementary dipole and introduce corresponding interaction operators.11 The dipolar moment di of the ith NP in the proximity of a surface can be expressed as: X ^ ij dj W ð1Þ di ¼ REi0 þ R

’ THEORY AND MODEL The configuration under study is sketched in Figure 1. A nanostructured gold surface is modeled as a group of cluster aggregates lying on a gold substrate. This set of samples is illuminated by a polarized laser beam under an incident angle θ. The aggregate morphology could be classified into three different classes: nearly isolated gold NPs (Figure 1a), moderately aggregated NPs into small clusters (Figure 1b,c), and densely aggregated clusters (Figure 1 parts d-f). Each sample consists of a group of clusters which results from an initially random distribution of NPs attached to each other under collision during their random move-

If the electromagnetic beam incident on the substrate is plane and plane-polarized, then the reflected beam from substrate (with ε = εr þ iεi = ^n2 = (n þ iκ)2 and extinction coefficient κ) is also plane and plane-polarized. The electric field intensity incident on the ith NP (positioned at the point ri) can be expressed as:

where R is NP polarizability, E0i is the external electrical field ^ ij is the dipole-dipole interaction acting on the ith NP, and W tensor. Taking NPs to be spherical particles with radius R and complex electric response ε, the NP polarizability is assumed to be: R ¼ R 3 ðε - 1Þ=ðε þ 2Þ

ð2Þ

The external field at the position of the ith NP is a result of the direct incident field coming from the external plane wave Eiinc plus the reflected field from the substrate surface Eir: Ei0 ¼ Eiinc þ Eir

Ei0 ¼ E0 exp jðω t - k 3 r i Þ

ð3Þ

ð4Þ

In this equation k is the incident wave vector. From the Goos-H€anchen effect linearly polarized light undergoes a small shift, when reflected from substrate.49 Using the well-known 1562

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Figure 1. Schematic form of sample morphology used in the simulation of aggregation of gold clusters lying on a gold substrate. The number of NPs and their radius remain constant for all simulations, and each sample is characterized by the mean value of its cluster size. (a) ÆSæ = 2, (b) ÆSæ = 4, (c) ÆSæ = 8, (d) ÆSæ = 25, (e) ÆSæ = 50, (f) ÆSæ = 100.

Fresnel formula for reflection of p-polarized (and s-polarized) light, it is easy to obtain an expression for the phase shift of reflected field from substrate as:    u-v ð5aÞ δp ¼ Im ln uþv "

u - ^n2 v δs ¼ Im ln u þ ^n2 v

where u = ^n2 cos(θ) and v = (^n2 - sin2(θ))1/2 are complex quantities and θ is the angle of incidence. The subscript s and p stand for s- and p-polarized beams, respectively. Considering the electric field intensity of the incident beam to be known, the amplitude of the reflected beam can be calculated according to the Fresnel formulas:

!# ð5bÞ 1563

jEr jp ¼ rp jEinc j

ð6aÞ

jEr js ¼ rs jEinc j

ð6bÞ

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Figure 2. Distribution of normalized local fields in samples with sizes demonstrated in Figure 1 illuminated by the p polarized laser beam. The incident beam angle and wavelength are fixed typically at θ = 50 and λ = 800 nm, respectively.

With

difference is found to be:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðcos θ - nÞ2 þ k2 rp ¼ ðcos θ þ nÞ2 þ k2

ð7aÞ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðn cos θ - 1Þ2 þ k2 cos2 θ rs ¼ ðn cos θ þ 1Þ2 þ k2 cos2 θ

ð7bÞ

Since NPs are placed over the substrate, there would be small phase differences between the incident and the reflected field at NP's center. By simple geometrical calculation this phase

φ ¼ k½ðR þ R cosð2θÞÞ=cosðθÞ

ð8Þ

In this equation k is the incident wavenumber, and R is the NP radius (NP distance from substrate). Simultaneous solutions of eqs 3 to 8 give the external field on NPs. Solving eq 1 for d, the local fields on NPs can be obtained from: Elocal ¼ R - 1 d

ð9Þ

In this work, the spatial distributions of the dimensionless enhanced local field G(x,y) = (EE*)local/(EE*)inc, and the 1564

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Figure 3. Averaged local field enhancement as a function of incident angle for different value of ÆSæ while the incident beam wavelength is fixed typically at λ = 800 nm: (a) for p polarized wave, (b) for s polarized wave.

Figure 4. Evolution of the average local field enhancement of the samples as a function of cluster size ÆSæ for different incident angles while the incident beam wavelength is fixed typically at λ = 800 nm: (a) for p polarized laser beam, (b) for s polarized laser beam.

spatially averaged enhanced local field of cluster aggregates ÆGæ, were calculated for inclined incident laser beam with two polarizations s and p. In these calculations targets with different mean cluster sizes were considered. The calculations were also conducted for the incident laser beam with different azimutal angles θ. It will be shown that the spatial positions of the localized hot spots are located at different parts of the sample. The enhanced local field in the hot spots exceeds the average enhancement by several orders of magnitude.

’ RESULTS AND DISCUSSION The evolution of the field enhancement G(x,y) for gold cluster aggregates were calculated. Cluster aggregates with same size of those given in Figure 1 were considered in the simulation. Figure 2 shows the simulation results for samples with different ÆSæ, which are presented in a-f, respectively. In this figure, it was assumed that the incident wave associated with laser beam has p polarization, and the incident angle is fixed typically at θ = 50. Basically, the NP coupling effect depends on the interparticle distance. In fact local field distribution and enhanced field strength strongly depend on the interparticle distances. As it can be seen from the results, for aggregates of small clusters (results of the initial stages of the aggregation process as in Figure 2a), the structure is still scale-invariant and thus retains translational symmetry.

As a result, the background field over the surface could be assumed to be efficiently uniform. However, local anisotropy in some parts of the sample results in localized and strongly enhanced field due to near-field interacting NPs. Using near-field optical microscopy, such a feature was directly visualized for an array of NPs.22 The results also show that the local fields can be enhanced more effectively with raising ÆSæ in moderately aggregated NPs (Figure 2b,c). The asymmetry arises due to the emergence of distinct attractants over the sample. Despite the formal lack of translational symmetry, the aggregation of NPs for a moderate cluster increases the average number of nearest neighbor which results in increasing the NP coupling. It must be noted that next nearest neighbor dipolar coupling was also reported.2 However, such couplings are small in comparison with the exponential distance dependence of near-field interactions. Therefore, the nearest neighbor interactions are expected to dominate the process in this regime. As a result, numbers of localization spots as well as the local field strength are increased. The aggregation of clusters into a larger size leads to an increase in cluster distance (Figure 2 parts d-f). As a result, coupling effects of distinct clusters become less efficient due to the evanescent character of the scattering fields. Moreover, the anisotropy was enlarged due to several morphological arrangements of clustered NPs, which results in the delocalization of field enhancements over the sample with lower strength. 1565

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Figure 5. Average field enhancement spectrum profiles versus incident beam wavelength for samples with different cluster sizes ÆSæ: (a) normal incidence, (b) s polarized incident beam at angle θ = 65, (c) p polarized incident beam at angle θ = 65. The field enhancement peak increases in magnitude and shifts toward lower energies for increasing cluster sizes less than 10.

Predictions based on theoretical simulations can provide important insight to choose an optimal angle of incidence in which the maximum field enhancement occurs for a given sample. However, to our best knowledge, there are no detailed experimental studies of the field enhancement as a function of laser beam incidence angle to date. Figure 3 shows the dependence of field enhancement on the incidence angle of the incoming laser beam. The results are presented in parts a and b for p and s polarization, respectively. As Figure 3a shows, in the case of p polarized incident laser beam, the averaged enhanced local field, increasing with the incident angle, reaches a maximum at θ = θo ≈ 65 and then decreases at higher angles. It must be noted that considering the presence of the substrate provides such an optimal value in the calculations. The total vertical field in the NP position is strongly affected by the interference of the incident laser beam and the reflected beam from substrate. Indeed, although the amplitude of the reflected field from substrate reaches its maximum value as θf90; its phase is opposed to that of the incident field, and the interference results in a decreased intensity at the substrate surface. As a result, an optimum angle can be obtained below θ = 90 where the maximum value of the vertical component of the total field comes together with the constructive interference of the fields. A similar effect was observed in the theoretical study of tip-enhanced Raman scattering.47,48 Our results also show that the angle in which ÆGæ is maximized is independent of ÆSæ for all samples with the same concentration of NPs. On the other hand, the aggregation of fixed density of NPs into fractal clusters can modify the absorption cross section for the neighboring particles but does not affect the optimal angle θo.

However, if the p polarized laser illumination is changed to s polarized illumination, somehow different behavior will be seen (Figure 3b). Our simulation shows that in comparison to the p polarized beam, s polarized beam can produce a very small field enhancement. Also, the field enhancement decreases with increasing the incident angle. This is obvious since the s polarized beam does not meet the phase-matching condition for excitation of the surface plasmon at substrate surface. The results in Figure 3 are in good agreement to those that can be obtained from Fresnel relations at the substrate-ambient interface.49 For more details, the averaged local field enhancement is plotted as a function of average cluster size in Figure 4a,b, for p and s polarized laser beams, respectively. The results in these figures are presented for different incident angles. These results clearly show that, as the average cluster size grows, the field enhancement versus incident angles have similar trends. Aggregation of NPs into small clusters (ÆSæ ∼ 10) results in increasing ÆGæ to its maximum value. However, a further increase in the cluster sizes does not cause additional enhancement. To see the effect of laser wavelength in field enhancement, the calculations are performed for some wavelengths. The results are presented in Figure 5. Figure 5a shows the enhanced field ÆGæ as a function of incident beam wavelength for samples with different cluster sizes ÆSæ under normal illumination. Clearly, there is no difference between the results for S and P polarizations. These results show that for larger cluster the maximum field enhancement occurs at larger wavelength (red shift). According to these results the peak intensities and width also grow when larger clusters are used. This observation is one of the fundamental 1566

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The Journal of Physical Chemistry C physical features of electromagnetic interaction in fractal aggregates, known as inhomogeneous broadening.28,50 In other words, in such aggregates different electromagnetic modes (collective surface plasmon excitations) may be resonant at different wavelengths which form a continuous band extending from the optical to the far-IR spectral region.2 Additionally, the clusters in each sample may have a variety of morphological arrangements (and size distributed) which results in broadening the field enhancement spectrum. The emergence of a secondary peak is expected for large clusters where the optical field becomes nonuniform across the sample. These results have previously been observed for finite metal particle chain.21 Moreover, while the main peak is red-shifted as the cluster size is increased, it shows no tendency of shifting in samples with an average size greater than 10. For further understanding of the far-field properties of larger clusters, the influence of the incident angle and polarization are studied in this condition. Figure 5b,c represents the field enhancement profile, for s and p polarized beam illuminating samples at an incident angle θ = 65. For s polarization, the results resemble that of normal illumination but with much lower values for field enhancement. This behavior is due to no change in the in-plane wavelength λ|| and decrease in exerted field at NP position due to Fresnel continuity relations at the substrate boundary for large incidence angles. Increasing the angle of incidence in illumination by p polarized wave results in a dramatic field enhancement (Figure 5c). Excitation of the transverse mode as well as the longitudinal mode results in further broadening and red shift.51,52 Since the optimal in-phase interference of the incident beam and the reflected beam occur at larger angles for larger wavelength, the secondary peak increases more than the first peak.

’ CONCLUSION Local field enhancement of cluster aggregates of gold NPs, placed over a gold substrate, was investigated numerically. Spatial field distributions over the sample were calculated using DDA combined with Fresnel relations. The effects of the incident beam characteristics such as polarization, wavelength, and incident angle on the collective response of cluster aggregates as well as the effect of target morphology characteristics were all studied. It was shown that the field enhancement depends on the cluster size and incident wave characteristics. From the results it was concluded that the average local field enhancement depends strongly on the incident angle for both p and s polarized beams. It was also concluded that for the case of p polarized beam there is a specific angle in which the field is maximized while for the s polarized beam the field decreases with respect to the incident angle. According to these results, for any particular angle of incidence and polarization, the average local field enhancement is dramatically increased with cluster size if aggregation of NPs forms a cluster size ÆSæ less than 10. However, for a cluster size larger than ∼10 the field enhancement reaches saturated values and even may decreases slightly for larger cluster aggregates. It is also found that, for the conditions of our calculations, maximum field enhancement can be achieved by a p polarized laser beam with an incident angle around an optimum angle θo. This angle depends on NP concentration and incident beam wavelength but is independent of ÆSæ.

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’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ98-21-77240540. Fax: þ98-21-77240497. E-mail: mahdm@ iust.ac.ir.

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