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Collective Plasmonic Resonances on Arrays of CysteineFunctionalized Silver Nanoparticle Aggregates Mária Csete,*,† Anikó Szalai,† Edit Csapó,‡ László Tóth,§ Anikó Somogyi,† and Imre Dékány‡,§ †

Department of Optics and Quantum Electronics, University of Szeged, 6720 Szeged, Dóm square 9, Hungary MTA-SZTE Supramolecular and Nanostructured Materials Research Group, and §Department of Medical Chemistry, Faculty of Medicine, University of Szeged, 6720 Szeged, Dóm square 8, Hungary

‡

S Supporting Information *

ABSTRACT: UV−visible spectroscopy on biofunctionalized spherical silver nanoparticle containing dispersions has shown that bioconjugation with L-cysteine results in aggregate formation, which causes appearance of UV and red-shifted absorptance maxima simultaneously. On the basis of comparative study of spectra registered experimentally and computed numerically, the simplest linear and wavy aggregate array geometries resulting in splitting according to the measurements were determined. Inspection of the near-field distribution has shown that collective plasmonic resonances develop both on linear and on wavy aggregates, which are influenced by the γ azimuthal orientation qualifying the E-field oscillation direction and by the φ incidence angle during p-polarized light illumination. These resonances originate from hybrid near- and far-field coupling phenomena, of which relative dominance is determined by the aggregate-arrays’ geometry and by the illumination direction. At perpendicular incidence the collective resonances manifest themselves dominantly in even and odd eigenmodes at the UV and red-shifted maxima, respectively. The eigenmodes’ excitation efficiency sensitively depends on the E-field projection onto the aggregates’ long axes, when the azimuthal angle is varied. In addition to resonant eigenmodes developing at analogous azimuthal and polar angles, squeezed guided plasmonic and standing resonator modes accompanied by enhanced EM-field appear at oblique incidence, due to grating coupling on the aggregate arrays.

1. INTRODUCTION The investigation of localized surface plasmon resonance (LSPR) phenomenon occurring, when subwavelength metal objects are illuminated by light, initialized tremendous advances in applied nanophotonics.1−4 The primary studies on individual nano-objects demonstrated the most important advantages of LSPR, the achievable tight EM-field confinement, and the tuning possibility of the resonance wavelength by the nanoobjects’ composition, shape, size, and dielectric environment.5,6 Already the early experimental studies and near-field computations revealed that single noble metal spheres can exhibit dipolar and quadrupolar resonances at optical and higher frequencies, respectively, although with a relative dominance sensitively depending on their diameter.5 According to the general approach that all objects designed to efficiently convert free-propagating optical radiation to localized energy can be considered as optical antennas, plasmonic nano-objects are special kinds of optical antennas.7,8 The peculiarity of plasmonic antennas are that they can take various forms and their properties can be precisely tailored by the composition, shape, and size due to the sensitive dependence of LSPR on these parameters. LSPR research was later refocused onto complex systems composed of plasmonic nano-objects, because higher degrees of © 2014 American Chemical Society

freedom are attainable both in spectral engineering and in nearfield tailoring via multipartite systems. Nanoparticle (NP) dimers are the simplest complexes, where the near-field coupling made possible by overlapping EM-fields of individual nano-objects results in emergence of split spectra consisting of peaks originating from longitudinal and transversal resonances.9−13 The appearance of novel spectral lines on dimers was explained by the hybridization of different plasmonic modes.12 It was proven that the spectral lines emerging below the frequency corresponding to Fröhlich condition originate always from precisely tunable dipolar modes,11 while the peaks appearing in the UV originate from quadrupolar modes that are less sensitive to the geometry.10 In clusters composed of a large number of metallic nanoobjects embedded into dielectric media, both near- and far-field couplings are at play.14−22 The number of modes involved in resonance phenomena is determined by the interacting NPs’ number and by the cluster geometry,14 while the resulted spectral features can be tuned by the characteristics and distance of constituents.15 In addition to e-beam lithography, Received: April 8, 2014 Revised: June 27, 2014 Published: July 7, 2014 17940

dx.doi.org/10.1021/jp503465r | J. Phys. Chem. C 2014, 118, 17940−17955

The Journal of Physical Chemistry C

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ments have potential to create various biodetection platforms; for example, the nano-objects can be either aligned on surfaces or dispersed in solutions. As a result, observation of LSPR curves accompanying the aggregation process makes possible direct tailored-to-material biodetection, as well as realization of aggregation-based immunoassay.42 According to our previous studies, silver colloid spheres wrapped with L-cysteine covering compose aggregates through hydrogen bonds and second-order interactions between the amino acids.50−53 However, only two aggregate illumination configurations were investigated extensively in the previous literature, when the E-field oscillation direction is parallel or perpendicular to the long axes of extended ensembles. The aim of our present study is to investigate thoroughly the effect of versatile relative E-field oscillation directions as well as the impact of oblique light incidence on the spectral response and on the characteristics of resonant eigenmodes and of coupled guided modes excitable on ordered arrays of different aggregates composed of very closely packed silver nanoparticles.

deposition of chemically prepared nano-objects onto lithographically prepatterned templates can result in clusters with various well-defined geometry.17−22 On noble metal NP clusters arrayed on substrates, the hybridization results in coexistent sub- and super-radiant modes, which manifest themselves in narrow Fano-lines promising for many application areas.17 Linear chains of nanoparticles are the most extensively studied one-dimensional clusters, which exhibit longitudinal and transversal resonances, when the E-field oscillation direction is parallel and perpendicular to their long axes, respectively.23−29 It was shown that the guiding properties of linear chains embedded into homogeneous media can be precisely tuned by the constituent nano-objects’ characteristics and distance.25,26 In case of optimal parameters, light incoupling can result in negative phase velocity,24 and in highly localized energy distribution.27 Although the presence of a substrate has a significant effect on the type of supported modes,29 linear chains arrayed on substrates were proposed for waveguide applications.23 Two-dimensional random30,31 and ordered32−38 arrays of NPs were also investigated thoroughly. Spectral lines originating from collective resonance phenomena30 as well as from quadrupolar modes31 were observed on NPs distributed randomly in dielectric media. The coincidence of dipolar collective and quadrupolar particle modes was observed, when the periodicity of square-arrays consisting of large nanospheres was tuned.33 Two-dimensional ordered NP arrays were inspected also on substrates to realize spectral engineering, which can be realized by tuning both the NP and the unit cell parameters to involve localized and propagating modes into coupled resonance phenomena.35−38 A novel approach is to organize versatile nanoscaled building blocks into higher order architectures via biomolecular crosslinking, which can result in directed self-assembly of aggregates with parameters widely tunable via proper chemical synthesis.20,22,39−53 The extremely small interparticle distances attainable via biomolecular linkers in two- or three-dimensional architectures make possible more types of collective resonances.41,50−53 Moreover, two-dimensional nanorod assemblies and three-dimensional NP tetrahedra linked by DNA are capable of introducing a chirality.45,46,48,49 Our previous studies indicated that the relative dominance of near- and far-field couplings sensitively depends on the E-field oscillation orientation with respect to the long axes of elongated ensembles, as well as on the aggregates’ orientation with respect to the lattice.51,53 All above-described higher order architectures made of noble metal nano-objects are of great interest in biosensing applications of nanoplasmonics due to their unique spectral properties.14−53 Plasmon-enhanced biosensing exploits the capabilities of spectral engineering, because by increasing the EM-field intensity at the absorption bands of specific bioobjects both the sensitivity and the specificity of detection can be improved.54−59 According to this, a novel class of biosensing platforms has been developed on the basis of the monitoring of LSPR and coupled resonance phenomena. In chemical procedures used to create composite architectures, a targetreceptor method is usually applied to bound biomolecules onto nano-objects; as a result, the biomolecule-mediated aggregation inherently ensures the overlap of molecules with high intensity EM-field. A further important advantage of aggregate-based biosensors is that the attainable versatile geometrical arrange-

2. MATERIALS AND METHODS 2.1. Preparation and Experimental Study of Silver Nanoparticle Dispersions. The synthesis of citrate-reduced silver nanoparticles (Ag NPs) was presented in our previous works.51−53 First, UV−visible spectroscopic characterization of bare nanoparticles-containing dispersion was performed after incubation for several hours at room temperatures. The prepared silver nanoparticles were subsequently functionalized by L-cysteine amino acid, by adding aqueous solution of a desired compound to the citrate stabilized Ag NPs. For experimental spectral study, dispersions containing Ag NP−Cys bioconjugates with a 30:1 molar ratio corresponding to monomolecular coverage of NPs were applied. The pH of the dispersions was adjusted by using 0.01 M HNO3 and NaOH solutions. The aggregation process of the Ag NP dispersions in the presence of L-cysteine was followed by a diode array spectrophotometer (Ocean Optics USB2000) in λ = 300− 700 nm range using a 1 cm thick quartz cuvette. The spectra were registered after 2 min during the aggregation process. The maxima of the measured absorptance spectra were determined via spline fit. On the basis of an extended spectral study described in our previous article, pH = 5.7 is the highest pH value, where Ag NP aggregation occurs in the presence of thiol group-containing amino acid.52 The diameter of individual Ag NPs was determined by TEM, while the average size of the aggregates was inspected by dynamic light scattering (DLS) method using a Zetasizer Nano ZS ZEN 4003 apparatus (Malvern Ins., UK). Three parallel DLS measurements were carried out similarly to our previous works.49−52 3. THEORETICAL APPROACH 3.1. Computation of Absorptance Spectra and NearField Distribution by Finite Element Method. We used finite element method (FEM) by applying the Radio Frequency module of COMSOL Multiphysics software package (COMSOL AB) to calculate the spectra of different aggregates. The purpose was to determine the degree of aggregation that 17941



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Figure 1. Schematic drawing of linear and wavy Ag NP−Cys aggregates showing all computation parameters: N is the number of Ag nanoparticles, d indicates the diameter of Ag nanoparticles, t is the thickness of the Cys-shell, while the small gap between Ag NPs is indicated by g. The colored arrows indicate the directions of E-field oscillation during p-polarized light illumination. Both the azimuthal angle (γ) and the polar angle (φ) are varied during FEM computations. On the three-dimensional schematic drawings, A, B and Aw, Bw reveal that different types of far-field and near-field couplings are at play in arrays of linear and wavy aggregates, which are aligned parallel to the Y axes.

Helmholtz equation becomes homogeneous. This way the solutions, the eigenvalues, can be transformed to the resonant frequencies of the system. Because the PMLs and dielectric losses make the problem nonlinear, the eigenvalue equation was linearized and solved in close proximity of frequencies corresponding to the UV and red-shifted peaks. While performing these computations, attention was paid to the symmetry features of our models by applying a symmetrypreserving mesh. The contribution of near- and far-field coupling phenomena in arrays to the absorptance peaks was considered by analyzing the strength of near-field originating from the neighboring aggregates, according to the method described in our previous works.51,53 The unit-cell size parameter was taken into account via the kgrating,x/y = ex/y2π/P wave vector of the two-dimensional grating, where ex/y is a unit vector along the X and Y directions. The long linear chains were included in a larger P = 744 nm periodic array, while the shorter wavy aggregates were investigated in a P = 600 nm periodic array. The corresponding different strength near-field coupling between nearby aggregates is indicated by B and Bw coupling in the insets of Figure 1. To inspect the effect of the illumination direction, first we have varied the E-field oscillation direction by setting the γi,j azimuthal angle to 0°, 30°, 60°, and 90° for i = 1, j = 1,2,3,4 values at perpendicular incidence, that is, at φ1,j = 0° (Figure 3; c, d, e, f in Figures 5 and 7; a, b, e, f in Figures 6 and 8). In a second parametric sweep, we have set the light incidence angle to analogous φ2,j = γ1,j polar angle values at constant γ2,j = 0° azimuthal orientation (Figure 4; g, h in Figures 5, 7; c, d, g, h in Figures 6, 8). Finally, we have studied the normalized as well as the time-dependent E-field in the XY plane at 5 nm apart from the aggregates’ axes, to analyze the steady-state E-field intensity distribution (Figures 5−8), and the time-evolution of the nearfield on the chains (Supporting Information movies S1−16), respectively. The time-dependent E-field distributions at analogous azimuthal and polar angles (γ1,j =0°, 30°, 60°, 90° at φ1,j = 0°, φ2,j = γ1,j, and γ2,j = 0°, for j = 1,2,3,4) are presented in the same multimedia file, where the indices i = 1,2 correspond to the top and bottom movies, to make a detailed comparison of all excited eigenmodes and coupled guided modes possible.

explains the absorptance spectra measured on dispersions of aggregates at pH = 5.7. The spectral effect of the simplest one-dimensional linear and two-dimensional wavy aggregate geometries was investigated. Absorptance spectra of aggregates made of Ag NP−Cys bioconjugates arrayed along simple linear ensemble and along wavy chains composed of two quarter-circles were computed (Figure 1). It is important to notice that by changing the geometry, the type of dominant interparticle coupling as well as the number of efficiently interacting particles are altered under the same illumination conditions. The studied aggregate geometries are qualified by the N number and d diameter of Ag nanospheres, t thickness of the Cys-shell, and g small gap between the NPs. The d = 8.25 nm average diameter of Ag NPs was selected in computations according to TEM measurements (inset in Figure 2). The t thickness of the Cys-shell was 0.45 nm, which corresponds to monomolecular coverage by this amino acid.52 The gap considered in present work is g = 0.875 nm, which approximates the realistic case of nonintersecting shells. Further advantage of this gap is that the d/(d+g) diameter-to-distance ratio corresponds to the optimal parameter, which results in the largest spectral splitting according to the literature.25 In FEM computations, the complex refractive index of Ag was taken from the Palik database interpolating the measured data set with a spline-fit.60 The refractive index of L-cysteine was taken into account with a Cauchy-formula of proteins (ncys = AC + BC/λ2) including AC = 1.45, BC = 0.01 m2 parameters based on ref 61. The wavelength-dependent nwater refractive index of water was taken into account by neglecting the pH-dependence according to previous works in the literature.62 The spectra were first computed from 300 to 700 nm with 10 nm resolution, and then the simulation was completed with 1 nm resolution around the maxima at γ = 0° and φ = 0° illumination directions (Figures 2−4). The eigenfrequency analysis of COMSOL software was used to calculate the resonant eigenmodes of different aggregates and to map the corresponding near-field distribution in the frequency interval of absorptance maxima (Figures 5a,b and 7a, b). For this purpose, eigenfrequency study was added as a study type, and eigenvalue solver is used as the solver sequence. In this study, there is no source or excitation; as a result, the 17942



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4. RESULTS AND DISCUSSION 4.1. Comparison of Spectra Measured at pH = 5.7 and Computed on Single Ag NP and on Linear and Wavy Ag NP−Cys Aggregates in Arrays. According to TEM measurements, the average diameter of Ag NPs is d = 8.25 nm, while the DLS revealed that the hydrodynamic diameter of the aggregates is 431.7 ± 119 nm with PDI = 0.31, indicating that the system of aggregates is considerably polydisperse.

Although, both of these spectral positions are in the interval of UV peaks observed on Ag NPs−Cys dispersions, stand-alone Lcysteine coated particles cannot account for the high measured absorptance, because complementary TEM investigations proved the dominance of aggregated ensembles (inset in Figure 2). According to this, the contribution of aggregate arrays consisting of chains with linear and wavy geometries to the spectral response was considered, and the calculated absorptance curves were normalized to each other to ensure the same apparent concentration of aggregates with different geometries. Finally, the measured absorptance curve was normalized to that computed absorptance peak, which resulted in a better fit (Figure 2). The array of linear chains results in a narrow absorptance peak, while the absorption band of the wavy aggregate array has a fwhm commensurate with the fwhm of the measured maximum. The explanation is that the wavy aggregate array is more complex, possesses more types of farfield and near-field coupling phenomena indicated by Aw and Bw couplings in the insets of Figure 1, and most probably it is more likely to be the real system of aggregates. 4.2. Impact of Illumination Direction on the Spectra of Linear and Wavy Ag NP−Cys Aggregates in Arrays. We analyzed the spectra of linear and wavy aggregates at different illumination directions considering that the aggregates are oriented randomly in realistic solutions. Already in case of perpendicular incidence (φ = 0°) and in case of parallelism of the E-field oscillation direction to the long axes of aggregates (γ = 0°), both UV and red-shifted maxima are observable. However, the absorptance is considerably larger on both types of aggregates at the red-shifted peaks under these circumstances (Figure 2, as well as Figures 3 and 4). 4.2.1. Impact of γ Azimuthal Angle on the Spectra of Linear and Wavy Ag NP−Cys Aggregates in Arrays. By modifying the γ azimuthal orientation in case of perpendicular incidence (φ = 0°), the direction of the E-field oscillation with respect to the chain axis is varied; as a consequence, the corresponding E|| = Ey projection varies proportionally to cos γ values. The phase of the incident light is the same on every Ag NPs at perpendicular incidence; as a result, in-phase oscillating particles are involved in collective resonance phenomena, in contrast to the case when the φ polar angle differs from zero (Figures 3 to Figure 4). The increase of γ azimuthal angle has a considerable effect on the spectra; the red-shifted maximum gradually decreases, while

Figure 2. Absorptance spectra measured on Ag NP−Cys bioconjugates’ dispersion at pH = 5.7 (wine ), and absorptance spectra computed by FEM for bare (navy − − −) and cysteine coated (blue ·) Ag NP, as well as for the linear chain-like ensemble (red - - -) and wavy aggregate (orange − · − · −), with N, g parameters presented via legends, illuminated at γ = 0° and φ = 0° directions, which result in absorptance maxima surrounding the measured UV and red-shifted peaks. The inset indicates TEM picture about the extended aggregates.

On the basis of our FEM studies, the maximum appearing at 398 nm on the calculated spectrum of d = 8.25 nm diameter Ag spheres coincides with the absorptance maximum measured on bare Ag NPs in the absence of Cys.51,53 The Fröhlich-condition for spherical particles is fulfilled at this absorptance maximum, εAg,real/εH2O(398 nm) ≈ −2, in accordance with the literature.1 Our FEM computations have also shown that stand-alone Lcysteine coated silver nanospheres with the investigated diameter result in a single maximum at 402 nm.51,53 The shift as compared to the bare Ag NP spectrum is caused by the change in dielectric environment from water to L-cysteine.

Figure 3. Transformation of split spectra (a) of linear chains consisting of N = 63 Ag NPs positioned with a g = 0.875 nm gap in P = 744 nm periodic array, and (b) of wavy aggregates consisting of N = 34 Ag NPs positioned with a g = 0.875 nm gap in P = 600 nm periodic array, when the azimuthal orientation is tuned at perpendicular incidence of p-polarized light from γ = 0°, resulting in dominantly longitudinal resonance, to γ = 90°, resulting in exclusively and dominantly transversal resonance on linear and wavy aggregates, respectively. 17943



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Figure 4. Transformation of the split spectra (a) of linear chains consisting of N = 63 Ag NPs positioned with g = 0.875 nm gap in P = 744 nm periodic array, and (b) of wavy aggregates consisting of N = 34 Ag NPs positioned with a g = 0.875 nm gap in P = 600 nm periodic array, when ppolarized light is incident on the aggregates at γ = 0° azimuthal orientation and the polar angle is increased from φ = 0° resulting in dominantly longitudinal resonance, to φ = 81° resulting in dominantly transversal resonance.

angles approximating the grazing incidence, it might be extrapolated from the observed tendencies that the red-shifted peak gradually decreases, while the UV peak increases further, when the polar angle approximates φ = 90° value. By comparing the spectra at analogous azimuthal and polar angles, and also at the commensurate γ = 90° azimuthal and φ = 81° polar angles, one can conclude that both the UV and the red-shifted peaks are larger at oblique incidence (Figure 3 to Figure 4). Moreover, the red-shifted peak on the linear chain decreases with a significantly smaller rate during tilting, which results in a considerable remaining absorptance peak for this aggregate geometry as well. These results reveal that grating coupling phenomena on periodic aggregate arrays significantly influence the spectra at large tilting. The agreement between the computed and measured peaks in the UV proves that not only the single Ag NPs, but also the aggregates contribute significantly to the UV absorptance maximum. The coexistence of maxima in different spectral intervals indicates that significantly different collective resonances may develop on arrays of extended aggregates, with relative dominance depending on the E-field oscillation and illumination direction. Near-field evidence of different multipolar modes’ existence and proof of their origin, longitudinal and transversal couplings between individual NPs inside aggregates with different geometries, as well as grating coupling on the aggregate arrays, are presented in section 4.3. 4.3. Impact of Illumination Direction on the NearField Distribution around Linear and Wavy Ag NP−Cys Aggregates in Arrays. The closely packed silver nanospheres exhibit dipolar resonance inside both aggregates. On the linear aggregate, the same orientation of individual dipoles with respect to the tangential of the chain makes possible the most efficient longitudinal and transversal coupling uniformly, when the E-field oscillation direction is parallel (γ = 0°) and perpendicular (γ = 90°) to the long axes, respectively. Inside the wavy chain it depends on the location of individual spheres, whether they are coupled transversally or longitudinally with their neighbors at specific illumination direction. As a result of NP distribution-dependent coupling phenomena, more complex characteristic collective resonances develop on the wavy aggregates. The resonances on wavy ensembles depend more sensitively on the illumination direction than the resonances on simple linear NP chains described in the previous literature.23−29,51,53

the UV maximum gradually increases in case of both aggregate geometries (Figure 3a,b). The ratio of the red-shifted and UV peaks is larger on the spectra of linear aggregates at small γ values. Although the red-shifted peak is smaller on the wavy aggregate at perpendicular incidence, the absorptance decreases with a considerably smaller rate on this ensemble in this spectral interval. At γ = 90° azimuthal orientation on the linear aggregate, only a small UV peak is observable, and there is no remaining redshifted peak, while on the wavy aggregate beside the commensurate UV peak a smaller red-shifted peak persists. A further difference between the two investigated aggregate geometries is that the UV absorptance involves several little peaks on the linear chain, while a single small UV peak is observable on the wavy chain at any azimuthal orientation. The remaining small red-shifted peak reveals that the considerably larger extension of the wavy aggregate along the E-field oscillation direction makes it possible to excite longitudinal resonances also along the 62.5 nm short axes in the γ = 90° azimuthal orientation, as it is described in section 4.3. 4.2.2. Impact of φ Polar Angle on the Spectra of Linear and Wavy Ag NP−Cys Aggregates in Arrays. For the same values of γ and φ angles, the corresponding E|| = Ey projection is equal, while during tilting both the E|| = Ey and the k|| = ky wave vector components parallel to the chain are tuned. In addition to this, during φ polar angle variation, the phase difference between neighboring illuminated spheres is tuned as well, in contrast to constant phase maintenance during γ azimuthal angle tuning (Figures 4 to Figure 3). The increase of the φ polar angle has a very similar effect on the spectra, as the azimuthal angle enhancement; the dominance of the red-shifted maximum gradually decreases, while the UV maximum gradually increases (Figure 4a,b). However, on both aggregate arrays, by increasing the polar angle, the red-shifted maximum first slightly increases through 30° tilting, then monotonously decreases, while the UV maximum monotonously increases through the entire polar angle interval. The ratio of maxima at the UV and red-shifted peaks is similar on spectra of linear and wavy aggregates at small tilting. Moreover, at φ = 60° polar angle, the UV and redshifted maxima are commensurate on both aggregates. Both peaks modify more rapidly in case of a wavy aggregate, and an additional difference is that at 81° tilting the UV peak becomes split and the attained maximum is larger. Although FEM computations can be performed only throughout polar 17944



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φ polar angles (first γ1,j is set to 0°, 30°, 60°, 90°, at φ1,j = 0° and then γ2,j = 0°, φ2,j = γ1,j). The wave vector of the grating coupled guided modes was determined as the vectorial sum of photonic wave vector’s projection onto the XY lattice plane and of the grating wave vectors: kLSPR, coupled = kphotonic, xy + nxkgrating, x + nykgrating, y, where nx, ny = ...−1, 0, 1... refer to the order of grating coupling. Taking into account that kphotonic, xy = |kphotonic sin φ|ei reduces to kphotonic, y in all investigated oblique incidence cases, because γ = 0°, kLSPR, coupled = kphotonic, y + nxkgrating, x + nykgrating, y (Figure 5g,h; Figure 7g,h; c,d,g,h in Figures 6 and 8) was computed. At oblique incidence (nx, 0) couplings are capable of resulting in forward propagating guided modes for positive as well as negative values of nx; these cases are indicated by magenta continuous wavy arrows. In contrast, both (0, ny) and (nx, ny) grating couplings can result in forward as well as in backward propagating guided modes with wavelength commensurate with the observed ones. Backward propagating guided modes appear, when ny < 0, and |kphotonic, y| < |nykgrating, y|, and are indicated by magenta wavy arrows, when they result in the appearance of resonator modes. The normalized E-field reveals that dominantly even (e.g., quadrupolar) modes develop at the violet peaks in all of the investigated cases (a,c,e,g in Figures 5−8), while dominantly odd (e.g., dipolar) modes appear at the red-shifted maxima (b,d,f,h in Figures 5−8), Tables 1 and 2. The eigenmode study proved that the linear aggregates in the P = 744 nm periodic array prefer to resonate in 2*λLSPR/2 = L and λLSPR/2 = L antenna-like modes at the UV and red-shifted maximum corresponding to 2m = 2 and 2m+1 = 1 cases, similarly to strings with fixed ends (Figure 5a,b). These eigenmodes are resonant modes that are excitable on a linear chain with one particle diameter vertical cross-section in the frequency interval of the absorptance maxima. At γ = 0° azimuthal orientation and perpendicular incidence (γ = 0°), the linear aggregate indicates dominantly a quadrupolar oscillation in 2*λLSPR/2 = L mode at the UV peak (Figure 5c, Supporting Information movie S1), while at the red-shifted peak a resonance intermittently in two types of λLSPR/2 = L dipolar modes is observable (Figure 5d, Supporting Information movie S2). Even though the individual dipoles are uniformly longitudinally coupled at both absorptance maxima, different normalized E-field modulation corresponding to quadrupolar and dipolar modes appears along the linear chain at the UV and red-shifted peaks, respectively (insets in Figure 5c,d). The (±1,1) and (±1,−1) grating couplings on the P = 744 nm periodic array are capable of promoting resonant oscillation in ∼2*λLSPR/2 = L mode at the UV peak. At the red-shifted peak, the wavelength of grating coupled 1.5*λLSPR/2 = L modes is significantly shorter than the observed one. This indicates that the appearing oscillation corresponds to the resonant eigenmode of linear aggregate arrays at the 5.53 × 1014 Hz eigenfrequency. The UV peak appearance is promoted by the long extension of the linear chain, which inherently makes it possible to develop an intensity distribution corresponding to quadrupolar modes; however, the related absorptance remains small as compared to the red-shifted peak (Figures 3 and 4). At γ = 90° azimuthal orientation, when the light is incident again perpendicularly (φ = 0°), the E-field oscillates perpendicularly to the long axes of the aggregates. The linear chain exhibits an unambiguous 2*λLSPR/2 = L quadrupolar mode at the UV peak (Figure 5e, Supporting Information

On the basis of our computations, the dielectric covering with L-cysteine promotes these coupling phenomena; that is, the role of amino acid is not only initialization of aggregation, but also the modification of optical properties in the medium surrounding the Ag NPs.51,53 Illumination by p-polarized light results in fundamentally different resonances on extended aggregates in different spectral regions. To uncover these collective resonances, first the resonant eigenmodes excitable at frequencies in close proximity of the UV (Figures 5a, 7a) and red-shifted (Figures 5b, 7b) absorptance maxima were analyzed on the linear (Figure 5a,b) and wavy (Figure 7a,b) aggregates. These eigenmodes were compared to the near-field distributions observable at γ = 0° and φ = 0° angles (Figures 5c,d, 7c,d), that is, when the E-vector oscillates along the long axes of aggregates and the light is incident perpendicularly, which corresponds to excitation of dominantly longitudinal resonances. The near-field distribution was also studied at γ = 90°, φ = 0° illumination direction (Figures 3, 5e,f, 7e,f), when transversal resonances’ excitation occurs exclusively and dominantly on linear and wavy chains at perpendicular incidence, as well as at γ = 0°, φ = 81° (Figures 4, 5g,h, 7g,h), when the largest tilting is capable of exciting dominantly transversal resonances. Finally, the nearfield distribution was compared both on linear and on wavy aggregates, when they were illuminated at analogous intermittent relative E-field oscillation directions with respect to the long axes of chains, at γ = 30°, φ = 0° and γ = 0°, φ = 30° (a,b and c,d in Figures 6, 8) as well as at γ = 60°, φ = 0° and γ = 0°, φ = 60° azimuthal−polar angles (e,f and g,h in Figures 6, 8). On the basis of the literature, the eigenmodes’ excitation is accompanied by peaks in absorptance on wires, rods, and antennas, which support multipolar modes depending on their length.63−67 According to this, the wavelength of antenna-like resonant plasmonic eigenmodes was compared to the length of the aggregates by inspecting the possible wavenumber matching (Figures 5a,b, 7a,b).63−67 In the presence of even (e.g., quadrupolar) modes, 2m-times half-wavelength is commensurate with the L length of the ensemble |kLSPR| = 2m(π/L) (m = 1, 2, 3...), while in the presence of odd (e.g., dipolar) modes, 2m+1-times half-wavelength covers the entire aggregates |kLSPR| = (2m+1)(π/L) (m = 0, 1, 2...) (Table 1). Taking into account that the aggregates are in a twodimensional array, the coupling via nxkgrating,x as well as via nykgrating,y grating wave vectors along the X and Y axes has to be considered, where nx, ny = ...−1, 0, 1... are integers referring to grating coupling order. The grating wave vectors are indicated with continuous and dashed orange arrows for positive and negative X, Y directions on the diagrams of c, d, g, h in Figures 5−8. The 8.25 and 62.5 nm extension of the linear and wavy aggregates along their short axes is small as compared to the longer ones; as a consequence, grating coupling to guided modes only along their long axes was considered. The role of grating coupling was analyzed in case of γ azimuthal angle tuning at perpendicular incidence (φ = 0°), comparing the vectorial sum of grating wave vectors to the wavenumber of the observable resonant eigenmodes kLSPR, coupled = nxkgrating,x + nykgrating,y (Figure 5c,d, Figure 7c,d).51,53 Finally, grating-coupled guided modes appearing at different polar angles were analyzed by comparing the time-average as well as the time-evolution of the E-field along the aggregates at the absorptance maxima observed at analogous γ azimuthal and 17945



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Figure 5. Normalized E-field of the eigenmodes corresponding (a) to f1 = 7.40 × 1014 Hz eigenfrequency at the UV and (b) to f 2 = 5.53 × 1014 Hz eigenfrequency at the red-shifted peak on the P = 744 nm periodic array of linear aggregates. The normalized E-field distribution at the (c,e,g) UV peaks, and at the (d,f,h) red-shifted peaks, when the array of linear aggregates is illuminated at (c,d) γ = 0°, φ = 0°; (e,f) γ = 90°, φ = 0°; (g,h) γ = 0°, φ = 81° orientations. (c,d,g,h) Vectorial diagram of grating couplings that contribute to the observable modes.

movie S3a). Significant difference with respect to the γ = 0° case is that at γ = 90° azimuthal orientation antinodes appear at the aggregates’ end, instead of nodes (Figure 5e to c). At the wavelength corresponding to the suppressed red-shifted peak, the E-field indicates a weak and tiny dipolar mode perpendicularly to the linear chain (Figure 5f, Supporting Information movie S4a). The individual dipoles are coupled uniformly transversally at γ = 90° azimuthal orientation; moreover, the long extension of the linear chain makes possible the development of a quadrupolar mode. Both of these conditions promote absorptance at the UV peak (inset in Figure 5e). Caused by the small 8.25 nm extension of the linear chain, resonance in the transversal dipolar mode along the E-field oscillation direction is not capable of resulting in a red-shifted absorptance maximum at this azimuthal orientation (Figure 3a, inset in Figure 5f). The E-field distribution is more complex at both absorptance peaks in case of large tilting at γ = 0° azimuthal orientation (Figure 5g,h). At φ = 81° angle of incidence, squeezed guided plasmonic modes appear, which can be considered as modes

supported by the insulator−metal−insulator (IMI) waveguide consisting of Ag NPs (Figure 5g, Supporting Information movie S3b and Figure 5h, Supporting Information movie S4b). Surprisingly, a standing mode with almost zero group velocity is observable at the UV peak on the linear aggregate on the timedependent E-field distribution as well (Figure 5g, Supporting Information movie S3b). This standing mode is composed of ∼4*λLSPR/2 = L forward and backward propagating guided modes, which originate from grating couplings in (±2,−1) and (±2,−4), (0,−5) orders, respectively (Table 1). Peculiarity of this angle of incidence is that the NPs are illuminated at both chain ends by light with the same phase, because L sin φ = 2*λ/nwater condition is fulfilled. The phase matching is ensured by phase-shifts occurring upon launching of guided modes that propagate forward and backward at the UV peak, and is maintained due to the simple symmetry of the linear chain and to the commensurability of the coupled modes’ halfwavelength with the long axes. The resulted coupled standing mode is similar to the resonator mode described in the literature.26 The existence of such resonator modes on linear aggregates supporting squeezed IMI modes is important for 17946



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Table 1. Results of Measurements and Computations on Linear Aggregate Array (N = 63, d = 8.25 nm, L = 575 nm, P = 744 nm): Position of Maxima (λ1, λ2) and the Corresponding Split (Δλ) on the Resulted Spectra, the Order of Grating Coupling (nx, ny) and the Ratio of the Eigenmodes (Appearing at Perpendicular Incidence), and Dominant Coupled Guided Plasmonic Modes’ Half-Wavelength to the Aggregate Length (2m and 2m+1 Refer to Even and Odd Numbers, Respectively) λ1 (nm)

(nx, ny)

2m and 2m+1

398 388

λ2 (nm)

single measured γ−φ/linear 0°−0°

403

(±1,1) (±1,−1)

2.2 2.2

545

30°−0° 0°−30°

400 380 390 370

90°−0° 0°−81°

390 380

2.2 2.6 2.6 2.2 3.9 3.7 4.0 4.1 2.2 3.9 3.8 3.7

540 540

60°−0° 0°−60°

0°−0° cases (±1,0) (0,−3) 0°−0° cases (±1,0) (±2,−1) (±2,−4) (0,−5) 0°−0° cases (±2,−1) (±2,−4) (0,−5)

(nx, ny)

2m and 2m+1

548

540 540

540 540

Δλ (nm) 160

(0,1) (±1,0) (0,−1) 0°−0° cases (±1,0) (±1,−2) (±1,0) (±2,−2)

1.5 1.5 1.5 1.5 2.1 2.3 1.5 2.9 3.2

0°−0° cases (±1,0) (±2,−2) (0,−4)

1.5 3.2 3.1 3.4

142

140 160 150 170

150 160

At γ = 30° azimuthal orientation and at perpendicular incidence (φ = 0°), the linear aggregate supports a 2*λLSPR/2 = L quadrupolar and two types of λLSPR/2 = L dipolar modes at the UV and red-shifted peak, respectively (Figure 6a, Supporting Information movie S5a and Figure 6b, Supporting Information movie S6a). Because of the 30° tilting of NP dipoles with respect to the aggregates’ long axes, the transversal and longitudinal coupling between them is slightly promoted and suppressed, and the resulted quadrupolar and dipolar mode is slightly enhanced and decreased, respectively (inset in Figure 6a,b). At γ = 0° azimuthal orientation and analogous φ = 30° tilting, the (±1,0) and (0,−3) order grating couplings result in forward and backward propagating guided modes with 2.6*λLSPR/2 = L characteristics at the UV maximum (Figure 6c, Supporting Information movie S5b, Table 1). A standing resonator mode appears again, which is promoted at φ = 30° incidence angle by light illumination with the same phase of NPs at both chain ends, because L*sin φ = λ/nwater condition is fulfilled again. Taking into account the equivalence of the grating coupled modes’ wavelength, and the quarter wavelength scaled chain length, the phase matching reveals that there is a π difference between phase-shifts occurring upon launching of guided modes that propagate forward and backward. At the red-shifted maximum, the (±1,0) and (±1,−2) order grating couplings result in forward and backward propagating guided modes with ∼2*λLSPR/2 = L characteristics (Figure 6d, Supporting Information movie S6b, Table 1). The superimposed even coupled modes are noticeable on the normalized E-field at the red-shifted peak. This indicates that the parity of dominant modes was modified on the aggregates array, because modes of reversal parity are grating-coupled with good efficiency. At larger γ = 60° azimuthal angle and perpendicular incidence, the linear aggregate supports a 2*λLSPR/2 = L quadrupolar and λLSPR/2 = L dipolar mode at the UV and redshifted peak, similarly to the γ = 30° orientation (Figure 6e, Supporting Information movie S7a and Figure 6f, Supporting

applications, because these resonator modes are accompanied by a very large EM-field confinement. Accordingly, 5 times larger intensity is observable at 81° tilting as compared to perpendicular incidence (Figure 5g to c). At the red-shifted peak a forward propagating guided mode with ∼3*λLSPR/2 = L characteristics is observable, which originates from grating coupling in (±1,0) orders. Although, the (±2,−2) and (0,−4) grating couplings result in similar ∼3*λLSPR/2 = L backward propagating guided modes, these couplings do not result in a resonator mode (Table 1). Accordingly, a modulation with wavelength corresponding to the λLSPR/2 = L eigenmode is observable on the normalized Efield (Figure 5h, Supporting Information movie S4b). When L = 575 nm long linear aggregates are horizontally aligned with P = 744 nm periodicity, the 169 nm distance between them can result in end-fire coupling from neighboring unit cells. This end-fire coupling indicated as a B coupling in Figure 1a enhances the far-field grating coupling, manifests itself in a nonsymmetric normalized E-field distribution, and promotes the appearance of multipolar modes. The timeevolution of the near-field pictures reveals that especially in case of large tilting the end-fire coupling indeed results in intense guided plasmonic modes, which superimpose on the eigenmodes excitable under specific illumination conditions (Figure 5g, Supporting Information movie S3b and Figure 5h, Supporting Information movie S4b). Our previous computations realized by applying unit cells with the same periodicity, but containing vertically aligned aggregates, indicated less significant UV maxima, confirming the role of end-fire coupling in horizontal arrays.51,53 The comparison of the near-field distribution along the aggregates at analogous 30° and 60° azimuthal orientations and polar angles confirmed that squeezed guided IMI modes originating from grating coupling appear at specific polar angles, which are superimposed on well-defined eigenmodes excitable on the linear chains at specific relative E-field oscillation directions with respect to their long axes. 17947



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Figure 6. Normalized E-field distribution at the (a,c,e,g) UV peaks, and at the (b,d,f,h) red-shifted peaks, when the array of linear aggregates is illuminated at (a,b) γ = 30°, φ = 0°; (c,d) γ = 0°, φ = 30°; (e,f) γ = 60°, φ = 0°; (g,h) γ = 0°, φ = 60° orientations. (c,d,g,h) Vectorial diagram of grating couplings that contribute to the observable modes.

this relative E-field oscillation direction, and by the phase difference arising between aggregates’ ends at φ = 60° incidence angle. At the red-shifted peak, guided modes with ∼3*λLSPR/2 = L characteristics propagate forward due to grating coupling in (±1,0) orders (Figure 6h, Supporting Information movie S8b), while the grating coupling in (±2,−2) orders results in a similar ∼3*λLSPR/2 = L backward propagating guided mode (Table 1). The parity of dominant modes is not modified at the redshifted peak on the time-dependent E-field; 2m+1 = 1 and 2m+1 = 3 odd modes remain dominant. However, normalized E-field modulation with a wavelength significantly smaller than that of the eigenmode is noticeable due to the modes that are grating-coupled at φ = 60° tilting. On the basis of eigenmode computations, 2*λLSPR/2 = L and λLSPR/2 = L eigenmodes corresponding to 2m = 2 and 2m+1 = 1 are observable also on the wavy aggregate at the UV and redshifted peak, respectively (Figure 7a,b). However, the wavy aggregate prefers to oscillate similarly to a string with E-field maxima at the middle and ends of the chain at the UV peak, which differs from the field distribution of the 2*λLSPR/2 = L

Information movie S8a). A fundamental difference in normalized E-field distributions at the UV peak is that antinodes appear at both aggregate ends, revealing that different phase shift occurs upon launching at γ = 30° and at γ = 60° azimuthal orientations (Figure 6e to a,c). Caused by the intermediate 60° orientation of the NP dipoles with respect to the long axes, the transversal and longitudinal coupling between them is more significantly promoted and suppressed, respectively (inset in Figure 6e,f). As a result, the strength of quadrupolar and dipolar modes as well as the corresponding absorptance peaks become commensurate (Figures 3 and 4). At γ = 0° azimuthal orientation and analogous φ = 60° tilting at the UV maximum, the (±1,0) and (±2,−1) order grating couplings result in ∼4*λLSPR/2 = L forward propagating guided modes, and similar ∼4*λLSPR/2 = L backward propagating guided modes also originate from (±2,−4) and (0,−5) couplings (Figure 6g, Supporting Information movie S7b, Table 1). However, a less well-defined standing resonator mode appears, caused by phase and wavelength mismatch between forward and backward propagating guided modes coupled at 17948



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Figure 7. Normalized E-field of the eigenmodes corresponding (a) to f1 = 7.93 × 1014 Hz eigenfrequency at the UV and (b) to f 2 = 5.41 × 1014 Hz eigenfrequency at the red-shifted peak on the P = 600 nm periodic array of wavy aggregates. The E-field distribution at the (c,e,g) UV peaks, and at the (d,f,h) red-shifted peaks, at (c,d) γ = 0°, φ = 0°; (e,f) γ = 90°, φ = 0°; (g,h) γ = 0°, φ = 81°. (c,d,g,h) Vectorial diagram of grating couplings that contribute to the observable modes.

mode on the linear chain. At the red-shifted peak, zero-field is observable at both ends; that is, the main characteristics of the E-field distribution of λLSPR/2 = L mode are analogous on the two different aggregates. The degree of IMI modes’ squeezing is almost 2 times larger on the wavy chain, indicating that the E-field confinement is strongly influenced by the two-dimensional NP aggregates’ shape. However, in case of wavy aggregates, we expect more complex near-field phenomena, because as real two-dimensional architectures they inherently support higher order multipolar modes. Moreover, due to the commensurability of their 283 nm long axes with one-half of the P = 600 nm unit

cell size parameter, altogether seven different order grating couplings on the P = 600 nm periodic array enhance resonant oscillations corresponding to ∼2*λLSPR/2 = L modes, while the (0,1), (±1,0), and (0,−1) order couplings promote ∼1*λLSPR/2 = L modes’ appearance on the wavy aggregate, respectively (Table 2). This condition is fulfilled both at the UV and at the red-shifted maxima at perpendicular incidence at any azimuthal orientation; however, those couplings come to play exclusively, which are promoted by the charge distribution at specific γ azimuthal orientation. Resonator modes are not supported because of symmetry breaking on centrally symmetric ensembles of NPs; on the contrary, dominance of coupled guided modes that propagate forward is expected. 17949



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Table 2. Results of Measurements and Computations on Wavy Aggregate Array (N = 34, L = 283 nm/310 nm, P = 600 nm): Position of Maxima (λ1, λ2) and the Corresponding Split (Δλ) on the Resulted Spectra, the Order of Grating Coupling (nx, ny) and the Ratio of the Eigenmodes (Appearing at Perpendicular Incidence), and Dominant Coupled Guided Plasmonic Modes’ Half-Wavelength to the Aggregate Length (2m and 2m+1 Refer to Even and Odd Numbers, Respectively) γ−φ/wavy

λ1 (nm)

(nx, ny)

2m and 2m+1

λ2 (nm)

2m and 2m+1

Δλ (nm)

0°−0°

380

(0,1) (±1,0) (0,−1)

0.9 0.9 0.9

160

380 400

540 540

0°−0° cases (±1,0) (0,−2)

0.9 1.2 1.2

160 140

60°−0° 0°-60°

380 400

530 540

0°−0° cases (±1,0) (0,−3)

0.9 1.5 1.6

150 140

90°−0°

380

1.9 1.9 1.9 2.1 2.1 2.1 2.1 0.9 1.9 1.9 2.1 2.1 2.1 2.1 0.9 1.9 1.9 2.0 2.1 1.9 2.1

540

30°−0° 0°−30°

(0,2) (±2,0) (0,−2) (±1,2) (±2,1) (±2,−1) (±1,−2) 0°−0° cases (0,1) (±2,−1) (±1,1) (±2,−2) (±1,−3) (0,−3) 0°−0° cases (±1,0) (±2,−2) (±2,−1) (0,−4) 0°−0° cases

530

0°−0° cases

150

0°−81°

390

(±2,−2) (0,−4) (±1,0) (±2,−1) (±2,−3)

1.9 1.9 2.1 2.1 2.1

530

(0,−3) (±1,0)

0.9 1.9 2.1 1.4 1.7

At γ = 0° azimuthal orientation and perpendicular incidence (φ = 0°), the wavy aggregate indicates a quadrupolar oscillation corresponding to the 2*λLSPR/2 = L mode at the UV peak, which exhibits E-field maxima at the middle as well as at the chain-ends, in contrast to the linear aggregate (Figure 7c, Supporting Information movie S9 to Figure 5c, Supporting Information movie S1). The UV peak is larger on the wavy aggregate (Figures 3 and 4), because all nanoparticle dipoles distributed along the 62.5 nm short axes are coupled efficiently transversally, and as a result they are involved in quadrupolar resonant oscillation (inset in Figure 7c). At the red-shifted peak, the wavy chain oscillates intermittently in two types of λLSPR/2 = L dipolar modes, similarly to the linear chain (Figure 7d, Supporting Information movie S10 to Figure 5d, Supporting Information movie S2). The modes exhibiting antinode at the arcs of the wavy chain are dominant, which originate from longitudinally coupled dipoles (inset in Figure 7d). According to the commensurate absorptance peaks, the wavy aggregate indicates well-defined multipolar modes both at UV and at red-shifted maxima at γ = 90°; however, the types of these oscillations are fundamentally different (Figure 7e, Supporting Information movie S11a and Figure 7f, Supporting Information movie S12a). At the UV peak, the entire wavy chain oscillates dominantly in 2*λLSPR/2 = L quadrupolar mode with E-field nodes at the middle as well as at the ends of the aggregate (Figure 7e, Supporting Information movie S11a). Accordingly, the E-field

(nx, ny)

140

maxima appear at arcs of the aggregate, where the NPs are coupled transversally (inset in Figure 7e). At the red-shifted peak, the wavy ensemble oscillates intermittently in a λLSPR/2 = L dipolar and in a weak 2*λLSPR/2 = L quadrupolar mode. In both cases, there is dominantly an E-field antinode at the middle of the aggregates (Figure 7f, Supporting Information movie S12a). The dipolar mode is enhanced by (0,1), (±1,0), and (0,−1) order grating couplings, while seven different types of grating couplings listed for the case of perpendicular incidence promote the appearance of the quadrupolar mode (Table 2). The parity of the dominant mode is modified caused by grating coupling and by the unique distribution of NP dipoles at specific illumination direction. The E-field maxima appear at the middle and ends of the aggregates, where the NPs are coupled longitudinally (inset in Figure 7f). It is important to notice that in the presence of either 1 or 2*λLSPR/2 = L modes, a dipolar mode appears along the short axes of the wavy aggregate as well. This dipolar mode accounts for the remaining red-shifted peak on the wavy aggregate (Figure 3b). Although a similar 2*λLSPR/2 = L quadrupolar mode is observable on the wavy aggregate at large φ = 81° tilting at the UV peak, the normalized E-field intensity is 10 times larger than in case of perpendicular incidence (Figure 7g, Supporting Information movie S11b to Figure 7c, Supporting Information movie S9). This field-enhancement proves that intense squeezed guided IMI modes propagate on the chain in addition to the 2*λLSPR/2 = L eigenmode. Indeed, forward propagating ∼2*λLSPR/2 = L guided modes originate from (±2,−2), (±1,0), 17950



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Figure 8. Normalized E-field distribution at the (a,c,e,g) UV peaks, and at the (b,d,f,h) red-shifted peaks, when the array of wavy aggregates is illuminated at (a,b) γ = 30°, φ = 0°; (c,d) γ = 0°, φ = 30°; (e,f) γ = 60°, φ = 0°; (g,h) γ = 0°, φ = 60° orientations. (c,d,g,h) Vectorial diagram of grating couplings that contribute to the observable modes.

coupled guided modes causes that the parity of dominant modes is modified on the normalized E-field at the red-shifted peak. At γ = 30° azimuthal orientation and perpendicular incidence, the wavy aggregate supports λLSPR/2 = L dipolar modes both at the UV and at the red-shifted peaks (Figure 8a, Supporting Information movie S13a and Figure 8b, Supporting Information movie S14a). The appearance of a dipolar mode at the UV peak is promoted by all seven different grating couplings occurring on the P = 600 nm array at perpendicular incidence. The parity of the dominant mode at the UV peak is modified due to unique spatial distribution of longitudinally and transversally coupled NPs. The individual NP dipoles can

and (±2,−1) order grating couplings at this orientation (Table 2). Although analogous ∼2*λLSPR/2 = L counter-propagating guided modes are grating coupled in (0,−4) and (±2,−3) orders (Table 2), no resonator mode is observable on the wavy aggregate caused by symmetry breaking. The length of the wavy aggregate is commensurate with the quarter wavelength of the dominant guided mode appearing at the red-shifted peak at φ = 81° tilting (Figure 7h, Supporting Information movie S12b). Indeed, the (±1,0) order grating coupling results in forward propagating ∼1.5*λLSPR/2 = L guided mode, while (0,−3) order grating coupling results in backward propagating guided mode with characteristics similar to ∼1.5*λLSPR/2 = L, however, with a slightly smaller wavelength (Table 2). The coexistence of different grating 17951



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The observed spectral modifications are in accordance with the E-field enhancement dependence on the illumination direction, which is mainly determined by the E|| = Ey projection onto the long axis of resonant antenna-like objects, for example, on spheroids and antennas.65,66 By modifying either the γ azimuthal or the φ polar angle, the longitudinal coupling strength between the Ag NPs is varied according to the modification of the Ey ≈ cos γ and Ey ≈ cos φ field component parallel to the aggregates’ long axes, respectively. Moreover, the rotation of the E-field and k vectors with respect to the aggregate axes causes that the relative dominance of the longitudinal and transversal coupling inside aggregates is tuned; that is, not only the strength, but the type of dominant coupling also varies.51,53 The individual dipoles are coupled uniformly with their neighbors on the linear chain at any azimuthal orientations at perpendicular incidence (insets in Figure 5c−f and Figure 6a,b,e,f), while on the wavy aggregate it depends significantly on the NP location, whether a specific NP dipole is coupled transversally and longitudinally with their neighbors (insets in Figure 5c−f, Figure 6 a,b,e,f, Figure 7c−f, and Figure 8a,b,e,f). The cartoons about the orientation of individual dipoles show that at any transitional E-field projection the near-field intensity along the two-dimensional wavy aggregates is proportional to the amount of dipoles that are coupled transversally and longitudinally at the UV and red-shifted maximum, respectively. Figures 2−4, as well as Figure 5c,d and Figure 7c,d, indicate that in the case of illumination at γ = 0° azimuthal orientation and at φ = 0° polar angle, when the E-field oscillation direction is parallel to the long axes, dominantly longitudinal resonances develop both on linear and on wavy aggregates. Because of the parallelism of the E-field oscillation to the aggregates’ long axes, longitudinal coupling is dominant between in-phase oscillating dipoles on all individual spheres on the linear chain and on spheres located at the arcs on the wavy aggregate. The coupling strength is maximized at perpendicular incidence, because the light reaches all spheres with the same phase in both aggregates. On the basis of the literature, one could expect that these longitudinal resonances manifest themselves exclusively in redshifted peaks.67 Accordingly, the comparison of the near-field intensities shows that the E-field intensity is significantly larger at the red-shifted maxima (Figure 5c to d and Figure 7c to d). However, our computations indicate that collective resonances are excited and result in tiny UV peaks as well on both types of aggregates (Figures 2−4). This is due to the large extension of the aggregates; the long axes of both investigated chains are larger than the ∼40 nm size required for the appearance of a quadrupolar resonance according to the literature.5 In addition to this, on the wavy aggregate the NPs are transversally coupled at the middle as well as at the chain ends, which enhances the quadrupolar mode related UV peak. Increasing the azimuthal angle at perpendicular incidence from γ = 0° to 90° causes that on the linear chain the coupling between individual spheres modifies gradually from longitudinal to transversal (Figures 1, 3, Figure 5c−f, and a,b,e,f in Figure 6). On the wavy chain, the location of spheres, which are coupled transversally and longitudinally, is modified as well; as a consequence, the EM-field corresponding to collective resonances is redistributed (Figures 1, 3, Figure 7c−f, and a,b,e,f in Figure 8); moreover, the dominant resonant modes’ parity is modified at specific orientations (Figures 7f, 8a,e). At γ = 90° azimuthal orientation, when the E-field oscillates perpendicularly to the aggregates’ long axes, the interparticle

be transversally coupled exclusively at the middle of the wavy aggregate at γ = 30° azimuthal orientation (inset in Figure 8a). At the red-shifted peak, oscillation intermittently in two types of dipolar modes is observable; however, the modes with E-field maxima at the end parts of the arcs are dominant, due to the presence of longitudinally coupled individual dipoles (inset in Figure 8b). At γ = 0° and analogous φ = 30° tilting, the (0,1), (±2,−1), (±1,1), (±2,−2) order grating couplings result in forward propagating ∼2*λLSPR/2 = L guided modes, while the (±1,−3), (0,−3) order grating couplings result in similar backward propagating ∼2*λLSPR/2 = L guided modes at the UV peak (Figure 8c, Supporting Information movie S13b, Table 2). The coexistence of grating coupled modes at the UV maximum with different propagation directions causes that the normalized Efield distribution is altered as compared to the γ = 30° and φ = 0° case, and exhibits 2*λLSPR/2 = L characteristics again. At the red-shifted maximum, the same ∼1*λLSPR/2 = L modes propagate forward and backward due to (±1,0) order and (0,−2) order parallel grating coupling, respectively (Figure 8d, Supporting Information movie S14b, Table 2). The enhancement of the red-shifted peak at φ = 30° tilting is promoted by the same parity of the eigenmode and of the forward and backward propagating guided modes coupled by the grating. At γ = 60° azimuthal orientation, the wavy aggregate supports a λLSPR/2 = L mode, however, with nodes and antinodes at both ends of the UV and red-shifted peak, respectively (Figure 8e, Supporting Information movie S15a, Figure 8f, Supporting Information movie S16a). The odd mode appearance in the UV is promoted again by seven different grating couplings occurring on the P = 600 nm array at perpendicular incidence. The parity of the dominant mode at the UV peak is modified due to unique synergy of longitudinal and transversal couplings; the individual NP dipoles can be efficiently transversally coupled throughout the entire wavy chain except the chain ends at γ = 60° azimuthal orientation (inset in Figure 8e). At the red-shifted peak, the field maxima appear at the end of the arcs, where the dipoles on the individual NPs can be coupled longitudinally (inset in Figure 8f). At γ = 0° and analogous φ = 60° tilting, the (±1,0), (±2,−1), (±2,−2), and (0,−4) order grating couplings result in similar ∼2*λLSPR/2 = L forward and backward propagating guided modes at the UV maximum (Figure 8g, Supporting Information movie S15b, Table 2). The coexistence of grating coupled guided modes with different propagation directions results in normalized E-field distribution with shallow 2*λLSPR/2 = L characteristics, which is superimposed on the λLSPR/2 = L mode observable at γ = 60° and φ = 0° illumination directions (Figure 8g to e). At the red-shifted maximum, the (±1,0) and the (0,−3) order grating coupling results in ∼1.5*λLSPR/2 = L forward and backward propagating guided modes, respectively (Figure 8h, Supporting Information movie S16b, Table 2). As a result, the normalized E-field modulation exhibits quarter-wavelengthscaled characteristics, which is superimposed on the eigenmode observable at γ = 60° and φ = 0° illumination direction. In summary, either azimuthal angle variation or off-axis illumination of the aggregates does not effect neither the position of extrema nor the degree of splitting, revealing that collective resonance phenomena occur on the Ag NP ensembles. 17952



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and promotes the contribution of higher order modes, which manifest themselves in strongly enhanced UV peaks.

coupling is uniformly transversal on the linear chain (inset in Figure 5e,f), while hybrid longitudinal and transversal couplings occur on the wavy chain both at the UV and at the red-shifted peaks (insets in Figure 7e,f). Although the phase is the same on each constituent particle at perpendicular incidence, the type of supported modes sensitively depends on the distribution of individual NPs, and on the length of the aggregates’ short axes (Figure 5e,f; Figure 7e,f). Exclusively and dominantly transversal resonances develop on the linear and wavy chains, respectively; these resonances manifest themselves in a tiny split UV peak on the linear aggregate, while on the wavy aggregate UV and red-shifted peaks coexist. The persisting redshifted peak reveals that the condition both of transversal and of longitudinal coupled resonances is fulfilled on the twodimensional NP architecture. The 62.5 nm short axes of the wavy aggregate make possible that longitudinal resonance oscillation appears along this direction, which manifests itself in the remaining red-shifted peak. The presented results indicate that by changing the relative orientation of the E-field oscillation direction as well as of the kphotonic, xy wave vector with respect to the aggregates, fundamentally different multipolar modes can be excited by p-polarized light illumination (Figures 3−8). When the light is incident obliquely, the phase of the dipolar oscillations on the near-field coupled individual Ag spheres is polar angle dependent, which has an impact on the efficiency of coupling into resonant eigenmodes at specific E-field projection (Supporting Information movies S1−16). The larger is the φ polar angle, the larger is the phase difference between the neighboring particles (Figures 1, 4, Figure 5g,h, Figure 7g,h; c,d,g,h in Figures 6 and Figure 8). As a result, different gratingcoupled squeezed guided IMI modes appear at specific illumination directions, when the E|| = Ey ≈ cos φ projection gradually decreases, while the k|| = ky ≈ sin φ projection of the wave vector gradually increases.67 Inspection of the near-field proved that in case of oblique incidence, guided plasmonic modes originating from different order grating couplings appear, which superimpose on the resonant eigenmodes of the aggregates. Superposition of antenna-like eigenmodes and different coexistent gratingcoupled guided modes accounts for that the normalized Efield exhibits a modulation at oblique incidence, which differs from the field distribution observable at analogous azimuthal orientation at perpendicular incidence (Figures 5g, 6g,h, 7h, 8c,d,g,h). The (nx, ny ≠ 0) grating coupled backward propagating guided modes play a role in standing resonator modes’ appearance at the UV peaks on the linear aggregate. The peculiarity of the two illumination directions, which resulted in resonator modes, is that both ensure in-phase excitation at the ends of the linear chain. The red-shifted peaks and the corresponding near-field enhancement are slightly larger at φ = 30° than in the case of perpendicular incidence on both investigated aggregates, which is due to that all dipoles excited by modes originating from different grating couplings are concentrated into the largest fraction of NPs, that is into the same quarter of the NPs (Figure 4, Figure 6d, Figure 8d). Finally, tilting to φ = 81° (∼90°) causes that transversal coupling between dipolar oscillations on individual NPs on the entire linear chain and at the arcs of the wavy aggregate is promoted, while the highest phase gradient along the NP ensembles is maintained (Figure 1, Figure 5g,h, Figure 7g,h). This phase gradient causes symmetry breaking along the chains,

5. CONCLUSIONS We have inspected the origin of absorptance spectra on aggregates consisting of biofunctionalized silver nanoparticles. Our present FEM computations proved the effect of the E-field oscillation orientation as well as of the light illumination direction on the spectra, and uncovered the role of resonant eigenmodes and grating-coupled squeezed guided plasmonic and standing resonator modes in spectral splitting. On the basis of the presented results, the near-field phenomenon accompanying the appearance of UV peaks is the appearance of dominantly even eigenmodes, while at the red-shifted peaks odd eigenmodes develop dominantly on the aggregates. Both nonparallel E-field orientation and oblique incidence enhance the UV peak significantly, while during tilting grating coupling results in squeezed guided IMI modes enhancing both peaks on the aggregate arrays. We have demonstrated that under specific circumstances resonator modes appear, which manifest themselves in standing waves accompanied by large EM-field enhancement. Our present results uncovered that the local EM-field intensity on extended two-dimensional, for example, wavy aggregates at the UV and red-shifted absorptance maxima is directly proportional to the amount of resonantly oscillating NP dipoles that are efficiently coupled transversally and longitudinally with their neighbors, respectively. The knowledge of this relationship offers a tool for precious near-field tailoring on higher order architectures: it is possible to rearrange the E-field maxima corresponding to modes of specific parity simply by changing the azimuthal orientation at the same wavelength, as it is shown in Figure 5c to e and Figure 6a to e, Figure 7c to e. On the basis of our results, it is suggested to illuminate the aggregates at 90° azimuthal orientation, when a specific type of biomolecules has to be detected, which prefers to attach to the archs of the wavy aggregate, because this way the E-field can be enhanced at desired locations. Periodic structures designed to realize the appropriate biomolecule positioning and EM-field localization simultaneously can be fabricated by applying, for example, polydimethyl-siloxane (PDMS) templates. It was also proven that the parity of dominant eigenmodes can be modified via grating coupling, for example, by applying transitional azimuthal orientation during illumination of the wavy aggregate at the UV peak (Figure 7a,e to Figure 8a,e), as well as at the red-shifted peak (Figure 7b to ), which opens novel avenues in applications of aggregate arrays. By modifying the parity, it is possible to force the E-field concentration to the middle of the wavy aggregate at 30° and 60° azimuthal orientation, which is advantageous for selective excitation of biomolecules, preferring to adhere to this part of the ensemble. Moreover, the possibility of parity change will make it possible to generate different highorder harmonics at the same frequency, by modifying simply the azimuthal orientation during illumination of two-dimensional NP architectures. The investigated aggregate geometries can be considered as model systems applicable for LSPR sensors calibration. Measurement of spectra originating from coupled resonances will make it possible to determine the degree of aggregation, and the pH as well as biomolecule concentration based on the previously mapped dependence of aggregation on these parameters. A near-future prospect is that biomolecules 17953



Article

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captured during nanoscale heterostructures’ synthesis can be detected with extremely high sensitivity. Further studies are in progress on chiral effects of two- and three-dimensional wavy aggregates, as well as on nonlocal phenomena on arrays of closely packed NPs.

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ASSOCIATED CONTENT

S Supporting Information *

Time-evolution of the near-field on the linear and wavy Ag NP−Cys aggregates presented in the XY plane at 5 nm apart from the axes of both chains. To make a detailed comparison of the excited modes possible in one multimedia file, the timedependent ((Re Ex)2 + (Re Ey)2 + (Re Ez)2)1/2 quantity is presented under two different illuminations conditions. The azimuthal and polar angles (φij, γij) are set as follows: γ1j is set to 0°, 30°, 60°, and ∼90° at φ1j = 0°, then γ2j = 0°, and φ2j = γ1j, where the indices i = 1,2 correspond to the top and bottom movies, respectively. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This publication has been supported by the European Union and cofunded by the European Social Funds, project title “Impulse lasers for use in materials science and biophotonics”, project number TÁ MOP-4.2.2.A-11/1/KONV-2012-0060; and project title “Supercomputer, the national virtual lab”, project number TÁ MOP-4.2.2.C/11/1/KONV/2012-0010. This research was supported by the European Union and the State of Hungary, cofinanced by the European Social Fund in the framework of TÁ MOP-4.2.4.A/2-11/1-2012-0001 “National Excellence Program”. We acknowledge Á ron Sipos and József Balázs for their help in the preparation of the movies and figures.

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REFERENCES

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