Plasmon Hybridization in Stacked Double Crescents Arrays

Jan 10, 2011 - Chromium (1.5 nm), used as adhesion promoter, and gold (25 nm) were .... fundamental plasmon mode (termed c1) featuring one node in the...
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Plasmon Hybridization in Stacked Double Crescents Arrays Fabricated by Colloidal Lithography Nicolas Vogel,*,†,§ Janina Fischer,†,§ Reza Mohammadi,†,‡ Markus Retsch,† Hans-J€urgen Butt,† Katharina Landfester,† Clemens K. Weiss,† and Max Kreiter† † ‡

Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany Physics Department, Shahid Chamran University, Ahvaz, Iran

bS Supporting Information ABSTRACT: We apply colloidal lithography to construct stacked nanocrescent dimer structures with an exact vertical alignment and a separation distance of approximately 10 nm. Highly ordered, large arrays of these nanostructures are accessible using nonclosepacked colloidal monolayers as masks. Spatially separated nanocrescent dimers are obtained by application of spatially distributed colloids. The polarization dependent optical properties of the nanostructures are investigated in detail and compared to single crescents. The close proximity of the nanocrescents leads to a coupling process that gives rise to new optical resonances which can be described as linear superpositions of the individual crescents’ plasmonic modes. We apply a plasmon hybridization model to explain the spectral differences of all polarization dependent resonances and use geometric arguments to explain the respective shifts of the resonances. Theoretical calculations are performed to support the hybridization model and extend it to higher order resonances not resolved experimentally. KEYWORDS: Nanosphere lithography, nanostructures, split ring resonators, metamaterials, plasmons, plasmon hybridization

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n nanoscale metallic objects, collective oscillations of electrons, known as plasmon resonances are excited upon interaction with electromagnetic irradiation. Their resonance wavelength crucially depends on size and geometry of the metallic structure and has been subject to intensive research.1 An assembly of such structures, featuring sizes below the wavelength of the incident radiation can be approximately described by an effective homogeneous refractive index, in analogy to the refractive index of ordinary matter that is based on the collective response of many individual molecules.2 These assemblies have been termed metamaterials as they can be designed to possess unique properties not occurring in nature, most prominently negative refraction.3,4 Substantial attention has been focused on these metamaterials as they hold promise to be used in sophisticated applications as perfect lenses5,6 and optical cloaking devices.7-9 Split ring resonators have been found to be valuable building blocks for such materials as the incident light excites circulating currents in these structures, leading to local magnetic dipole moments that can counteract the incident magnetic field and result in negative permeability, a prerequisite for negative refraction.4,10,11 Since the size of the objects must be substantially smaller than the wavelength of the electromagnetic field, the fabrication of metamaterials at or close to optical wavelengths remain challenging. Major efforts have been undertaken to design periodic arrays of split ring resonators in two and three dimensions with high precision. Predominantly, modern lithographic techniques as electron beam lithography or focused ion beam milling are employed. Metamaterials in two and three dimensions have thus been produced1,12 and negative refraction has been demonstrated at various wavelengths approaching the visible range.3,13-15 These methods, priced for their resolution and positioning precision, however, intrinsically feature drawbacks that hamper r 2011 American Chemical Society

widespread applications, both in larger scale technological applications as well as in academic research. First, expensive equipment is needed not being readily available at every facility. Second, due to their serial character the production of arrayed structures, consisting of many individual objects, is time-consuming; large area patterning thus becomes cumbersome if not impossible. Third, the quality of the noble metals used, and with them the optical properties of the structures, are in general compromised due to contaminations. These arise from residues of photoresist and amorphous carbon for electron beam processes as well as contamination and doping with heavy ions employed by focused ion beam milling. A conceptually simple, yet powerful alternative consists of the use of colloidal particles for the formation of nanostructures. Sacrificing the possibility to generate any desired object shape, it overcomes the major drawbacks of serial processing. Without the use of expensive instruments, large areas can be structured in a highly parallel fashion. Furthermore, as noble metals are deposited by vacuum evaporation, impurities and contaminations can be reduced to a negligible level. As colloidal monolayers feature a high degree of symmetry and can be fabricated with particles of a broad range of sizes, precise control of size and lateral spacing of structures at the nanoscale is readily achieved. Originally, closed-packed monolayers were used to design arrays of nanotriangles with sizes between several tens to several hundred of nanometers.16-18 Using more sophisticated processes and nonclose-packed arrangements, arrays of Received: September 3, 2010 Revised: October 26, 2010 Published: January 10, 2011 446

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more complex structures have been fabricated, including embedded objects,19,20 discs,21 rings22 and nanoscale crescents.23,24 The latter are of special interest as they support several multipolar resonances25-27 and can be considered the optical equivalent to split ring resonators. Thus, a possibility to design metamaterials in a cost-efficient way was introduced. Recently, 3D arrays of nanocrescents have been fabricated in a layer-by-layer fashion using colloidal lithography.23 The approach uses a sol-gel process to cover one layer of nanostructures with insulating material followed by another lithography step. Thus, the mutual orientation of the crescents can be controlled. However, vertical alignment of the crescents with respect to the underlying layer has not yet been achieved using a colloidal approach for structuring. The vertical alignment, paired with short separation distances introduces intriguing changes in the optical spectra of nanostructures arising from interaction of the plasmonic resonances. A theoretical model, termed plasmon hybridization, has been established to explain such coupling effects for nanoparticle dimers.28,29 This hybridization model can be seen as an electromagnetic analogue to molecular orbital theory: the plasmonic resonances of two nanostructures in close proximity to each other undergo a coupling process that gives rise to new resonances as linear superpositions of the original resonances. In this picture, the two particles can be described as a plasmonic molecule,30,31,34 similar to two atoms chemically bound to form a molecule. As the wave function of these atoms can be superimposed to give rise to a binding- and an antibinding molecular orbital in the molecule, the plasmonic modes hybridize as well. Recently, the concept has been extended to describe the coupling of the fundamental mode of split ring resonators.30,32 Here, we present a quasi 3D fabrication technique leading to stacked nanocrescents arrays with precise vertical alignment using a colloidal lithographic approach. The process leaves ample degrees of freedom to control various aspects of the structures, including size, lateral spacing, vertical spacing as well as mutual orientation, thus allowing for precise adjustment of the plasmonic resonances of the particle array. Extended 3D structure generation as demonstrated by Retsch et al.23 is sacrificed in favor of precise control over the vertical alignment of the crescents and thus to gain access to the observation of strong coupling effects in the stacked crescents. Large areas of highly ordered stacked crescents arrays were produced by a colloidal lithography approach. A hexagonally closed packed colloidal monolayer was assembled on a glass substrate by preassembly of latex particles at the air water interface using a process developed by Retsch et al.33 (experimental details are given in the Supporting Information). This monolayer was subjected to a mild plasma treatment to shrink the colloids in size and hence produce nonclose-packed monolayers. The hexagonal symmetry of the original monolayer was preserved as the colloids effectively kept their positions during the etching procedure. The nonclose-packed monolayer (Scheme 1a) was used as a mask for the patterning process. Chromium (1.5 nm), used as adhesion promoter, and gold (25 nm) were evaporated under an angle of 30° with respect to the surface normal (Scheme 1b). Afterward, the sample was rotated by 180° and silicon dioxide (20 nm), chromium (1.5 nm), and gold (25 nm) were evaporated under an angle of -30°. In this way material was deposited in the areas under the colloids shaded by the colloidal spheres in the previous evaporation step (Scheme 1c). Reactive ion beam etching (RIE) perpendicular

Scheme 1. Process Flow for the Fabrication of Stacked Nanocrescent Arraysa

a

(a) Assembly of the colloidal monolayer and subsequent plasma induced size reduction. (b) Evaporation of gold under an angle of 30° with respect to the surface normal. (c) Evaporation of silicon dioxide and gold under an angle of -30° with respect to the surface normal. (d) Reactive Ion Beam Etching (RIE) normal to the surface to remove gold and SiO2 from the areas not protected by the colloids. (e) Removal of the colloids to uncover the stacked crescent arrays. (f) Close up of the crescent arrays to highlight the separation of the two crescents by the intermediate SiO2 layer.

to the surface was used to remove all material not protected by the colloids. Material deposited under the colloids was not affected by the ion beam and therefore, remained on the surface (Scheme 1d). Using rubber glue, the colloidal monolayer was selectively removed without inducing damage to the nanostructure array (Scheme 1e). The process led to the formation of arrays of stacked double crescents. The individual double crescents are separated by a thin layer of insulating silicon dioxide and hence, represent two individual plasmonic structures in very close proximity. Because of the 180° rotation in between the two evaporation processes, the two crescents are symmetric with their tips facing each other and overlapping over a length of approximately 40 nm. The 3D arrangement with one nanocrescent being on top of the other is visualized in Scheme 1f. The diameter of the individual crescents was 450 nm (see Supporting Information Figure SI3 for a detailed sketch of the crescent dimensions). The lattice spacing in the array of the crescents is determined by the colloidal monolayer as well and reflects its symmetry. For the actual structure array in this study, the interparticle spacing was approximately 100 nm. 447

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Figure 1. Scanning electron microscopy (SEM) images of the stacked nanocrescents arrays. Top row: single crescents arrays representing the first layer in the stacked crescent configuration. (a) Top view; (b) side view. Bottom row: stacked crescents arrays. (c) Top view; (d) side view. The black arrows highlight the separation layer between the two crescents. For a better illustration of the preparation method, the side-view images were taken on a sample where the colloidal monolayer used as mask was not removed.

Figure 1 shows SEM images of the structures prepared. In the top insets, the high symmetry of the arrays is well visible. The slightly undefined edges of the structures result from the fact that during the plasma etching process, the surface of the colloids roughened. This roughness is transferred to the nanostructures during the evaporation process. The side view images give information about the vertical structure of the nanostructures. To investigate the process at different stages and to produce reference samples with single crescents arrays, reactive ion etching was performed after the first evaporation of gold (upper part of Figure 1). This leads to the formation of single gold crescents in the areas protected by the colloids (Figure 1b). The complete, stacked double crescents structures are shown in Figure 1c,d. Again, the high symmetry of the structure can be seen in the top view images while the side view images (Figure 1d) show the separation of the individual single crescents by the silicon dioxide layer (indicated by arrows). The total lateral extension of the structure array is determined by the colloidal monolayer and extends to several square centimeters (Supporting Information Figure SI1). The process leaves ample degrees of freedom to tune the resulting structures. First, choosing colloids with different diameters and varying the etching time used to reduce the size of the particles, both, the size of the nanostructures as well as the lattice spacing in the array can be precisely adjusted. Second, varying the height of the silicon dioxide layer separating the stacked crescents enables the fine-tuning of the coupling efficiency of the two separate resonators and, thus, gives access to tailor-made optical resonances. Another parameter to tune the structural design is the evaporation angle of gold that can be used to vary the overlap of the stacked double crescents. Finally, changing the azimuthal angle for the second gold evaporation relative to the first one gives rise to completely different symmetries in the architectures of the stacked crescents as the second crescent can be oriented with any chosen angle with respect to the first one (please refer to

Supporting Information Figure SI2 for an exact definition of all relevant parameters). An azimuthal angle of 180°, being subject of this study, leads to structures with a strong overlap on the edges with optical phenomena described below. Furthermore, the high symmetry of the stacked structures gives rise to resonances without a dipole moment; commonly referred to as dark modes. Such resonances are of importance for the creation of negative refraction materials as they can possess negative values for the permeability.10,11,32,35 A drawback of the fabrication technique presented in this paper is the inherent restriction in 3D space for the structure generation. This stems from the fact that colloids are used for the crescents generation that provide limited space underneath to shade the structures to be formed during the reactive ion etching step (compare Figure 1d). Therefore, the stacking of multiple crescent structures will be difficult. However, choosing bigger colloids, the stacking of several layers of larger crescents is feasible due to their comparably low height (typically, the height of a single crescent is 25 nm). Sacrificing extended 3D structure design, we gain access to perfect alignment of the nanostructures, a feature that has not yet been accomplished with a colloidal lithography process. As demonstrated by samples prepared by electron beam lithography with all the limitations discussed above, the vertical alignment of the separate crescents makes them valuable as plasmonic molecules with strong interparticle coupling of the individual resonators plasmonic resonances.32 UV-vis-NIR spectroscopy was used to gain fundamental understanding of the optical properties of the stacked double crescent structures (Figure 2). The incident beam was normal to the crescent coated substrate surface and linearly polarized for all measurements. As objects, single crescents, stacked double crescents and rings were investigated and compared. The latter were generated by a similar process as the double crescents but without the intermediate silicon dioxide layer. 448

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Figure 2. UV-vis-NIR spectra of spatially separated single crescents (a) and stacked crescents pairs (b) and arrays of the respective objects (c,d). SEM images are depicted in the insets. Panels (e,f) illustrate the plasmonic hybridization model used to explain the shifts of the plasmonic resonances in the double crescent structures. (e) Linear superposition of two single crescents in c resonance; the close proximity results in a new coupled pair consisting of symmetric mode cþ and an antisymmetric mode c- with c- being energetically lower compared to cþ due to the off-phase oscillation that leads to charges with opposite sign to be in direct vicinity. (f) Coupling scheme for resonances excited upon irradiation with u polarized light. Similar to (e), the close proximity of the two crescents lead to hybridization of the single plasmon resonances that split up into the symmetric mode uþ and the antisymmetric mode u-. In analogy to (e), the antisymmetric mode u- is lower in energy.

The optical properties of the individual stacked double crescents were examined on samples with randomly distributed, spatially separated objects as well. For that, colloidal particles were diluted with ethanol to a concentration of 0.01 wt %, a drop added to the glass slide and the solvent evaporated by a gentle nitrogen stream. This procedure led to individual colloidal particles being sparsely distributed over the substrate.26,27 To fabricate structures with a similar size as in the arrays, colloids with a diameter of 400 nm were used in the process (following an equal process as for the size-reduced arrays). The objects show multiple plasmonic resonances that, in most cases, are highly sensitive to the orientation of the crescents relative to polarization of the incident light beam. In accordance to work published earlier,25-27 linear polarization along the symmetry plane of a crescent will be referred to as “u” polarization, polarization perpendicular to the symmetry plane will be termed “c” polarization (Figure 2e,f).26 Figure 2 presents the extinction spectra recorded for the different nanostructures and compares the optical properties of spatially separated objects and nanostructure arrays. Scanning electron microscopy images of the respective crescent structures are shown as insets in the spectra. For better comparison, the wavelengths of the peak maxima are indicated. Simplified sketches of charge distributions in the objects at resonance are

shown in Figure 2e,f. Figure 2a shows the characteristic resonances of spatially separated, single crescents. In c polarization, a strong resonance at 2460 nm is visible that is attributed to the fundamental plasmon mode (termed c1) featuring one node in the middle of the crescent26,27 (see isolated crescent in Figure 2e). In u polarization, the c1 resonance disappears and a resonance at 1446 nm is excited. This resonance, termed u1, is attributed to the first harmonic (see isolated crescent in Figure 2f). Another peak at approximately 658 nm is visible in both spectra. This peak, previously termed pp (particle plasmon) as it roughly matches the resonance observed for very small gold objects, is assigned to a polarization of the crescents perpendicular to the contour.26,27 For connected crescent structures forming a closed ring, two resonances are excited at 2436 and 692 nm, none of which shows any dependence on the polarization of the incident light (spectra shown in the Supporting Information Figure SI4). This behavior reflects the symmetry of a ring which does not show any anisotropy and thus, no polarization dependence. The low energy peak at 2436 nm is assigned to the fundamental ring resonance that is comparable in energy to the fundamental resonance of the single crescents.26 The high energy peak arises from the particle plasmon resonance excited perpendicular to the ring contour. Spatially separating the two crescents to the stacked structure (Figure 2b) has drastic 449

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influences on the plasmonic resonances. It is obvious that the spectra differ strongly from the ones for rings, indicating that the thin separation layer has a dramatic influence on the optical properties. In agreement with the electron microscopy characterization, it becomes clear that the stacked crescent structures are indeed not ringlike. For c-polarized incident light, a peak emerges at 2004 nm that is blue shifted compared to the single crescents. the u polarization gives rise to a resonance at 2324 nm being strongly red shifted with respect to the single crescents. These shifts can be understood from plasmon hybridization as will be discussed below. The fundamental resonance c1 for single crescents is energetically lower compared to the first harmonic (u1) appearing in u polarization, in accordance to the number of nodes of the standing wave excited in the crescent (see single crescents in Figure 2e,f). The introduction of a second crescent in close proximity, however, leads to a resonance visible in u polarization with a lower energy compared to the plasmon mode excited in c polarization. In total, the energetic order of the resonances is reversed compared to the parent resonances c1 and u1 of the bare crescents. A high energy peak, being visible in both polarizations, is present at 658 nm. The latter appears at the same wavelength as for the single crescents and similarly is attributed to the resonance perpendicular to the contour of the crescents To explain the striking differences in the optical properties, we adopted a plasmon hybridization model to the stacked structures.28-31 The hybridization model can be seen as an electromagnetic analogue to molecular orbital theory: the plasmonic resonances of two nanostructures in close proximity to each other undergo a coupling process that gives rise to new resonances as linear superpositions of the original resonances. In this picture, the two resonators can be described as a plasmonic molecule.30,32,34 Similar to wave functions of atoms in a molecule, which can be superimposed to form a binding molecular orbital and an antibinding molecular orbital, the plasmonic modes hybridize as well. Figure 2e,f shows the formation of hybridized plasmon modes both for the c1 and u1 resonance of the single crescent. In both cases, the linear superposition leads to a pair of new modes. In the symmetric mode, termed cþ and uþ, respectively, the two crescents oscillate in phase, whereas in the antisymmetric hybrid mode (c- and u-), the oscillation occurs out of phase. The antisymmetric mode is reduced in energy compared to the symmetric one. For c-polarized light, the symmetric mode cþ features an enhanced dipole moment compared to the single crescents as the two crescents oscillate in phase (Figure 2e). Hence, the coupling efficiency to the external electric field is high and the cþ mode is detected in the spectrum shown in Figure 2b. In contrast, the out of phase oscillation of the antisymmetric mode c- leads to an electric field distribution in the stacked structure with no effective dipole moment present. Therefore, this mode cannot be excited by the external field and does not appear in the spectra.35 In total, the plasmonic resonance visible in the spectra is blue shifted compared to the single crescents’ fundamental mode c1. For u-polarized light, the physical model is similar to the c resonance; linear superposition of the u1 resonance gives rise to a new pair of resonances uþ and u- (Figure 2f). However, due to the different symmetry of the u1 mode, the situation is inverted. The symmetric mode uþ shows an electric field distribution resembling an electric quadrupole without a dipole present in the

Figure 3. Simulated UV-vis-NIR absorption spectra for single- and stacked double crescents for c and u polarization. The simulations reproduce the features of the experimental data and support the hybridization model.

plasmonic molecule. Hence, the coupling efficiency to the external light field is weak and the resonance does not appear in the spectrum of Figure 2c. The antisymmetric mode u- however, does feature an electric dipole and thus is excited by u-polarized light. Compared to the single crescents’ u1 resonance, the hybrid resonance being visible in the spectrum is red shifted. The coupling efficiency between the two crescents is sufficiently strong to induce a crossover of the plasmonic resonances compared to the single crescents with the lowest energy mode appearing in u-polarization. The picture given is in agreement with theoretical and experimental investigations of double split ring resonators produced by electron beam lithography, where plasmon hybridization was observed for the fundamental mode of the split rings.30,32 The spectra for separated objects and crescent arrays closely resemble each other (Figure 2a-d). In the particle arrays, all optical features are retained, including the crossover of resonances upon hybridization. Compared to the separated objects, the peaks of both hybridized plasmon modes in the stacked double crescents arrays are shifted by about 100 nm in the direction of the resonances for single crescents. This indicates a slightly decreased coupling efficiency, which is probably caused by a small deviation in the height of the silicon dioxide spacer layer and by the increase in roughness of the arrayed structure. The broadening of the peaks in the arrays is attributed to the increase in inhomogeneities. The higher surface coverage of the arrays is reflected by the increased extinction that was more than 1 order of magnitude higher than for the separated objects. To gain further insight into the response of the nanostructures to an external optical field, computer simulations of the optical properties using JCMwave were performed.36 The dielectric function used to model Au was based on the Drude model and fitted to experimental data of Johnson and Christy.37 The single and double crescents’ geometries were adapted from SEM images to match the experimental design. Schemes of the simulated crescents as well as exact dimensions are given in the Supporting Information. First, single crescents were simulated and reproduced the experimental data. Figure 3 shows the simulated spectra. In c polarization, three 450

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resonances are visible. The fundamental plasmon mode c1 appears at 2176 nm and thus agrees with the value observed experimentally with a blue shift of 200 nm. Additionally, the second harmonic resonance c2 appears at 960 nm. This resonance is not resolved in the experimental spectra, most probably due to insufficient intensity caused by a higher sensitivity of this mode to inhomogeneities in the nanoparticles structures. Finally, the mode assigned to as particle plasmon appears at approximately 550 nm. In u polarization, the first harmonic mode u1 becomes visible while the other modes are not excited, being in perfect agreement with both experimental data and models proposed. The mode peaks at 1265 nm. Compared to the experimental spectra, the peak shows a blue shift of 200 nm. The near field distributions at the different peak wavelengths is given in the Supporting Information Figure SI5 and agrees with the simplified sketches of the charge distributions presented in Figure 2e,f. The shifts of the resonances of the stacked double crescents with respect to the single crescents are in good agreement with the experimental results and support the plasmon hybridization model. For c-polarized incident light, the hybrid resonance cþ is strongly blue shifted compared to the c1 resonance of the single crescents. Thus, it corroborates with the plasmon hybridization model, which predicts the only visible resonance to be the higher energy mode cþ. The peak appears at 1690 nm, a value that is approximately 300 nm blue shifted compared to the experimental value. The hybrid analogue to the c2 resonance appears at 910 nm and is blue shifted compared to the c2 resonance of the single crescents. The hybridization behavior of this resonance will be discussed in more detail further below. In u polarization, the simulated spectrum shows one hybrid resonance at 1750 nm. Compared to the first harmonic resonance u1 of the single crescents, the hybrid resonance u- is red shifted and qualitatively agrees with the experimental results and the hybridization model. Moreover, the computer simulations also feature the crossover of resonances observed experimentally. Hence, it validates the finding that the coupling efficiency of the plasmon modes is strong enough to shift the lowest energy mode from being observed in c polarization to the perpendicular u polarization. Quantitatively, the hybrid mode u- is blue shifted compared to the measured data. In general, we attribute the quantitative discrepancies between simulation and experiments to the following differences. First, roughness effects are known to cause a significant red shift of the plasmon resonances as has been shown for gold nanodots.38 A detailed description of such effects on nanocrescent structures is under investigation in our group. Second, the precise determination of size and geometry of the double crescents is difficult as the first crescent is partially hidden underneath the second one. Additionally, the layer thickness of both gold and insulating layer is not constant for the complete crescent but diminishes around the wings and tips (see Figure 1). In the simulations however, it was taken as constant. Alteration of simulation parameters (such as values for the gold permittivity) as well as adapting more sophisticated models for the crescents (as including of the nonconstant gold and SiO2 layers) could improve the quantitative agreement between simulation and experiment. However, as all essential features of the experimental data are reproduced, no further refinements were performed. The c2 resonance and its hybridized analogue were examined in further detail by means of simulations. According to literature, the resonance is the second harmonic mode and features two nodes and a charge distribution as illustrated in Figure 4b.25-27

Figure 4. Hybrid plasmon mode arising from coupling of the c2 resonance. (a) Simulated spectra of stacked double crescents with varying overlap region. The hybrid c2þ resonance is highly sensitive to variations of the overlap. Compared to the single crescents’ c2 mode, the hybrid mode blue shifts with small overlap (40 nm) while a strong red shift is induced for the big overlap (120 nm). All c2þ resonance positions are indicated by a dotted line. (b) Model of plasmon hybridization for the c2 resonance. Linear superposition of the resonances lead to two hybrid modes termed c2þ and c2with c2þ being higher in energy. (c) Schematic representations of the charge distribution of the c2þ mode for a small and a big overlap of the crescents. For the small overlap, the charges at the tips of the crescents are in close proximity. The mode is blue shifted compared to the single resonance. With a big overlap, the tip charges cross the first node and come into closer proximity of the region with an opposing charge. Hence, the total energy of the hybrid mode is reduced.

Upon hybridization, the mode splits into the symmetric c2þ and the antisymmetric c2- hybrid resonances (Figure 4b). In analogy to the hybridization of c1, only the symmetric c2þ mode features a sufficient dipole moment to be excited by the external field. Therefore, a blue shift of the hybrid resonance compared to the single crescents c2 resonance is expected and can be seen in the simulations of Figure 3. Strikingly, the hybrid c2þ mode shows a strong dependency on the overlap in the stacked dimer architecture while c1 and u1 are not affected dramatically. The overlap describes the tip areas that directly face each other in the stacked structure. Experimentally, it can be increased by increasing the evaporation angle of gold and silicon dioxide (see Supporting Information Figures SI2 and 451

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Figure 5. Near-field distributions of the stacked double crescents at resonance wavelengths. First row: near field in the xy-plane cutting half of the glass layer in between the crescents. Second row: near field in the xz-plane cutting the stacked structure along the tip region. The cut plane is indicated by dashed lines in the top row images. For better visibility, the crescents have been highlighted by a dotted frame. (a,d) cþ resonance mode at a wavelength of 1690 nm. The symmetric mode has similar charges at the tips of the crescents. Hence, no field enhancement in between the tips is visible. (b,e) uresonance mode at wavelength of 1750 nm. The field enhancement in the overlap part is clearly resolved and shows that the tips are oppositely charged. (c,f) c2þ resonance mode at a wavelength of 910 nm. The additional nodes of the mode are visible in the xy-plane. The tips have similar charges, leading to a depletion of the electric field in the middle of the gap between the crescents in the xz-plane. The enhancement visible at both sides of the gap is a result of the proximity of the tip charge and the opposite charges in the wings of the tips.

3 for geometric details). Figure 4a shows the simulated resonance spectra for single crescents and stacked double crescents with 40 and 120 nm overlap region of the crescents tips with the first one representing the data shown in Figure 3. Upon hybridization, the peak shifts from 960 to 910 nm for a small overlap region of 40 nm. The increase of the crescents’ overlap region to 120 nm drastically changes the energetic situation for the c2þ resonance. A strong shift to longer wavelengths is induced and the hybrid mode now peaks at 1295 nm. Remarkably, the differences in overlap cause a change in shift direction with respect to the single crescents resonances. This behavior is attributed to regions with opposite charge in the crescents wings as illustrated in Figure 4c. For a small overlap region, only the charges at the tips of the crescents interact and lead to the high energy mode c2þ. With an increase in overlap, the charges present at the tips are getting into closer proximity to the opposite charges present in the wings of the crescents, leading to a substantial decrease in energy of the hybrid mode. Both the fundamental c1 resonance and the first harmonic u1 do not have additional charges in the wings and therefore, are not sensitive to changes of the overlap region (compare Figure 4a for c1 resonance and Supporting Information Figure SI6 for u1 resonance). However, this qualitative interpretation of the c2þ resonance shift is complicated by the appearance of a sharp Fano resonance at 1418 nm in the simulated spectra of the stacked double crescents with big overlap.39-41 The appearance of this type of resonance in plasmonic nanostructures has recently attracted significant attention. A Fano dip arises from destructive coupling between the broad, bright c1þ resonance with the subradiant c2mode and is characterized by a sharp minimum in the extinction spectra in the broad, super-radiant resonance mode. As the Fano dip strongly alters the extinction in the spectral region, it is difficult to assign the exact position of the c2þ resonance shifted by the differences in overlap. Nevertheless, the qualitative picture

for the coupling behavior of the hybrid c2þ resonance using geometrical arguments is further supported by near field distributions shown below. The effect of the separation distance on the optical properties was examined by simulations as well. With increasing separation distance, the hybrid mode shifts toward the resonances observed for the single crescents (see Supporting Information, Figure SI7). To examine the charge distributions of the crescent dimers for the different hybrid resonances excited, near field distributions were mapped at the resonance frequencies (Figure 5). The upper part of the figure gives the field distributions in the xy plane, parallel to the substrate. The cuts were taken in the middle of the insulating barriers. Thus, both crescents are in equal distance to the displayed plane. The field essentially probes the distribution of charges predicted by the hybridization model. The lower part of Figure 5 shows the near-field distribution along the gap between the interacting tips of the two crescents. The cut shows the xz plane, being perpendicular to the substrate surface, and cuts the crescents parallel to the symmetry axis along the tip region. The dotted line inserted into the upper images shows the plane of the cut. Figure 5a,d visualizes the field distribution for the cþ resonance at 1690 nm. A strong field is present in the regions of the tips of the crescents, reflecting the areas with higher electron densities as predicted in the hybridization model. The node at the symmetry plane in the middle of the crescents is visible as well. In the gap between the tips of the crescents, no field enhancement is visible as the resonance is a symmetric mode and the tips have similar charges (see Figure 5d). The field distribution for the u- resonance at a wavelength of 1750 nm is presented in Figure 5b,e. The xy plane shows a strong field enhancement at the tips and a minor enhancement in the middle of the crescents. It agrees well with the charge distribution postulated by the hybridization model. Furthermore, the field is depleted at the wings of the crescents, thus imaging the two nodes of the wave function. As the resonance is antisymmetric, 452

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Nano Letters the tips facing each other bear opposite charges. Therefore, the electric field is strongly enhanced in the gap between the tips (Figure 5e). The hybrid c2þ mode at 910 nm is investigated in Figure 5c,f. Again, the field distribution agrees well with the theoretical model proposed. The cut in the xy plane shows a field distribution with three nodes resembling the sketch of the charge distribution given in Figure 4b. As the mode is symmetric and the tips have similar charges, no field enhancement should be visible in the gap between the tips. Figure 5f shows a depletion region in the middle of the gap while an enhancement is visible at the edges of the gap. The depletion visualizes the region where similar charges interact strongly. The field enhancement at both sides of the gap reflects the proximity of the tip charges to the opposite charges present at the wings of the crescents and supports the hybridization model for the c2 resonance given in Figure 4b. Concluding, a novel technique for the fabrication of large-area arrays of stacked double crescents by colloidal lithography is introduced. Sophisticated nanoscale objects can thus be aligned vertically with a precision of several nanometers, a feature that formerly required expensive, serial techniques as electron beam lithography or focused ion beam milling. The arrays feature a high degree of lateral symmetry that reflects the hexagonal order of the colloidal monolayer. The process is parallel, cheap and enables to structure large areas. Ample degrees of freedom exist for the process that allow for precise adjustment of the nanocrescents’ size, shape, overlap, and mutual orientation. All of these characteristics have a strong effect on the optical properties of the objects and can be used to tailor plasmonic resonances according to the desired applications. Furthermore, the precise vertical alignment also gives access to observe fundamental aspects of the coupling process between nanostructures. Polarization dependent UV-vis-NIR absorption spectroscopy showed that the close proximity in space led to drastic differences in the plasmon resonances compared to single crescents. In the presence of the second crescent, the fundamental plasmon mode blue shifted while the energy of the first harmonic mode decreased. The effects were sufficiently strong that a crossover between the two resonances took place, thus giving the impression that the first harmonic mode became energetically favored to the fundamental mode. A plasmon hybridization model was adapted to explain the resonance positions. Symmetry considerations showed that for each polarization, only one of the hybrid modes features a dipole and hence, is excited efficiently by the external electric field. As the symmetric situation for the fundamental and first harmonic mode is inverted, the shifts in energy for the stacked double structure are readily explained. A complete hybridization model for all polarization dependent resonances of nanocrescents dimers was elaborated, thus shedding light into the fundamental understanding of the behavior of complex structures in close proximity. Theoretical calculations reproduced all essential spectral features and thus supported the proposed hybridization model.

LETTER

u-polarization. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: 0049-6131-379572. Fax: 0049-6131-379100. E-mail: vogel@ mpip-mainz.mpg.de. Author Contributions §

These authors contributed equally to this work.

’ ACKNOWLEDGMENT N.V. appreciates financial support from the Materials Science in Mainz graduate school. Andreas Unger is acknowledged for fruitful discussions. ’ REFERENCES (1) Murray, W. A.; Barnes, W. L. Plasmonic Materials. Adv. Mater. 2007, 19 (22), 3771. (2) Pendry, J. B. Negative Refraction. Contemp. Phys. 2004, 45 (3), 191. (3) Shelby, R. A.; Smith, D. R.; Schultz, S. Experimental Verification of a Negative Index of Refraction. Science 2001, 292 (5514), 77. (4) Smith, D. R.; Pendry, J. B.; Wiltshire, M. C. K. Metamaterials and Negative Refractive Index. Science 2004, 305 (5685), 788. (5) Wiltshire, M. C. K.; Pendry, J. B.; Hajnal, J. V. Sub-Wavelength Imaging at Radio Frequency. J. Phys.: Condens. Matter 2006, 18 (22), L315. (6) Pendry, J. B. Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett. 2000, 85 (18), 3966. (7) Pendry, J. B.; Schurig, D.; Smith, D. R. Controlling Electromagnetic Fields. Science 2006, 312 (5781), 1780. (8) Schurig, D.; Mock, J. J.; Justice, B. J.; Cummer, S. A.; Pendry, J. B.; Starr, A. F.; Smith, D. R. Metamaterial Electromagnetic Cloak at Microwave Frequencies. Science 2006, 314 (5801), 977. (9) Cai, W. S.; Chettiar, U. K.; Kildishev, A. V.; Shalaev, V. M. Optical Cloaking with Metamaterials. Nat. Photonics 2007, 1 (4), 224. (10) Pendry, J. B.; Holden, A. J.; Robbins, D. J.; Stewart, W. J. Magnetism from Conductors and Enhanced Nonlinear Phenomena. IEEE Trans. Microwave Theory Tech. 1999, 47 (11), 2075. (11) Smith, D. R.; Padilla, W. J.; Vier, D. C.; Nemat-Nasser, S. C.; Schultz, S. Composite Medium with Simultaneously Negative Permeability and Permittivity. Phys. Rev. Lett. 2000, 84 (18), 4184. (12) Liu, N.; Guo, H. C.; Fu, L. W.; Kaiser, S.; Schweizer, H.; Giessen, H. Three-Dimensional Photonic Metamaterials at Optical Frequencies. Nat. Mater. 2008, 7 (1), 31. (13) Shalaev, V. M.; Cai, W. S.; Chettiar, U. K.; Yuan, H. K.; Sarychev, A. K.; Drachev, V. P.; Kildishev, A. V. Negative Index of Refraction in Optical Metamaterials. Opt. Lett. 2005, 30 (24), 3356. (14) Shalaev, V. M. Optical Negative-Index Metamaterials. Nat. Photonics 2007, 1 (1), 41. (15) Soukoulis, C. M.; Linden, S.; Wegener, M. Negative Refractive Index at Optical Wavelengths. Science 2007, 315 (5808), 47. (16) Fischer, U. C.; Zingsheim, H. P. Sub-Microscopic Pattern Replication with Visible-Light. J. Vac. Sci. Technol. 1981, 19 (4), 881. (17) Hulteen, J. C.; Vanduyne, R. P. Nanosphere Lithography - a Materials General Fabrication Process for Periodic Particle Array Surfaces. J. Vac. Sci. Technol., A 1995, 13 (3), 1553. (18) Haynes, C. L.; Van Duyne, R. P. Nanosphere Lithography: A Versatile Nanofabrication Tool for Studies of Size-Dependent Nanoparticle Optics. J. Phys. Chem. B 2001, 105 (24), 5599. (19) Vogel, N.; Jung, M.; Retsch, M.; Knoll, W.; Jonas, U.; Koper, I. Laterally Patterned Ultraflat Surfaces. Small 2009, 5 (7), 821. (20) Vogel, N.; Jung, M.; Bocchio, N. L.; Retsch, M.; Kreiter, M.; Koper, I. Reusable Localized Surface Plasmon Sensors Based on Ultrastable Nanostructures. Small 2010, 6 (1), 104.

’ ASSOCIATED CONTENT

bS

Supporting Information. Experimental details, photograph of array dimensions, sketches to clarify all parameters of the process, exact dimensions of the stacked double crescents used for simulations, optical spectra for ring structures without separation, near field distributions of single crescents resonances, effect of crescents’ overlap, and effect of separation distance for 453

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Nano Letters

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