Letter pubs.acs.org/NanoLett
Standing Wave Plasmon Modes Interact in an Antenna-Coupled Nanowire Jared K. Day,†,∥ Nicolas Large,†,∥ Peter Nordlander,†,‡,∥ and Naomi J. Halas*,†,‡,§,∥ †
Department of Electrical and Computer Engineering, ‡Department of Physics, §Department of Chemistry, ∥Laboratory for Nanophotonics, and the Rice Quantum Institute, Rice University, MS-378, 6100 Main Street, Houston, Texas 77005, United States S Supporting Information *
ABSTRACT: In a standing wave optical cavity, the coupling of cavity modes, for example, through a nonlinear medium, results in a rich variety of nonlinear dynamical phenomena, such as frequency pushing and pulling, mode-locking and pulsing, modal instabilities, even complex chaotic behavior. Metallic nanowires of finite length support a hierarchy of longitudinal surface plasmon modes with standing wave properties: the plasmonic analog of a Fabry−Pérot cavity. Here we show that positioning the nanowire within the gap of a plasmonic nanoantenna introduces a passive, hybridization-based coupling of the standing-wave nanowire plasmon modes with the antenna structure, mediating an interaction between the nanowire plasmon modes themselves. Frequency pushing and pulling, and the enhancement and suppression of specific plasmon modes, can be controlled and manipulated by nanoantenna position and shape. KEYWORDS: Plasmonic nanoantenna, Fabry-Pérot, cathodoluminescence, dark-field spectroscopy, plasmon hybridization, frequency pulling, antinode drift
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cavity modes exist in macroscopic optical systems such as inhomogeneously broadened lasers and cavities filled with nonlinear optical media, where a nonlinear or gain medium provides the mechanism for intermodal coupling. Mechanical or other symmetry-breaking perturbations on an optical cavity can also result in mode coupling phenonena. These systems give rise to a wealth of rich nonlinear physical phenomena, including frequency pushing19 and pulling,20,21 optical bistability,22−24 self-pulsing,25−27 and chaotic time-dependent behavior.28 Here we report a plasmonic system consisting of a finitelength plasmonic nanowire placed within the gap of a twoarmed nanoantenna structure. The hybridization coupling of the nanowire modes to the antenna also induces an effective coupling between the nanowire standing wave modes themselves. This rudimentary system of coupled standing wave plasmon modes exhibits frequency pushing and pulling and modifications of the mode intensities. The spectral envelope of the coupled nanowire system is observed using dark-field microscopy, and detailed field distribution of the coupled standing wave plasmon modes is imaged using cathodoluminescence. Results and Discussion. Individual Au nanowires were fabricated by electron beam (e-beam) lithography on a Si wafer
anowires are an essential building block for device design in nanophotonics because they are capable of supporting propagating one-dimensional (1D) surface plasmons. When the nanowire length is longer than the plasmon propagation distance, nanowires can function as plasmon waveguides,1−3 typically supporting multiple plasmon modes with transverse confinement along the nanowire surface.4−6 They can be used to realize plasmonic splitters,7,8 quarter wave polarization converters,9 and when branched can even support logic and mathematical functions.10,11 Thinner and shorter-length nanowires support multiple longitudinal localized surface plasmon resonances (LSPRs) as well as transverse modes. The longitudinal plasmon modes in this regime are essentially standing waves described by 1D damped Fabry-Pérot cavity models.12−17 Plasmon standing waves in these structures are identified by a positive integer mode index, l, for the standing wave geometric condition: l·(λsp/2) = Lnw, where λsp is the surface plasmon wavelength and Lnw is the length of the nanowire.4,5 As the longitudinal mode number is increased, the modes have increasingly small net dipole moments, making these otherwise bright modes poor far-field radiators, resembling rather the confined modes of an optical cavity. One way to enhance the weakly radiative properties of the plasmonic standing wave modes would be to couple them to a more radiative plasmonic structure such as a nanoantenna. This coupling of multiple plasmon standing-wave modes to a nanoantenna, however, will also induce an indirect interaction between the plasmon cavity modes themselves.18 Coupled © XXXX American Chemical Society
Received: November 26, 2014 Revised: January 6, 2015
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Figure 1. Optical and e-beam excitation of single Au nanowire. (A) FDTD (red) and dark-field (black) scattering and CL emission spectrum (blue) of a single finite Au nanowire (420 × 35 nm) show the standing-wave eigenmodes l = 2−4. Inset: Expanded nanowire FDTD scattering spectrum showing the hierarchy of l = 1−4 plasmon modes. (B,C) Bandpass filtered (40 nm FWHM) CL images of the nanowire at (B) 650 nm and (C) 750 nm. Integrated line scans for each CL image display the standing wave nature of the nanowire resonances. Inset in (B): SEM image of the nanowire. Scale bars represent 100 nm.
to collect emitted photons that were then transmitted to the detector. The collected light was linearly polarized along the longitudinal axis of the nanowire (in correspondence with the dark-field optical configuration) and either dispersed by a grating across a CCD for spectroscopy or directed to a PMT to produce CL excitation images when the electron beam was rastered over the structure. Bandpass filters were inserted into the optical path before the PMT to create wavelength-specific raster-scanned images. Background correction for all spectra was performed to reduce additional sources of stray light from substrate luminescence and transition radiation.32 The dark-field scattering spectrum for an isolated nanowire (Figure 1A, black line) clearly resolves a single nanowire resonance peak within our detector range (500−1000 nm) at ∼760 nm, and a broad shoulder at 680 nm. This spectrum is in good agreement with FDTD simulations (Figure 1A, red line). These two features can clearly be identified as the l = 3 and l = 4 standing wave nanowire plasmon modes. Optical excitation only weakly excites even-order modes for the off-normal incident excitation angle of the dark-field optical geometry (NA = 0.75). In contrast, the CL emission spectrum (Figure 1A, blue line) resolves the l = 3 and l = 4 higher-order mode resonances of the nanowire more clearly, because the selection rules for e-beam excitation allow for both even and odd nanowire modes to be excited.31,35,36 The lower energy tail from nanowire resonances l = 1 and l = 2, observed from the FDTD results cannot be detected experimentally due to the low detection efficiency of the detectors beyond 900 nm. Bandpass-filtered CL excitation images were created at the two nanowire standing-wave resonance frequencies and shown in Figure 1B,C. The standing wave nature of these modes is most clearly seen in the CL excitation image at 750 nm (Figure 1C) for the l = 3 mode.4,6,14 Photon emission from the l = 4 mode, by contrast, is damped, and its standing wave structure is not as well observable, most likely due to the weaker radiative character of this higher-order mode. Higher-order nanowire modes have been shown to have a suppression of photo emission at nanowire ends resulting in an inherent deviation away from ideal standing wave distributions. The exact cause
with a 100 nm oxide layer. Thirty-five nanometer thick Au nanowires were deposited with e-beam evaporation following deposition of a 2 nm thick Ti adhesion layer. All nanowires in these experiments had dimensions of 420 nm length and 35 nm width. Scattering spectra of individual nanowires were obtained using a dark-field microscope (Figure 1A). Unpolarized white light from a halogen lamp was focused onto the nanowires using an epi-illumination configuration in a Zeiss Imager A2 microscope (NA = 0.75, Zeiss LD EC Epiplan-Neofluar 100× objective). The scattered light was collected and passed through a linear polarization analyzer oriented along the longitudinal axis of the nanowire prior to the spectrograph and CCD detector (Synapse, Jobin Yvon). The spectrum of an individual nanowire was also calculated using the finitedifference time-domain method (FDTD, Lumerical Solutions). The specific geometry was obtained from SEM images of the nanowires. The 2 nm Ti adhesion layer and the SiO2 substrate were taken into account in the simulations. The simulations used the Johnson and Christy bulk dielectric function for Au29 and the dielectric functions of Palik for Ti and SiO2.30 The simulations were performed for optical excitation at oblique incidence, just as in the experimental configuration. Cathodoluminescence (CL) imaging and spectroscopy were used to characterize the isolated nanowire and the nanowire− nanoantenna coupled system. In CL, the electron beam excitation of surface plasmon modes has no symmetry restrictions, allowing all plasmon modes to be excited in a weighted response corresponding to the position of the electron excitation beam on the structure.31,32 The high spatial localization of the electron beam excitation allows for nanoscale-resolution images to be constructed that are proportional to the radiative local density of optical states (LDOS).33,34 CL measurements were obtained using a combined Gatan (MonoElite CL4) spectrometer, light probe, and software acquisition unit attached to a scanning electron microscope (SEM, FEI Quanta 650) chamber. A parabolic mirror (NA = 0.89), containing a hole to transmit the electron beam (30 keV) onto the sample, was focused above the sample B
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Figure 2. Plasmon hybridization in a coupled nanowire−nanoantenna structure. (A) Schematic of the system: finite Au nanowire symmetrically positioned between two identical Au square structures, separated by gap size, g. (B) FDTD (top) and dark-field (bottom) scattering of nanowire− nanoantenna system at various gap sizes, g. (C) Plasmon hybridization energy diagram of hybridized antenna structure identifying scattering spectra for isolated building blocks (blue, green, and black lines) and a fully coupled system (red line) composed of two side nanoantennas (140 × 140 nm) and a nanowire of 420 × 35 nm with a gap size g = 15 nm. Coupling of l = 3 and l = 4 modes mediated by the l = 1 plasmon mode of the dimer plasmon is highlighted in yellow. (D) Surface charge distributions associated with the primitive plasmon modes (blue, green, and black outlined images) and with the hybridized modes (red outlined images) of the coupled structure.
gap size g = 15 nm. The fabricated structure had g ∼ 20 nm with a spectral response in good agreement with the theory. To examine the nanowire−nanoantenna interaction, we apply plasmon hybridization theory to the coupled system (Figure 2C). In the absence of the central nanowire, the nanoantenna structure forms a weakly coupled dimer separated by ∼70 nm (Figure 2C, green). For transverse antenna dimer polarization (polarization along the nanowire), the plasmon frequency of the dimer blue shifts slightly from that of a single structure (Figure 2C, blue).39 In the visible frequency range, the isolated Au nanowire (Figure 2C, black) supports two oddorder standing wave plasmon modes (l = 3, 5) and an evenorder (l = 4) mode. In the coupled nanowire−nanoantenna structure, these modes hybridize (Figure 2C, red). The strong resonant interaction between the l = 1 antenna mode and the l = 3 nanowire mode results in a splitting of the antenna mode that dominates the spectral response of the coupled structure (Figure 2C). The higher energy spectral feature corresponds to a mixed mode where both the l = 3 and l = 4 nanowire modes couple strongly to the l = 1 antenna mode (iv), and through this coupling, to each other. This interaction is highlighted in yellow in Figure 2C. The higher order l = 5 nanowire mode couples less strongly to the nanoantenna mode (v). The l = 3 nanowire mode also contributes individually to
for the reduced field strength at the nanowire ends is currently unknown but the reflectivity of the nanowire terminating points,5,37 the phase delay due to the reactance of the fields interacting with the surrounding medium,38 and enhanced electron scattering12 are all thought to play a role in the suppressed near-field intensity at nanowire ends. However, the characteristic lower photon emission from isolated nanorods end points5,12,37 can still be generally observed at both wavelengths in Figure 1B,C. The coupled nanowire−nanoantenna structure shown in Figure 2A was fabricated using the same one-step e-beam lithography process used for the isolated Au nanowire. The dimensions of the Au square antennas were 140 nm on each side, chosen by matching the length of the square antenna dipole to the half wavelength λsp of the l = 3 nanowire mode. This dimension ensures particularly strong coupling between the antenna mode and the l = 3 nanowire mode. FDTD calculations were performed to analyze the spectral evolution of the coupled nanowire−nanoantenna system as a function of the gap spacing, g, between the side antenna structures and the nanowire (Figure 2B). As the gap size is decreased, the spectrum changes from one broad peak encompassing various overlapping resonances to a scattering spectrum consisting of two distinct spectral features at 700 and 850 nm for the smallest C
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Figure 3. Symmetric and asymmetric nanowire−nanoantenna modes. (A) SEM images for symmetric and asymmetric arrangements of square nanoantennas (140 × 140 nm) coupled to nanowires (420 × 35 nm). Asymmetric geometry has square antennas aligned in parallel with a longitudinal offset of Δx = 140 nm. (B) Standing wave plasmon modes identified through CL imaging. Image borders correspond to the hybridized mode observed in each image, (hybrid-iii, purple; hybrid-iv, green; hybrid-v, blue). Line profiles taken through the center of the nanowire are plotted below each image. Scale bars represent 100 nm. (C) Scattering and CL emission spectra for coupled nanowire−nanoantenna systems. Upper panel shows dark-field (black) and FDTD (red) scattering spectra. Center and lower panels display CL emission spectra and corresponding Lorentzian peak fits (hybrid-iii, brown; hybrid-iv, orange; hybrid-v, yellow), respectively. Color-coded vertical bars are associated with CL images in (B).
modified by the relative position Δx of the two antenna arms along the nanowire. The spatial distributions of the standing wave modes are all a function of the spatial offset of the antenna arms except when physical deformations of the nanostructures caused by the CL scanning alter the spatial distribution at isolated sites. CL scanning deformations can be seen in Figure 3B for hybrid modes iv and v near the 0.4 μm e-beam position. The CL spectra can be decomposed into three Lorentzian peaks (Figure 3C, lower panel) corresponding to the hybridized peaks predicted in Figure 2B. In order to provide a more detailed understanding of how the antenna longitudinal offset modifies the properties of the plasmon near-field in the nanowire, we acquired CL images of the coupled nanowire−nanoantenna system as the longitudinal displacement between the two antenna arms was increased by 70 nm increments on opposing sides of the nanowire (Supporting Information S1). From the CL excitation images we extract the intensities along the longitudinal axis of the nanowire at selected wavelengths that allow us to observe the evolution of the plasmon standing wave intensity profiles (Figure 4).
the lower energy spectral feature (iii) that is essentially the bonding combination of the nanowire l = 3 and antenna l = 1 modes. Charge distributions for all of the primitive and hybridized plasmon modes are shown in Figure 2D. For nanoantennas positioned either symmetrically or asymmetrically on both sides of the nanowire (Figure 3A), line profiles extracted from CL images (Figure 3B) show three distinct resonances of the coupled nanowire−nanoantenna system. Unlike the modes observed for an isolated nanowire, in the nanowire−nanoantenna system three hybridized modes (iii, iv, and v) are observable. In the isolated nanowire, the l = 5 mode was previously strongly suppressed, but it is now visible due to the addition of the nanoantenna to the structure. A characteristic feature of this system is the strong modulation of the standing-wave plasmon in the nanowire due to the nanowire−nanoantenna coupling. Varying the longitudinal spacing between the two arms of the antenna (Figure 3, right panels) modifies this coupling in a complex manner. Comparison of the spectra of the symmetric and asymmetric nanowire−nanoantenna system shows that for the asymmetric case the overall coupling is weaker, but the main characteristics (hybridized modes) are retained and also D
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Figure 4. Integrated CL line profiles for an isolated nanowire and the coupled nanowire−nanoantenna systems. Wavelength-specific horizontal line scans between 20 and 35 pixels wide were integrated and plotted against e-beam position for an isolated nanowire and for nanowire−nanoantenna systems with different longitudinal separation distances (Δx = 0, 70, 140, 210, 280 nm). Each line profile was taken from a bandpass filtered (40 nm FWHM) CL image taken at 50 nm increments between 600−850 nm. SEM images for each nanowire system are shown above each respective line profile graph. Scale bars correspond to 100 nm.
The near-field coupling of the nanoantennas can greatly alter the spatial distribution of the nanowire standing wave resonances. For each nanowire system, the antinode positions along the nanowire change with the emission wavelength, as can be seen in Figure 4. The antinode spacing is a direct measurement of the half-wavelength, λsp/2,6 and the variation in antinode spacing as a function of excitation wavelength indicates that the λsp also varies at different emission wavelengths. Using the multiple antinode separation distances along the nanowire we calculated an average λsp for each line profile in Figure 4 to illustrate how the λsp changes across the spectral bandwidth of the different nanowire−nanoantenna systems (Figure 5). The data in this figure is obtained by analysis of multiple nanowire−nanoantenna systems over a systematic range of emission wavelengths (Supporting Information Figure S1). The average λsp values reported in Figure 5 were determined by excluding the antinode spacing values measured from the terminal antinodes to eliminate distortions caused by the reflections from the nanowire ends.5,6,37 Tracking λsp across multiple excitation wavelengths for each nanowire−nanoantenna system reveals an overall declining trend of λsp values with decreasing emission wavelength (Figure 5). However, within a given mode (hybrid-iii, purple; hybrid-iv, green; hybrid-v, blue), λsp increases for decreasing emission
The offset nanoantenna−nanowire coupling leads to modified spatial near-field profiles for the nanowire LSPRs that differ from an isolated nanowire. Because the radiative decay of a point-source emitter (i.e., electron) is directly influenced by nearby cavity modes,33 CL imaging provides a useful method for mapping the spatial distribution of these optical modes.5,16,31,33,34,40 In Figure 4, the hybrid-iii nanowire mode at 850 nm (top scan, brown) for the symmetric configuration (Δx = 0 nm) closely resembles the l = 3 resonance for the isolated nanowire at that same frequency but is strongly enhanced by the symmetric nanoantenna. Breaking nanoantenna symmetry (Δx = 70 nm) causes the relative intensity between the antinodes at 850 nm to become skewed to the left center antinode. The antinode intensity variation along the nanowire is the result of the modification of the LDOS caused by the interaction with the antenna.41 The antenna offset also shifts the energies of the nanowire standing wave modes: at 650 nm, the standing wave plasmon mode is tuned from hybrid-iv to hybrid-v for small antenna offset and evolves to the hybrid-iii mode for the largest nanoantenna offset (Δx = 280 nm). The energy shift of nanowire modes can be better understood by analyzing the spatial distortions of the standing wave modes that are most strongly hybridized when their antinodes are aligned with the antinodes (corners) of the nanoantennas. E
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The red-shifted energy level of the weakly coupled nanoantenna dimer mode and the positional alignment of the nanoantenna antinodes at the nanowire ends (Figure 4) are also responsible for stretching the λsp to more than double the expected values for an ideal l = 3 Fabry-Pérot mode (Figure 5, Δx = 280 nm). Although this configuration has rotational symmetry, the longitudinally polarized collection of the CL photon emission cancels any rotational symmetry effects. The combination of the red-shifted energy of the weakly coupled dimer mode and favorable positional alignment contribute to the extension of the CL imaging bandwidth of the hybrid-iii mode (purple) from 650−850 nm (emission wavelengths). This extended bandwidth allows the hybridization to pull the nanowire antinodes further apart at shorter wavelengths leading to the largest measured spatial distortion of the cavity modes (Figure 5, bottom panel). In this configuration the hybrid-iv mode is only weakly observable at 600 nm while the hybrid-v mode was completely damped. The lack of symmetry of the hybrid-iv resonance at 600 nm with respect to the transverse axis of the nanowire−nanoantenna structure is due entirely to shape irregularities from e-beam fabrication and defects formed during the CL scanning procedure. In conclusion, we demonstrated the enhancement of the scattering strength of weak higher-order nanowire resonances through near-field coupling with nanoantennas. Strong coupling responsible for the enhancement is the result of energy overlap and the positional alignment between the nanowire LSPRs and the dipole moment of the adjacent nanoantennas. The simple nanowire−nanoantenna design allowed us to easily compare both optical and electron spectroscopy techniques to better understand mode hybridization in such coupled nanostructures. CL imaging revealed that antinodes of uncoupled nanowire resonances do not remain in stationary positions throughout its spectral bandwidth as expected from eigenmode solutions of nanowire resonances. Instead, the antinodes of the nanowire LSPRs are shown to “drift” between stationary positions as a function of wavelength. Near-field coupling to nanoantennas can control the behavior of antinode “drift” directly affecting the spectral bandwidth of a given mode. The hybridization of the multipolar nanowire resonances with the nanoantenna dipoles not only enhances the far-field emission of these resonances but also alters their near-field intensities, spatial distribution, and spectral bandwidth. Near-field coupling of nanoantennas to nanowire optical cavities illustrates that plasmon hybridization can control the radiative LDOS of nanowires. This type of coupled geometry, when combined with active media, could ultimately enable strategies for active control of emission properties in nanowire-based device geometries.
Figure 5. Mode compression/relaxation behavior for isolated nanowire and nanowire−nanoantenna systems. The local plasmon wavelength, λsp, calculated by averaging the distances between internal antinodes of nanowire resonances are plotted at a range of CL emission wavelengths for each system. Data points are colored according to nanowire mode excited: l = 3, purple and l = 4, green for the isolated nanowire; hybrid-iii, purple, hybrid-iv, green, and hybrid-v, blue for the nanowire−nanoantenna systems. Dashed lines are used to highlight λsp trends within a given nanowire mode.
wavelengths for the hybridized nanowire systems in direct contrast to the behavior observed for the standing wave modes in an isolated nanowire. For the isolated nanowire l = 3 mode (Figure 5, top panel, purple) the decreasing values of λsp at shorter wavelengths indicates the central antinodes are pushed together (compressed) before the appearance of the next higher-order mode (l = 4, green). Alternatively, the central antinodes of nanowire−nanoantenna systems spread apart at shorter excitation wavelengths before the onset of the next higher order mode abruptly reduces λsp. The antinode expansion at shorter wavelengths is then restarted within the new resonance mode. The measured values of λsp at snapshots within the active spectral region of nanowire systems reveal that even for isolated nanowires the distance between antinodes monotonically “drifts” to higher or lower values within an individual resonant mode when probing the blue or red side of the resonant peak. “Antinode drift” within resonant modes can be controlled by hybridization with adjacent nanoantennas and between the individual standing modes themselves. The energy shifts of the hybridized nanowire standing wave modes can be more easily observed in Figure 5. The increasing longitudinal offset (Δx) between the nanoantennas reduces the dimer mode coupling causing a red-shift in the nanoantenna energy level. At 600 nm, the hybrid-v mode (blue) of the symmetric nanowire−nanoantenna system (Δx = 0) changes to the hybrid-iv mode (green) with a 70 nm offset because the nanoantenna dimer red-shifts away from the high energy hybrid-v mode. For a 140 nm offset, the hybrid-v mode becomes dominant again despite the red-shifting energy of the nanoantenna dimer because the location of the antinodes of nanoantenna are now close to four antinodes of the l = 5 nanowire mode, increasing coupling to this mode. Increasing the offset beyond 140 nm decreases the interaction so that the hybrid-iv mode is the highest order mode excited at 600 nm.
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ASSOCIATED CONTENT
S Supporting Information *
S1: Spectral and imaging bandwidth of nanowire−nanoantenna systems. S2: T-shaped antenna. S3: Gap (g) effect on thick and thin nanowires. S4: Side antenna size effects on thick and thin nanowires. S5: Far-field optical and electron spectra for hybridnanowire systems. 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]. F
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(N.L.) Department of Chemistry, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208-3113. Author Contributions
J.K.D. and N.L. contributed equally to this work. J.K.D. fabricated the nanostructures, performed the optical and cathodoluminescence measurements. N.L. performed the theoretical study and numerical simulations. J.K.D. and N.L. performed the data analysis and wrote the manuscript. N.J.H. and P.N. designed the project. This material is available free of charge via the Internet at http://pubs.acs.org. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors wish to thank Mark Knight for insightful discussions about cathodoluminescence. This work was financially supported by the Robert A. Welch Foundation under Grants C-1220 (N.J.H.) and C-1222 (P.N.), the National Security Science and Engineering Faculty Fellowship (NSSEFF) N00244-09-1-0067, the National Science Foundation (NSF) ECCS-1040478, the ONR Grant N00014-10-10989, and the Cyberinfrastructure for Computational Research funded by NFS under Grant CNS-0821727.
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