Role of Resonances in the Transmission of Surface Plasmon

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Role of Resonances in the Transmission of Surface Plasmon Polaritons between Nanostructures Paul Johns, Kuai Yu, Mary Sajini Devadas, and Gregory V Hartland ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b07185 • Publication Date (Web): 11 Feb 2016 Downloaded from http://pubs.acs.org on February 15, 2016

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Role of Resonances in the Transmission of Surface Plasmon Polaritons between Nanostructures Paul Johns,1 Kuai Yu,2 Mary Sajini Devadas,3 and Gregory V. Hartland1,* 1

Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana

46556, United States 2

Current address: Department of Chemistry, Stanford University, Stanford, California 94305,

United States 3

*

Department of Chemistry, Towson University, Towson, Maryland 21252, United States

Corresponding author: e-mail [email protected]

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Abstract: Understanding how surface plasmon polaritons (SPPs) propagate in metal nanostructures is important for the development of plasmonic devices. In this paper we study the transmission of SPPs between single-crystal gold nanobars on a glass substrate using transient absorption microscopy. The coupled structures were produced by creating gaps in single nanobars by focused ion beam milling. SPPs were launched by focusing the pump laser at the end of the nanobar, and the transmission across the gaps was imaged by scanning the probe laser over the nanostructure. The results show larger losses at small gap sizes. Finite element method calculations were used to investigate this effect. The calculations show two main modes for nanobars on a glass surface: a leaky mode localized at the air-gold interface, and a bound mode localized at the glass-gold interface. At specific gap sizes (approximately 50 nm for our system) these SPP modes can excite localized surface plasmon modes associated with the gap, which dissipate energy. This increases the energy losses at small gap sizes. Experiments and simulations were also performed for the nanobars in microscope immersion oil, which creates a more homogeneous optical environment, and consistent results were observed.

KEYWORDS: plasmonics, surface plasmon, waveguide, resonance, nanobar, electromagnetic coupling


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Surface plasmon polaritons (SPPs) are the collective oscillations of the free electrons of a metal that occurs between a metal surface and a dielectric medium.1 SPPs are able to confine light to a subwavelength scale in noble metal waveguides,2 which is important for a variety of applications, including sensors,3-9 nanocircuits,10-11 and plasmonic lasers.12-13 A key issue in this field is damping,13 which can negatively impact performance in these applications. This has led to research in using gain materials to increase the propagation lengths.14-15 Another fundamental issue that affects SPP devices is coupling between nanostructures.16-18 Plasmon coupling has been extensively studied for particles, as it is central to the creation of the hot-spots that are important in surface enhanced Raman spectroscopy (SERS).19-22 However, less is known about coupling between nanostructures for propagating SPPs.17, 23-24 Recently we have used transient absorption microscopy to image propagating SPP modes in metal nanobars (nanowires with square cross-sections) supported on glass substrates.25-26 These modes can also be imaged by light scattering27-29 or through the use of fluorescent reporter dyes.30-34 Compared to these alternative techniques, transient absorption microscopy has higher signal-to-noise than light scattering, and does not suffer from photobleaching of the reporter dyes.31, 33 Multiple measurements can also be performed on the same wire, allowing studies of how changes in the environment change the properties of the SPP modes. However, transient absorption microscopy is more complex to set up than fluorescence or light scattering measurements, and it takes significantly longer to obtain an image. Substrate supported nanowires generally display two SPP modes: a bound mode that propagates at the nanobar-substrate interface, and a leaky mode that propagates at the nanobarair interface.35-38 Our previous studies examined the propagation lengths of these modes, and how they are affected by discontinuities (trenches) in the substrate.26, 39 The results showed that the


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bound mode is strongly damped by substrate discontinuities, whereas, the leaky mode is relatively unaffected. In this paper we investigate how the propagating SPP modes couple between two nanobars. The coupled structures were created by cutting gaps in long, chemically synthesized nanobars using focused ion beam (FIB) milling. Individual chemically synthesized nanobars are highly uniform, which means that the structures are essentially identical on either side of the gap. This allows us to obtain precise information about the coupling efficiency by comparing the magnitude of the transient absorption signal in the different segments. The transient absorption measurements yield information about the loss of the SPP intensity at the gap, and how this depends on gap size. The experimental results were compared to three-dimensional finite element simulations carried out using COMSOL Multiphysics® (v. 4.4). The simulations were performed in the frequency domain using either the bound or the leaky modes as excitation sources (the mode shapes and propagation constants for these modes were found from a boundary mode analysis of the system).17 The fields obtained from the simulations allow us to determine the spatial distribution for energy dissipation for the mode, which is directly related to the transient absorption signal. Both the experiments and simulations show larger losses at small gap sizes. This is attributed to the excitation of localized surface plasmons associated with the gap in the nanostructures. These modes are resonances that appear at specific gap widths, and provide an additional decay channel for the SPPs.

Results and Discussion: Gaps with widths between 20–90 nm were made in a number of different nanobars by FIB milling. The gold nanobars in our sample typically had rectangular cross-sections, with


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average sizes of 600 ± 220 nm, 380 ± 140 nm and 15 ± 4 µm for the width, height and length, respectively.26 Note that the dimensions of the nanobars used in this study are much larger than the sizes typically proposed for device applications.40-41 This is because small nanowires have short SPP propagation lengths,37 which makes them difficult to study by far field optical techniques. A scanning electron microscopy (SEM) image of a cut nanobar is shown in Figure 1(a). The widths of the gaps were determined from high-resolution SEM images (examples are presented in the Supporting Information). Because the gaps are not perfectly flat (see Supporting Information), the widths reported here were taken at the mid-point of the nanobar. SPPs were launched by focusing the pump laser at the end of the nanobar, with the polarization of the pump parallel to the long axis of the nanobar. Figure 1(b) shows a scattered light image, where the leaky mode can be clearly seen.29 Although the scattered light image shows SPP propagation and coupling across the gaps, the signal-to-noise is not good enough to provide accurate information about the propagation lengths or the coupling efficiency. Figure 1(c) shows a transient absorption image, where the probe laser was temporally overlapped with the pump and spatially scanned over the sample while the pump laser was held fixed. A line profile of the transient absorption signal along the nanobar is show in Figure 1(d). Note that both the image and the line profile are plotted on a natural log scale. The signal in these measurements arises from the hot electrons created by dephasing of the SPPs, and reports directly on the SPP intensity.26, 39 The transient absorption signal shows a drop at the gaps, and the percentage decrease at each of the gaps is given in Figure 1(d). The percentage decrease was determined by fitting the signal on either side of the gap to an exponential function, and extrapolating to the middle of the gap. This provides for a more reliable estimate of the SPP losses compared to using single points to determine the SPP intensity on either side of the gap.


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This method also accounts for the decay of the SPP along the nanobar. Additional transient absorption images and line profiles are shown in Figure S3 of the Supporting Information.

Figure 1. (a) SEM image of a nanobar with three cuts created by FIB milling. The width of the gaps from left to right are 20 nm, 30 nm and 25 nm respectively. Note that some cutting into the substrate is also visible (see the Supporting Information for more details). (b) Scattered light image where the pump-laser was focused on the right end of the nanobar. (c) Transient absorption image of the nanobar plotted on a natural log scale. (d) Line profile taken from the image in panel (c). The percentage drop in the signal for each gap is given in the figure. The lines represent exponential fits to the SPP signal in the different segments of the nanobar. Figure 2 shows the average percentage drop in the SPP intensity as a function of gap width for the supported nanobars in air (Fig. 2(a)), and in microscope immersion oil (Fig. 2(b)). Placing microscope immersion oil over the sample creates a nearly homogeneous optical environment for the nanobars, and changes the form of the propagating SPP modes (see Figure 3 below). Each point in Figure 2 corresponds to several repeated measurements, and the y-axis error bars represent 95% confidence limits. Note that the propagation lengths are much shorter for the nanobars in oil.26 This reduces the SPP intensity at the gap, and means that we were not


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able to obtain reliable data for the larger gap sizes. Plots of the experimental percentages losses for the 2nd and 3rd gaps in the nanobars (see Figure 1(d)) are presented in Figure S11 of the Supporting Information document. This data is not as reliable as the data form the 1st gap, due to the much smaller signal levels and, thus, will not be discussed in detail.

Figure 2. (a) Plot of the average percentage loss in intensity of the SPP as a function of gap width for supported nanobars in air. (b) Plot of the average percentage losses versus gap width for the nanobars in microscope immersion oil. In both panels the symbols are the experimental data and the lines show results from finite element method simulations. Error bars represent 95% confidence limits. Panels (c) and (d) show the calculated percentage losses over a wider range of gap sizes. Our hypothesis for these experiments was that SPP transfer across the gaps would occur through a dipole-dipole coupling mechanism, analogous to how electromagnetic energy is transported in chains of nanoparticles,40, 42 and how the localized surface plasmon resonances of particles couple to SPPs in nanowires.7, 17, 23-24 This coupling should depend on the overlap of the SPP fields in the gap and, thus, decrease as the gap between the nanostructures increases – causing larger losses at larger gap sizes.17, 43 However, the experimental data in Fig. 2(a) shows


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larger losses at smaller gap sizes, opposite our expectations. To understand this effect, finite element method (FEM) simulations of SPP propagation were conducted. The FEM simulations were performed with a three-dimensional model of the nanobar, which is described in detail in the Supporting Information. A boundary mode analysis was performed to find the electric field distributions and wavevectors for the SPP modes supported by the nanobar. These modes were then used as the excitation source for a second calculation that solved for the electric field over the entire structure. The calculations were performed with the Frequency Domain Solver in COMSOL, using the Electromagnetic Waves, Beam Envelope study from the Wave Optics Module. The nanobars were modeled as having square cross-sections, with an edge length of 500 nm (this is representative of the average size and geometry of the structures interrogated in our experiments), and lengths of 900 nm for each segment of the nanobar. Figure 3(a) shows the results from the boundary mode analysis. For the supported nanobars in air, two primary SPP modes are excited for laser polarization parallel to the long axis of the nanobar: a bound mode that propagates at the glass-gold interface, and a leaky mode that propagates at the air-gold interface.26, 29 Only half of the mode is shown since it is symmetrical, and the symmetry was used to minimize computational demand. The white horizontal line indicates the air-glass boundary, with glass being in the lower portion of the image, and the dark rectangle is the nanobar. The propagation constants for the different modes are given in the Figure. Note that the leaky mode has a much smaller propagation constant than the bound mode, which allows some light to couple into the substrate - this can be seen in the field plot in Figure 3(a). Results are also shown for the nanobar in microscope immersion oil. The supported SPP mode in this case is approximately symmetrical around the nanobar, with more amplitude in the higher index material (which is the immersion oil in this calculation).29


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Figure 3. (a) Electric field plots for the bound and leaky modes, and the SPP mode for the nanowires in oil, determined from the boundary mode analysis. These calculations took advantage of the symmetry of the nanostructure, so only half of the mode is shown. The refractive indexes of the glass and oil used in the simulations are nglass = 1.5 and noil = 1.515. (b) Field plots for the propagation of the SPP modes over the gap structure. Excitation is from the left side of the structure, and the images represent a slice in the y-z plane. (c) Field plots for the propagation of the different modes for a continuous nanobar.

Figure 3(b) shows plots of the electric fields for the bound and leaky modes over the gap structure obtained from the three-dimensional FEM simulations, and Figure 3(c) shows the corresponding plots for the continuous structures. In all these plots (and the plots in Figure 4 below) the SPP modes are introduced on the left hand side of the simulation box, and propagate to the right. The calculations show that the modes are damped as they move across the gap, and that the fields are enhanced in the gap. The gap also causes some scattering of the SPPs into


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photons. Comparing the simulations for the nanobars with a gap to those for the continuous structures also shows that the presence of the gap changes the distribution of the fields. For example, for the continuous nanobar in air the bound mode is exclusively localized at the metalglass interface. In contrast, for the gap structure there is also significant field strength at the metal-air interface. Note that the transient absorption experiments do not directly monitor the SPP fields— the signal arises from the electron heating created by the propagating SPP modes.26 To simulate the transient absorption signal, the power dissipation per unit volume was calculated for the SPP modes. This data was averaged over each segment, and the difference in the average power dissipated in the two segments was used to determine the loss of the SPP intensity due to the gap. This analysis matches the experiments, where the transient absorption signal on either side of the gap was compared to determine the SPP losses. Note that in the experiments we used an exponential fitting procedure to account for the decay of the SPPs in the nanobar. This is not necessary in the simulations because the segments are short compared to the SPP propagation lengths. The results of these calculations for the supported nanobars in air are presented as the lines in Figure 2(a). Consistent with the experimental data, the calculations show higher losses at smaller gap sizes (40 – 50 nm in the simulations). Figure 2(c) shows a plot of the calculated losses over a wider range of gap sizes. This plot shows the expected increase in losses at large gap sizes (greater than 100 nm). A similar behavior is seen for the nanobars in microscope immersion oil. In this case the calculated losses show a sharp peak around a 30 nm gap width, followed by an increase in the percentage losses at larger gap sizes. Plots of the dissipated power for the bound and leaky modes for the supported nanobars in air for a gap size of 50 nm (corresponding to the peak in the


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losses at small gap widths), and for a large gap size (100 nm), are shown in Figures 4(a) – (d). Figures 4(e) and (f) show analogous data for the nanobars in microscope immersion oil. The data in Figure 4 shows that there is increased power dissipation within the gap at specific gap sizes, which suggests a resonance effect. We assign this resonance to a localized (nonpropagating) surface plasmon mode associated with the gap that is excited by the propagating SPP modes.

Figure 4. Images of the power dissipation for a gap size of 50 nm for (a) the bound mode, and (b) the leaky mode. Panels (c) and (d) show images at a 100 nm gap size. Results for the nanobars in oil are shown in panels (e) and (f) for gap sizes of 20 nm and 100 nm, respectively. To further investigate the nature of the localized modes in these experiments, the power dissipation in the vicinity of the gap was calculated for a range of gap sizes for the supported nanobars in air, for supported nanobars in oil, and for unsupported nanobars in air. The results are presented in Figures 5(a) and (b). This data was generated by performing a volume integration of the power dissipation density over the last 50 nm of the first nanobar and the first 50 nm of the second nanobar. The plots show peaks at specific gaps sizes that depend on the


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environment of the nanobar. Note that the maximum in the power dissipation in Figure 5 does not occur at exactly the same gap width as the maximum for the calculated losses in Figure 2. This is presumably because the SPP losses arise from a combination of heat dissipation (Figures 4 and 5) and scattering (Figure 3), and that these two effects are maximized at different gap widths.

Figure 5. (a) Power dissipation as a function of gap width for the bound (black) and leaky (blue) modes of a supported nanobar. (b) Data for a nanobar in microscope immersion oil (red) and completely surrounded by air (green). The excitation wavelength for both plots was 800 nm. Maximum power dissipation occurs at a gap width around 50 nm for the supported nanobar, 20 nm for the nanobar in oil and 50 nm for the nanobar in air.


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The effect of wavelength was also investigated in the FEM simulations. Calculations were performed for nanobars with a 20 nm gap in microscope immersion oil, for pump wavelengths ranging from 700 nm to 1200 nm (see Figure S5 of the Supporting Information). (An oil environment was chosen for these simulations for simplicity, as only one SPP mode has to be considered.) The results show a peak in the power dissipation at 800 nm. This is further evidence of a resonance effect, that is, that the losses at small gap sizes arise from excitation of a localized surface plasmon mode associated with the gap. While the simulations and experiments in Figure 2 show the same trend (greater losses at smaller gap sizes), they are not in quantitative agreement. One possibility for this is that the real nano-structures have imperfections that are not present in the simulations. The computational model assumes an idealized structure where the cuts in the bars were perfectly flat, and the bars are symmetrical with no surface irregularities. However, SEM images (see Figure S1 of the Supporting Information) show that the cuts are wider at the top of the bar than at the bottom (this is a natural consequence of the FIB milling process), and that there is a significant amount of cutting into the substrate (again see Figure S1 in the Supporting Information). FEM simulations were performed to examine how these imperfections in the milling process affect propagation of the SPP modes across the gap. First, simulations were performed where the gap between the wires was extended into the substrate. Our previous work showed that trenches created by photolithography (several µm width and several hundred nm deep) can completely damp the bound mode.39 However, the cuts created by the FIB milling process are much narrower and shallower. Calculations were performed for a 50 nm cut in the nanobar that extended 100 nm into the substrate. The results of this calculation are presented in Figure S8 in the Supporting Information. Cutting into the


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substrate minimally affects the SPP propagation, causing an additional loss of only about 5% for each mode. Calculations were also performed for nanobars that had a curved top surface, similar to those observed in the SEM images (see Figures S9 and S10 of the Supporting Information). These calculations show that the bound mode is only moderately affected by curvature on the top surface (as expected). However, the leaky mode suffers greater losses, especially at small gap sizes.

Thus, surface curvature offers a partial explanation for the difference between the

experiments and simulations in Figure 2. Note that the larger damping of the leaky mode due to surface curvature also offers an explanation for the difference in the losses for the first and second gaps (see Figure 1(d) and Figure S11). Specifically, at the first gap the experiments measure the attenuation of both the bound and the leaky modes. The greater attenuation of the leaky mode means that at the second gap the bound mode dominates, which has a smaller attenuation. The change in the mode composition due to the different transmission probabilities also explains why the decay of the transient absorption signal in Figure 1(d) is different in the different segments.39 Another possibility for the difference between simulations and experiments in Figure 2 is that the FIB milling process damages the nano-structures in the vicinity of the gap,44-45 causing a decrease in the SPP transmission. Damage from FIB milling has been shown to be an issue in electrical conductivity measurements across nanogaps in gold nanowires.45 Likewise, for SPPs creating defects in the crystal structure of the metal decreases the propagation length,46 which implies that damage from FIB milling in the gap region would decrease the transmission probabilities measured in our experiments.


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Conclusions: Transient absorption microscopy has been used to image SPP propagation in coupled gold nanobars. The results show that the SPP modes are attenuated by 60 – 80% for cut widths ranging from 20–100 nm, with greater losses occurring at smaller gap widths. The larger losses at small gap sizes are attributed to coupling between the SPP modes of the nanowire and localized surface plasmon resonances associated with the gap.

These resonances cause

additional losses through energy dissipation and scattering. The resonant nature of the gap modes was confirmed through FEM simulations by calculating the power dissipation in the vicinity of the gap versus wavelength for a given gap size, and versus gap size for a given wavelength. Coupling between propagating SPP modes and localized gap plasmon modes has not been previously observed in experiments, and represents a fundamental energy loss mechanism for the SPP modes that must be considered in designing plasmonic devices. Methods: Finite Element Method Calculations: Three dimensional finite element method simulations were performed using COMSOL Multiphysics®, v. 4.4. These calculations were done in two main steps. First, a boundary mode analysis was performed to determine the supported plasmon modes. Second, one of the modes was used as an input for the full three dimensional model.17 The simulations were performed in the frequency domain, using the Electromagnetic Waves, Beam Envelope study from the Wave Optics Module of COMSOL. Additional details can be found in the Supporting Information. Nanofabrication: The cuts in the nanobars were produced using FIB milling with a Helios NanoLab DualBeam 600 (FEI). Before cutting, the nanobars were plasma cleaned for 15 minutes, then sputtered with a thin (< 2 nm) layer of iridium to provide a conductive surface.


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Nanobars were cut at 3-4 µm increments, resulting in one, two or three cuts per bar depending on the length of the bar. Various cut widths were produced to study the gap size dependence of SPP coupling. The effect of the iridium layer on the SPP modes was examined by FEM calculations (See Figure S12 of the Supporting Information). These calculations show that a thin iridium layer has very little effect on the form and propagation constant of the SPP modes, however, the propagation length is significantly reduced. Transient Absorption Microscopy: Transient absorption measurements were performed with a ultrafast Ti:Sapphire oscillator/optical parametric oscillator laser system, which provided pump and probe wavelengths of 800 nm and 570 nm, respectively. The pump beam was linearly polarized and the polarization was adjusted to be parallel to the long axis of the nanobar, and the probe was circularly polarized. The pump and probe pulses were temporally overlapped, combined with a dichroic mirror and sent through a 4f lens system to a high numerical aperture objective. The reflected probe beam was collected by the objective and sent to an avalanche photodiode. A low-pass filter was used to prevent the 800 nm pump light from reaching the detector. The pump beam was modulated at 400 kHz using an acousto-optic modulator, and the change in reflectivity of the probe induced by the pump was measured by a high frequency lockin amplifier. The probe was scanned over the sample using a galvo-scanning mirror system to form a transient absorption image.25-26, 47 A diagram of the experimental setup is shown in the Supporting Information. The pump and probe beam powers were kept below 800 µW and 200 µW, respectively. No melting or reshaping of the materials was observed at these powers.

Supporting Information: Example SEM images of cuts, details of the finite element method calculation, cross sectional electric field plots, power dissipation plots of nanobars with rounded


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corners and nanobars with small substrate cuts, second and third gap percentage loss, and experimental layout. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgment: This research was supported by the United States National Science Foundation (CHE-1110560 and CHE-1502848), and the University of Notre Dame Strategic Research Initiative.

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References: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Ritchie, R. H., Plasma Losses by Fast Electrons in Thin Films. Phys. Rev. 1957, 106, 874-881. Maier, S. A., Plasmonics: Fundamentals and Applications; Springer Science: New York, 2007. Barnes, W. L.; Dereux, A.; Ebbesen, T. W., Surface Plasmon Subwavelength Optics. Nature 2003, 424, 824-830. Murray, W. A.; Barnes, W. L., Plasmonic Materials. Adv. Mater. 2007, 19, 3771-3782. Bozhevolnyi, S. I., Plasmonic Nanoguides and Circuits; Pan Stanford Publishing: Singapore, 2008. Ebbesen, T. W.; Genet, C.; Bozhevolnyi, S. I., Surface-Plasmon Circuitry. Phys. Today 2008, 61, 44-50. Sun, M.; Hou, Y.; Xu, H., Can Information of Chemical Reaction Propagate with Plasmonic Waveguide and be Detected at Remote Terminal of Nanowire? Nanoscale 2011, 3, 4114-4116. Lal, S.; Hafner, J. H.; Halas, N. J.; Link, S.; Nordlander, P., Noble Metal Nanowires: From Plasmon Waveguides to Passive and Active Devices. Acc. Chem. Res. 2012, 45, 1887-1895. Cohen, M.; Zalevsky, Z.; Shavit, R., Towards Integrated Nanoplasmonic Logic Circuitry. Nanoscale 2013, 5, 5442-5449. Dai, W. H.; Lin, F. C.; Huang, C. B.; Huang, J. S., Mode Conversion in High-Definition Plasmonic Optical Nanocircuits. Nano Lett. 2014, 14, 3881-3886. Kumar, M. S.; Piao, X.; Koo, S.; Yu, S.; Park, N., Out of Plane Mode Conversion and Manipulation of Surface Plasmon Polariton Waves. Opt. Express 2010, 18, 8800-8805. Noginov, M. A.; Zhu, G.; Belgrave, A. M.; Bakker, R.; Shalaev, V. M.; Narimanov, E. E.; Stout, S.; Herz, E.; Suteewong, T.; Wiesner, U., Demonstration of a Spaser-Based Nanolaser. Nature 2009, 460, 1110-1112. Berini, P.; De Leon, I., Surface Plasmon–Polariton Amplifiers and Lasers. Nat. Photonics 2011, 6, 16-24. Paul, A.; Zhen, Y. R.; Wang, Y.; Chang, W. S.; Xia, Y.; Nordlander, P.; Link, S., DyeAssisted Gain of Strongly Confined Surface Plasmon Polaritons in Silver Nanowires. Nano Lett. 2014, 14, 3628-33. Im, S.-J.; Ho, G.-S., Plasmonic Amplification and Suppression in Nanowaveguide Coupled to Gain-Assisted High-Quality Plasmon Resonances. Laser Phys. Lett. 2015, 12, 045902. Solis, D., Jr.; Paul, A.; Olson, J.; Slaughter, L. S.; Swanglap, P.; Chang, W.-S.; Link, S., Turning the Corner: Efficient Energy Transfer in Bent Plasmonic Nanoparticle Chain Waveguides. Nano Lett. 2013, 13, 4779-4784. Zhang, S.; Gu, C.; Xu, H., Single Nanoparticle Couplers for Plasmonic Waveguides. Small 2014, 10, 4264-4269. Pan, D.; Wei, H.; Jia, Z.; Xu, H., Mode Conversion of Propagating Surface Plasmons in Nanophotonic Networks Induced by Structural Symmetry Breaking. Sci. Rep. 2014, 4, 4993.


18

Page 18 of 20

Page 19 of 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.

ACS Nano

Ward, D. R.; Grady, N. K.; Levin, C. S.; Halas, N. J.; Wu, Y. P.; Nordlander, P.; Natelson, D., Electromigrated Nanoscale Gaps for Surface-Enhanced Raman Spectroscopy. Nano Lett. 2007, 7, 1396-1400. McMahon, J. M.; Li, S. Z.; Ausman, L. K.; Schatz, G. C., Modeling the Effect of Small Gaps in Surface-Enhanced Raman Spectroscopy. J. Phys. Chem. C 2012, 116, 16271637. Osberg, K. D.; Rycenga, M.; Harris, N.; Schmucker, A. L.; Langille, M. R.; Schatz, G. C.; Mirkin, C. A., Dispersible Gold Nanorod Dimers with Sub-5 nm Gaps as Local Amplifiers for Surface-Enhanced Raman Scattering. Nano Lett. 2012, 12, 3828-3832. Tong, L. M.; Xu, H. X.; Kall, M., Nanogaps for Sers Applications. MRS Bull. 2014, 39, 163-168. Knight, M. W.; Grady, N. K.; Bardhan, R.; Hao, F.; Nordlander, P.; Halas, N. J., Nanoparticle-Mediated Coupling of Light into a Nanowire. Nano Lett. 2007, 7, 23462350. Wei, W.; Li, S. Z.; Qin, L. D.; Xue, C.; Millstone, J. E.; Xu, X. Y.; Schatz, G. C.; Mirkin, C. A., Surface Plasmon-Mediated Energy Transfer in Heterogap Au-Ag Nanowires. Nano Lett. 2008, 8, 3446-3449. Lo, S. S.; Shi, H. Y.; Huang, L. B.; Hartland, G. V., Imaging the Extent of Plasmon Excitation in Au Nanowires Using Pump-Probe Microscopy. Opt. Lett. 2013, 38, 12651267. Yu, K.; Devadas, M. S.; Major, T. A.; Lo, S. S.; Hartland, G. V., Surface Plasmon Polariton Propagation and Coupling in Gold Nanostructures. J. Phys. Chem. C 2014, 118, 8603-8609. Dickson, R. M.; Lyon, L. A., Unidirectional Plasmon Propagation in Metallic Nanowires. J. Phys. Chem. B 2000, 104, 6095-6098. Sanders, A. W.; Routenberg, D. A.; Wiley, B. J.; Xia, Y.; Dufresne, E. R.; Reed, M. A., Observation of Plasmon Propagation, Redirection, and Fan-out in Silver Nanowires. Nano Lett. 2006, 6, 1822-1826. Song, M.; Bouhelier, A.; Bramant, P.; Sharma, J.; Dujardin, E.; Zhang, D.; Colas-desFrancs, G., Imaging Symmetry-Selected Corner Plasmon Modes in Penta-Twinned Crystalline Ag Nanowires. ACS Nano 2011, 5, 5874-5880. Verhagen, E.; Tchebotareva, A. L.; Polman, A., Erbium Luminescence Imaging of Infrared Surface Plasmon Polaritons. Appl. Phys. Lett. 2006, 88, 121121 Solis, D.; Chang, W.-S.; Khanal, B. P.; Bao, K.; Nordlander, P.; Zubarev, E. R.; Link, S., Bleach-Imaged Plasmon Propagation (BLIPP) in Single Gold Nanowires. Nano Lett. 2010, 10, 3482-3485. Wild, B.; Cao, L. N.; Sun, Y. G.; Khanal, B. P.; Zubarev, E. R.; Gray, S. K.; Scherer, N. F.; Pelton, M., Propagation Lengths and Group Velocities of Plasmons in Chemically Synthesized Gold and Silver Nanowires. ACS Nano 2012, 6, 472-482. Solis, D., Jr.; Paul, A.; Chang, W.-S.; Link, S., Mechanistic Study of Bleach-Imaged Plasmon Propagation (BLIPP). J. Phys. Chem. B 2013, 117, 4611-4617. Nauert, S.; Paul, A.; Zhen, Y.-R.; Solis, D., Jr.; Vigderman, L.; Chang, W.-S.; Zubarev, E. R.; Nordlander, P.; Link, S., Influence of Cross Sectional Geometry on Surface Plasmon Polariton Propagation in Gold Nanowires. ACS Nano 2014, 8, 572-580. Chen, W. P.; Ritchie, G.; Burstein, E., Excitation of Surface Electromagnetic Waves in Attenuated Total-Reflection Prism Configurations. Phys. Rev. Lett. 1976, 37, 993-997.


19

ACS Nano

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.

Berini, P., Plasmon-Polariton Waves Guided by Thin Lossy Metal Films of Finite Width: Bound Modes of Symmetric Structures. Phys. Rev. B 2000, 61, 10484-10503. Zia, R.; Selker, M.; Brongersma, M., Leaky and Bound Modes of Surface Plasmon Waveguides. Phys. Rev. B 2005, 71, 165431. Zhang, S. P.; Xu, H. X., Optimizing Substrate-Mediated Plasmon Coupling toward HighPerformance Plasmonic Nanowire Waveguides. ACS Nano 2012, 6, 8128-8135. Johns, P.; Yu, K.; Devadas, M. S.; Li, Z.; Major, T. A.; Hartland, G. V., Effect of Substrate Discontinuities on the Propagating Surface Plasmon Polariton Modes in Gold Nanobars. Nanoscale 2014, 6, 14289-96. Maier, S. A.; Kik, P. G.; Atwater, H. A.; Meltzer, S.; Harel, E.; Koel, B. E.; Requicha, A. A. G., Local Detection of Electromagnetic Energy Transport Below the Diffraction Limit in Metal Nanoparticle Plasmon Waveguides. Nat. Mater. 2003, 2, 229-232. Lal, S.; Link, S.; Halas, N. J., Nano-Optics from Sensing to Waveguiding. Nat. Photonics 2007, 1, 641-648. Solis, D., Jr.; Willingham, B.; Nauert, S. L.; Slaughter, L. S.; Olson, J.; Swanglap, P.; Paul, A.; Chang, W.-S.; Link, S., Electromagnetic Energy Transport in Nanoparticle Chains via Dark Plasmon Modes. Nano Lett. 2012, 12, 1349-1353. Wei, H.; Pan, D.; Xu, H. X., Routing of Surface Plasmons in Silver Nanowire Networks Controlled by Polarization and Coating. Nanoscale 2015, 7, 19053-19059. Burek, M. J.; Greer, J. R., Fabrication and Microstructure Control of Nanoscale Mechanical Testing Specimens via Electron Beam Lithography and Electroplating. Nano Lett. 2010, 10, 69-76. Shi, P.; Zhang, J. Y.; Lin, H. Y.; Bohn, P. W., Effect of Molecular Adsorption on the Electrical Conductance of Single Au Nanowires Fabricated by Electron-Beam Lithography and Focused Ion Beam Etching. Small 2010, 6, 2598-2603. Ditlbacher, H.; Hohenau, A.; Wagner, D.; Kreibig, U.; Rogers, M.; Hofer, F.; Aussenegg, F. R.; Krenn, J. R., Silver Nanowires as Surface Plasmon Resonators. Phys. Rev. Lett. 2005, 95, 257403. Gabriel, M. M.; Kirschbrown, J. R.; Christesen, J. D.; Pinion, C. W.; Zigler, D. F.; Grumstrup, E. M.; Mehl, B. P.; Cating, E. E. M.; Cahoon, J. F.; Papanikolas, J. M., Direct Imaging of Free Carrier and Trap Carrier Motion in Silicon Nanowires by SpatiallySeparated Femtosecond Pump–Probe Microscopy. Nano Lett. 2013, 13, 1336-1340.


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Role of Resonances in the Transmission of Surface Plasmon

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