Dynamics of Surface Plasmon Polaritons in Metal Nanowires

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Dynamics of Surface Plasmon Polaritons in Metal Nanowires Paul Johns,† Gary Beane,† Kuai Yu,‡ and Gregory V. Hartland*,† †

Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States College of Electronic Science and Technology, Shenzhen University, Shenzhen, 518060, P. R. China

‡

ABSTRACT: Metal nanostructures have found extensive use in a variety of applications in chemistry, including as substrates for molecular sensing and surface enhanced spectroscopy and as nanoscale heaters for photothermal therapy. These applications depend on the strong absorption and field enhancements associated with localized surface plasmon resonance (LSPR). This has led to a number of studies of how the LSPR line width, which measures energy losses for the coherent electron motion, depends on the size and shape of different types of metal nanoparticles, and the environment around the particle. Extended metal nanostructures, such as nanowires and nanoplates, display propagating surface plasmon modes, termed surface plasmon polaritons (SPPs), in addition to LSPRs. These modes are important for applications where metal nanostructures are used as waveguides. However, less is known about the damping of the propagating SPPs compared to the LSPRs. The energy losses for the propagating SPP modes can be investigated by measuring propagation lengths. The goal of this Feature Article is to review recent experiments that have provided quantitative information about the propagation lengths of SPPs in metal nanostructures, and to provide a physical understanding of the important factors in SPP damping. energy losses for the SPP mode,4,49,50,66−68 and is the counterpart of the line width for the LSPRs. Compared to the LSPRs of metal nanoparticles, there have been fewer studies of the dephasing of SPPs. Primarily this is because it is more difficult to couple photons to propagating SPPs due to momentum matching restrictions.1,4,6,63 This article will focus on calculations and experimental results for the propagating SPP modes of metal nanowires,48,49,69,70 rather than thin films2,65−67,71 and nanoplates.72,73 Finite element simulations will be used to elucidate the different types of SPP modes that are supported in the nanowires, and how the propagation lengths depend on the dimensions of the nanowire and the refractive index of the environment.74−77 Examples will also be given of experimental measurements that provide quantitative information about the complex wavevector of the SPP modes.47,49,51,75,78−88 The focus will be on chemically synthesized nanowires, as these have been the most studied extended metal nanostructures to date. These materials are crystalline with smooth surfaces and, thus, are expected to have longer propagation lengths compared to the polycrystalline nanowires made by electron-beam lithography or template deposition.49,80,89 A major goal of the article will be to make a connection between the line widths of LSPRs and the propagation lengths of SPPs.

1. INTRODUCTION The interaction between metal nanostructures and light generates surface plasmon polaritonswhich are mixtures of photonic and plasmonic states.1−8 For nanoparticles, these excitations are confined, and give rise to resonances that are termed localized surface plasmon resonances (LSPRs).9−11 The LSPRs of Ag and Au nanoparticles have been extensively studied, primarily because of the applications of these materials to surface enhanced spectroscopies,12−19 molecular sensing,20−23 and imaging and photothermal therapy.24−31 For most of these applications, it is desirable to have resonances with high quality factors, that is, narrow line widths.32,33 The line widths are hard to measure accurately in conventional ensemble experiments, because of inhomogeneous broadening effects from the different sizes and shapes present in the samples.34 Thus, this field has benefitted tremendously from the development of optical techniques that can record spectra of single metal nanoparticles.35−43 There have been a number of such studies in the past decade, so that the way the LSPR line width depends on size, shape, and material is now reasonably well understood.34,44−46 In extended metal nanostructures, such as metal nanowires, the electron motions can have a well-defined momentum.47−52 These types of modes are termed propagating surface plasmon polaritons (SPPs).4,6,53 The propagating SPPs have also found applications in materials science and engineering. For example, SPPs in metal nanowires provide a way of guiding electromagnetic fields with subdiffraction spatial resolution,54−60 which is useful for creating photonic devices with ultrasmall mode volumes.2,61−65 In these applications, it is desirable to have SPP modes that are strongly confined with long propagation lengths. The propagation length depends on the © 2017 American Chemical Society

Received: December 19, 2016 Revised: January 23, 2017 Published: February 3, 2017 5445

DOI: 10.1021/acs.jpcc.6b12748 J. Phys. Chem. C 2017, 121, 5445−5459

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The Journal of Physical Chemistry C

Figure 1. (a) Extinction spectra σext for the LSPR of different sized Ag spheres in water. (b) Contributions from Landau damping Γh (nonradiative relaxation) and radiation damping Γr to the line width for the spectra in panel a. (c) Extinction spectra σext for the transverse LSPR of different sized Ag nanowires in water. (d) Contributions from Γh and Γr to the line width for the spectra in panel c. The spectra were calculated through COMSOL Multiphysics, using the dielectric constant data from ref 96.

2. SIMULATIONS OF POWER DISSIPATION IN METAL NANOSTRUCTURES The starting point for our discussion is a classical description of power losses in metal nanostructures, and how these are calculated through finite element methods. Before discussing propagating SPPs in nanowires, we first look at LSPRs of particles. The width of the LSPR directly reports on energy losses for the electron system. Traditionally, the LSPR line width is divided into three contributions: nonradiative decay or Landau damping (Γh decay of the coherent electron oscillation into electron−hole pairs and, eventually, heat), radiation damping (Γr energy loss by emission of photons), and electron−surface scattering (Γsurf dephasing of the electron oscillation due to collisions with the particle surface).34,36,37,42,44,46,90−94 Electron−surface scattering will not be discussed in this article, as the nanowires that have been examined in experiments to date have lateral dimensions greater than 20 nm, which is larger than the characteristic size where electron−surface scattering effects are significant.42,44,46,92,93 There have been several recent reviews of electron−surface scattering effects in metal nanostructures, and the interested reader is referred to these.34,44 Neglecting electron−surface scattering means that the total line width is simply given by Γ = Γh + Γr. Figure 1a shows simulated extinction spectra for different sized Ag nanospheres in water. The spectra were calculated through finite element analysis, using the Wave Optics module of COMSOL Multiphysics (v 5.2a). In these calculations, the extinction cross section σext is obtained from the sum of the absorption and scattering cross sections, σabs and σscat, respectively.95 These cross sections were calculated from the power losses for the incident electromagnetic field due to absorption and scattering by the particle. Specifically, the absorption cross section is calculated by integrating the power dissipation Qrh over the volume of the sphere: σabs = ∭ Qrh dV/ P0, where P0 is the incident power of the electromagnetic field.

In turn, the scattering cross section is obtained by integrating the time-averaged power flow from the scattered field over a spherical surface placed at some distance from the nanoparticle: S dA/P0, where ⇀ S is the Poynting vector for the σscat = ∬ n̂·⇀ scattered field and n̂ is a unit vector normal to the surface.95 S are specified in our COMSOL More details on how n̂ and ⇀ simulations are given in the Appendix to this article. The Johnson and Christy dielectric constant data was used for all of the simulations presented below.96 The plasmon resonance for the spheres becomes more intense and broader as size increases. The increase in the line width arises from radiation damping: at large sizes, decay of the plasmon oscillation into photons becomes a significant energy loss mechanism.36,91,92,97,98 The radiative and nonradiative contributions to the total line width can be determined by analyzing the power dissipation from each process. Specifically, by analogy with molecular quantum yields, Γh = (Ph/Ptot)Γ and Γr = (Pr/Ptot)Γ, where Ptot = Ph + Pr is the total dissipated power and Ph and Pr are the power dissipated by resistive heating and radiation, respectively. Ph and Pr are given by Ph = S dA as before. Figure 1b shows a plot ∭ Qrh dV and Pr = ∬ n̂·⇀ of Γh and Γr versus the size obtained from the spectra in Figure 1a. In this calculation, Ph and Pr were determined at the peak of the LSPR, and Γ was obtained by fitting the spectra to a Fano profile A(1 + (ω − ω0)/qw)2/(1 + ((ω − ω0)/w)2), where ω0 is the resonance frequency, A is the amplitude, w = Γ/2, and q is the asymmetry factor.99,100 A Fano profile was used, rather than the conventional Lorentzian profile,46,92 to provide a consistent analysis with the LSPRs of the metal nanowires presented below, which show asymmetrical lineshapes. This profile has been extensively used to analyze the spectra of metal nanostructures and, thus, is a natural choice for these simulations.99−101 Figure 1b shows that, at sizes greater than 15−20 nm, light scattering becomes the dominant energy loss mechanism for the LSPR of Ag spheres.34 Note that, because the absorption and scattering cross sections are proportional to 5446


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Figure 2. (a) Propagation length LSPP versus radius for Au nanowires with circular cross sections in air, water, and microscope immersion oil. (b) LSPP versus width for Au nanowires with a square cross section in microscope immersion oil and supported on a glass surface. Panels c and d show the corresponding propagation constants β/k0 for the nanowires in panels a and b, respectively. (e) Plots of the norm of the electric field for (from left to right) nanowires with a circular cross section in microscope immersion oil, a square nanowire in oil, and the bound and leaky modes for a square nanowire on a glass surface. The dimensions of the nanowires (diameter or width) were 500 nm.

greater than approximately 15 nm. The Γh contribution to the line width is larger for the nanowires compared to that for the spheres because the LSPRs of the nanowires are blue-shifted and closer to the interband transitions of Ag.102 Note that the spectra calculated through the finite element simulations are in good agreement with spectra calculated using the full Mie theory expressions for the extinction and scattering cross sections of spheres,34 or the equivalent expressions for infinite cylinders.95,103 For both the spheres and the cylinders, the contribution from radiation damping to the line width increases with size. For the spheres, Γr is simply proportional to volume.36,91,92 To understand this scaling, we note that the damping constant for the LSPR can be expressed as Γ = −(dW/dt)/W, where W is the stored electromagnetic energy. The power dissipation from emitting photons (−(dW/dt)r) is proportional to the scattering cross section, which scales as the volume squared for not too large particles (i.e., at sizes where retardation effects are relatively small). In contrast, the stored energy W is simply proportional to volume. Thus, for spheres, Γr increases with volume. The size dependence for Γr is more complicated for the cylinders, most likely because of retardation effects at large sizes. Note that for both the spheres and the cylinders the damping from nonradiative processes is roughly independent of

Ph and Pr, the nonradiative and radiative contributions to the LSPR line width can equivalently be calculated by Γh = (σabs/ σext)Γ and Γr = (σscat/σext)Γ (this form is convenient for Mie theory calculations, for example). Extended metal nanostructures also display LSPRs. Figure 1c shows calculated spectra for the transverse LSPR (electron oscillation across the nanowire) for cylindrical silver nanowires of different dimensions in water. These calculations were performed in a two-dimensional simulation, which effectively assumes infinitely long nanowires. The powers dissipated by resistive heating and radiation were calculated in an analogous way to what was done for the spheres, except now the volume and surface integrals for Ph and Pr become area and line integrals, respectively. Specifically, Ph = ∬ Qrh dA and Pr = S dl where the integral for Ph is over the area of the ∫ n̂·⇀ nanowire and the integral for Pr is over a circle placed at a distance from the nanowire. Note that the cross sections have units of m2 per unit length, which we have expressed as nm in Figure 1c. Figure 1d shows the contributions from radiative and nonradiative damping determined using the analysis described above, where the total line width was obtained from the spectra in Figure 1c using the Fano profile. Similar to the spheres, the radiation damping contribution increases as the lateral dimensions of the nanowire increase, and dominates for radii 5447


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Figure 3. (a) Plot of the relative amount of electromagnetic energy inside the nanowire Win/(Win + Wout) versus width for the different sized nanowires in Figure 2. Note that Win/(Win + Wout) decreases as size increases. (b) Attenuation constant α versus Win/(Win + Wout). (c) Plots of the normalized electric field for the bound mode of a square nanowire with different widths. (d) Plots of the normalized electric field for the different nanowires in microscope immersion oil.

size. This is because the amount of energy dissipated by heating is proportional to the volume of the nano-object, so that the size dependent terms in −(dW/dt)/W cancel. We now turn our attention to the propagating SPP modes of the nanowires. We start with Au nanowires, as these have been the most studied. The different SPP modes that are supported by a nanowire can be determined in COMSOL by a twodimensional Mode Analysis calculation.74−77,84−88 This analysis ̃ = β + iα, yields the complex wavevector of the SPP mode kSPP where β and α are the propagation and attenuation constants, respectively. The SPP propagation length is given by LSPP = 1/ 2α.74−77,84−88 Parts a and b of Figure 2 show the propagation lengths versus size for several different cases: cylindrical Au nanowires in homogeneous environments (air, water, and microscope immersion oil) (Figure 2a) and Au nanowires with square cross sections on a glass surface and in microscope immersion oil (Figure 2b). The corresponding propagation constants (β/k0) are presented in Figure 2c and d. Note that only the lowest order SPP modes are examined, as these are the ones generally seen in experiments. Plots of the electric fields associated with the different modes are shown in Figure 2e. Square cross sections were investigated for the substrate supported nanowires, because this shape roughly matches the shape of the nanowires examined in our previous papers.84,86,87 For the square nanowire on glass, there are two supported modesa bound mode where the field is localized at the nanowire glass interface and a leaky mode where the field appears on both the metal−air and metal−glass interfaces.50,75,84,86 The propagation constant β for the leaky mode is much smaller than that for the bound mode, and is small enough that the leaky mode can couple to photons in the substrate.75,76,85,88 In contrast, for the bound mode and for nanowires in a homogeneous environment, β/k0 is always greater than nmed, which means that SPPs cannot couple to free space photons.50

For all of the different cases in Figure 2, the propagation length of the SPP modes increases (power losses decrease) with increasing dimensions. For all of the modes except the leaky mode, this has a fairly simple physical reason: for metal nanostructures, the decay length of the field into the environment increases as the diameter increases.52,66,67 However, the decay length for the field inside the nanostructure is determined by the optical penetration depth in the metal,6,8 which does not depend on size. Thus, as the size of the structure increases, the SPP modes are less confined in the metal: proportionally more of the field is outside the nanowire. Because the power losses arise from resistive heating inside the metal, the propagation lengths increase as the dimensions increase. To illustrate this effect, Figure 3 shows plots of the attenuation constant α and the relative amount of electromagnetic energy inside the nanowire Win/(Win + Wout) for the nanowires in a homogeneous environment and for the bound mode. For our two-dimensional calculations, 1 Wi = 2 ∬ (ϵiϵ0 |Ei|2 + |Bi |2 /(μi μ0 )) dA , where ϵi, Ei, μi, and Bi are the dielectric constant, the electric field, the permittivity, and the magnetic field in region “i”, respectively. In Figure 3a, Win/(Win + Wout) is plotted versus dimensions for the nanowires in a homogeneous environment and for the bound mode of the substrate supported nanowires. The relative amount of energy inside the nanowires decreases (the SPP modes become less confined) as the dimensions increase.52,67 Figure 3b shows a plot of α versus Win/(Win + Wout). The attenuation constant increases (LSPP decreases) as Win/(Win + Wout) increases. This shows that as the SPP modes become more confined they suffer greater attenuation. Parts c and d of Figure 3 show plots of the normalized electric field for the bound mode of a square nanowire and the field for a square nanowire in microscope immersion oil. These plots show that, as the dimensions of the nanowire increase, the 5448


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Figure 4. (a) Attenuation constant α versus width for the leaky mode of Au nanowires with square cross sections. αh and αr are the contributions from resistive heating and radiation damping, respectively. (b) Field plots for the leaky mode for several different sized square Au nanowires. (c) Attenuation constants and (d) field plots for the leaky mode for pentagonal Ag nanowires.

field extends out further into the medium. However, the length scale for the decay of the field inside the nanowire does not change with size. Thus, the relative amount of electromagnetic energy inside the nanowire Win/(Win + Wout) decreases as size increases. This has an interesting consequence for the bound mode: for large nanowires, the field inside is completely damped, so that the field only appears at the glass−metal interface. In contrast, for smaller nanowires, the field inside does not decay completely, and some electric field appears at the metal−air interface. The leaky mode for the substrate-supported nanowires shows a different behavior from the modes in Figure 3. Like the other SPP modes, LSPP increases as the dimensions increase for the leaky mode; however, the leaky mode becomes less confined at small dimensions rather than at large dimensions (see Figure 4). The analysis in Figure 3 cannot be used for the leaky mode, because the leaky mode couples to propagating fields in the substrate rather than evanescent fields. This means that Win/(Win + Wout) changes with the size of the simulation area. Thus, to understand the behavior of the leaky SPP mode, we look at the power losses due to radiative and nonradiative processes. Following the procedure for the LSPRs, we write the total attenuation constant as α = αh + αr, where αh and αr are the contributions from resistive heating and radiation, respectively. The values of αh and αr can be calculated from αh = (Ph/Ptot)α and αr = (Pr/Ptot)α, where the total attenuation constant α is obtained from the Mode Analysis calculation in COMSOL. The powers dissipated by resistive heating and radiation were calculated in the same way as that for the LSPRs in Figure 1. Figure 4a shows a plot of αh and αr for the leaky mode of a Au nanowire with a square cross section determined from this analysis. The data shows that αr decreases rapidly as size increases, and that it is the decrease in αr that causes the increase in LSPP seen in Figure 2. This is in contrast to the other (“regular”) SPP modes, where the increase in LSPP with size arose from a decrease in αh due to the modes becoming less

confined. This behavior is also very different from that for the LSPRs of the spheres and cylinders in Figure 2, where radiation damping becomes stronger as size increases. Figure 4b shows plots of the norm of the electric field ( Ex 2 + Ey 2 + Ez 2 , where Ex, Ey, and Ez are the x-, y-, and z-components of the electric field) for the leaky mode for square Au nanowires with different widths (200−2000 nm). The calculations show very clearly that the leaky mode is coupled to a propagating (photonic) field in the substrate that radiates away from the nanowire at an angle. The angle is a consequence of the momentum matching conditions, and is discussed in more detail below. The coupling to the photonic modes of the substrate is clearly much stronger at small sizes. The stronger coupling to photonic modes in the substrate at small sizes is surprising given that there is very little change in the propagation constant for the leaky mode with size (see Figure 2d). However, we believe that this can be explained by a simple geometric effect. Starting at the larger nanowires, we note that the leaky mode is primarily localized at the top metal−air interface; see Figure 4b.50,77,84−88 To couple to the photonic modes in the substrate, the field at the top of the metal nanostructure must overlap with the field in the substrate. As the size of the metal nanostructure decreases, the two fields become closer together, so the coupling between them increases. Figure 4c and d shows an analogous analysis of αh and αr and mode plots for Ag nanowires with pentagonal cross sections (which is the common shape for chemically synthesized Ag nanowires). The results are very similar to those for the square Au nanowiresthe leaky mode is strongly attenuated at small sizes due to increased coupling to photonic modes in the substrate. It is interesting to compare the damping for the LSPRs to that for the propagating SPPs. To do this, we compare quality factors. For the LSPR resonances, the quality factor is given by Q = ωrW/(−dW/dt), where ωr is the resonance frequency, W is the total stored energy in the oscillator, and dW/dt is the 5449


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Figure 5. Quality factors versus size (radius) for the plasmon modes of Ag nanoparticles in water. (a) LSPR of a Ag sphere and transverse LSPR for a cylindrical Ag nanowire; (b) propagating SPP mode for a cylindrical Ag nanowire.

power dissipation for the oscillator.104 dW/dt = −ΓW which means that Q has the simple form of Q = ωr/Γ. For the propagating SPPs, we use the expression for the quality factor of a waveguide Q = ωτSPP, where τSPP is the lifetime of the SPP mode and ω is the angular frequency.105−107 The lifetime τSPP is related to the propagation length by τSPP = LSPP/vg, where vg is the group velocity of the SPP mode.105−107 Figure 5a shows a plot of the quality factor versus size for the LSPRs of Ag spheres and the transverse LSPR of cylindrical Ag nanowires (both in water). The quality factor for the propagating SPP mode of cylindrical Ag nanowires in water is presented in Figure 5b. For the propagating SPP modes, the group velocity was calculated by vg = (∂ω/∂k) ≈ Δω/Δk. The quality factors for the LSPRs of both the Ag spheres and the cylindrical Ag nanowires decrease with increasing size. This is expected, as the LSPRs suffer increased radiation damping with increasing size. Note that the LSPR quality factors for the cylinders are lower than those for the spheres. This is because Γh is larger for the cylinders, due to the blue shift in the resonancesee Figure 1. Figure 5b shows that the quality factor for the propagating SPPs of the nanowires increases as size increasesopposite the trend that occurs for the LSPRs. As discussed above, this is because the energy losses are smaller at large sizes due to field confinement effects. Interestingly, the quality factors for the propagating SPPs for the larger nanowires are comparable to those for the LSPRs at small sizes. It is also important to note that in real systems electron− surface scattering effects would reduce the quality factors for the LSPRs at sizes less than 10 nm.34,44

Figure 6. Scattered light images of Ag nanowires. Left: images of silver nanowires under white light illumination. Right: images recorded with a near-IR laser (880 nm) focused at one end of the wire. Parts a and b show a straight wire with no kinks or defects, and parts c and d show a kinked wire. In the laser images, light emission can be seen from the distal end of the wire and at sharp bends in the wire. Reproduced with permission from ref 108. Copyright © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

3. VISUALIZING SURFACE PLASMON POLARITONS IN METAL NANOWIRES A variety of different optical techniques have been used to image SPPs. In the following, we will discuss some of the more common measurements. The example images are taken from our work; however, this is not meant to imply that we are main workers in this field. Figure 6 shows scattered light images of silver nanowires recorded with a standard optical microscope in reflection mode.108 The images on the left were obtained using a lamp to illuminate the sample. The wires reflect strongly, and appear bright on a dark background. This configuration does not excite the propagating SPP modes because the momentum of the photons is not matched to the SPP wavevector. The panels on the right in Figure 6 show images where a near-IR laser beam has been focused at one end of a nanowire.49,69,70,108 The break in symmetry at the end of the wire relaxes the momentum matching conditions and allows excitation of the SPP modes. This is the simplest way to interrogate SPPs in

metal nanowires. For the wires in Figure 6, only bound modes were detected: scattered photons were only observed at the end of the wire or at kinks, not along the wire.49,69,70,108 This could be because only bound modes were excited, or because the propagation length for the leaky mode is very short so that this mode does not appear in the images. The scattered light images in Figure 6b and d clearly show that SPPs are excited and that they travel down the wire. In principle, the intensity of the light emitted at the distal end of the nanowire provides a way of measuring the decay length for the SPP modes.70 However, the details of the end structure will also affect the scattered intensity, which means that analysis of images such as those in Figure 6c and d does not provide accurate information about the SPP propagation lengths. On the other hand, scattered light measurements can provide information about the propagation length for the leaky modes.75,81,85,88 In the following, we will discuss light scattering measurements for the leaky mode, before moving onto more 5450


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Figure 7. (a) Scattered light image of the leaky mode for a Ag nanowire. (b) Fourier image of the nanowire in panel a. Panels c and d show line profiles extracted for the images in panels a and b, respectively. Fitting the data in panel c to an exponential decay yields the propagation length for the SPP mode (note that panel c is plotted on a natural log scale), and panel d yields the propagation constant β/k0. The inset of panel c shows a line profile across the nanowire.

Figure 8. (a) Momentum matching conditions for coupling between SPPs of a metal nanowire and photonic modes in the substrate. (b) Plot of the value of θ needed to achieve momentum matching for a given value of ϕ. (c) Polar plot of the projection of the wavevectors in panel a onto the (x, y) plane. (d) Calculated real space image of the leaky mode. Note that the distances for the x- and y-axes are in μm.

shape is characteristic of the leaky mode and is a consequence of momentum matching (see below). In the Fourier space image, the leaky mode appears as a line that corresponds to the wavevector for the mode.75,81,85,88 To understand the information content in these images, Figure 8a shows a wavevector diagram for coupling between the SPP modes of the nanowire and photons in the substrate (adapted from refs 82 and 85). The wavevectors are matched when the propagation constant for the SPP mode (β) equals

complex optical measurements that can interrogate both the bound and leaky modes. Figure 7 shows scattered light images for the leaky mode of a Ag nanowire. Two images are presented, a real space image where the camera is placed at a primary focal plane of the microscope, and the conjugate Fourier space image that is obtained by projecting the back focal plane of the objective onto the camera.75,81,85,88 In the real space image, emission can be seen along the length of the nanowire. The double lobe 5451


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The Journal of Physical Chemistry C nk0 sin(θ) cos(ϕ), where n is the refractive index of the substrate, k0 = 2π/λ is the free space wavevector of the light, and θ and ϕ are indicated in Figure 8a. Figure 8b shows a plot of the value of θ = arcsin(β/(nk0 cos(ϕ))) that matches the wavevectors for the SPP and light for a given ϕ. As ϕ increases, the projection of the light wavevector onto the axis of the nanowire (the y-axis in Figure 8) decreases, which means that θ must increase to achieve momentum matching. The limiting value of ϕ, beyond which momentum matching cannot be achieved, occurs when β/(nk0 cos(ϕc)) = 1, or ϕc = arccos(β/ nk0). The value of ϕc is shown as the vertical dotted blue line in Figure 8b. Note that in far-field optical microscopy measurements the numerical aperture (NA) of the objective limits the range of θ values and, thus, the values of ϕ. The maximum value of θ assuming a NA = 1.4 (denoted as θNA) and the corresponding maximum value of ϕ (denoted as ϕNA) are shown as the dashed horizontal and vertical red lines in Figure 8b. Also shown in Figure 8b is the critical angle for total internal reflection (θc dashed horizontal blue line). Figure 8c shows a plot of the projection of the different wavevectors in Figure 8a onto the (x, y) plane. The magnitude of the wavevector of light parallel to the axis of the nanowire is ky/k0 = β/k0, and the wavevetor for the perpendicular component is kx/k0 = n sin(θ) sin(ϕ) = (β/k0) tan(ϕ). This analysis shows that the SPP should appear as a line perpendicular to the reciprocal space vector corresponding to the long axis of the nanowire, which is exactly what is seen in the Fourier space images in Figure 7. The outer circle in Figure 8c indicates the maximum wavevector allowed by the NA of the objective, and the inner circle corresponds to the critical angle for total internal reflection (which is not related to detecting the SPPs but appears in the images).75,81,85,88 The Fourier space image in Figure 8c can be converted to a real space image by performing a spatial Fourier transform.109 Specifically, the fields in the real space image f(x, y) and the Fourier space image g(kx, ky) are related through the Fourier transform pair f (x , y) = and g (kx , k y) =

∞

∞

The images and analysis in Figures 7 and 8 show that light scattering measurements can yield both the real and imaginary ̃ components of the leaky mode wavevector kSPP = β + iα. Specifically, the real space image provides information about the propagation length LSPP = 1/2α, and the Fourier space image yields β/k0.75,81,85,88 These types of measurements have been used to study propagation lengths and constants in nanowires with different sizes,81,88 and how the propagation constant depends on the environment of the nanowire.85 They have also demonstrated that pentagonal silver nanowires (which is the characteristic shape for chemically synthesized wires) support multiple leaky modes.88 The propagation constant and the damping for the leaky SPP modes can also be measured by near-field scanning optical microscopy (NSOM).47−49,51,110 In these experiments, the SPP modes are launched at one end of the nanowire, and the tip of the NSOM microscope is used to sample the SPP field near the surface. However, NSOM measurements are very challenging, and require highly specialized equipment. Thus, there have been no systematic NSOM studies of how the SPP wavevector depends on the size and shape of the nanowires, and their environment. The bound SPP modes are more difficult to quantitatively study by far field optical microscopy because they only scatter photons at defects in the nanowires or at the ends. The most popular method for measuring the propagation lengths of these modes is to coat the nanowires with emitters, such as inorganic quantum dots or organic dyes.78−80,82,83,111,112 Similar to the leakage microscopy measurements, SPPs are launched by focusing a laser at one end of the nanowire. The electric field from the SPPs couples to the transition dipole moment of dye molecules near the surface of the nanowire, causing an electronic transition. Recording an image of the dye emission provides a map of the SPP field strength, which yields the propagation length.78−80,82,83,111,112 Images have been produced using both single- and two-photon emission. Note that both bound and leaky SPP modes are excited in these measurements, and assigning the measured propagation lengths to a specific SPP mode requires comparison to theory.78−80,83 An obvious issue with these experiments is the possibility of bleaching the electronic transitions of the dye. To overcome this problem, Link and co-workers developed a technique termed bleach-imaged plasmon propagation (BlIPP),78,79,82,83 where confocal fluorescence images of dye-coated samples are recorded before and after excitation of the SPPs in the nanowire. Dye molecules near the surface of the nanowire are bleached by the SPP, and the rate of bleaching depends on the field strength. Subtracting the before and after images shows the distribution of bleached molecules, which can be analyzed to generate information about LSPP.78,79,82,83 A nice aspect of these experiments is that prolonged excitation of the SPP modes can bring out weak features, and allow modes to be studied that are hidden in regular direct emission images.79,83 Recently, our laboratory has developed an alternative approach for studying SPP propagation in nanostructures based on transient absorption microscopy (TAM).84,86,87,113−115 In these experiments, a near-IR pump laser is used to excite the SPP modes of the nanowire. The SPPs move down the wire, and as they move, they lose energy via nonradiative and (for the leaky mode) radiative processes. The nonradiative relaxation channel creates hot electrons that cause a transient absorption signal in the nanowire, which is monitored by a visible probe laser.84,86,87,114 The magnitude of

( 21π )∬−∞ g(kx , ky)ei(k x+k y) dkx dky x

y

( 21π )∬−∞ f (x , y)e−i(k x+k y) dx dy. We model x

y

the time-averaged fields in the Fourier space image as g (kx , k y) = E0δ(k y − β)kx for |kx /k 0| ≤

NA2 − (β /k 0)2

for |kx /k 0| >

NA2 − (β /k 0)2

=0

Fourier transforming g(kx, ky) yields f(x, y) = (iE0/π)eiβy(sin(kcx) − kcx cos(kcx))/x2 for the field in the real space image, where kc = k 0 NA2 − (β /k 0)2 . The intensity pattern f(x, y)2 created by this field is plotted in Figure 8d. The calculated real space image shows the characteristic two lobes, which are separated by 570 nm for the choice of parameters in Figure 8d (NA = 1.4 and β/k0 = 1.05). These lobes are a consequence of the momentum matching conditions that introduce wavevectors for the light that are perpendicular to the SPP wavevector. The spacing between the lobes depends on the NA of the objective and, thus, does not carry any useful physical information about the SPP. Note that the calculations presented above assume an infinitely long nanowire with no attenuation of the SPP mode. Damping can be included by modeling g(kx, ky) as a Lorentzian in ky, rather than a delta function. This introduces an exponential decay of the intensity in the real space image. 5452


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Figure 9. (a) Scattered light image of a gold nanowire and (b) the corresponding AFM image. The dimensions determined from the AFM measurements are 450 nm × 250 nm × 15 μm (width × height × length). (c and d) Transient absorption images with pump excitation parallel and perpendicular to the long axis of the nanowire, respectively. The pump beam is fixed at the end indicated by the arrows. (e and f) Line profiles of the signal extracted from the images in parts c and d. Note that the intensities are on a log scale. A fit to the linear portion (red lines) gives an estimate of the SPP propagation length. Reproduced with permission from ref 84. Copyright 2014 American Chemical Society.

experiments (which detect electron heating), the magnitude of the signal depends on the SPP field inside the nanowire.84,86,87 In principle, this could lead to different results for the two measurements. Neither the TAM nor the fluorescence images provide information about the propagation constant, which is a disadvantage of these techniques compared to the Fourier imaging measurements in Figure 7. TAM experiments are more complex to implement than the fluorescence detection experiments, but they have the advantage that they do not require additional processing of the samples, and do not suffer from bleaching. This means that repeated measurements can be performed on the same nanowire. This is demonstrated in Figure 9, where measurements with the pump laser polarized parallel and perpendicular to the axis of the nanowire are presented.84 The observation that the propagation lengths are essentially the same in the two experiments implies that the same SPP modes are excited by the two polarizations. In general, the propagation lengths measured in these experiments are in good agreement with the calculated values, although it is important to note that the details of the shape of the nanowire and effects such as rounding of the edges affect the propagation length.84 The TAM images typically show a single decay length (see Figure 9), and our interpretation of this is that they report on the SPP mode with the longest propagation length. Comparison between the experimental results and the simulations shows that the leaky mode is detected for large nanowires (dimensions greater than 500 nm) and the bound mode is detected for smaller nanowires.84 The measurements also show that the propagation lengths are reduced when the refractive index of the environment is increased, for example, by adding microscope immersion oil to the samples,84 consistent with the results presented in Figure 2 above. The relatively simple sample preparation and optical alignment of the TAM experiments means that they can be used on a variety of different systems. For example, we have used these measurements to examine nanowires suspended over trenches,86 and with cuts fabricated by focused ion-beam

the transient absorption signal is proportional to the number of hot electrons, which depends on the intensity of the SPP modes. Thus, scanning the probe over the nanowire generates an image that directly reports on the SPP field strength. Example TAM images for a gold nanowire are presented in Figure 9, along with scattered light and atomic force microscopy (AFM) images.84 Note that the TAM data is plotted on a natural log scale. Fitting the line profiles to an exponential yields the propagation length, which is 16.7 ± 0.8 μm for the nanowire in Figure 9 (for the pump laser polarized parallel to the long axis of the nanowire).84 The nanowires examined in ref 84 had relatively large lateral dimensions (average heights of 550 ± 140 nm and widths 600 ± 220 nm) and correspondingly long propagation lengths (between 10 and 20 μm). In contrast, the smaller 60 ± 10 nm diameter Au nanowires examined in our initial report in ref 114 had much shorter propagation lengths, on the order of 1−2 μm, consistent with the results in Figure 2 above. In order to maximize the signal, the wavelength of the probe is chosen to be resonant to the transverse LSPR of the nanowire, and the pump and probe are temporally overlapped. A possible problem with these experiments is that the timing between the pump and probe pulses could change when the probe is scanned over the sample to form an image, due to differences in the path length between the two beams.114 Transient absorption measurements for a long nanowire recorded with the pump and probe separated by up to 25 μm show very little change in the form of the signal versus time trace.84 This indicates that the path length differences created by scanning the probe relative to the pump do not significantly affect the signal in these experiments. The TAM microscopy measurements provide similar information to the fluorescence detection experiments described above. Both bound and leaky modes are excited in the experiments, and the measurements yield an effective propagation length for the excited modes. For the fluorescence detection experiments, the magnitude of the signal depends on the SPP field outside the nanowire,78,83 whereas, for the TAM 5453


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Figure 10. (a) SEM image of a nanobar with three cuts created by FIB milling. The widths of the gaps from left to right are 20, 30, and 25 nm, respectively. (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. (e) Simulated power dissipation as a function of gap width for the bound (solid line) and leaky (dashed line) modes of a supported nanobar. The experimental measurements are shown as the symbols. (f) Data for a nanobar in microscope immersion oil. The excitation wavelength was 800 nm. Reproduced with permission from ref 87. Copyright 2016 American Chemical Society.

(FIB) milling.87 Both of these systems would be difficult to study by either the light scattering, NSOM, or fluorescence detection methods. The experiments on the nanowires suspended over trenches showed an unexpected effect: for approximately half the nanowires, the propagation lengths were different on the two sides of the trench. The pump laser excites both the bound and leaky modes; however, finite element simulations show that the bound mode (which is localized at the metal−glass interface) is strongly attenuated by the trench, so that only the leaky mode is detected on the far side of the trench. Thus, different propagation lengths can be measured in these experiments when the bound mode dominates the signal on the near side of the trench.86 Figure 10 shows results for a system with a different type of discontinuity: Au nanowires with gaps that have been fabricated by FIB milling.87 Figure 10a shows a scanning electron microscopy image of the nanowire, and a scattered light image recorded by focusing a near-IR laser at one end of the nanowire is presented in Figure 10b. The scattered light image shows that the leaky mode is definitely excited, although the bound mode could also be excited, and that the leaky mode couples across the gaps created by the FIB. Although it is not evident from the figure, the signal-to-noise in the scattered light image is not good enough to accurately measure the probability for transmission across the gaps. Figure 10c shows a TAM image of the nanowire where the near-IR pump laser is focused at one end of the nanowire, and the probe laser is scanned across the sample to form an image. There is a clear drop in the signal at each cut, and analysis of the image (Figure 10d) yields

the relative loss in the SPP intensity (which is related to the transmission probability) at each gap. The results show that the SPP modes are attenuated by 60− 80% for cut widths ranging from 20 to 100 nm. Interestingly, on average, larger losses are observed at smaller gap widths see Figure 10e and f. Intuitively, one would expect the oppositelarger losses should be observed at larger gap sizes because the coupling between the SPPs on either side of the gap should be reduced.87 Finite element simulations show that the increased losses at small gap sizes arise from coupling between the SPP modes of the nanowire and localized surface plasmon resonances associated with the gap.87 These resonances cause additional losses through energy dissipation and scattering. In the finite element simulations, the power dissipation in the vicinity of the gap was calculated versus wavelength for a given gap size and versus gap size for a given wavelength. Both data sets show resonances. The dissipated powers as a function of gap size for 800 nm excitation for the bound and leaky modes and for the nanowires in microscope immersion oil are presented in Figure 10e and f.87 The increased losses at approximately 50 nm gap size for the bound and leaky modes are consistent with the experimental results.87 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. 5454


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4. SUMMARY AND PERSPECTIVES A number of far-field optical techniques have been developed to study the properties of propagating SPP modes in extended metal nanostructures. These techniques provide information about the propagation lengths LSPP of the SPPs, and in some cases can also determine the propagation constant β. The different techniques have different strengths and weaknesses. For example, light scattering measurements are easy to implement and provide information about β as well as LSPP,47−51,75,76,81,85,88 but they can only be used to study leaky modes. The propagation lengths for both the bound and leaky SPP modes can be interrogated by observing emission from dye molecules or quantum dots coated on the sample.78−80,82,83,111,112 These experiments provide high signal-to-noise images but suffer from photobleaching. Our group has used TAM to measure SPP propagation.84,86,87,114 This technique allows repeated measurements on the same sample but is more complex than light scattering or fluorescence imaging and requires specialized laser sources. The results from experiments on Au nanowires show that LSPP increases as the lateral dimensions of the nanowire increase, which means that the SPPs suffer reduced losses at large sizes.84,114 This is opposite to what occurs for the LSPRs of particles, where the energy losses increase at large sizes due to increased radiation damping.36,46,91,92 Finite element simulations show that for the bound modes this effect arises because the coupling between the field is outside the nanowire, which means that resistive heating effects are reduced. For the leaky SPP modes, the increased propagation lengths at large sizes are due to reduced radiative damping. This is counterintuitive given that radiation damping strongly increases with size for the LSPRs of nanoparticles. We believe that this effect arises because the coupling between the field at the surface of the nanowire and photonic modes in the substrate decreases as size increases. It is also interesting to note that the quality factors for the propagating SPP modes for large nanowires are comparable to those for the LSPRs of small particles. We have also used TAM to study how the SPP modes couple between nanostructures.87 TAM is well suited for these types of measurements, as it does not require special sample preparation and multiple measurements can be performed in different environments. The results from the experiments on cut nanowires show increased losses at small gap sizes. This is attributed to excitation of LSPRs associated with the gaps in the structure.

complicated and involves separating the Poynting vector into its x-, y-, and z-components: n̂ ·⇀ S = ewfd.relPoavx*onx + ewfd.relPoavy*ony (A1)

+ ewfd.relPoavz*onz

The functions ewfd.relPoavx, ewfd.relPoavy, and ewfd.relPoavz call for the x-, y-, and z-components of the relative Poynting vector. onx, ony, and onz are defined as onx = nx*ofact

(A2a)

ony = ny*ofact

(A2b)

onz = nz*ofact

(A2c)

where nx, ny, and nz are the normal vectors in each direction. The value of ofact takes into account the quadrant of the simulation and takes the value of ±1 according to if

(nx*x + ny*y + nz*z) ≥ 0, 1, −1

(A3)

For the two-dimensional case (i.e., the infinite nanowire), the zcomponent of all of the above equations was omitted. For the two-dimensional calculations, it was not necessary to break the Poynting vector into its components to calculate the value of S . This was simply called by ewfd.nPoav. n̂·⇀ Stored Electromagnetic Energy 1

The value Wi = 2 ∬ (ϵiϵ0 |Ei|2 + |Bi |2 /(μi μ0 )) dA is called in COMSOL as ewfd.Wav.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1 (574) 631-9320. ORCID

Gary Beane: 0000-0001-5312-0477 Gregory V. Hartland: 0000-0002-8650-6891 Notes

The authors declare no competing financial interest. Biographies

■

APPENDIX In this section, we give details of the COMSOL commands used to calculate the extinction cross sections, dissipated powers, attenuation constants, and stored electromagnetic energy for the different nanostructures. Extinction Cross Sections, Power Dissipation, and Attenuation Constants

When calculating the absorbance cross section, σabs = ∭ Qrh dV/P0, the value of P0 is defined as

P0 =

(

(1 V / m)2 2Z 0

)n

med ,

where Z0 is the characteristic impedance

Paul Johns is a Ph.D. Candidate in Physical Chemistry at the University of Notre Dame and a Graduate Assistance for Areas of National Need (GAANN) Teaching Fellow. He received his B.S. in Chemistry from Saint Francis University in Loretto, PA. His research focuses on finite element calculations of surface plasmon polaritons in different types of metal nanostructures.

of vacuum and nmed is the refractive index of the surrounding medium. The value Qrh is called by ewfd.Qrh, and the integral is over the volume of the nanostructure (this becomes an integral over area for the two-dimensional calculations). Calculating the S dA/P0, is more scattering cross section, σscat = ∬ n̂ ·⇀ 5455


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applying novel spectroscopy techniques to study single nanostructures, with the goal to understand energy relaxation processes in nanomaterials, and how these materials interact with their environment. Prof. Hartland is a Fellow of the AAAS, the ACS, and the RSC.

■

ACKNOWLEDGMENTS This work has been supported by the US National Science Foundation, most recently through CHE-1502848. K.Y. acknowledges financial support from the National Natural Science Foundation of China (NSFC) (Grant Nos. 11274247, 11574218). The authors would also like to thank their coworkers who have been involved in these projects, most notably Mary Sajini Devadas, Libai Huang, Shun-Shang Lo, and Hristina Musto.

■

Gary Beane received his Ph.D. in chemistry with Prof. Paul Mulvaney at The University of Melbourne in 2014. From 2014 to 2016, he worked with Professor David F. Kelley at the University of California, Merced, as a postdoctoral scholar in the Department of Natural Sciences on Auger recombination in graded semiconducting nanocrystals. He is currently a postdoctoral scholar with Prof. Gregory Hartland in the Department of Chemistry and Biochemistry at the University of Notre Dame, where he studies single metal nanostructures.

REFERENCES

(1) Raether, H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings; Springer-Verlag: Berlin, 1977; Vol. 111. (2) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 2003, 424, 824−830. (3) Dintinger, J.; Klein, S.; Bustos, F.; Barnes, W. L.; Ebbesen, T. W. Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 035424. (4) Barnes, W. L. Surface plasmon-polariton length scales: a route to sub-wavelength optics. J. Opt. A: Pure Appl. Opt. 2006, 8, S87−S93. (5) Pitarke, J. M.; Silkin, V. M.; Chulkov, E. V.; Echenique, P. M. Theory of surface plasmons and surface-plasmon polaritons. Rep. Prog. Phys. 2007, 70, 1−87. (6) Maier, S. A. Plasmonics: Fundamentals and Applications; Springer Science+Business Media LLC: New York, 2007. (7) Pelton, M.; Aizpurua, J.; Bryant, G. Metal-nanoparticle plasmonics. Laser Photonics Rev. 2008, 2, 136−159. (8) Novotny, L.; Hecht, B. Principles of Nano-Optics, 2nd ed.; Cambridge University Press: Cambridge, U.K., 2012. (9) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment. J. Phys. Chem. B 2003, 107, 668−677. (10) Wiley, B. J.; Im, S. H.; Li, Z. Y.; McLellan, J.; Siekkinen, A.; Xia, Y. N. Maneuvering the surface plasmon resonance of silver nanostructures through shape-controlled synthesis. J. Phys. Chem. B 2006, 110, 15666−15675. (11) Zhao, J.; Pinchuk, A. O.; McMahon, J. M.; Li, S. Z.; Ausman, L. K.; Atkinson, A. L.; Schatz, G. C. Methods for describing the electromagnetic properties of silver and gold nanoparticles. Acc. Chem. Res. 2008, 41, 1710−1720. (12) Campion, A.; Kambhampati, P. Surface-enhanced Raman scattering. Chem. Soc. Rev. 1998, 27, 241−250. (13) Kneipp, K.; Kneipp, H.; Itzkan, I.; Dasari, R. R.; Feld, M. S. Ultrasensitive chemical analysis by Raman spectroscopy. Chem. Rev. 1999, 99, 2957−2976. (14) Kneipp, J.; Kneipp, H.; Kneipp, K. SERS - a single-molecule and nanoscale tool for bioanalytics. Chem. Soc. Rev. 2008, 37, 1052−1060. (15) Qian, X. M.; Nie, S. M. Single-molecule and single-nanoparticle SERS: from fundamental mechanisms to biomedical applications. Chem. Soc. Rev. 2008, 37, 912−920. (16) Stewart, M. E.; Anderton, C. R.; Thompson, L. B.; Maria, J.; Gray, S. K.; Rogers, J. A.; Nuzzo, R. G. Nanostructured plasmonic sensors. Chem. Rev. 2008, 108, 494−521. (17) Camden, J. P.; Dieringer, J. A.; Zhao, J.; Van Duyne, R. P. Controlled plasmonic nanostructures for surface-enhanced spectroscopy and sensing. Acc. Chem. Res. 2008, 41, 1653−1661. (18) Fan, M. K.; Andrade, G. F. S.; Brolo, A. G. A review on the fabrication of substrates for surface enhanced Raman spectroscopy and their applications in analytical chemistry. Anal. Chim. Acta 2011, 693, 7−25.

Kuai Yu obtained his Ph.D. degree from the National University of Singapore in 2013. He was then a postdoctoral researcher in Professor Hartland’s group. In 2016, He started working at Shenzhen University, China, where he is currently an Associate Professor. His research interests are applying nonlinear spectroscopy for nanomaterials and cell biology.

Gregory V. Hartland is a Professor in the Department of Chemistry and Biochemistry at the University of Notre Dame. He obtained a Ph.D. from UCLA in 1991 and was a postdoctoral researcher at the University of Pennsylvania. His current research interests are in 5456


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(40) Billaud, P.; Marhaba, S.; Cottancin, E.; Arnaud, L.; Bachelier, G.; Bonnet, C.; Del Fatti, N.; Lerme, J.; Vallee, F.; Vialle, J. L.; et al. Correlation between the extinction spectrum of a single metal nanoparticle and its electron microscopy image. J. Phys. Chem. C 2008, 112, 978−982. (41) Davletshin, Y. R.; Lombardi, A.; Cardinal, M. F.; Juve, V.; Crut, A.; Maioli, P.; Liz-Marzan, L. M.; Vallee, F.; Del Fatti, N.; Kumaradas, J. C. A quantitative study of the environmental effects on the optical response of gold nanorods. ACS Nano 2012, 6, 8183−8193. (42) Juve, V.; Fernanda Cardinal, M.; Lombardi, A.; Crut, A.; Maioli, P.; Perez-Juste, J.; Liz-Marzan, L. M.; Del Fatti, N.; Vallee, F. Sizedependent surface plasmon resonance broadening in nonspherical nanoparticles: Single gold nanorods. Nano Lett. 2013, 13, 2234−2240. (43) Yorulmaz, M.; Nizzero, S.; Hoggard, A.; Wang, L. Y.; Cai, Y. Y.; Su, M. N.; Chang, W. S.; Link, S. Single-particle absorption spectroscopy by photothermal contrast. Nano Lett. 2015, 15, 3041− 3047. (44) Crut, A.; Maioli, P.; Del Fatti, N.; Vallee, F. Optical absorption and scattering spectroscopies of single nano-objects. Chem. Soc. Rev. 2014, 43, 3921−3956. (45) Myroshnychenko, V.; Rodriguez-Fernandez, J.; Pastoriza-Santos, I.; Funston, A. M.; Novo, C.; Mulvaney, P.; Liz-Marzan, L. M.; de Abajo, F. J. G. Modelling the optical response of gold nanoparticles. Chem. Soc. Rev. 2008, 37, 1792−1805. (46) Hu, M.; Novo, C.; Funston, A.; Wang, H. N.; Staleva, H.; Zou, S. L.; Mulvaney, P.; Xia, Y. N.; Hartland, G. V. Dark-field microscopy studies of single metal nanoparticles: understanding the factors that influence the linewidth of the localized surface plasmon resonance. J. Mater. Chem. 2008, 18, 1949−1960. (47) Lamprecht, B.; Krenn, J. R.; Schider, G.; Ditlbacher, H.; Salerno, M.; Felidj, N.; Leitner, A.; Aussenegg, F. R.; Weeber, J. C. Surface plasmon propagation in microscale metal stripes. Appl. Phys. Lett. 2001, 79, 51−53. (48) Ditlbacher, H.; Krenn, J. R.; Schider, G.; Leitner, A.; Aussenegg, F. R. Two-dimensional optics with surface plasmon polaritons. Appl. Phys. Lett. 2002, 81, 1762−1764. (49) 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. (50) Zia, R.; Selker, M. D.; Brongersma, M. L. Leaky and bound modes of surface plasmon waveguides. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 165431. (51) Zia, R.; Schuller, J. A.; Brongersma, M. L. Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 74, 165415. (52) Berini, P. Long-range surface plasmon polaritons. Adv. Opt. Photonics 2009, 1, 484−588. (53) Stockman, M. I. Nanoplasmonics: The physics behind the applications. Phys. Today 2011, 64, 39−44. (54) 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. (55) Stockman, M. I. Nanofocusing of optical energy in tapered plasmonic waveguides. Phys. Rev. Lett. 2004, 93, 137404. (56) Gramotnev, D. K.; Bozhevolnyi, S. I. Plasmonics beyond the diffraction limit. Nat. Photonics 2010, 4, 83−91. (57) Stockman, M. I. Nanoplasmonics: past, present, and glimpse into future. Opt. Express 2011, 19, 22029−22106. (58) Wiener, A.; Fernandez-Dominguez, A. I.; Horsfield, A. P.; Pendry, J. B.; Maier, S. A. Nonlocal effects in the nanofocusing performance of plasmonic tips. Nano Lett. 2012, 12, 3308−3314. (59) 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. (60) Anderson, L. J. E.; Zhen, Y. R.; Payne, C. M.; Nordlander, P.; Hafner, J. H. Gold nanobelts as high confinement plasmonic waveguides. Nano Lett. 2013, 13, 6256−6261.

(19) Sharma, B.; Frontiera, R. R.; Henry, A. I.; Ringe, E.; Van Duyne, R. P. SERS: Materials, applications, and the future. Mater. Today 2012, 15, 16−25. (20) Haes, A. J.; Van Duyne, R. P. A unified view of propagating and localized surface plasmon resonance biosensors. Anal. Bioanal. Chem. 2004, 379, 920−930. (21) Haes, A. J.; Zou, S. L.; Schatz, G. C.; Van Duyne, R. P. A nanoscale optical biosensor: The long range distance dependence of the localized surface plasmon resonance of noble metal nanoparticles. J. Phys. Chem. B 2004, 108, 109−116. (22) Willets, K. A.; Van Duyne, R. P. Localized surface plasmon resonance spectroscopy and sensing. Annu. Rev. Phys. Chem. 2007, 58, 267−297. (23) Lal, S.; Link, S.; Halas, N. J. Nano-optics from sensing to waveguiding. Nat. Photonics 2007, 1, 641−648. (24) West, J. L.; Halas, N. J. Engineered nanomaterials for biophotonics applications: Improving sensing, imaging, and therapeutics. Annu. Rev. Biomed. Eng. 2003, 5, 285−292. (25) Perez-Juste, J.; Pastoriza-Santos, I.; Liz-Marzan, L. M.; Mulvaney, P. Gold nanorods: Synthesis, characterization and applications. Coord. Chem. Rev. 2005, 249, 1870−1901. (26) Hu, M.; Chen, J. Y.; Li, Z. Y.; Au, L.; Hartland, G. V.; Li, X. D.; Marquez, M.; Xia, Y. N. Gold nanostructures: engineering their plasmonic properties for biomedical applications. Chem. Soc. Rev. 2006, 35, 1084−1094. (27) Skrabalak, S. E.; Chen, J. Y.; Sun, Y. G.; Lu, X. M.; Au, L.; Cobley, C. M.; Xia, Y. N. Gold nanocages: Synthesis, properties, and applications. Acc. Chem. Res. 2008, 41, 1587−1595. (28) Schwartzberg, A. M.; Zhang, J. Z. Novel optical properties and emerging applications of metal nanostructures. J. Phys. Chem. C 2008, 112, 10323−10337. (29) Jain, P. K.; Huang, X. H.; El-Sayed, I. H.; El-Sayed, M. A. Noble metals on the nanoscale: optical and photothermal properties and some applications in imaging, sensing, biology, and medicine. Acc. Chem. Res. 2008, 41, 1578−1586. (30) Boisselier, E.; Astruc, D. Gold nanoparticles in nanomedicine: preparations, imaging, diagnostics, therapies and toxicity. Chem. Soc. Rev. 2009, 38, 1759−1782. (31) Xia, Y. N.; Li, W. Y.; Cobley, C. M.; Chen, J. Y.; Xia, X. H.; Zhang, Q.; Yang, M. X.; Cho, E. C.; Brown, P. K. Gold nanocages: From synthesis to theranostic applications. Acc. Chem. Res. 2011, 44, 914−924. (32) Sherry, L. J.; Chang, S. H.; Schatz, G. C.; Van Duyne, R. P.; Wiley, B. J.; Xia, Y. N. Localized surface plasmon resonance spectroscopy of single silver nanocubes. Nano Lett. 2005, 5, 2034− 2038. (33) Sherry, L. J.; Jin, R. C.; Mirkin, C. A.; Schatz, G. C.; Van Duyne, R. P. Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms. Nano Lett. 2006, 6, 2060−2065. (34) Hartland, G. V. Optical studies of dynamics in noble metal nanostructures. Chem. Rev. 2011, 111, 3858−3887. (35) Sonnichsen, C.; Geier, S.; Hecker, N. E.; von Plessen, G.; Feldmann, J.; Ditlbacher, H.; Lamprecht, B.; Krenn, J. R.; Aussenegg, F. R.; Chan, V. Z. H.; et al. Spectroscopy of single metallic nanoparticles using total internal reflection microscopy. Appl. Phys. Lett. 2000, 77, 2949−2951. (36) Sonnichsen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J.; Wilson, O.; Mulvaney, P. Drastic reduction of plasmon damping in gold nanorods. Phys. Rev. Lett. 2002, 88, 077402. (37) Berciaud, S.; Cognet, L.; Tamarat, P.; Lounis, B. Observation of intrinsic size effects in the optical response of individual gold nanoparticles. Nano Lett. 2005, 5, 515−518. (38) Arbouet, A.; Christofilos, D.; Del Fatti, N.; Vallee, F.; Huntzinger, J. R.; Arnaud, L.; Billaud, P.; Broyer, M. Direct measurement of the single-metal-cluster optical absorption. Phys. Rev. Lett. 2004, 93, 127401. (39) Muskens, O. L.; Bachelier, G.; Del Fatti, N.; Vallee, F.; Brioude, A.; Jiang, X.; Pileni, M.-P. Quantitative absorption spectroscopy of a single gold nanorod. J. Phys. Chem. C 2008, 112, 8917−8921. 5457


Feature Article

The Journal of Physical Chemistry C (61) Maier, S. A.; Brongersma, M. L.; Kik, P. G.; Meltzer, S.; Requicha, A. A. G.; Atwater, H. A. Plasmonics - A route to nanoscale optical devices. Adv. Mater. 2001, 13, 1501−1505. (62) Nikolajsen, T.; Leosson, K.; Bozhevolnyi, S. I. Surface plasmon polariton based modulators and switches operating at telecom wavelengths. Appl. Phys. Lett. 2004, 85, 5833−5835. (63) Maier, S. A. Plasmonics: The promise of highly integrated optical devices. IEEE J. Sel. Top. Quantum Electron. 2006, 12, 1671− 1677. (64) Ebbesen, T. W.; Genet, C.; Bozhevolnyi, S. I. Surface-plasmon circuitry. Phys. Today 2008, 61, 44−50. (65) Berini, P.; De Leon, I. Surface plasmon-polariton amplifiers and lasers. Nat. Photonics 2012, 6, 16−24. (66) Berini, P. Plasmon polariton modes guided by a metal film of finite width. Opt. Lett. 1999, 24, 1011−1013. (67) Berini, P.; Charbonneau, R.; Lahoud, N.; Mattiussi, G. Characterization of long-range surface-plasmon-polariton waveguides. J. Appl. Phys. 2005, 98, 043109. (68) Jung, J.; Søndergaard, T.; Bozhevolnyi, S. I. Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 035434. (69) Dickson, R. M.; Lyon, L. A. Unidirectional plasmon propagation in metallic nanowires. J. Phys. Chem. B 2000, 104, 6095−6098. (70) 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. (71) Boltasseva, A.; Nikolajsen, T.; Leosson, K.; Kjaer, K.; Larsen, M. S.; Bozhevolnyi, S. I. Integrated optical components utilizing longrange surface plasmon polaritons. J. Lightwave Technol. 2005, 23, 413− 422. (72) Major, T. A.; Devadas, M. S.; Lo, S. S.; Hartland, G. V. Optical and Dynamical Properties of Chemically Synthesized Gold Nanoplates. J. Phys. Chem. C 2013, 117, 1447−1452. (73) Luo, S.; Yang, H. B.; Yang, Y. Q.; Zhao, D.; Chen, X. X.; Qiu, M.; Li, Q. Controlling wave-vector of propagating surface plasmon polaritons on single-crystalline gold nanoplates. Sci. Rep. 2015, 5, 13424. (74) Li, Z.; Bao, K.; Fang, Y.; Guan, Z.; Halas, N. J.; Nordlander, P.; Xu, H. Effect of a proximal substrate on plasmon propagation in silver nanowires. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 241402. (75) Song, M.; Bouhelier, A.; Bramant, P.; Sharma, J.; Dujardin, E.; Zhang, D.; Colas-des-Francs, G. Imaging symmetry-selected corner plasmon modes in penta-twinned crystalline Ag nanowires. ACS Nano 2011, 5, 5874−5880. (76) Wei, H.; Zhang, S. P.; Tian, X. R.; Xu, H. X. Highly tunable propagating surface plasmons on supported silver nanowires. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 4494−4499. (77) Zhang, S.; Xu, H. Optimizing substrate-mediated plasmon coupling toward high-performance plasmonic nanowire waveguides. ACS Nano 2012, 6, 8128−8135. (78) 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. (79) Paul, A.; Solis, D.; Bao, K.; Chang, W.-S.; Nauert, S.; Vidgerman, L.; Zubarev, E. R.; Nordlander, P.; Link, S. Identification of higher order long-propagation-length surface plasmon polariton modes in chemically prepared gold nanowires. ACS Nano 2012, 6, 8105−8113. (80) 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. (81) Hartmann, N.; Piatkowski, D.; Ciesielski, R.; Mackowski, S.; Hartschuh, A. Radiation channels close to a plasmonic nanowire visualized by back focal plane imaging. ACS Nano 2013, 7, 10257− 10262.

(82) 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. (83) 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. (84) 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. (85) Wang, Z.; Wei, H.; Pan, D.; Xu, H. Controlling the radiation direction of propagating surface plasmons on silver nanowires. Laser & Photonics Reviews 2014, 8, 596−601. (86) 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. (87) Johns, P.; Yu, K.; Devadas, M. S.; Hartland, G. V. Role of resonances in the transmission of surface plasmon polaritons between nanostructures. ACS Nano 2016, 10, 3375−3381. (88) Yang, H. B.; Qiu, M.; Li, Q. Identification and control of multiple leaky plasmon modes in silver nanowires. Laser & Photonics Reviews 2016, 10, 278−286. (89) Wiley, B. J.; Lipomi, D. J.; Bao, J.; Capasso, F.; Whitesides, G. M. Fabrication of surface plasmon resonators by nanoskiving singlecrystalline gold microplates. Nano Lett. 2008, 8, 3023−3028. (90) Averitt, R. D.; Westcott, S. L.; Halas, N. J. Linear optical properties of gold nanoshells. J. Opt. Soc. Am. B 1999, 16, 1824−1832. (91) Sonnichsen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J. Plasmon resonances in large noble-metal clusters. New J. Phys. 2002, 4, 93. (92) Novo, C.; Gomez, D.; Perez-Juste, J.; Zhang, Z.; Petrova, H.; Reismann, M.; Mulvaney, P.; Hartland, G. V. Contributions from radiation damping and surface scattering to the linewidth of the longitudinal plasmon band of gold nanorods: a single particle study. Phys. Chem. Chem. Phys. 2006, 8, 3540−3546. (93) Baida, H.; Billaud, P.; Marhaba, S.; Christofilos, D.; Cottancin, E.; Crut, A.; Lerme, J.; Maioli, P.; Pellarin, M.; Broyer, M.; et al. Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles. Nano Lett. 2009, 9, 3463−3469. (94) Lombardi, A.; Loumaigne, M.; Crut, A.; Maioli, P.; Del Fatti, N.; Vallee, F.; Spuch-Calvar, M.; Burgin, J. Surface Plasmon Resonance Properties of Single Elongated Nano-objects: Gold Nanobipyramids and Nanorods. Langmuir 2012, 28, 9027−9033. (95) Bohren, C. F.; Huffman, D. R. Absorption and scattering of light by small particles; John Wiley & Sons: New York, 1983. (96) Johnson, P. B.; Christy, R. W. Optical constants of the noble metals. Phys. Rev. B 1972, 6, 4370−4379. (97) Wokaun, A.; Gordon, J. P.; Liao, P. F. Radiation damping in surface-enhanced Raman-scattering. Phys. Rev. Lett. 1982, 48, 957− 960. (98) Munechika, K.; Smith, J. M.; Chen, Y.; Ginger, D. S. Plasmon line widths of single silver nanoprisms as a function of particle size and plasmon peak position. J. Phys. Chem. C 2007, 111, 18906−18911. (99) Luk’yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T. The Fano resonance in plasmonic nanostructures and metamaterials. Nat. Mater. 2010, 9, 707−715. (100) Miroshnichenko, A. E.; Flach, S.; Kivshar, Y. S. Fano resonances in nanoscale structures. Rev. Mod. Phys. 2010, 82, 2257− 2298. (101) Lassiter, J. B.; Sobhani, H.; Fan, J. A.; Kundu, J.; Capasso, F.; Nordlander, P.; Halas, N. J. Fano resonances in plasmonic nanoclusters: Geometrical and chemical tunability. Nano Lett. 2010, 10, 3184−3189. (102) Wang, X.; Zhang, Z. Y.; Hartland, G. V. Electronic dephasing in bimetallic gold-silver nanoparticles examined by single particle spectroscopy. J. Phys. Chem. B 2005, 109, 20324−20330. 5458


Feature Article

The Journal of Physical Chemistry C (103) Ruppin, R. Extinction by a circular cylinder in an absorbing medium. Opt. Commun. 2002, 211, 335−340. (104) Chiasera, A.; Dumeige, Y.; Feron, P.; Ferrari, M.; Jestin, Y.; Conti, G. N.; Pelli, S.; Soria, S.; Righini, G. C. Spherical whisperinggallery-mode microresonators. Laser Photonics Rev. 2010, 4, 457−482. (105) Berini, P. Figures of merit for surface plasmon waveguides. Opt. Express 2006, 14, 13030−13042. (106) Maier, S. A. Plasmonic field enhancement and SERS in the effective mode volume picture. Opt. Express 2006, 14, 1957−1964. (107) Min, B.; Ostby, E.; Sorger, V.; Ulin-Avila, E.; Yang, L.; Zhang, X.; Vahala, K. High-Q surface-plasmon-polariton whispering-gallery microcavity. Nature 2009, 457, 455−458. (108) Staleva, H.; Hartland, G. V. Vibrational dynamics of silver nanocubes and nanowires studied by single-particle transient absorption spectroscopy. Adv. Funct. Mater. 2008, 18, 3809−3817. (109) Saleh, B. E. A.; Teich, M. C. Fundamentals of Photonics, 2nd ed.; John Wiley & Sons: New York, 2007. (110) Weeber, J. C.; Krenn, J. R.; Dereux, A.; Lamprecht, B.; Lacroute, Y.; Goudonnet, J. P. Near-field observation of surface plasmon polariton propagation on thin metal stripes. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64, 045411. (111) Ditlbacher, H.; Krenn, J. R.; Felidj, N.; Lamprecht, B.; Schider, G.; Salerno, M.; Leitner, A.; Aussenegg, F. R. Fluorescence imaging of surface plasmon fields. Appl. Phys. Lett. 2002, 80, 404−406. (112) Verhagen, E.; Tchebotareva, A. L.; Polman, A. Erbium luminescence imaging of infrared surface plasmon polaritons. Appl. Phys. Lett. 2006, 88, 121121. (113) 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 spatially-separated femtosecond pump−probe microscopy. Nano Lett. 2013, 13, 1336−1340. (114) Lo, S. S.; Shi, H. Y.; Huang, L.; Hartland, G. V. Imaging the extent of plasmon excitation in Au nanowires using pump-probe microscopy. Opt. Lett. 2013, 38, 1265−1267. (115) Gabriel, M. M.; Grumstrup, E. M.; Kirschbrown, J. R.; Pinion, C. W.; Christesen, J. D.; Zigler, D. F.; Cating, E. E. M.; Cahoon, J. F.; Papanikolas, J. M. Imaging charge separation and carrier recombination in nanowire P-I-N junctions using ultrafast microscopy. Nano Lett. 2014, 14, 3079−3087.

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Dynamics of Surface Plasmon Polaritons in Metal Nanowires

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