Chemical interface damping for propagating surface plasmon polaritons in gold nanostripes

Surface plasmon polaritons are created when light couples to the collective motion of electrons at the surfaces of conductors.^1–3 In nanoparticles, spatial confinement creates resonances which are known as localized surface plasmon resonances (LSPRs).^4,5 Extending one or two of the dimensions of the structure to create a nanowire or nanoplate leads to surface plasmons with a definitive momentum, which are denoted as propagating surface plasmon polaritons (PSPPs).^1,6–9 In contrast to LSPRs that are defined by their resonance frequency (ω₀) and linewidth (Γ), PSPPs are described by their wavevector (k_SPP) and propagation length (L_SPP).^1–3,6–9 PSPPs can be excited over a wide range of frequencies; however, coupling to light relies on matching the momentum of the photons with that of the electron motion.^1–3 

For nanostructures, the momentum matching condition can be overcome by focusing the light source at a point in the structure where there is a break in symmetry, such as at the ends of the nanostructure.^10–12 Among the techniques that can probe PSPPs are transient absorption microscopy (TAM),^13,14 near-field scanning optical microscopy (NSOM),^11,15 photoemission electron microscopy (PEEM),^16–18 and leakage radiation microscopy.^8,9,19–23 The first three techniques suffer from the fact that there are two PSPP modes for metal nanostructures on a surface. There is a “bound” mode that propagates at the metal-substrate interface and a “leaky” mode that propagates at the metal-air interface.^24,25 In general, both of these modes can be excited and detected in TAM, NSOM, and PEEM experiments.²⁶ However, in leakage radiation microscopy, only the leaky PSPP mode is imaged. The bound mode is not detected since its wavevector is typically outside the range of wavevectors that can be collected in a conventional optical microscope.^8,9 Having only one mode contribute to the experiments greatly simplifies the analysis.⁹ 

Leakage radiation microscopy has recently been used to study the PSPP modes in Au nanostripes—rectangular nanostructures created by photolithography.²⁷ It was found that the lifetimes of the leaky PSPP modes for the nanostripes are an order of magnitude longer than those of LSPRs. The long lifetimes of the leaky modes and the fact that these modes travel at the metal-air interface create an interesting system for studying chemical interface damping (CID).²⁸ CID arises due to coupling of hot electrons in the metal with the lowest unoccupied molecular orbitals of the surface attached molecules.^29,30 For nanoparticles, CID can be studied by measuring the linewidth of the LSPR.^28,30 These types of measurements are best done on single nanostructures to remove inhomogeneous broadening effects from the distribution of sizes and shapes in the sample.^31–33 Several recent papers have used single particle light scattering measurements to study how CID depends on the size of the particle and the nature of the adsorbed molecules.^34–36 In particular, it was shown that CID is affected by the molecular packing density,^34,35 and whether the adsorbed molecules contain electron donating or withdrawing groups.³⁶ 

In the present study, leakage radiation microscopy measurements were used to study CID in gold nanostripes. In these experiments, real space imaging was used to measure the PSPP propagation length, and back-focal plane (BFP) imaging was used to determine the wavevector, k_SPP, and, from this, the PSPP group velocity v_g.²⁷ The combination of these two measurements yields the lifetime of the PSPP mode,²⁷ which can be used to determine the rate for CID (Γ_CID).³³ Thiols were chosen for study due to their strong binding to gold and their ability to form well-defined, close packed monolayers on gold surfaces.^37,38 Several different thiol chain lengths were used to probe how molecular packing affects Γ_CID.³⁹ In addition, a comparison between octanethiol and perfluoro-octanethiol was made to study the effect of changing the electronic properties of the molecule. However, the CID effects in our measurements are very small and are similar (within experimental uncertainties) for all the studied thiols. The small Γ_CID values are attributed to the relatively large size of the structures in these experiments.

The nanostripe samples were prepared using photolithography and electron beam deposition of the Au. A 3 nm titanium wetting layer was used to promote adhesion to number 1.5 borosilicate glass coverslips. The samples prepared had widths of 2.5, 3, and 4 µm, the length of 100 µm, and height of 40 or 50 nm. Atomic Force Microscopy (AFM) was used to characterize the dimensions of the structures (see the supplementary material for details). Thiol deposition was performed by either vapor deposition or liquid immersion. Hexanethiol and octanethiol were deposited by vapor deposition at 70 °C in multiple increments of 4 h blocks.⁴⁰ For perfluoro-octanethiol and dodecanethiol, a solution containing 10⁻²M of thiol was used for deposition. The solution was placed on the sample for a set time. The sample was then rinsed with ethanol to remove excess liquid and dried before use.^34,41 The same nanostripes were interrogated before and after thiol deposition, and a new sample was used for each thiol. The difference in PSPP propagation lengths between the uncoated and thiol coated nanostripes was used to determine Γ_CID, as described in detail below.

The optical system used to record the propagation lengths, and group velocities of the PSPP modes has been described in detail elsewhere.^9,14,27 Briefly, the PSPP modes are excited by focusing a supercontinuum laser (Fianium SC450-4) at the end of the nanostripes with a high numerical aperture (NA) objective (1.35NA Olympus UPlan-Apo, 100× oil objective), where the break in symmetry relaxes the momentum matching conditions. The polarization of the laser beam was aligned along the long axis of the nanostripes. Specific wavelengths from the supercontinuum were selected using an acousto-optic tunable filter (Fianium AOTF-DUAL). Scattered light from the sample was collected with the same objective and sent to a DVC1500m CCD camera. A diagram of the optical system is presented in the supplementary material. A beam stop was placed at the image plane of the microscope to block the backscattered light from the focused laser spot. Real space images were used to determine the propagation length, and Fourier space/BFP images were used to determine the PSPP wavevector. The optical system was switched from real space to Fourier space imaging by simply flipping a lens in and out of the light path.²⁷ Propagation lengths were determined at a wavelength of 850 nm, selected by the AOTF. In these measurements, the intensity of the scattered light in the real images was averaged over the width of the nanostripe.

Figure 1 shows a schematic diagram of the wavevectors for the PSPP modes and the photons in the glass substrate in leakage radiation microscopy.^9,20,22,23 The inner dashed circle in the Fourier plane image shows the condition for total internal reflection (k/k₀ = 1), and the cropped edge corresponds to the numerical aperture of the objective. These two features calibrate the wavevector scale in the Fourier images.^9,20,22,23 For a nanostripe orientated along the x-axis, as in Fig. 1, momentum matching occurs when

and

where n is the refractive index of the glass substrate and k₀ is the wavevector of free space photons.⁹ Thus, the leaky PSPP mode creates a line in the Fourier plane image that allows k_SPP to be measured. Dispersion curves were generated by measuring the PSPP wavevector from the Fourier plane images over a range of different wavelengths.

Finite element simulations were used to calculate the wavevector and propagation lengths of the PSPP modes. These calculations were performed in COMSOL Multiphysics (v. 5.3) using a two-dimensional mode analysis calculation. This analysis yields the complex mode index for the system $ñ=neff+iα/k0$⁠, where n_eff is the effective index and α is the attenuation constant.^{8,9,13,20–25,42} The real part of $ñ$ gives the PSPP wavevector k_SPP = n_effk₀, and the imaginary part is related to the propagation length by L_SPP = 1/2α. Note that the 2D simulations effectively assume infinitely long nanostripes. The dielectric constant data from Johnson and Christy were used for the calculations,⁴³ and a 3 nm titanium wetting layer was included in the simulations to match the experimental geometry. The effect of thiol adsorption was modeled by creating a 1.1 nm thick film over the gold nanostripe with a refractive index of 1.455. The COMSOL simulations do not include the CID effect, as this arises from a quantum mechanical interaction between the electrons in the nanostripe and the orbitals of the adsorbed molecules.^28–30 These simulations were performed as a control to test whether a thin molecular layer changes the radiation damping and/or damping from resistive heating for the leaky PSPP mode.⁹ 

Fourier space images for 2.5 µm and 4 µm wide nanostripes are presented in Figs. 2(a) and 2(b), respectively. These images were recorded at a wavelength of 750 nm. This wavelength was chosen to clearly show the higher order leaky PSPP mode of the wider nanostripes. As discussed above, the inner circles in these images correspond to the condition for total internal reflection of light (k/k₀ = 1), and the image is cropped at k/k₀ = NA.^9,20,22,23 The wavevector for the leaky mode appears as a horizontal line, which is very close to the light line (k/k₀ slightly greater than 1). Figures 2(c) and 2(d) show line profiles extracted from the Fourier space images in panels (a) and (b). The black markers are the experimental measurements, and the red lines are the results of the finite elements simulations. The peaks in the experimental line profiles give the values of k_SPP. In the calculations, the features in the Fourier space images were modeled as Lorentzians with peaks at k/k₀ = n_eff and widths of 2α.

The most important point from Fig. 2 is that there is only one feature in the BFP image for the 2.5 µm wide nanostripe, whereas two features appear for the 4 µm nanostripes. Noble metal nanostructures on dielectric substrates have a series of leaky modes that suffer width and wavelength dependent cutoffs.^23,27 The smaller wavevector feature in Fig. 2(d) near k/k₀ = 1.01 is assigned to the second order leaky mode for the 4 µm nanostripe. The presence of this mode complicates the analysis of the experiments in several ways. First, it makes it harder to measure the propagation lengths in the real space images. The different order leaky modes have different propagation lengths,²⁴ which can be difficult to deconvolute in the images. The presence of two or more leaky modes also complicates the analysis of the Fourier space images, which means that the wavevector measurements are less accurate. Indeed, the agreement between the simulations and the experiments is much better for the 2.5 µm nanostripes in Fig. 2(c) compared to 4 µm nanostripes in Fig. 2(d). Thus, in our study of CID effects, only nanostripes with widths under 4 µm were interrogated so that only a single leaky mode is present at the wavelengths used in the experiments (λ = 850 nm for the experiments reported below).

In principle, the width of the features in the BFP images could be used to determine the attenuation constant.²⁰ However, the widths in the BFP images are always broader than the calculated widths for our system, indicating that the resolution in the Fourier images is not sufficient for measuring PSPP damping. It is not clear why this is the case, but because of this, only the real space images were used to measure the PSPP propagation lengths. Figure 3(a) shows a false color reflected light image of a 2.5 µm wide nanostripe. In Fig. 3(b), a real space leakage radiation image of the PSPP modes for the bare (uncoated) gold nanostripe is presented. Here, the beam is focused at the end of the nanostripe to launch the PSPPs, and the beam stop was used to block the undesired backscattered laser intensity. A line profile from this image (averaged over the width of the nanostripe) is shown in Fig. 3(c), along with an exponential fit to the data which yields the propagation length (11.6 ± 0.2 µm for this nanostripe). Figure 3(d) shows frequency vs wavevector dispersion curves for bare and thiol coated 2.5 µm wide nanostripes measured from BFP experiments performed at different wavelengths. The slopes of these curves yield the group velocity v_g. The markers in this figure are the experimental results. The solid and dashed lines are the wavevectors calculated from the finite element simulations and fitted to the experimental data, respectively. The experimental and theory dispersion curves are in excellent agreement for the bare nanostripes but are slightly different for the thiol coated nanostripes.²⁷ 

Chemical interface damping for different thiols was studied by measuring the PSPP wavevectors and propagation lengths as a function of thiol exposure time.^34,35 Figure 4(a) shows a plot of the propagation length as a function of deposition time for octanethiol. The error bars in this figure are standard deviations determined from measurements of 5 nanostripes. The same five nanostripes were interrogated before and after thiol deposition, with new nanostripe samples being studied for each different thiol. The horizontal line in Fig. 4(a) is the calculated propagation length for bare Au, which is in good agreement with the experimental measurements. The propagation length was calculated using a height of 50 nm and a width of 2.5 µm, matching the width of the measured nanostripes determined from the real space images. The propagation length decreases when the nanostripes are exposed to octanethiol. The results show that after approximately 20 h exposure time, there are no further changes in the propagation length. This implies that we have created a saturated surface at 20 h for this system. This length of time for saturation is consistent with previous results for vapor phase deposition under the conditions used in our experiments.⁴⁰ Figure 4(b) shows a similar plot for perfluoro-octanethiol, which was deposited from solution. The nanostripes for these experiments had a height of 40 nm and were 3.2 µm wide [this is why the calculated propagation length for the bare nanostripe in Fig. 4(b) is different to that in Fig. 4(a)]. Surface saturation is reached in a much shorter time for solution phase deposition compared to vapor phase deposition. In the following, only data for saturated coatings of thiol will be presented and discussed.

The dispersion curve for the octanethiol coated nanostripes is included in Fig. 3(d). The experimental data show a shift to larger wavevectors for the coated nanostripes. The finite element simulations also predict a shift in the wavevectors for the coated samples; however, the shift is much smaller so that the lines for the bare and coated samples appear overlapped in Fig. 3(d). The group velocity, found by taking the slope of the dispersion curve, has the same value of v_g = (0.89 ± 0.01)c₀ for both the bare nanostripes and the coated nanostripes. Dispersion curves measured for the other thiol molecules examined in this work give similar values for the group velocity.

The propagation lengths and the group velocities determined from the leakage radiation microscopy experiments can be used to determine the lifetime T₁ of the PSPP mode by^27,44–47

Previous studies showed that the lifetimes of the PSPP modes in these nanostripes are an order of magnitude longer than the LSPRs for gold nanorods,²⁷ which would make them potentially useful for studying CID. The PSPP lifetime has contributions from resistive heating (decay of the plasmon into excited electron-hole pairs), radiation damping, electron-surface scattering, and CID.^9,27,33 The finite element simulations, which capture radiation damping and resistive heating effects in metal nanostructures, show that there is no change in the calculated propagation lengths when the nanostripes are coated with a 1.1 nm thick layer with a refractive index of 1.455 (the approximate thickness of an octanethiol monolayer). This implies that the resistive heating and radiation damping effects for the nanostripes do not change with thiol deposition. In this case, the change in lifetime due to CID can be simply determined from the measurements for thiol coated and bare nanostripes by

Table I shows the values of T_1,CID obtained for different height nanostripes and different thiols. In order to compare the results to linewidth measurements from LSPR studies, the lifetimes were also converted to dephasing rates by

where T_2,CID = 2T_1,CID.³³ The calculated values of Γ_CID are included in Table I. Note that the T_1,CID values in Table I were obtained by subtracting the values of 1/T_1,thiol and 1/T_1,bare for the individual nanostripes and averaging the results. The average values of T_1,thiol and T_1,bare for the different samples are reported in the supplementary material.

The data show that the CID effect from surface bound molecules is small and that there are no significant differences between the different thiols or with changing the height of the nanostripes—the different Γ_CID values in Table I are essentially the same within experimental error. The relatively large scatter in the values of Γ_CID for these experiments is attributed to surface roughness (AFM images that provide information about the surface roughness are presented in the supplementary material). Surface roughness changes thiol packing, which affects the value of Γ_CID. This will lead to variations in the measured values of Γ_CID for different nanostripes in a given set of experiments and limits the precision of the measurements.⁴⁸ 

The results in Table I show that adsorbed thiol molecules produce a change in the PSPP dephasing rate of Γ_CID ≈ 2 meV for the Au nanostripes. In contrast, recent measurements for gold nanorods with widths ranging from 10 to 30 nm gave values of Γ_CID = 20–40 meV, with larger values being observed for nanorods with smaller dimensions.^34–36 However, in order to properly compare the results for the PSPP modes to the nanorod experiments, the data have to be scaled for the different path lengths for the electrons for the two systems. The effective path length for electron-surface scattering in nanostructures can be calculated by L_eff = 4V/S,^49,50 where V is the volume and S is the surface area of the structure. Modeling the nanorods as circular cylinders and the stripes as infinitely long rectangular structures yields

and

where d and L are the diameter and length of the nanorods, and w and h are the width and thickness of the nanostripes, respectively. In the derivation of Eq. (5b), we have assumed that L ≫ w ≫ h for the nanostripes and that the bottom surface of the nanostripe does not contribute to CID (this surface is masked by the substrate).

If the CID process for the PSPP modes of the nanostripes is the same as that for the LSPRs of the nanorods, then we expect

To test Eq. (6), two examples from Ref. 34 are compared to our results: 27 × 78 nm (d × L) nanorods, where $ΓCIDrod≈19$ meV, and 14 × 41 nm nanorods, where $ΓCIDrod≈42$ meV. For the 27 × 78 nm nanorod sample, $Leffstripe/Leffrod≈8.3$ and $ΓCIDrod/ΓCIDstripe≈9.5$⁠, and for the 14 × 41 nm nanorod sample, $Leffstripe/Leffrod≈16$ and $ΓCIDrod/ΓCIDstripe≈21$⁠. In both cases, the ratio of the L_eff values for the nanorods and nanostripes matches the ratio of the Γ_CID values. Thus, the CID process for the leaky PSPP modes of the nanostripes is essentially the same as that for the LSPRs of Au nanorods—it is simply reduced in magnitude because of the larger overall dimensions of the nanostripes.

A major problem with the experiments described in this paper is that the CID effect is very small and similar to the uncertainty in the measurements. This makes it hard to systematically study CID using this system. In principle, larger values of $ΓCIDstripe$ could be obtained by decreasing the dimensions of the nanostripes—specifically decreasing their height [see Eq. (5b)]. However, the propagation lengths for the leaky PSPP modes of metal nanostripes decrease with decreasing dimensions due to increased radiation damping.⁵¹ This effect arises because the field for the leaky PSPP mode becomes less confined and more strongly coupled to substrate photons as the dimensions decrease.^{9,24,27,51,52} The competition from radiation damping means that it will be difficult to make accurate measurements of Γ_CID for the leaky modes of the nanostripes. For the LSPRs of nanoparticles, the opposite effect occurs: at small sizes, radiation damping is reduced and CID enhanced so that $ΓCIDrod$ can be more accurately measured, that is, until the nanorods become so small that they are hard to detect in light scattering measurements.^32,33

Leakage radiation microscopy has been used to study CID in gold nanostripes for several different thiol molecules. The measurements show that there is a decrease in the propagation length of the leaky PSPP modes when the nanostripes are coated by thiol. The difference between the propagation lengths for the bare and thiol coated nanostripes was used to calculate a CID rate for the nanostripes. The values obtained were on the order of 1–3 meV, which is much smaller than the rates typically observed for Au nanorods.^35,36 This difference is due to the differences in the size of the nanostripes compared to the nanorods. Scaling the results by the effective path length for electrons in the two systems shows that the CID dephasing rates measured for the leaky PSPP modes of the nanostripes are consistent with those from the LSPRs of nanorods. This is an interesting result given that the field distributions and properties (well defined momentum compared to spatial localization) of PSPPs and LSPRs are very different. Unfortunately, despite the long lifetimes of PSPP modes compared to LSPRs, it will be difficult to use the PSPP modes of the nanostripes for systematic measurements of Γ_CID. This is because at small dimensions, where CID becomes more prominent, the leaky PSPP modes suffer severe radiation damping.^9,51

See the supplementary material for a schematic of the optical system for BFP imaging, atomic force microscopy images of the nanostripes, propagation length vs exposure time measurements for different thiol molecules, average PSPP lifetimes for the coated and uncoated nanostripes, and details of the finite element method simulations.

The authors acknowledge the support of the National Science Foundation through Award No. CHE-1502848. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors would like to thank Professor Masaru Kuno for the use of the Fianium Supercontinuum light source.

The authors declare that there are no conflicts of interest for the present work.