Surface Plasmon Polariton Interference in Gold Nanoplates

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Surface Plasmon Polariton Interference in Gold Nanoplates Gary Beane, Kuai Yu, Tuphan Devkota, Paul Johns, Brendan Brown, Guo Ping Wang, and Gregory V Hartland J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02079 • Publication Date (Web): 25 Sep 2017 Downloaded from http://pubs.acs.org on September 25, 2017

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The Journal of Physical Chemistry Letters

Surface Plasmon Polariton Interference in Gold Nanoplates

Gary Beane,#,a,* Kuai Yu,#,b Tuphan Devkota,a Paul Johns, a Brendan Brown, a Guo Ping Wang, b Gregory Hartlanda,†

a

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

46556, United States

b

College of Electronic Science and Technology, Shenzhen University, Shenzhen, 518060, P. R.

China

* Corresponding author: e-mail: [email protected] # GB and KY contributed equally to this work † e-mail: [email protected]

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Abstract: Transient absorption microscopy (TAM) measurements have been used to study the optical properties of surface plasmon polariton (SPP) modes in gold nanoplates on a glass substrate. For thin gold nanoplates the TAM images show an oscillation in the signal across the plate due to interference between the ‘bound’ and ‘leaky’ SPP modes. The wavelength of the interference pattern is given by λ = 2π Δk where Δk is the difference between the wavevectors for the bound and leaky modes, and is sensitive to the dielectric constant of the material above the gold nanoplate. Back focal plane imaging was also used to measure the wave-vector of the leaky mode which, in combination with the Δk information from the TAM images, enabled the bound mode wavevector to be determined. These experiments represent the first far-field optical measurement of the wavevector for the bound mode in metal nanostructures.

TOC Graphic:

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Metal nanostructures represent an area of physical chemistry that continues to provide many avenues for research, and a number of emerging applications. The most common studied particles are those with high symmetry, such as spherical nanoparticles. In these structures the optical spectra are dominated by localized surface plasmon resonances (LSPRs), which are collective oscillations of the conduction band electrons that are sensitive to the size and shape of the particle.1-3 The LSPRs in Ag and Au nanoparticles have found applications in theranostics,4-7 molecular sensing,8-9 and surface enhanced spectroscopies.10-12 However, in extended metal nanostructures, such as nanowires, nanoplates or thin films, propagating surface plasmon polaritons (SPPs) can also occur.13-17 Unlike LSPRs, these modes do not directly couple to light due to the momentum mismatch between photons and electron motion.18 They can be excited in several ways, for example, by using a prism or grating structure,18-20 or by focusing light at the end of the nanostructure, where the break in symmetry relaxes the momentum matching restrictions.21-23 For nanostructures supported on a glass surface, two types of SPPs are observed in general: bound modes that are localized at the metal-glass interface, and leaky modes that exist predominantly at the metal-air interface.24-28 A number of different experimental techniques have been used to study these modes. Near-field techniques, such as scanning near-field optical microscopy (SNOM), can provide information about both the wavevector and propagation length of the SPP modes that have significant electric fields at the top of the nanostructure.22, 29-36 In general these are the leaky modes,31-32, 36 although bound modes can also be detected in nearfield experiments on thin nanostructures.22,

33-35

More recently, two-photon photoemission

electron microscopy (PEEM) has been used to image propagating SPP modes in gold nanoplates.37-38 These measurements also provide wavevector information, and both bound and

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leaky modes have been observed.37-38 The PEEM experiments are near-field measurements in the sense that the electrons which form the image are generated by the electric fields at the surface of the nanostructure. The SPP propagation lengths can also be measured by coating the nanostructure with a thin layer of fluorescent material and recording an emission image,39-43 or by transient absorption microscopy (TAM) experiments.44-46

These far-field optical

measurements do not have the spatial resolution needed to measure the SPP wavevector. However, the wavevector of the leaky mode can be measured by leakage radiation microscopy.26, 47-50

Specifically, imaging the back focal plane (BFP) of the objective onto a camera produces a

Fourier space image that yields the leaky mode wavevector.26, 47-50 In this contribution, we employ TAM and BFP imaging to investigate the SPP modes of Au nanoplates.49, 51 The TAM images show a periodic modulation in the signal intensity across the plate, which is assigned to interference between the bound and leaky modes. The wavelength of the modulation gives the difference in wavevector Δk between the two modes. Modulations in the SPP intensity have been observed in several previous optical experiments. However, the signal in these cases was attributed to either an interference between the photons emitted by the leaky mode and the excitation laser,47 or an interference between different leaky modes.50 Thus, the modulations in our experiments arise from a fundamentally different physical mechanism. Importantly, the signal in the TAM images carries information about the wavevector for the bound mode. By combining the Δk values from the TAM images with the wavevector of the leaky mode obtained from the BFP images, we are able to determine the wavevector of the bound mode. To the best of our knowledge, this is the first experimental measurement of the bound mode wavevector by a far-field optical experiment. Measurements were performed at different wavelengths, and the results of the measurements are in good agreement with

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electromagnetic simulations. Transient absorption images also were collected for the nanoplates in water. The results show that the interference pattern is very sensitive to the dielectric constant of the environment, potentially making these measurements useful for sensing applications. The Au nanoplates were synthesized using the procedure described in Ref. [51], and were deposited onto a glass coverslip for the optical imaging experiments. While there was a large degree of heterogeneity in the lateral dimension of the Au plates, most of the plates investigated had a thickness of around 50 nm (see the Figure 1 below and Figure S1 of the Supporting Information). Figure 1(a) shows a transient absorbance microscopy (TAM) image of a Au nanoplate. These experiments were performed with 720 nm pump pulses and 560 nm probe pulses. The SPPs were launched by focusing the pump laser at one of the edges of the nanoplate, midway between adjacent corners.49, 51 The image was constructed by scanning the probe laser over the sample.52-53 A step size of 0.1 μm was used, and the total image size is 20 x 20 μm2. The probe laser detects a transient absorption signal in the nanoplates, which arises from hot electrons created by dephasing of the SPPs.44, 54 The most noticeable feature in the TAM image is a series of concentric rings centered on the pump laser focus. Figure 1(b) shows a TAM image for the same nanoplate with water added to the top of the sample.

A scanning electron

microscope (SEM) image of the nanoplate is shown in Figure 1(c). The inset of this image shows that the nanoplate has a height of 42 ± 1 nm. Line profiles through the TAM images are presented in Figure 1(d) that show clear differences in the wavelength of the oscillations: 1.24 ± 0.01 µm for the nanoplate in air compared to 5.1 ± 0.5 µm in water. The pattern in the transient absorption image is assigned to interference between the bound and leaky modes of the nanoplate. Specifically, the wavelength λ is related to the difference in wavevectors by:

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Δk = kbound − kleaky = 2π λ

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(1)

where kbound and kleaky are the wavevectors of the bound and leaky modes, respectively. To confirm this assignment finite element simulations were performed to calculate kbound and kleaky , and to model the transient absorption signal. In the first step of the simulations, a 2D mode analysis calculation was used to determine the SPP modes supported by the plate.24-28

In this

calculation the nanoplate was supported on glass, with a width x height of 5 μm x 50 nm. The dielectric constants for Au were taken from Johnson and Christy.55 This calculation gives a complex eigenvalue, where the real part corresponds to the wavevector and the imaginary part gives the attenuation constant. For a 720 nm pump wavelength the finite element analysis gives kbound = 1.6136k0 and kleaky = 1.0269k0 for the nanoplate in air, and kbound = 1.6156k0 and

kleaky = 1.4025k0 for the nanoplate in water, where k0 is the wavevector of free space light. In the second step the propagation of the SPP modes in the plate was simulated. A full 3D calculation was used with a Au nanoplate with dimensions of 5.0 μm x 15.0 μm x 50 nm. A relatively long nanoplate was chosen so that the wavelength could be accurately measured in the simulations. One end of the NP was defined as an input port, and the other end as a scattering boundary condition to absorb the electromagnetic fields. The bound and leaky modes from the 2D analysis were input into the simulation and allowed to propagate along the structure. Figures 2(a) and 2(b) show the norm of the electric field for the leaky and bound modes in air from the 2D analysis, along with the wavevector for each mode. These images were generated for an excitation at a wavelength of 720 nm. Figure 2(c) shows a top-down view of the energy dissipation density, which is proportional to the transient absorption signal,46, 54 from the 3D simulation. The image is a slice through the nanoplate at a distance of 10 nm from the

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bottom (metal-glass) surface. This distance was chosen because the probe laser interrogates the nanoplate from the glass side in these experiments, and the optical penetration depth of the 560 nm probe beam in gold is 11 nm. The energy dissipation density shows an oscillation that is similar to the oscillations in the TAM images in Figure 1. A line profile through the image in Figure 2(c) is presented in Figure 2(d). A fit to the data for the nanoplate in air gives a wavelength of 1.24 µm, which is in excellent agreement with the experimentally measured wavelength (see Figure 1(d)), confirming the assignment of the modulations to interference between the bound and leaky modes. Analogous calculations for the nanoplate in water are presented in Figures 2(e) and 2(f). In this case the wavelength of the modulations is 3.13 µm, which does not agree as well with the experimental results (5.1 ± 0.5 µm). As expected, the wavelengths in the 3D simulations are equal to 2π Δk , where Δk is the difference in wavevectors from the 2D mode analysis calculation. Note that the calculated images in Figure 2 show a lateral interference pattern that is not evident in the experimental images. This pattern arises from structure in the electric field for the leaky mode near the bottom of the plate (see Figure 2(a) and Figure S7 of the Supporting Information). Finite element simulations show that this structure becomes less pronounced as the width of the nanoplates increases (see Figure S7), which is presumably why the structure does not appear for the large nanoplates interrogated in the experiments. Also note that the interference fringes are less visible in the experiments than the simulations. This is because the experiments integrate over a range of depths in the nanoplate, and the magnitude of the fringes is depth dependent. For example, the fringes are maximized when the fields from the bound and leaky modes have a similar magnitude, and fall off when one field is much larger than the other – which occurs near the surfaces of the nanoplate.

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The discrepancy between the calculated wavelength and the experimental value for the nanoplates in water is surprising, given the excellent agreement between the calculations and experiments for air. To investigate this issue, simulations were performed with nanoplates with different thicknesses, with a layer of surfactant at the surface, and with a water film in between the plate and the substrate. None of these effects produced better agreement between the experiments and theory. Thus, we believe that the reason for the discrepancy is simply that the experimental measurements are not very accurate for the nanoplates in water. This is because for water the wavelength is on the order of the dimensions of the plate and, thus, not well defined in the measurements. The damping of the interference pattern is also of interest. The damping constant for the modulations should be equal to the average of the damping constants for the bound and the leaky modes: α = (α bound + α leaky ) 2 . For the simulations α bound and α leaky where taken from the complex wavevectors from the Boundary Mode analysis, rather than the decay length in the 3D calculations. This is because a coarser mesh size was used for the 3D calculations compared to the 2D Boundary Mode analysis, which reduces their accuracy. The length scale for the decay of the oscillations is given by L = 1 2α , which is calculated to be 8.2 μm for the nanoplates in air and 11.3 μm for water. In comparison, the experimentally measured length scale in air is 2.2 ± 0.1 μm. Note that the damping cannot be determined experimentally for water because of the size effects described above. The shorter length scale for the measurements is attributed to a diffraction effect. The pump laser launches the SPPs from a small region of the nanoplate. As the SPP modes move away from this region they spread out. This spreading, which can be clearly seen in the TAM images, decreases the amplitude of the interference pattern along any specific direction, and

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leads to a larger than expected damping constant. Assuming that the SPPs diffract as circular waves, the amplitude should decrease as 1/R. Scaling the data in Figure 1 by this factor changes the experimental decay length to 7.5 ± 0.3 μm, which is now in reasonable agreement with the value calculated from the finite element simulations. The analysis presented above shows that the transient absorption images yield the difference in the wavevectors between the bound and leaky modes. On the other hand, Back Focal Plane (BFP) imaging can be used to measure the absolute value of the wavevector of the leaky mode.26, 47-50 This means that by combining these two measurements we can measure both and . This is demonstrated in Figure 3.

Figure 3(a) shows a real-space scattered

light image of a Au nanoplate in air excited by a 720 nm laser. The Fourier image that coincides with the real-space image is presented in Figure 3(b). This image was obtained by projecting the back focal plane of the objective onto the camera.

The white dotted line in Figure 3(b)

represents k k0 = 1 (the critical angle for total internal reflection) and the outer diameter is determined by the numerical aperture of the objective ( k k0 = NA ). The arc of intensity in the BFP image corresponds to the wavevector of the leaky mode.49 For nanowires the leaky mode shows up in the BFP images as a line at constant k k0 .26, 47, 54

This is because there is only a single direction for kleaky for a one-dimensional nanowire.

On the other hand, for nanoplates a range of directions are possible for kleaky , as can be seen from Figure 1. Qualitatively, this gives a series of lines at different angles which add up to an arc in the BFP image.49 A diagram of the momentum matching conditions for SPPs of a nanoplate is presented in Figure 3(c).47-48 When the wavevector for the leaky mode makes an angle α with the

y-axis,

momentum

matching

with

photons

9

in


the

substrate

occurs

when


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kleaky = nk0 sin θ cos(ϕ − α ) , where n is the refractive index of the substrate, and θ and ϕ are defined in Figure 3(c). The projection of the wavevector for light onto the (x,y) plane (which is what

is

measured

in

the

Fourier

images)

is

given

by

(k x ,k y ) = (kleaky cosϕ cos(ϕ − α ),kleaky sin ϕ cos(ϕ − α )) , which appears as a line in the image. Figure 3(d) shows a plot of kleaky k0 for different values of α, chosen to match the angles in the experimental image. Note that the lengths of the lines are limited by the NA of the collection objective. The range of angles produces a collection of lines which, when added together, gives an arc in the Fourier image. The average values of kleaky measured from three different gold nanoplates for pump laser wavelengths of 720, 760 and 800 nm are given in Figure 3(e). Also shown in Figure 3(e) are the values of kbound determined from kleaky and the Δk values measured in the TAM images (

kbound = Δk + kleaky ). For the nanoplates in water, BFP imaging cannot be used to measure kleaky . This is because adding water to the sample increases kleaky , and pushes it out of the range of wavevectors that can be detected with our objectives.26, 47-50 However, the simulations show that the wavevector of the bound mode does not change significantly when water is added to the sample. Thus, if we assume that kbound remains relatively unchanged as we change the refractive index of the dielectric above the Au nanoplate, the interference pattern from the TAM images can be used to determine kleaky for the Au nanoplate in water. The values determined from this analysis are included in Figure 3(e). The dashed lines in Figure 3(e) show the calculated values of kbound and kleaky for air and water from the finite element simulations. The experimental and

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calculated values of kbound and kleaky are in good agreement for air. The agreement between the experimental and calculated values of kleaky is not as good for water. This is attributed to the lower accuracy of the experimental Δk values for water, as noted above. The results presented above show that TAM and BFP imaging can provide a wealth of detail about the SPP modes in metal nanostructures. However, one of the difficulties associated with these experiments is that not all the nanoplates show interference effects in the TAM images.

There are several possibilities for this.

For example, unknown details about the

structure of the edges of the nanoplates could control whether the bound and/or leaky modes are excited by the pump laser. However, we think that a more likely explanation is the penetration of the fields into the nanoplate. The interference effect relies on overlap of the fields associated with the bound and leaky modes, which are primarily localized on opposite surfaces of the nanoplate. These fields are damped in the metal, see Figure 2, which means that the magnitude of the interference pattern will decrease with plate thickness.

Simulations of the SPP

interference pattern for plate thicknesses of 25-100 nm are presented in Figure S5 of the Supporting Information. These simulations show that the interference effects quickly drop off with thickness, and would be hard to see for plates that are over 50 nm thick. It is interesting to compare our results to those of Frank et. al.,38 who also observed an interference pattern in their two-photon PEEM measurements.

In these experiments the

wavelengths in the PEEM images are directly related to the wavevectors of the bound and leaky SPPs, not the difference in wavevector. In the two-photon PEEM experiments the intensity of 2

the observed signal is proportional to I 2 (r,t) = ET∗ (r,t) ⋅ ET (r,t) , where ET (r,t) is the total electric field at the surface of the nanoplate, which has contributions from the probe laser (

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E0 (r,t) ) and the SPPs ( Ebound (r,t) and Eleaky (r,t) ): ET (r,t) = E0 (r,t) + Ebound (r,t) + Eleaky (r,t) . This means that

ET∗ (r,t) ⋅ ET (r,t)

has terms that scale as

E0∗ (r,t) ⋅ Ebound (r,t)

and

E0∗ (r,t) ⋅ Eleaky (r,t) , which will give spatial modulations in the PEEM images at the SPP ∗ wavelengths. The terms that go as Ebound (r,t) ⋅ Eleaky (r,t) will be much smaller in the PEEM

experiments, because E0 >> Ebound , Eleaky . In contrast, the intensity of the TAM signal is ∗ (r,t) ⋅ ESPP (r,t) × E0∗ (r,t) ⋅ E0 (r,t) , where ESPP (r,t) is the sum of the fields proportional to ESPP

from

the

bound

and

leaky

SPPs

generated

from

the

pump

laser:

ESPP (r,t) = Ebound (r,t) + Eleaky (r,t) . In this case the spatially modulated terms in the signal go as ∗ Ebound (r,t) ⋅ Eleaky (r,t) + c.c. , which means that the TAM measurements provide information

about the difference in the wavevectors of the bound and the leaky modes. Note that whether the bound mode can be detected or not is dependent on the thickness of the nanoplate for both the PEEM and the TAM experiments. For the PEEM measurements the plate must be thin enough so that the field from the bound mode can penetrate to the top surface where the electrons are generated. For the TAM experiments, the fields from the bound and leaky modes must overlap to produce an interference pattern which, as discussed above, also requires thin plates.

Summary and Conclusions: A combination of TAM and BFP imaging has been used to investigate the SPP modes in Au nanoplates. The TAM images show spatial oscillations that are attributed to interference between the bound and leaky SPP modes of the nanoplate. The wavelength of the interference is

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very sensitive to the dielectric material above the gold nanoplate. For example, adding water to the sample increases the wavelength by approximately a factor of five. This is a much larger effect than the shifts in the LSPRs of nanoparticles due to changes in the refractive index of the environment.56-57 However, the instrumental complexity and long data acquisition times for these measurements mean that this technique is unlikely to be useful in sensing applications. In addition to the TAM images, we also utilized BFP imaging to extract the wavevector of the leaky mode of the Au nanoplates.49 Combining the values of kleaky from the BFP images with the Δk data from the TAM images allows us to experimentally determine the wavevector of the bound SPP mode. For the nanoplates in air the values of kbound were found to be in excellent agreement with the results of finite element simulations. The agreement between the calculated and experimental wavevectors is not as good for the nanoplates in water, which is attributed to problems with the accuracy of the experiments when the wavelength of the modulations becomes similar to the lateral dimensions of the nanoplate.

To the best of our knowledge, these

experiments are the first measurement of the wavevector for the bound mode by a far-field optical method. They provide a way of studying the bound modes for nanostructures in different environments, which is hard to do with near-field SNOM or PEEM experiments.

Methods: The Au nanoplates were synthesized using the procedure described in the Ref. [51]. The samples for optical studies were prepared by spin-casting a dilute solution of nanoplates in water onto a cleaned glass coverslip (Electron Microscopy Services, No 1 glass coverslips). The sample was then mounted on a piezoelectric stage in an inverted optical microscope. For the SEM analysis the samples were coated with iridium prior to imaging. Real space scattered light

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images of the nanoplates were obtained by placing a camera at the primary focal plane of the microscope.

The conjugate Fourier space images, which provide information about the

wavevectors of the leaky modes, were obtained by projecting the back focal plane of the objective onto the camera.26, 47-50 Transient Absorption Microscopy images were generated using a single particle pumpprobe spectroscopy setup described previously.44-46, 52-53 The instrument is based on a Coherent Chameleon Ultra-II Ti:sapphire oscillator (80 MHz repetition rate) that was tuned to either 720, 760 or 800 nm. The output of the oscillator was split with a 90/10 beamsplitter. The weaker portion was used as the pump and was chopped by an acousto-optical modulator (IntraAction) at 400 kHz, triggered by the internal function generator of a lock-in amplifier (Stanford Research Systems SR844). The stronger portion of the laser output pumped an optical parametric oscillator (Coherent Mira-OPO), which provided the probe pulses. The wavelength of the OPO depends on the pump wavelength, for example, pumping at 720 nm produces a probe pulse at 560 nm. A Thorlabs DDS600 linear translation stage was used to control the time delay between the pump and probe beams. For imaging measurements the pump and probe are temporally overlapped to maximize the signal. The intensities of the pump and probe beams were controlled by half-wave plate/polarizer combinations, and quarter-wave plates were used to create circularly polarized beams at the sample. The pump and probe pulses were combined with a dichroic mirror and sent through a 4f lens system to a high NA objective (Olympus UPlan FLN 100×, 1.35 NA, oil immersion). A galvo-scanning mirror system was placed in the path of the probe beam at the focus of the 4f lens system before the dichroic mirror. This allows the probe to be scanned over the sample independently from the pump to form a transient absorption image.44-46, 52-53

The reflected probe beam was collected by the focusing objective and sent to an avalanche

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photodiode. A short-pass filter was used to prevent the pump light from reaching the detector, and the change in reflectivity of the probe induced by the pump was measured by the lock-in amplifier.

Typical powers were 500 and 100 μW for the pump and probe, respectively,

corresponding to energies of 12 and 1.2 pJ/pulse at the sample. Under these conditions, the signal is stable and no melting or reshaping of the nanoplates was observed.

Acknowledgements: This work was supported by the US National Science Foundation through grant CHE-1502848. K.Y. acknowledges financial support from the National Natural Science Foundation of China (NSFC) (Grant Nos 11274247, 11574218) and the Natural Science Foundataion of SZU (Grant No 2017005). This research was supported in part by the Notre Dame Center for Research Computing through access to the computing cluster.

Author Contributions: # GB and KY contributed equally to this work.

ORCID IDs: Gary Beane: 0000-0001-5312-0477 Kuai Yu: 0000-0001-6138-0367 Tuphan Devkota: 0000-0002-0572-5874 Paul Johns: 0000-0002-1134-7566 Gregory V. Hartland: 0000-0002-8650-6891

Supplemental Information: SEM images of nanoplates; TAM and BFP images for a second nanoplate; wavelength dependent measurements for all the nanoplates examined; details of the finite element simulations, and simulations of the thickness dependence of the TAM signal.

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a)

c)

5 μm 5 μm

b)

42 nm

d) λ = 1.24 ± 0.01 μm Log (Signal)

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λ = 5.2 ± 0.5 μm

5 μm 0

3

6

9

12

Distance ( m)

Figure 1: Transient Absorbance Microscopy images of a Au nanoplate on glass in air a) and in water b). c) Scanning electron microscope micrograph of the Au nanoplate. d) Line profiles and fits for TAM images in air (blue markers) and water (red markers). Note that the transient absorption signal is plotted on a log scale in (d). The wavelengths determined from the fit are given in the panel. The TAM images were obtained by exciting the nanoplate with a 720 nm pump beam, and detecting the change in the intensity of the reflected 560 nm probe beam.

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#

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! #

#

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#

! #

#

Figure 2: Finite element simulation for a 50 nm thick 5x15 µm Au nanoplate on glass in air and in water with 720 nm excitation. Panels (a) and (b) show the norm of the electric field for the leaky and bound modes, respectively, for the nanoplate in air determined from the 2D mode analysis calculations. Panels (c) and (d) show images of the energy dissipation density for a horizontal plane 10 nm from the bottom of the nanoplate in air and water. (d) Line profile from the data in panel (c). (f) Line profile from the data in panel (e).

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Figure 3: False color scattered light images from a Au nanoplate. (a) real space image and (b) back focal plane image. (c) Diagram of the momentum matching conditions for the wavevectors of the leaky SPP mode and photons in the substrate. (d) Simulation of the range of possible wavevectors for the leaky modes of a nanoplate. (e) Measured wavevectors for the bound and leaky modes for the nanoplates in different environments and for different wavelengths. The dashed lines show the results from the finite element simulations. The error bars for the measurements are 95% confidence limits determined from analysis of 3 nanoplates.

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ournal of Physical Page Chemistry 26 of 28 L

1 2 3 4 5 ACS 6 Paragon Plus Environmen 7 8

Page 27 of 28

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a)


c)

5 µm 5 µm

b)

42 nm

d) L = 1.24 ± 0.01 µm

L = 5.15 ± 0.06 µm 5 µm 0 Environment ACS Paragon Plus

3

6

Distance ( m)

9

12


a)

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

b)

c)

d)

1.8

k / k0

1.6 1.4

k bound k leaky(air)

1.2 1 1.55

k leaky(water)

1.6

1.65

Energy ( eV )

1.7

1.75


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Surface Plasmon Polariton Interference in Gold Nanoplates

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