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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 13938–13948
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Edge scattering of surface plasmons excited by scanning tunneling microscopy

Yang Zhang, Elizabeth Boer-Duchemin, Tao Wang, Benoit Rogez, Geneviève Comtet, Eric Le Moal, Gérald Dujardin, Andreas Hohenau, Christian Gruber, and Joachim R. Krenn  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 13938-13948 (2013)
http://dx.doi.org/10.1364/OE.21.013938


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Abstract

The scattering of electrically excited surface plasmon polaritons (SPPs) into photons at the edges of gold metal stripes is investigated. The SPPs are locally generated by the inelastic tunneling current of a scanning tunneling microscope (STM). The majority of the collected light arising from the scattering of SPPs at the stripe edges is emitted in the forward direction and is collected at large angle (close to the air-glass critical angle, θc). A much weaker isotropic component of the scattered light gives rise to an interference pattern in the Fourier plane images, demonstrating that plasmons may be scattered coherently. An analysis of the interference pattern as a function of excitation position on the stripe is used to determine a value of 1.42 ± 0.18 for the relative plasmon wave vector (kSPP/k0) of the corresponding SPPs. From these results, we interpret the directional, large angle (θ~θc) scattering to be mainly from plasmons on the air-gold interface, and the diffuse scattering forming interference fringes to be dominantly from plasmons on the gold-substrate interface.

© 2013 OSA

1. Introduction

Propagating surface plasmon polaritons (SPPs) may be used to transfer information and energy in metallic nanostructures with spatial resolution below the diffraction limit [1

1. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005). [CrossRef]

, 2

2. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

]. Plasmon-guiding structures, such as metal nanowires [3

3. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

9

9. C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett. 12(1), 45–49 (2012). [CrossRef] [PubMed]

] and stripes [10

10. J.-C. Weeber, Y. Lacroute, and A. Dereux, “Optical near-field distributions of surface plasmon waveguide modes,” Phys. Rev. B 68(11), 115401 (2003). [CrossRef]

15

15. R. Zia, J. A. Schuller, and M. L. Brongersma, “Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides,” Phys. Rev. B 74(16), 165415 (2006). [CrossRef]

], and their coupling to quantum emitters [16

16. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007). [CrossRef] [PubMed]

18

18. A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, “Controlled coupling of a single nitrogen-vacancy center to a silver nanowire,” Phys. Rev. Lett. 106(9), 096801 (2011). [CrossRef] [PubMed]

] have been extensively studied. However, there are comparatively few experimental reports on the scattering of plasmons into photons at nanostructure edges [8

8. T. Shegai, V. D. Miljković, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, “Unidirectional broadband light emission from supported plasmonic nanowires,” Nano Lett. 11(2), 706–711 (2011). [CrossRef] [PubMed]

, 19

19. P. Dawson, F. D. Fornel, and J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72(18), 2927–2930 (1994).

22

22. J. Berthelot, F. Tantussi, P. Rai, G. Colas des Francs, J.-C. Weeber, A. Dereux, F. Fuso, M. Allegrini, and A. Bouhelier, “Determinant role of the edges in defining surface plasmon propagation in stripe waveguides and tapered concentrators,” J. Opt. Soc. Am. B 29(2), 226–231 (2012). [CrossRef]

], despite the fundamental and practical importance of this issue. One of the challenges of these studies is the separation of the light originating from the edge scattering of plasmons from the light due to the optical excitation.

We use a scanning tunneling microscope (STM) to electrically excite SPPs on electron beam-lithographed Au metal stripes and study the scattering behavior. STM-excitation of plasmons [23

23. R. Berndt, J. K. Gimzewski, and P. Johansson, “Inelastic tunneling excitation of tip-induced plasmon modes on noble-metal surfaces,” Phys. Rev. Lett. 67(27), 3796–3799 (1991). [CrossRef] [PubMed]

26

26. P. Bharadwaj, A. Bouhelier, and L. Novotny, “Electrical excitation of surface plasmons,” Phys. Rev. Lett. 106(22), 226802 (2011). [CrossRef] [PubMed]

] has several advantages over the more common optical excitation, for example i) low energy electrical excitation (< 4 eV), which is compatible with current microelectronics, ii) very localized excitation (~10 nm) [27

27. L. Douillard and F. Charra, “High-resolution mapping of plasmonic modes: photoemission and scanning tunnelling luminescence microscopies,” J. Phys. D Appl. Phys. 44(46), 464002 (2011). [CrossRef]

] and iii) the absence of background excitation light. Thanks to this local excitation and the absence of any background excitation light we have demonstrated a new method for measuring the relative wave vector of scattered SPPs.

In this article, we use real and Fourier plane measurements of the collected light from STM-excited plasmons to investigate their scattering properties. Both directional, large angle (θ~θc) and diffuse, isotropic contributions to the scattered light are observed. The diffuse emission, observed in the Fourier plane, is modulated by interference fringes. From the excitation point dependence of these interferences, the relative wave vector of the corresponding SPPs (kSPP/k0) is determined to be 1.42 ± 0.18. From these measurements it is proposed that the directional, large angle (θ~θc) scattering is mainly from plasmons on the air-gold interface, and the diffuse scattering is mostly due to plasmons on the gold-substrate interface.

2. Experiment

The experiment is shown schematically in Fig. 1(a)
Fig. 1 (a) Schematic of the experiment: the STM excites SPPs (red arrows) which propagate radially on an Au stripe (5 μm × 2 μm × 100 nm) on an ITO/glass substrate. Inset: the edge scattered light is collected through the transparent substrate by the objective below the sample. (b) and (c) Real plane emission patterns from an Au stripe excited by STM, as collected with an oil objective (NA = 1.45) and an air objective (NA = 0.95), respectively. The yellow dotted lines indicate the Au stripe edges. The green spot indicates the STM tip position. The STM excitation parameters are Vs = 2.5 V, I = 2 nA, Pt/Ir tip, accumulation time t = 30 s in (b) and Vs = 2.8 V, I = 6 nA, accumulation time t = 120 s in (c).
. The experimental setup consists of a commercial STM (Veeco D3100 Nanoscope IVa) operated in air and mounted on an inverted optical microscope (Zeiss Axiovert 200) [25

25. T. Wang, E. Boer-Duchemin, Y. Zhang, G. Comtet, and G. Dujardin, “Excitation of propagating surface plasmons with a scanning tunnelling microscope,” Nanotechnology 22(17), 175201 (2011). [CrossRef] [PubMed]

]. Typical tunnel current values are I = 2-6 nA and typical sample voltages are Vs = 2.5 - 2.8 V. These parameters lead to tip-sample separation distances typically on the order of ~1 nm [28

28. C. J. Chen, Introduction to Scanning Tunneling Microscopy (Oxford University, 1993).

]. Commercially cut Pt/Ir and sharp electrochemically etched W tips [29

29. Y. Nakamura, Y. Mera, and K. Maeda, “A reproducible method to fabricate atomically sharp tips for scanning tunneling microscopy,” Rev. Sci. Instrum. 70(8), 3373–3376 (1999). [CrossRef]

] are used for STM imaging and plasmon excitation. An air objective (63X, NA = 0.95) and oil immersion objective (100X, NA = 1.45) are used to obtain real and Fourier plane images of the light emitted through the transparent substrate and collected with a charge coupled device (CCD) camera (Roper Scientific). Emission spectra are obtained using a liquid nitrogen-cooled spectrometer (Jobin Yvon).

The samples are electron beam-lithographed Au stripes deposited on a 30 nm-thick indium tin oxide (ITO) film on a glass substrate (refractive index nglass = 1.52). The ITO layer is necessary since the surface must be conducting for STM measurements, yet transparent so that the scattered light may be collected through the substrate. The length and width of the Au stripes used are 5 ± 0.05 μm and 2 ± 0.05 μm respectively. Their thickness is chosen to be 100 nm in order to suppress SPP leakage radiation and thus enable us to concentrate on SPP edge scattering. The experiment is repeated using several different tips and stripes (>20).

3. Results and discussion

Figure 1(b) shows the real plane image of the light generated when STM-excited SPPs are scattered at the edges of an Au stripe. For this image, the oil immersion objective was used so that light emitted at angles of up to almost 72° was collected (nglass = 1.52). The STM tip position is in the center of the stripe (green dot) and the scattered light is seen along all four edges. STM excitation of SPPs on flat Au films has been shown to produce 2D outgoing circular waves [25

25. T. Wang, E. Boer-Duchemin, Y. Zhang, G. Comtet, and G. Dujardin, “Excitation of propagating surface plasmons with a scanning tunnelling microscope,” Nanotechnology 22(17), 175201 (2011). [CrossRef] [PubMed]

, 26

26. P. Bharadwaj, A. Bouhelier, and L. Novotny, “Electrical excitation of surface plasmons,” Phys. Rev. Lett. 106(22), 226802 (2011). [CrossRef] [PubMed]

]. As the dimensions of the Au stripe are larger than the SPP wavelength in the visible spectrum range (i.e., for λ0 = 700 nm, λSPP ~680 nm for air-Au interface SPPs), an outgoing circular wave is also expected in this case (see Fig. 1(a)). Thus it is plausible that SPP scattering into light is observed on all edges of the Au stripe in the real plane image. Note that no leakage radiation through the Au stripe is observed since the stripe is relatively thick (100 nm) [30

30. A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. Aussenegg, A. Leitner, and J. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Philos. Roy. Soc. A 149, 220–229 (2008).

]. The fringe structures seen outside the stripe are believed to be due to optical aberrations from the imaging system.

Figure 1(c) shows the real plane image for the same STM-surface plasmon excitation experiment, but this time for collection the air objective is used (maximum collection angle is about 39°). In this case, only four light emission spots are observed, located at the edges on the tip-stripe axes. The differences between the real plane images recorded with the oil and air objectives (Figs. 1(b) and 1(c)) are understood by considering the conservation of the kSPP component parallel to the edge of the stripe, as detailed in the appendix.

The real plane and Fourier plane images in Fig. 2
Fig. 2 Real and Fourier plane images of the light generated when STM-excited SPPs are scattered at the edges of an Au stripe, obtained with the oil objective (NA = 1.45) and a polarizer before the CCD camera. (a) Real plane image, polarizer axis perpendicular to the Au stripe long axis. (b) Real plane image, polarizer axis parallel to the Au stripe long axis. Red double arrows indicate the polarizer orientation. Yellow dashed lines show the position of the Au stripe and the green dot represents the STM tip position. (c) and (d) The corresponding Fourier plane images. (e) and (f) Normalized cross sections of the Fourier plane images along the white dashed lines in (c) and (d) respectively. nglasssinθ=1corresponds to the air-glass interface critical angle (the angle θ is measured with respect to the optical axis, see also Fig. 3(a)). The STM excitation is carried out with a Pt/Ir tip (Vs = 2.5 V, I = 2 nA, accumulation time t = 60 s). As the usable wavelength range of the polarizer is 380 - 780 nm, a 775nm short pass filter is also used during these measurements. The Fourier plane measurements obtained with the oil immersion objective were calibrated from molecular fluorescence data by assigning the critical angle to the inflection point, i.e., where the intensity increases rapidly [25, 31].
were obtained with the oil objective and with a polarizer before the CCD camera, using the same stripe and same STM tip. The polarizer axis was oriented either perpendicular (Figs. 2(a), 2(c) and 2(e)) or parallel (Figs. 2(b), 2(d) and 2(f)) to the long axis of the stripe. In the real plane images of Figs. 2(a) and 2(b), we see that there is little scattered light detected from SPPs which propagates in a direction perpendicular to the polarizer axis. Thus it appears that the scattered light from SPPs incident on a stripe edge maintains its initial polarization (i.e. TM with respect to the SPP propagation direction) [32

32. Z. Li, K. Bao, Y. Fang, Y. Huang, P. Nordlander, and H. Xu, “Correlation between incident and emission polarization in nanowire surface plasmon waveguides,” Nano Lett. 10(5), 1831–1835 (2010). [CrossRef] [PubMed]

].

Figures 2(c)-2(f) show the corresponding Fourier plane images and their cross-sections. From this data it may be estimated that more than 60% of the collected light is emitted into a narrow θ angle range (FWHM ≈6°) with a maximum at an angle of θ = 41.3° ± 0.6°. This angle is close to the critical angle of the air-glass interface θc=arcsin(1/nglass)=41.1°(nglass = 1.52). This result shows that the majority of the scattered light is emitted at large angles.

In Fig. 2 we note that the intensities are asymmetric in opposite directions. Such an asymmetry is common for the STM-excitation of plasmons on metal structures [33

33. T. Wang, “Electrical excitation of surface plasmons with a scanning tunneling microscope,” Ph.D thesis (Université Paris-Sud, 2012).

]. An artifact from the imaging system may be ruled out as the source of the observed asymmetry as it is not always in the same direction. While local roughness may play a role, it is unlikely to be the main cause of the asymmetry since the same phenomenon is seen to vary with time on thin gold films [33

33. T. Wang, “Electrical excitation of surface plasmons with a scanning tunneling microscope,” Ph.D thesis (Université Paris-Sud, 2012).

]. Thus we conclude that the observed asymmetry arises from a local asymmetry of the STM tip.

The data of Fig. 2 was acquired using the same tip and no evolution of the tip was observed during the experiment. From the Fourier plane cross-sections of Figs. 2(e) and 2(f), we see that the highest intensity arc is in the same direction as the brightest edge in the real plane images of Figs. 2(a) and 2(b) respectively. This observation implies that SPPs are mainly scattered in the forward direction at stripe edges. This result is similar to the unidirectionality of light emitted from laser-excited metal nanowires of large diameter (> 300 nm) [8

8. T. Shegai, V. D. Miljković, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, “Unidirectional broadband light emission from supported plasmonic nanowires,” Nano Lett. 11(2), 706–711 (2011). [CrossRef] [PubMed]

] and to the theoretical studies of SPP scattering on a metal wedge [34

34. V. B. Zon, “Reflection, refraction, and transformation into photons of surface plasmons on a metal wedge,” J. Opt. Soc. Am. B 24(8), 1960–1967 (2007). [CrossRef]

]. Thus SPPs excited by STM are shown to scatter principally in the forward direction at large angle θ (collected light observed close to the critical angle) when scattered at stripe edges.

If the grayscale is changed in Figs. 2(c) and 2(d), fringes are seen in the center of the image, i.e. for angles θ less than the air-glass critical angle, as shown in Figs. 3(c)
Fig. 3 Fringes observed in the Fourier plane. (a) Schematic of the experiment: a sharp tungsten STM tip is placed above the center of the stripe and launches SPPs. SPPs at both the air/Au (dark blue curve) and Au/substrate interface (red curve) are excited. The radiative scattering at opposite edges (A and B) is collected using an air objective (NA = 0.95) and a polarizer. The distance (L) between opposite edges is either the width or length of the stripe. The STM tip, located initially at d = 0, is then displaced by an amount Δd along the width or length of the stripe and the experiment is repeated. (b) and (f) Real plane images recorded with the polarizer axis perpendicular or parallel to the stripe long axis respectively. Yellow dashed lines indicate the profile of the stripe, and green dots indicate the STM tip excitation position. The excitation conditions are Vs = 2.5 V, I = 6 nA, and the accumulation time is t = 120 s (W tip). (c)-(e) and (g)-(i) Fourier plane images recorded with a polarizer perpendicular or parallel to the Au stripe long axis respectively, when the STM tip is displaced from the center by different values of Δd. The excitation conditions are Vs = 2.8 V, I = 6 nA, and the accumulation time t = 600 s (W tip). The dashed lines in (c)-(e) and (g)-(i), as well as j) and k) indicate the central fringe. (j) and (k) Cross sections of the Fourier plane images (vertical lines in (c)-(e) and (g)-(i)) are plotted together (raw data and smoothed curves). The red ■ are for Δd = 0, the blue ● for Δd = 100 nm, and the green ▲ for Δd = 200 nm. Curves in (j) and (k) are shifted vertically for clarity. The Fourier plane images obtained with the air objective were calibrated using the fringe pattern spacing from a known laser-illuminated diffraction grating. The fringes in (d) and (e) are seen to curve slightly due to the fact that phase difference between the light scattered from each edge depends on the incident angle of the SPP when the tip is not in the center of the stripe.
and 3(g), (Fig. 3 data is obtained with the air objective in order to avoid collecting as much as possible the light emitted at large angle, thus increasing the signal-to-noise ratio for the data at small angle). The fringe period is inversely proportional to the distance between the opposite edges (width or length). This strongly suggests that the fringes are the result of the interference of the scattered light from each edge (labeled A and B in Fig. 3(a)). This implies that at least part of the STM-excited plasmon wave scatters coherently. Note that two perpendicular sets of fringes are superimposed when Fourier plane images are collected without a polarizer.

Figures 3(c)-3(e) and Figs. 3(g)-3(i) show how the fringe pattern shifts as a function of STM tip excitation position. This fringe shift indicates that the SPPs which give rise to the Fourier plane interference pattern are not standing waves, since the phase difference between the scattered light from the opposite edges would be independent of the STM tip excitation position in that case. SPP standing waves in this system would give rise to interference oscillations in the emission spectrum [6

6. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

] but these are not seen (see Fig. 4
Fig. 4 Spectrum of the light emitted at one end of a gold stripe after STM excitation. The data is obtained using an aperture so that light from a 2 µm diameter area is collected (red dashed circle in inset). Note that no Fabry-Perot oscillations are observed in the spectrum. Smoothed (red curve) and raw data (grey curve) are shown. The excitation conditions are Vs = 2.5 V, I = 1 nA, W tip, and the accumulation time is t = 60 s (oil immersion objective used). The green dot shows the position of the STM tip on the gold stripe (inset).
). This suggests that losses are too high and/or the reflectivity of the plasmons at the edges is too low, resulting in standing waves that are too weak to be detected.

If only scattering perpendicular to the edge is considered for simplicity, the intensity of the inference pattern in the Fourier plane is equal to:
I(nglasssinθ)=IA+IB+2IAIBcos(ΦAΦB+μAμB+δAδB)
(1)
whereIA=|EA|2,IB=|EB|2, δA(δB) is the phase delay due to the light propagation from A(B) to the Fourier plane. The position of the STM tip is d (d = 0 in the middle of the stripe). With kSPP the wave vector of the propagating surface plasmons, we have ΦAΦB=2kSPPd.We assume that the phase difference due to scattering at the stripe edges is independent of the tip excitation position, i.e., μAμB does not depend on d. The phase difference from the optical path difference is:δAδB=k0Lnglasssinθ(see Fig. 3(a)), wherek0=2π/λ0is the wave vector of the emitted light in air.

Bright fringes appear if the total phase difference(ΦAΦB+μAμB+δAδB)=2mπ, where m is an integer. Thus, the position of a bright fringe in the Fourier plane is:

(nglasssinθ)bright(d)=λ0Lm2dLkSPPk0μAμBk0L
(2)

From the Fourier plane data in Fig. 3 we measure the separation between bright fringes to be 0.347 (L = 2 μm) or 0.142 (L = 5 μm). The spacing between fringes in the Fourier plane is equal to Δ(nglasssinθ)bright|spacing=λ0/L, as may be seen from Eq. (2). Thus from these measurements we determine values of 694 nm (L = 2 μm) or 710 nm (L = 5 μm) for the wavelength of the emitted light. From Fig. 4, we see that the light emitted from an STM-excited gold stripe has a central wavelength at about 700 nm and a FWHM of ~150 nm. The photon wavelengths determined from Eq. (2) are thus in agreement with our broad emission spectra measurements.

When the excitation position of the STM tip is displaced by Δd the bright fringe shift is equal to:
Δ(nglasssinθ)bright|shift=2ΔdLkSPPk0
(3)
Rearranging Eq. (3) we get

kSPPk0=L2ΔdΔ(nsinθ)bright|shift
(4)

Thus from Eq. (4), the kSPP/k0 value can be deduced from the fringe shift for a displacement Δd of the STM tip excitation position. The obtained kSPP/k0 values are 1.37 ± 0.16 for L = 2 μm and 1.49 ± 0.20 for L = 5 μm. Combining these two sets of measurements gives us an average value of 1.42 ± 0.18. This value is large compared to the kSPP/k0 value measured previously for stripes [22

22. J. Berthelot, F. Tantussi, P. Rai, G. Colas des Francs, J.-C. Weeber, A. Dereux, F. Fuso, M. Allegrini, and A. Bouhelier, “Determinant role of the edges in defining surface plasmon propagation in stripe waveguides and tapered concentrators,” J. Opt. Soc. Am. B 29(2), 226–231 (2012). [CrossRef]

]. Sources of error include thermal drift of the STM tip with respect to the sample, as we are working in air at room temperature, and the fact that the precise fringe positions are difficult to determine due to the broadband nature of STM excitation (see Fig. 4) and the low signal-to-noise ratio.

In order to verify the validity of our experimental method for the determination of the plasmon relative wave vector kSPP/k0, we perform similar fringe shift measurements on a 200 nm thick Au film perforated with two 250 nm-diameter holes [33

33. T. Wang, “Electrical excitation of surface plasmons with a scanning tunneling microscope,” Ph.D thesis (Université Paris-Sud, 2012).

], see Fig. 5
Fig. 5 Complementary experiment performed on a 200 nm thick Au film perforated with two 250 nm-diameter holes. The purpose of this experiment is to test the validity of the fringe shift method for measuring the relative plasmon wave vector kSPP/k0. (a) Diffraction-limited real plane image obtained when the STM excitation is equidistant from the two holes (as represented by the green dot). The hole separation is 2 µm. The excitation conditions are Vs = 2.5 V, I = 6 nA, W tip, and the accumulation time is t = 180 s. (b) and (c) Fourier plane images obtained when the tip is equidistant from the two holes (Δd = 0) or shifted 100 nm along the tip-hole axis (Δd = 100 nm). As in the case of the stripe, fringes are seen in the Fourier plane image and these fringes shift with excitation position. The bright fringe denoted by the red dashed line in (b) shifts to the position denoted by the blue dashed line in (c). Note that this shift is smaller than that which is seen in Fig. 3, giving rise to a smaller measured relative plasmon wave vector kSPP/k0 and note also that the fringes are not curved in this case. The excitation conditions are Vs = 2.5 V, I = 6 nA, W tip, and the accumulation time is t = 300 s (air objective used).
. The center-to-center distance between the holes is 2 μm and the same experimental setup is used. By measuring the shift of the center fringe as a function of STM tip excitation position between the holes, kSPP/k0 is determined to be about 1.06 ± 0.08 from Eq. (4). This value agrees to within experimental uncertainty with the theoretical value of kSPP/k0 = 1.03 [38

38. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

] estimated for a gold film. (εAu = −16.78 + 1.317i [39

39. R. Innes and J. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F Met. Phys. 17(1), 277–287 (1987). [CrossRef]

], λ0 = 700 nm), thus confirming the validity of the method.

Other possible explanations for this surprisingly large value of kSPP/k0 should be considered. The STM tip and the localized plasmons located beneath it might contribute to the scattered light in the case where the tip radius of curvature is large compared to the stripe width. However, in our case the STM tip radius is less than 100 nm, an order of magnitude smaller than the stripe width. Another possibility might be the influence of corner modes. SPP modes on Au stripes are hybrid due to the coupling of SPPs on the Au/air interface with corner modes which are highly confined at Au stripe edges [10

10. J.-C. Weeber, Y. Lacroute, and A. Dereux, “Optical near-field distributions of surface plasmon waveguide modes,” Phys. Rev. B 68(11), 115401 (2003). [CrossRef]

]. This hybridization leads to a modification of the kSPP [22

22. J. Berthelot, F. Tantussi, P. Rai, G. Colas des Francs, J.-C. Weeber, A. Dereux, F. Fuso, M. Allegrini, and A. Bouhelier, “Determinant role of the edges in defining surface plasmon propagation in stripe waveguides and tapered concentrators,” J. Opt. Soc. Am. B 29(2), 226–231 (2012). [CrossRef]

, 43

43. M. Song, A. Bouhelier, P. Bramant, J. Sharma, E. Dujardin, D. Zhang, and G. Colas-des-Francs, “Imaging symmetry-selected corner plasmon modes in penta-twinned crystalline Ag nanowires,” ACS Nano 5(7), 5874–5880 (2011). [CrossRef] [PubMed]

]. However, changes in kSPP due to corner plasmons are small for L = 2 µm (ΔkSPP/k0<0.1) and cannot completely account for the large value of kSPP measured here. Thus the idea that the fringes arise from light scattered from plasmons on the gold-substrate interface appears to be the most probable.

The question of how these Au/ITO/glass interface plasmons are excited is an interesting one. It is known that the inelastic tunnel current of an STM excites both localized and propagating surface plasmons on air-gold film [25

25. T. Wang, E. Boer-Duchemin, Y. Zhang, G. Comtet, and G. Dujardin, “Excitation of propagating surface plasmons with a scanning tunnelling microscope,” Nanotechnology 22(17), 175201 (2011). [CrossRef] [PubMed]

, 26

26. P. Bharadwaj, A. Bouhelier, and L. Novotny, “Electrical excitation of surface plasmons,” Phys. Rev. Lett. 106(22), 226802 (2011). [CrossRef] [PubMed]

]. The localized plasmons might in turn excite the “bottom” interface plasmons. Another possibility might be that the scattered light from the top interface is the excitation source. This last possibility may be ruled out, as the measured fringe shift as a function of the STM tip excitation position would not reflect the relative kSPP value of the Au/substrate plasmon. We thus propose that it is the localized surface plasmons directly beneath the STM tip that excite the Au/substrate plasmons which lead to the observed fringe shift.

Since the contribution from these SPPs on the gold-substrate interface is expected to be small due to the thickness of the gold stripe (100 nm), it appears that the majority of the scattered light from this lower interface is coherently and diffusely scattered, and is thus quite different from the mainly directional forward scattering from the upper interface. If the plasmons from the two interfaces scattered in a similar fashion, we would expect that the relative k-vector measured by the fringe shift method would be closest to the value for the air/gold interface plasmons, which is not the case. (It is assumed that the air/gold interface plamons are more efficiently excited by STM). Thus, in this way we have identified two different scattering regimes for SPPs on gold stripes, depending on from which interface the SPPs originate.

4. Conclusion

We have investigated the scattering of electrically exited SPPs on a gold stripe. Two different scattering components have been identified: a strong directional contribution that is scattered at large angle (i.e., 60% in a 6° range around the air/glass critical angle and more than 80% at angles above θc) and a weaker (≿0.5%) contribution that is diffusely, yet coherently scattered, and observed at low angle (nglasssinθ0.5). Using an original method to determine the wave vector of SPPs, we attribute the weak, small θ angle scattering primarily to light from SPPs on the Au/substrate interface and the directional, large θ angle scattering to light principally from SPPs on the Au/air interface. This knowledge of how SPPs are scattered at edges is important in the context of coupling plasmonic stripes with other plasmonic nanostructures or with quantum emitters.

Appendix: Real plane images recorded using the air and oil immersion objectives

In order to satisfy the boundary conditions of Maxwell's equations and conserve momentum, the x components of the SPP and scattered light wave vectors must be equal, i.e., kx_glass=kSPPsinα (see Fig. 6(b)
Fig. 6 Radiative scattering of STM-excited SPPs on an Au stripe edge. (a) 3D view and (b) top view. The incident and reflected SPP wave vectors (kSPP) are represented by red arrows. α is the SPP incident angle with respect to the stripe edge normal. The wave vector of the scattered radiation in the glass medium (kglass) is represented by a blue arrow. The projection of kglass on the stripe top surface (kxy_glass) is represented by a green arrow. kx_glass, ky_glass, kz_glass (black arrows) are the x,y,z components of kglass respectively. The direction of the scattered radiation is defined by the polar angle θ with respect to the z axis and the in-plane angle φ. Momentum conservation implies thatkx_glass=kSPPsinα. The optical axis of the microscope is in the z direction.
, kSPP is the SPP wave vector, α the SPP incident angle and kx_glass the x component of the scattered light wave vector in glass). In order to see how the SPP incident angle α relates to the collection angle θ (i.e., the angle the scattered light makes with the optical axis, see Fig. 6(a)) we consider kxy_glass, the component of the scattered light wave vector in the glass substrate that lies in the xy plane (kxy_glass=kglasssinθ, see Fig. 6). Since by definition, kxy_glass is equal to kxy_glass=|kx_glass+ky_glass|, it is always larger or equal to kx_glass, or in other words, kglasssinθkSPPsinα. With kglass=nglassk0, we get:

θarcsin(1nglasskSPPsinαk0)
(5)

The maximum angle θmax at which the scattered light may be detected is limited by the objective numerical aperture NA, θmax=arcsin(NA/nglass).

Thus, when SPPs hit the stripe edge at a large incident angle α, the scattered photons emitted at a large θ angle may be collected with the oil objective (NA = 1.45) but not with the air objective (NA = 0.95). Thus in this way we can explain the difference between the real plane images recorded with the oil (see Fig. 1(b)) and air objectives (see Fig. 1(c)).

Acknowledgments

We thank A. Drezet, S. Huant and J. M. Hao for fruitful discussions. We also acknowledge technical support from the “Centrale de Technologie Universitaire IEF-Minerve” in Orsay and the “Laboratoire de Photonique et de Nanostructures” in Marcoussis. We thank Christophe David and Jean-Christophe Girard for providing us with tungsten tips. This work is supported by the ANR project NAPHO (contract ANR-08-NANO-054) and the European STREP ARTIST (contract FP7 243421). Y.Z. also thanks the ESF for a travel grant (PLASMON BIONANOSENSE).

References and links

1.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005). [CrossRef]

2.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

3.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997). [CrossRef] [PubMed]

4.

J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B 60(12), 9061–9068 (1999). [CrossRef]

5.

R. M. Dickson and L. A. Lyon, “Unidirectional plasmon propagation in metallic nanowires,” J. Phys. Chem. B 104(26), 6095–6098 (2000). [CrossRef]

6.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

7.

E. J. R. Vesseur, R. de Waele, M. Kuttge, and A. Polman, “Direct observation of plasmonic modes in Au nanowires using high-resolution cathodoluminescence spectroscopy,” Nano Lett. 7(9), 2843–2846 (2007). [CrossRef] [PubMed]

8.

T. Shegai, V. D. Miljković, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, “Unidirectional broadband light emission from supported plasmonic nanowires,” Nano Lett. 11(2), 706–711 (2011). [CrossRef] [PubMed]

9.

C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett. 12(1), 45–49 (2012). [CrossRef] [PubMed]

10.

J.-C. Weeber, Y. Lacroute, and A. Dereux, “Optical near-field distributions of surface plasmon waveguide modes,” Phys. Rev. B 68(11), 115401 (2003). [CrossRef]

11.

J. R. Krenn and J. C. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos Trans A Math Phys Eng Sci 362(1817), 739–756 (2004). [CrossRef] [PubMed]

12.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63(12), 125417 (2001). [CrossRef]

13.

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71(16), 165431 (2005). [CrossRef]

14.

E. S. Barnard, T. Coenen, E. J. R. Vesseur, A. Polman, and M. L. Brongersma, “Imaging the hidden modes of ultrathin plasmonic strip antennas by cathodoluminescence,” Nano Lett. 11(10), 4265–4269 (2011). [CrossRef] [PubMed]

15.

R. Zia, J. A. Schuller, and M. L. Brongersma, “Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides,” Phys. Rev. B 74(16), 165415 (2006). [CrossRef]

16.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007). [CrossRef] [PubMed]

17.

H. Wei, D. Ratchford, X. E. Li, H. Xu, and C.-K. Shih, “Propagating surface plasmon induced photon emission from quantum dots,” Nano Lett. 9(12), 4168–4171 (2009). [CrossRef] [PubMed]

18.

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, “Controlled coupling of a single nitrogen-vacancy center to a silver nanowire,” Phys. Rev. Lett. 106(9), 096801 (2011). [CrossRef] [PubMed]

19.

P. Dawson, F. D. Fornel, and J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72(18), 2927–2930 (1994).

20.

B. Steinberger, “The passive and dynamic control of surface plasmon polariton propagation,” Ph.D thesis (Karl-Franzens-University Graz, 2007).

21.

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, “Directional light emission from propagating surface plasmons of silver nanowires,” Nano Lett. 9(12), 4383–4386 (2009). [CrossRef] [PubMed]

22.

J. Berthelot, F. Tantussi, P. Rai, G. Colas des Francs, J.-C. Weeber, A. Dereux, F. Fuso, M. Allegrini, and A. Bouhelier, “Determinant role of the edges in defining surface plasmon propagation in stripe waveguides and tapered concentrators,” J. Opt. Soc. Am. B 29(2), 226–231 (2012). [CrossRef]

23.

R. Berndt, J. K. Gimzewski, and P. Johansson, “Inelastic tunneling excitation of tip-induced plasmon modes on noble-metal surfaces,” Phys. Rev. Lett. 67(27), 3796–3799 (1991). [CrossRef] [PubMed]

24.

S. Egusa, Y.-H. Liau, and N. F. Scherer, “Imaging scanning tunneling microscope-induced electroluminescence in plasmonic corrals,” Appl. Phys. Lett. 84(8), 1257–1259 (2004). [CrossRef]

25.

T. Wang, E. Boer-Duchemin, Y. Zhang, G. Comtet, and G. Dujardin, “Excitation of propagating surface plasmons with a scanning tunnelling microscope,” Nanotechnology 22(17), 175201 (2011). [CrossRef] [PubMed]

26.

P. Bharadwaj, A. Bouhelier, and L. Novotny, “Electrical excitation of surface plasmons,” Phys. Rev. Lett. 106(22), 226802 (2011). [CrossRef] [PubMed]

27.

L. Douillard and F. Charra, “High-resolution mapping of plasmonic modes: photoemission and scanning tunnelling luminescence microscopies,” J. Phys. D Appl. Phys. 44(46), 464002 (2011). [CrossRef]

28.

C. J. Chen, Introduction to Scanning Tunneling Microscopy (Oxford University, 1993).

29.

Y. Nakamura, Y. Mera, and K. Maeda, “A reproducible method to fabricate atomically sharp tips for scanning tunneling microscopy,” Rev. Sci. Instrum. 70(8), 3373–3376 (1999). [CrossRef]

30.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. Aussenegg, A. Leitner, and J. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Philos. Roy. Soc. A 149, 220–229 (2008).

31.

M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210–1215 (2004). [CrossRef]

32.

Z. Li, K. Bao, Y. Fang, Y. Huang, P. Nordlander, and H. Xu, “Correlation between incident and emission polarization in nanowire surface plasmon waveguides,” Nano Lett. 10(5), 1831–1835 (2010). [CrossRef] [PubMed]

33.

T. Wang, “Electrical excitation of surface plasmons with a scanning tunneling microscope,” Ph.D thesis (Université Paris-Sud, 2012).

34.

V. B. Zon, “Reflection, refraction, and transformation into photons of surface plasmons on a metal wedge,” J. Opt. Soc. Am. B 24(8), 1960–1967 (2007). [CrossRef]

35.

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol. 2(7), 426–429 (2007). [CrossRef] [PubMed]

36.

S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B 26(12), B28–B33 (2009). [CrossRef]

37.

S. A. Guebrou, J. Laverdant, C. Symonds, S. Vignoli, and J. Bellessa, “Spatial coherence properties of surface plasmon investigated by Young’s slit experiment,” Opt. Lett. 37(11), 2139–2141 (2012). [CrossRef] [PubMed]

38.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

39.

R. Innes and J. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F Met. Phys. 17(1), 277–287 (1987). [CrossRef]

40.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

41.

P. Li and T. Taubner, “Broadband subwavelength imaging using a tunable graphene-lens,” ACS Nano 6(11), 10107–10114 (2012). [CrossRef] [PubMed]

42.

Theoretically it may be shown that by assuming that the scattered light is driven by a weighted coherent sum of SPP modes from both interfaces, the effectively observed kSPP/k0 determined from the above fringe shift method is neither that of the air/Au mode nor that of the Au/ITO/glass mode but a weighted average of the two. If both modes mix at the edge, there is some change in fringe visibility (due to partly constructive or destructive interference) and the fringes in the Fourier plane shift as if only one SPP with an effective kSPP is excited.

43.

M. Song, A. Bouhelier, P. Bramant, J. Sharma, E. Dujardin, D. Zhang, and G. Colas-des-Francs, “Imaging symmetry-selected corner plasmon modes in penta-twinned crystalline Ag nanowires,” ACS Nano 5(7), 5874–5880 (2011). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(240.7040) Optics at surfaces : Tunneling
(300.2140) Spectroscopy : Emission
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: March 25, 2013
Revised Manuscript: May 16, 2013
Manuscript Accepted: May 16, 2013
Published: June 3, 2013

Citation
Yang Zhang, Elizabeth Boer-Duchemin, Tao Wang, Benoit Rogez, Geneviève Comtet, Eric Le Moal, Gérald Dujardin, Andreas Hohenau, Christian Gruber, and Joachim R. Krenn, "Edge scattering of surface plasmons excited by scanning tunneling microscopy," Opt. Express 21, 13938-13948 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-13938


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References

  1. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005). [CrossRef]
  2. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010). [CrossRef]
  3. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.22(7), 475–477 (1997). [CrossRef] [PubMed]
  4. J.-C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J.-P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B60(12), 9061–9068 (1999). [CrossRef]
  5. R. M. Dickson and L. A. Lyon, “Unidirectional plasmon propagation in metallic nanowires,” J. Phys. Chem. B104(26), 6095–6098 (2000). [CrossRef]
  6. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95(25), 257403 (2005). [CrossRef] [PubMed]
  7. E. J. R. Vesseur, R. de Waele, M. Kuttge, and A. Polman, “Direct observation of plasmonic modes in Au nanowires using high-resolution cathodoluminescence spectroscopy,” Nano Lett.7(9), 2843–2846 (2007). [CrossRef] [PubMed]
  8. T. Shegai, V. D. Miljković, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, “Unidirectional broadband light emission from supported plasmonic nanowires,” Nano Lett.11(2), 706–711 (2011). [CrossRef] [PubMed]
  9. C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett.12(1), 45–49 (2012). [CrossRef] [PubMed]
  10. J.-C. Weeber, Y. Lacroute, and A. Dereux, “Optical near-field distributions of surface plasmon waveguide modes,” Phys. Rev. B68(11), 115401 (2003). [CrossRef]
  11. J. R. Krenn and J. C. Weeber, “Surface plasmon polaritons in metal stripes and wires,” Philos Trans A Math Phys Eng Sci362(1817), 739–756 (2004). [CrossRef] [PubMed]
  12. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B63(12), 125417 (2001). [CrossRef]
  13. R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B71(16), 165431 (2005). [CrossRef]
  14. E. S. Barnard, T. Coenen, E. J. R. Vesseur, A. Polman, and M. L. Brongersma, “Imaging the hidden modes of ultrathin plasmonic strip antennas by cathodoluminescence,” Nano Lett.11(10), 4265–4269 (2011). [CrossRef] [PubMed]
  15. R. Zia, J. A. Schuller, and M. L. Brongersma, “Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides,” Phys. Rev. B74(16), 165415 (2006). [CrossRef]
  16. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007). [CrossRef] [PubMed]
  17. H. Wei, D. Ratchford, X. E. Li, H. Xu, and C.-K. Shih, “Propagating surface plasmon induced photon emission from quantum dots,” Nano Lett.9(12), 4168–4171 (2009). [CrossRef] [PubMed]
  18. A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, “Controlled coupling of a single nitrogen-vacancy center to a silver nanowire,” Phys. Rev. Lett.106(9), 096801 (2011). [CrossRef] [PubMed]
  19. P. Dawson, F. D. Fornel, and J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett.72(18), 2927–2930 (1994).
  20. B. Steinberger, “The passive and dynamic control of surface plasmon polariton propagation,” Ph.D thesis (Karl-Franzens-University Graz, 2007).
  21. Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, “Directional light emission from propagating surface plasmons of silver nanowires,” Nano Lett.9(12), 4383–4386 (2009). [CrossRef] [PubMed]
  22. J. Berthelot, F. Tantussi, P. Rai, G. Colas des Francs, J.-C. Weeber, A. Dereux, F. Fuso, M. Allegrini, and A. Bouhelier, “Determinant role of the edges in defining surface plasmon propagation in stripe waveguides and tapered concentrators,” J. Opt. Soc. Am. B29(2), 226–231 (2012). [CrossRef]
  23. R. Berndt, J. K. Gimzewski, and P. Johansson, “Inelastic tunneling excitation of tip-induced plasmon modes on noble-metal surfaces,” Phys. Rev. Lett.67(27), 3796–3799 (1991). [CrossRef] [PubMed]
  24. S. Egusa, Y.-H. Liau, and N. F. Scherer, “Imaging scanning tunneling microscope-induced electroluminescence in plasmonic corrals,” Appl. Phys. Lett.84(8), 1257–1259 (2004). [CrossRef]
  25. T. Wang, E. Boer-Duchemin, Y. Zhang, G. Comtet, and G. Dujardin, “Excitation of propagating surface plasmons with a scanning tunnelling microscope,” Nanotechnology22(17), 175201 (2011). [CrossRef] [PubMed]
  26. P. Bharadwaj, A. Bouhelier, and L. Novotny, “Electrical excitation of surface plasmons,” Phys. Rev. Lett.106(22), 226802 (2011). [CrossRef] [PubMed]
  27. L. Douillard and F. Charra, “High-resolution mapping of plasmonic modes: photoemission and scanning tunnelling luminescence microscopies,” J. Phys. D Appl. Phys.44(46), 464002 (2011). [CrossRef]
  28. C. J. Chen, Introduction to Scanning Tunneling Microscopy (Oxford University, 1993).
  29. Y. Nakamura, Y. Mera, and K. Maeda, “A reproducible method to fabricate atomically sharp tips for scanning tunneling microscopy,” Rev. Sci. Instrum.70(8), 3373–3376 (1999). [CrossRef]
  30. A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. Aussenegg, A. Leitner, and J. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Philos. Roy. Soc. A149, 220–229 (2008).
  31. M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B21(6), 1210–1215 (2004). [CrossRef]
  32. Z. Li, K. Bao, Y. Fang, Y. Huang, P. Nordlander, and H. Xu, “Correlation between incident and emission polarization in nanowire surface plasmon waveguides,” Nano Lett.10(5), 1831–1835 (2010). [CrossRef] [PubMed]
  33. T. Wang, “Electrical excitation of surface plasmons with a scanning tunneling microscope,” Ph.D thesis (Université Paris-Sud, 2012).
  34. V. B. Zon, “Reflection, refraction, and transformation into photons of surface plasmons on a metal wedge,” J. Opt. Soc. Am. B24(8), 1960–1967 (2007). [CrossRef]
  35. R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nat. Nanotechnol.2(7), 426–429 (2007). [CrossRef] [PubMed]
  36. S. Ravets, J. C. Rodier, B. Ea Kim, J. P. Hugonin, L. Jacubowiez, and P. Lalanne, “Surface plasmons in the Young slit doublet experiment,” J. Opt. Soc. Am. B26(12), B28–B33 (2009). [CrossRef]
  37. S. A. Guebrou, J. Laverdant, C. Symonds, S. Vignoli, and J. Bellessa, “Spatial coherence properties of surface plasmon investigated by Young’s slit experiment,” Opt. Lett.37(11), 2139–2141 (2012). [CrossRef] [PubMed]
  38. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
  39. R. Innes and J. Sambles, “Optical characterisation of gold using surface plasmon-polaritons,” J. Phys. F Met. Phys.17(1), 277–287 (1987). [CrossRef]
  40. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  41. P. Li and T. Taubner, “Broadband subwavelength imaging using a tunable graphene-lens,” ACS Nano6(11), 10107–10114 (2012). [CrossRef] [PubMed]
  42. Theoretically it may be shown that by assuming that the scattered light is driven by a weighted coherent sum of SPP modes from both interfaces, the effectively observed kSPP/k0 determined from the above fringe shift method is neither that of the air/Au mode nor that of the Au/ITO/glass mode but a weighted average of the two. If both modes mix at the edge, there is some change in fringe visibility (due to partly constructive or destructive interference) and the fringes in the Fourier plane shift as if only one SPP with an effective kSPP is excited.
  43. M. Song, A. Bouhelier, P. Bramant, J. Sharma, E. Dujardin, D. Zhang, and G. Colas-des-Francs, “Imaging symmetry-selected corner plasmon modes in penta-twinned crystalline Ag nanowires,” ACS Nano5(7), 5874–5880 (2011). [CrossRef] [PubMed]

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