1. Introduction

Scattering type apertureless near-field scanning optical microscopy (ANSOM) [1-13] has been widely used in near-field study to overcome the optical resolution limits originating from the cut-off frequency [14] and the finite skin depth of coating material [15] in aperture based NSOM. The optical resolution of ANSOM where a sharp metal tip scatters the local field into far-field is, in principle, determined by the size of tip apex where high field enhancement is induced [4-8]. In the analysis of the measured signal, the effective scattering center can be regarded as a point-like dipole by virtue of the field localization at the proximity of the tip end, and this enables plausible explanations of the signals [4-6, 9-11].

Unlike the light scattering by a tip in homogeneous media, the light scattered from the tip placed close to a surface suffers significant modifications due to the existence of the surface. The dipolar coupling between the real dipole at the tip apex and its image dipole induced at the sample surface has been applied in the analysis of the signals [4-6, 8-13].

Image dipole has a significant meaning in the energy transfer between nano-objects as well. It is well-known that the fluorescence from molecules placed close to flat metal surfaces or gold nanoparticles (GNP) are efficiently quenched. This can be explained, depending on situations mainly, by the increased non-radiative energy transfer from the molecule to metal surfaces [16] and also by the reduced radiative decay rate originated from the destructive interference of the radiations from the single dye molecule and its image dipole at the metal surfaces when molecules are aligned tangentially to the adjacent metal surfaces [17, 18].

In spite of the vital importance of the image dipole – dipole interaction occurring between nano-objects, there have been experimental obstacles hindering the systematic studies of the coupling mechanism. In particular, there has been no proper way of detecting the local field polarization direction on nano-scales. For example, in the vicinity of metal surfaces, a dipole aligned vertically to the surface induces an image dipole on the surface in the same polarization direction as the real dipole, which causes constructive interference. On the other hand, the horizontally aligned dipole induces an image dipole in the opposite direction, which causes destructive interference (Fig. 1) [5].

An intrinsic limitation of ANSOM, the large background signals also prevent the systematic study of the image dipole effects. In side illumination geometry of the plane wave, a significantly large background enforces the detection of high harmonics of the modulated signal, from those quantitative studies are hardly carried out [5, 6, 8-12].

Despite all of aforementioned obstacles, there have been pioneering works on image dipole effects. Cvitkovic et al. have recently presented the ‘finite-dipole model’ in ref. 13 for a quantitative description of effective scattering shapes of sharp metal tips and the image dipole effects. Because sharp metal tips scatter the vertical field component (parallel to the tip axis) more efficiently than the horizontal field component due to the lighting rod effect [19, 20], it needs to use other type of tips to study the orientation dependent image dipole effects.

In this study, we systematically investigate the polarization dependent image dipole effects near a flat gold surface. We use a propagating surface plasmon polaritons (SPP) as an excitation source. The well-characterized field profile of SPP and sufficiently reduced background noise by virtue of the evanescent nature of SPP make it possible to carry out quantitative studies of the image dipole effects. We use a GNP functionalized tip as a local field scatterer and apply the polarization-resolved detection scheme [21, 22] to completely separate the vertical and the horizontal dipole contributions to the signal from each other. We show how the far-field detected signal of the dipole drastically changes depending on the polarization direction, vertically or horizontally to the metal surface.

 

Fig. 1. Polarization direction dependence of the image dipole effects at the vicinity of metal surfaces.

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2. Experimental methods and principles

Figure 2 shows our experimental schematics. A propagating SPP is generated at the slit position by impinging a beam of cw-mode Ti-Sapphire laser (wavelength λ ₀=780 nm) at the back side of the sample. The incident polarization is adjusted perpendicular to the silt direction for the coupling of the incident light to the SPP. The thickness of the gold film and the slit width are 80 nm and 400 nm, respectively. A lens (focal length of 5 cm) focuses the excitation beam at the slit position to eliminate the position dependent interference between the directly transmitted light through the thin metal film and the propagating SPP at the tip position [23]. The tip is fixed at one selected x-position at about 50 µm away from the slit exit to diminish unwanted backgrounds resulting from the deflected light at the tip shaft when the propagating light transmitted at the slit position touches the tip surface [24].

The electric field of the propagating SPP on a flat gold surface can be described as follows [21, 25];

where E ₀ is a constant amplitude, $\kappa =\mathrm{Im}\left[\frac{2\pi }{{\lambda }_0}\sqrt{\frac{{\epsilon }_{\mathit{air}}^2}{{\epsilon }_{\mathit{air}}+{\epsilon }_{\mathit{Au}}}}\right]$ the reciprocal skin depth of the SPP into air (ε _air=1), and $k_{\mathit{spp}}=\frac{2\pi }{{\lambda }_0}\sqrt{\frac{{\epsilon }_{\mathit{air}}·{\epsilon }_{\mathit{Au}}}{{\epsilon }_{\mathit{air}}+{\epsilon }_{\mathit{Au}}}}$ the wave-number of the SPP. As a dielectric constant of GNP, ε _Au≈-22.5+1.4i of bulk gold at the wavelength λ ₀=780 nm is used [25]. This propagating SPP induces the dipole moment at the GNP attached to the apex of an etched glass fiber (Thorlab, FS-SN-4224) [26]. The time integrated intensity ratio of the horizontal and the vertical field components of propagating SPP is determined by the dielectric constant of gold;

which is directly related to the dipole moment strength ratio of two orthogonal dipoles induced at the GNP,

where α⃡ is the polarizability tensor of the GNP [22] and x̂ and ẑ denote the unit vectors in x- and z-axes, respectively. Please refer Ref. 22 and 27 for a detailed α⃡ measurement. The tensor value of GNP used in this measurement is determined as $\stackrel{⃡}{\alpha }=\left(\begin{array}{cc}1.34& 0\\ 0& 1\end{array}\right)$ .

 

Fig. 2. Schematic diagram of the experimental setup. An etched glass fiber functionalized with GNP of 100 nm diameter is placed above a flat gold surface about 50 µm away from the slit position. A 780 nm cw Ti-Sapphire laser beam is incident from the bottom side of the sample to generate SPPs propagating in ± x-direction on air-gold interface. This propagating SPP is scattered by the GNP functionalized tip and a linear analyzer is placed in front of the detector for the axis resolved detection. The tip-sample distance (h) is varied from near- to far-field region, and the detection angle (ϕ) between the sample surface and the detector position vector is also changed.

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The scattered light intensity is measured while varying the tip-sample distance h and the detection angle ϕ between the sample surface and the detector position vector d̂=(0,-cosϕ,sinϕ). A long working objective lens (Mitutoyo M Plan Apo 10×) collects the scattered light and delivers it to an avalanche photo diode (APD, Hamamastu, 4777-01). A linear polarizer placed before the detector resolves the polarization direction of the scattered light.

3. Results and discussion

Figure 3(a) shows the plot of the signal intensities versus the tip-sample distance (h) obtained with the detection polarizer oriented along the horizontal (black solid line) and vertical (red solid line) directions to the sample surface. The elliptical scattering shape of the GNP is taken into account by dividing the horizontal signal intensity with (1.34)² [22]. Here, the detection angle (ϕ) is 33°. To account for these features one by one, we firstly consider the interference between the direct radiation from the GNP and its reflection from the sample surface to the detector by using a simple image dipole model ((i) in Fig. 3(b)). The reflected light from the surface can be considered as the radiation from the image dipole located at the opposite side to the interface. The relative strength of the radiation from the real and the image dipole is determined by the magnitude of the reflection coefficient $\left(R^{s\left(p\right)}=\mid R^{s\left(p\right)}\mid e^{i{\phi }_{\mathit{delay},s\left(p\right)}}\right)$ of the s- and the p-polarized light at air-gold interface [28]. The relative phase difference between the real and the image dipoles is determined by the argument of the reflection coefficient, φ_delay,s(p), as well as the phase difference caused by the optical path length difference φ_diff=k ₀·d, where d=2h sin ϕ is the path difference in Fig. 3(b). For analytical calculations, we applied the single dipole model (SDM) where the real (above the surface) and the image (below) dipoles are assumed to be point-like dipoles. We note that the reflection coefficient of the plane wave is used in this analysis because the scattered light is detected in far-field region. The effects of the higher nonlinear terms included in the effective polarizability change will be discussed in later part.

 

Fig. 3. (a). Experimentally measured tip-sample distance dependent signal intensity with the detection analyzer direction vertical (red) and horizontal (black) to the sample surface. Here, ϕ=33°. (b) The reflected light at the sample surface (dashed line) can be considered as the radiated field from the image dipole (i). And the mutual interaction of the real (upper) and the image (below) dipoles modifies the radiation properties of their own (ii). (c) Analytical calculation of the signal intensities depending on tip-sample distance for the vertical (red) and the horizontal (black) dipoles. Here, the strength ratio of two orthogonal dipoles (p_z/p_x) is determined by the magnitude ratio of the z- and the x-components of the excitation field, i. e. |E_{z, SPP}|/|E_{x, SPP}|. (d) Oscillation periods from the calculation (solid line) and the experiment (open circles). Inset: the solid angle of the objective, φ_s=16.3°.

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The signal intensity of the horizontal (s) and the vertical (p) dipoles in the SDM is written by

Here, |E_s(p)-orig|² is determined by the relative time-integrated strength of the horizontal (s) and the vertical (p) field components of the propagating SPP as in Eq. (2). With the detection angle ϕ=33° being the same as our measurements, Fig. 3(c) shows the analytically calculated signal intensity with the detection polarizer angle direction horizontal (black solid) and vertical to the sample surface (red solid). For the vertical polarization case, i.e., p-polarization case, cos² ϕ term should be multiplied to Eq. (4) to compare with experimentally measured one because of that an oscillating dipole cannot radiate light in its oscillation direction. In a detailed explanation, the electric field at a detection position r⃗ radiated by a dipole moment p⃗ located at origin is described as follows [28];

where k is the wave-vector and r is the distance from the dipole to the detector. With p⃗=(0,0,p_z) and the detection position vector d̂=(0,-cosϕ,sinϕ), the radiated electric field in far-field region with consideration of the surface reflection is given by substituting Eq. (5) into Eq. (4).

Note that the vertical polarizer direction in Fig. 2 is differ from the z-axis in the laboratory frame but parallel to E⃗ _{det ector} giving the measured intensity proportional to cos² ϕ.

The peak and the dip positions of both the horizontal and the vertical components in Fig. 3(c) are almost coincident to those of experiments in Fig. 3(a). The oscillation period $\frac{{\lambda }_0}{2\sin \varphi }$ is determined by the condition of φ_diff=k ₀ d=2π. In Fig. 3(d), the calculated values of oscillation period are plotted in solid line and experimentally measured values for three different detection angles are marked with open circles. For larger detection angles of ϕ=21° and 33° the values from the calculations and the experiments agree well to each other, but for ϕ=8.5° there is a relatively large discrepancy between them. This difference seems to result from the gradually confined numerical aperture (NA) of the collection objective. The used objective lens of NA=0.28 has the collection solid angle φ_s=16.3° (inset in Fig. 3(d)), which means that for a smaller detection angle ϕ<φ_s, the lower part of the lens does not collect the signal, implying the bigger value of effective collection angle.

In the next step, we consider the radiating property modifications of the GNP caused by the reflected fields directly back to the GNP ((ii) in Fig. 3(b)). This effective polarizability (α _eff) change of the GNP can be dealt with the mutual interaction between the real and the image dipoles. The radiated field from the real dipole (upper sphere in the Fig. 3(b)) influences the image dipole (below), and the resultant altered field of the image dipole modifies the real dipole again. This mutually repeating effect on the α _eff can be calculated in a self-consistent manner. In many of the earlier studies [4-6, 8-12], the α _eff is calculated in the quasi-electrostatic limit assuming a small distance from the particle (or the tip apex of a metal tip) to the interface. Moreover the finite size of the scattering particle is not considered in the SDM.

 

Fig. 4. (a). Squared values of the effective polarizability of GNP calculated in SDM for the vertical (red) and the horizontal (black) polarizations. Each value is normalized by the squared value of polarizability calculated in a homogeneous environment. (b) Signal intensities calculated by applying SDM (dashed lines) and CDM in Green-function formalism (solid lines) are shown together with the experimental results (open circles).

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In Fig. 4(a), we plotted the squared value of the effective polarizability of GNP as a function of the tip-sample distance according to the SDM. Here, all terms of Eq. (5) are included compared to the quasi-electrostatic limited calculation. The values are normalized by the un-perturbed polarizabilities calculated in a homogeneous environment. Note that our definition of the α _eff is different from that of the Ref. 5 in that we include only the modified radiation from the real dipole not the modified radiation of the image dipole. Using the SDM and α _eff derived from it, we fail to reproduce the experimentally measured signals (dashed lines in Fig. 4(b)). The relative signal intensities of the vertical and the horizontal components are different in calculation and experiment. In addition, the lifted valley of the vertical polarization signal appeared in experiment at h~300 nm of the tip-sample distance cannot be recovered because the magnitude of the reflection coefficient |R_s(p)| is close to unity for all polarization directions and detection angles for gold surfaces.

In order to understand the origin of the observed deviation, we applied the coupled dipole method (CDM) [29-31] where the GNP of radius 50 nm is divided into approximately 500 identical sub-volumes, which act as point dipoles. In this calculation, all mutual interactions between sub-volumes including the reflected field from the sample surface are considered. In Fig. 4(b), the theoretical calculations with CDM (solid lines) are compared to the experimental data (open circles) for two orthogonal detection polarizer angle directions. The theory and the experiment are in excellent agreements to each other. Furthermore, the lifted non-zero value of the minimum at h~300 nm is clearly recovered by the theory.

 

Fig. 5. The whole volume of spherical shaped GNP is divided into approximately 500 identical sub-volumes and the relative contribution strength to the signal intensity is displayed in different size and color. The largest red one has the biggest contribution. Normalization applied for each case. For the vertical (a) and the horizontal (c) dipole cases at h=300 nm, the corresponding schematic pictures of the signal intensity profile are shown in (b) and (d), respectively.

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For a deeper understanding of these phenomena, the individual contribution strength of sub-volumes to the detected signal is shown in Fig. 5. Here, the whole effects, the interference between the direct radiation and the reflection and the mutual interactions between all sub-volumes, are included. Note that the size of the sub-volumes is not the spatial expansion in space but denotes the relative strength combined with different colors. Figure 5(a) shows the vertically induced dipole case around the lifted valley position (h=300 nm). At this tip-sample distance, the reflected field to the detector mainly destructively interferes with the directly radiated field from the GNP. The center part negligibly contributes to the signal but the sub-volumes at the top and the bottom positions have rather bigger contributions. The tip-sample distance dependent signal intensity is schematically drawn in Fig. 5(b) paraphrasing the overall contributing distribution of the GNP to the signal. For the horizontal-component at the same tip-sample distance, on the other hands, the center part contributes most efficiently to the signal, as can be expected from the constructive interference (Fig. 5(c)). One interesting feature is that the right part of the GNP from the detector, where the propagating SPP is incident on, contributes to the detected signal much more than the left part. The schematic signal intensity profile for the horizontal detection polarizer direction is also shown in Fig. 5(d). These results clearly demonstrate that finite size effects of the scatterer should be applied even when the GNP size (100 nm diameter) is suitably small compared to the excitation beam wavelength (780 nm), to explain the details of the detected signals.

4. Conclusion

The dipole radiation is one of the fundamentals in optics, on the other hand, the experimental verification of its effects engaged with metal surfaces has been challenging due to its highly polarization dependent nature. In this study, we experimentally demonstrate how the image dipole modifies the far-field detected signal depending on its polarization direction to the metal surface. By using a propagating SPP as an excitation source, well characterized local dipoles are generated at the GNP attached to an etched glass fiber. Contributions of dipoles aligned vertically and horizontally to the surface are completely separated from each other in our measurement for a systematic analysis of the polarization dependent image dipole effects on the signal. Measured signals are fully explained by the Fabry-Perot like interference between the radiations from the GNP and from the image dipole induced at the flat gold surface, and by the finite size effects of the GNP. We believe that our study gives a deeper understanding of the image dipole effects on the detected signal in scattering type ANSOM.