1. Introduction

It has been shown that metal nanoparticles exhibit distinct physical/chemical properties from their bulk counterparts due to plasmon resonance, which strongly depends on the particle’s size and shape [1–3]. The effect of optical enhancement of nanoparticles has been studied in various experiments of surface-enhanced spectroscopy for a long time [4–7]. The optical field scattering around a nanoparticle may be viewed as an instantaneous absorption and re-radiation process. When the wavelength of incident light coincides with the wavelength of plasmon resonance, the absorption/scattering cross-section of a particle expands significantly [8]. The re-radiated electromagnetic (EM) field from the particle exhibits phase difference (ϕ) relative to the incident EM field. It is known that while the wavelength of incident EM field is tuned from long to short wavelengths across the plasmon resonance, the phase difference changes from 0 to π [9].

It is very difficult to observe such a phase response with a far-field excitation scheme, where a large number of nanoparticles are excited at the same time and the resultant multiple re-radiation will interfere with each other, leaving only the collective behavior observable [10]. It’s better to study the nanoparticles once at a time, but the far-field excitation area is limited by diffraction. Moreover, it is difficult to decouple the weak re-radiated field from the much stronger incident propagating field when using a far-field excitation. Instead, near-field excitation provides not only more localized interaction, but also less propagating field with a predominant evanescent field through a sub-wavelength aperture. The evanescent field is capable to excite an isolated nanoparticle in the vicinity of the aperture and decays rapidly within the distance of a single wavelength. The excited nanoparticle shall give out subsequent re-radiation, which interferes with the residual propagating field from the near-field aperture in the far-field regime. Therefore, with a near-field excitation and far-field collection scheme, the SP phase response within a single nanoparticle may be extracted.

Such observation of SP phase response has been recently demonstrated in NSOM experiments on a single particle basis [11, 12], but the SP phase dependency on particle size has not been well addressed. To avoid the acquisition error induced by the residual difference of individual NSOM probes and to avoid the risk of damaging tips from repetitively approaching, silver nanoparticles of various sizes are arranged on a quartz surface through high-temperature annealing [13]. In this paper, we report a series of NSOM experiments to directly observe and analyze the size-dependent optical enhancement of a single nanoparticle through an isolated excitation. The phase differences of diversely-sized nanoparticles across the absorption of plasmon resonance are quantitatively analyzed with different excitation wavelengths. The EM field distribution within a single nanoparticle is the interfered result between the re-radiated and the incident propagating field. Through the study of size-wavelength-dependent optical enhancement, we retrieved the phase shift of plasmonic re-radiation from the EM field distribution for each nanoparticle. Our observations indicate the potential to control spatial distribution of SP modes on a nanostructured surface via wavelength manipulation [14].

2. Experimental setup

2.1 Near-field scanning optical microscopy (NSOM)

Figure 1(a) shows the scheme of experimental setup. A NSOM scanner (Aurora-3, Veeco) and a tapered Al-coated fiber probe with a 50-nm aperture were used. Due to the high reflectivity of aluminum and the tapered characteristic given by thermal pulling technique, the incident light was fully constrained at the tip of the probe as a point source. One He-Ne laser (λ=633 nm) and two solid-state lasers (λ=532 nm and 488 nm) were individually coupled into the probe as the light source for exciting Ag nanoparticles. The fiber-based probe mounted on a tuning fork was perpendicular to the sample surface where the distance between the tip and surface was controlled by a shear force feedback system [15]. In our measurements, the set point was maintained at half of the free oscillation amplitude in a constant-gap scanning mode. The constant scanning rate was set at 5 µm/s. The scattered light from samples was detected in the far field by a photomultiplier tube (PMT) through a microscope objective (Olympus 50×, NA=0.8). Both the topography and near-field scanning optical images were simultaneously recorded for subsequent analyses.

 

Fig. 1. (a). NSOM setup. (b) The absorption spectrum of Ag nanoparticles. The spectral positions of the NSOM excitations are shown with RGB lines. Inset: SEM image of Ag nanoparticles.

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2.2 Samples

A random distribution of Ag nanoparticles with different sizes was fabricated by a hightemperature annealing technique. First, the quartz substrate was coated with a 10-nm silver layer by thermal evaporation (physical vapor deposition, PVD) in a 10^-6 torr vacuum chamber. Then the coated substrate was put into a 600 °C furnace (Lindberg/Blue M Tube Furnaces, Thermo Electron Co.) for 30 min and drawn out to cool down to room temperature. To minimize surface energy of congregated metal atoms, the annealed silver layer gradually formed well-separated silver nanospheres during the cooling period. The inset in Fig. 1(b) shows the scanning electron microscope (SEM) picture of the resultant Ag nanospheres. The diameter ranges from 15 nm to 150 nm. Figure 1(b) gives the far-field absorption spectrum of Ag nanoparticle film measured by a UV/VIS/NIR spectrometer (U-3010, HITACHI). The broad plasmon resonance spectrum reflected the size variation of our Ag nanoparticles. Our excitation wavelengths were chosen within the broad region to observe the near-field optical enhancement which depends on the size of nanoparticle and the phase of near-field SP coupling. The major advantage of this fabrication method is to obtain diversely-sized and well-separated nanoparticles on the same surface. As a consequence, there is no need to frequently change or re-approach the scanning tips to study the size-dependent behaviors, avoiding the risk of damaging tips.

 

Fig. 2. Simulation results of the far-field interference from E_tip and E_s with phase difference (a) ϕ=0, (b) ϕ=π/2, and (c) ϕ=π. (d) Their cross-sectional views are combined in (d), showing the dramatic difference between on- and off-resonance.

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3. Theoretical considerations

The purpose of this theoretical simulation is to qualitatively analyze the far-field interference between the re-radiated field from the nanoparticles and the propagating field from the fiber tip. The point source from the fiber tip is modeled as [11]:

where r is the distance from light source to the nanoparticle, k is the wave number, and ω is the angular frequency. A and B are constants that individually represent the amplitude of propagating EM field and evanescent EM field. η is the decay length of evanescent field. The dipole moment induced in a nanoparticle is

where the polarizability α depends on the size of the nanoparticle and the wavelength of excitation EM field. α can be written as

where ϕ is the phase-difference between the displacement of the oscillator and the field that excites it. Thus, the particle dipolar radiation generated from the oscillating dipole can be shown as

 

Fig. 3. Measured NSOM images of a 50-nm nanoparticle with (a) λ=633 nm, (b) λ=532 nm, and (c) λ=488 nm. Their cross-sectional views are combined in (d).

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Z ₀ is the free space impedance and r ₁ is the distance from nanoparticle to detector. The measured intensity (I_m) in the far-field detector is I_m∝|E_tip+E_s|². For ualitative analyses of the interference pattern, the relative optical signal I is defined as I=(I_m-I _m0)/I _m0, where I _m0∝|E_tip|² is the plane intensity without nanoparticles. Figure 2 shows the simulation results with various phase shifts. Figure 2(a) and (c) are the two off-resonance cases of ϕ=0 and ϕ=π, respectively. A constructive interference pattern with a bright center is found in Fig. 2(a) while a ring-shaped destructive interference component with a dark center is observed in Fig. 2(c). At SP resonance condition, ϕ=π/2, the nanoparticle has the strong re-radiation EM field and the interference result is dominated by particle dipolar re-radiation, as shown in Fig. 2(b). Figure 2(d) shows the corresponding profile of three cases. It is evident that if the excitation is resonant with the nanoparticle, the optical enhancement effect is significant. If the excitation wavelength is longer or shorter than the plasmon resonant wavelength, the phase shift ϕ is either less or more than π/2, resulting in a constructive or destructive interference respectively. Therefore, metal nanoparticles may be effectively applied to modulate the phase of localized EM field. Moreover, based on these simulations, the SP phase response of re-radiation in the near field may be obtained from the far-field observation.

 

Fig. 4. Particle size spectra for RGB excitations. The tendency of shorter wavelength resonant with smaller silver nanoparticles is evident.

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4. Results and discussion

Figure 3 displays NSOM images of a single silver nanoparticle of 50-nm diameter with 488-, 532-, and 633-nm excitations, respectively. For this particle, the plasmon resonance wavelength is about 530 nm and thus significantly larger resonance enhancement is provided by the 532-nm excitation. The near-field distribution of the optical field intensity is very different for the 633- and 488-nm excitations in the same particle. A dip is observed in the position of the nanoparticle with the 488-nm excitation while a bump is observed with the 633-nm excitation. Since the observed signal is the result of interference between optical field from the fiber-tip and plasmonic re-radiation from the nanoparticle, the phase of induced polarizability inside the particle would strongly affect the result. Note that the polarizability experiences a π phase-shift across the plasmon resonance absorption. With the 633-nm excitation, though not at resonance, constructive interference exhibits between excitation and re-radiation, resulting in a weak, but positive signal. At 532 nm, which is on resonance, the particle dipolar re-radiation dominates, producing a stronger signal. But for the 488-nm excitation, theπ phase-shift of the polarizability resulted in a destructive interference between excitation and re-radiation, and thus a dip is observed. These results agree well with the simulations.

Figure 4 outlines the particle size spectra of interfered optical far-field intensity with RGB excitations. The ordinate is the relative optical signal (I) and the abscissa is sizes of silver nanoparticle. The plasmon resonance peak of 633-nm excitation is located at the diameter of 75 nm, while that of 532-nm excitation is at 50 nm. The resonance peak of 488-nm excitation approaches its maximum toward a diameter of smaller than 40 nm. Thus, for the 633-nm excitation, a SP phase shift of π/2 is expected for the near-field re-radiation from a 75-nm Ag nanoparticle. In other words, Ag nanoparticles with diameters larger than 75 nm can be employed to modulate the phase between π/2 and π. Those are smaller than 75 nm can be used to control the phase between 0 and π/2. Similarly, for the 532-nm excitation, the phase-modulation of π/2 is expected with 50-nm nanoparticles. These results validate the possibility of spatial manipulation of SP phases by modulating the size of metal nanoparticle or by selecting appropriate wavelengths.

5. Conclusion

In conclusion, our result manifests the correlation between plasmon resonance and the size of a single metal nanoparticle with the aid of a multiple-wavelength NSOM. We have shown that the size-/wavelength-dependent optical enhancement within a single silver nanoparticle can be revealed through isolated excitations. By visualizing the interference pattern between the plasmonic re-radiation and the excitation wave in the far field, the relative SP phase-shift across the resonant wavelength can be quantitatively extracted. The phase-response properties may be employed in allocating the spatial distribution of localized SP modes on a nanostructured surface.