**2. Theory of** *s***-SNOM**

324 Advanced Photonic Sciences

concept. In 1984, two groups have simultaneously demonstrated it in the visible wavelength range [7-8]. Light through a sub-wavelength diameter aperture, which is evanescent in character, illuminates a sample within its near-field range. The optical response thus recorded while the sample is scanned laterally constructs a near-field optical image scanning nearfield optical microscope (SNOM). Its resolution depends on the diameter of aperture. Although breaking the Abbe's resolution limit, this new type of optical microscope holds three restrictions. The first one is that the resolution cannot be better than 50 nm, caused by the finite penetration into the optical field-confinement metal structure that defines the aperture. The second one is the trade-off between spatial resolution and collected signal intensity the smaller the aperture is, the smaller the optical signal is collected [9]. The third one is that the throughput of the aperture is highly wavelength dependent, thus distorting the recorded optical spectrum. The aforementioned restrictions thus restrain the practice of aperture-type

In contrast to the aperture-type SNOM, Wickramasinghe and coworkers in 1994 demonstrated an apertureless SNOM with a 10-nm resolution on the basis of sensing the dipole-dipole coupling between a tip end and a sample [10]. Later, Keilmann's team furthermore extended this approach to extract both amplitude and phase of such electromagnetic coupling simultaneously, concocting a comprehensive scattering-type SNOM (*s*-SNOM) [11-15], as depicted in Fig. 1. The collimated optical radiation impinges onto the site where the apex of an atomic force microscopic tip (AFM probe) is in close proximity of sample surface (enclosed by green dotted ellipse). Right-handed image of the figure 1 shows a blow-up view of the induced localized field at the tip apex. The restrictions of aperture-type SNOM are unleashed in such new-generation SNOM. Firstly, the resolution of s-SNOM is only limited by the tip radius. Secondly, the enhanced local field at the tip apex, owing to plasmon resonance, intensifies the electromagnetic interaction at the tip-

SNOM from the applications in nanophotonics and nanotechnology in general.

sample system and thus boosts up the resulted scattered radiation for detection.

Fig. 1. Schematic view of scattering-type scanning near-field optical microscope.

systems. Finally, Section 8 concludes this chapter.

In this chapter, we delineate the fundamental theory of *s*-SNOM (Section 2) and show its experimental setup (Section 3). Section 4 describes issues relevant to extracting near-field images. Its spatial resolution is demonstrated and discussed in Section 5. We show that *s*-SNOM is a powerful tool to unravel local optical properties in nanocomposite systems in Section 6. Furthermore in Section 7, we illustrate that it is possible to extract both amplitude and phase of surface plasmon polariton. The two cases above exemplify the great potential of *s*-SNOM to explore plasmonics and metamaterials, as well as nano-structured composite The field enhancement of a metallic tapered tip apex could be up to 1000-fold higher than the field of an incident optical wave that impinges onto it in an optimum condition for electromagnetic resonance [16]. As a consequence, the electromagnetic interaction between the tip and the incident field can be greatly altered owing to the presence of a near-by surface within the near-field enhancement zone, conferring an enhanced scattered radiation to the far field. Understanding the electromagnetic interaction taking place between the tip apex and the sample surface entails the detailed structure of the tip and solving the electromagnetic field in vicinity of the tip-surface composite system. Nonetheless, a simple model that can reveal the fundamental nature of such electromagnetic interaction would assist in understanding the limits of *s*-SNOM and in furthering its advancement and generalization. The first simplification is that only the response of the tip to the incident optical wave coming from the region around the tip apex is considered, whose dimension is much smaller than the wavelength of the incident wave, such that phase retardation is negligible over such region and thus a quasi-static treatment is justified [17-19]. Secondly, in spite that many multipole fields could be produced from the interaction between the incident wave and the tip apex of finite size and of complicated shape, only the dipole field from a sphere that approximates the tip apex is considered for it dominates the far-field radiation characteristics from the tip-surface system. Lastly, only a flat sample surface is considered for extracting the far-field scattered radiation, though a corrugated surface is expected to modify the outcome. The influence of the surface structure will be discussed later.

Fig. 2. Schematic of quasi-electrostatic dipole model illustrating the electromagnetic interaction happening in *s*-SNOM of side-illuminating geometry.

High-Resolution Near-Field Optical Microscopy: A Sub-10

the sample surface; *a* is the radius of the sphere.

thousand folds difference for a metallic tip [23].

reaches the maximal value at

**3. Setup of** *s***-SNOM** 

complicated models.

Nanometer Probe for Surface Electromagnetic Field and Local Dielectric Trait 327

makes *s*-SNOM in theory a near-field probe. As a final note to the near-field electromagnetic interaction mechanism, although more complete models have been proposed [22] the physical nature illustrated by the simple model still remains the main results from these

Fig. 3. Calculated scattering intensity, *Isca*, of near-field interaction between a chromium sphere and three different samples Au (red line), Si (blue line) and SiO2 (green line) *vs*. *z* based on quasi-static dipole model. *r* is the separation between the center of the sphere and

For a *p*-polarized incident wave, the induced dipole at the sphere has a component normal to the surface, owing to the non-zero field component of the incident wave along the surface normal direction. The induced image dipole is also along the same direction, resulting in an effective polarizability that is larger than *<sup>T</sup>* . Furthermore, according to Eqs. (1) and (2),

scattered radiation is maximized. On the other hand, for an *s*-polarized incident wave, its field component is parallel to the surface, producing a point dipole that also follows the same direction. The image dipole beneath the sample surface is on the other hand along the opposite direction and thus produces a dipole field that counteracts the incident field. Effectively, it partially cancels the dipole above the surface. The resultant effective polarizability in this case is smaller than *<sup>T</sup>* . That is, the scattered radiation is much smaller than that produced in the case of the *p*-polarized wave excitation. The distinction can be

One major challenge facing the development of *s*-SNOM is how to separate the extremely weak near-field signal originated from the tip apex from the huge background signal originated from the giant scattering radiation from the shaft of the tip and the sample. This is caused by the fact that the illuminated region of the incident optical wave cannot be smaller than the one defined by the diffraction limit. This practical problem was solved by

i = 60º in most cases. Namely, at this incident angle, the

*eff*

Figure 2 shows the geometric schematic of the interaction of a *p*-polarized incident electromagnetic wave with an electric field *E*<sup>0</sup> that impinges onto the surface with an incident angle i. A sphere with a radius of *a* and a dielectric constant of *<sup>T</sup>* that symbolizes the tip apex, residing at *r* above the surface of sample that has a dielectric constant of , in *s*-SNOM. The gap between the sphere and the surface is *zra* . According to the Mie's theory of a sphere [20], the sphere illuminated by the incident light gives an induced point dipole with a dipole moment of *p* that is equal to *<sup>T</sup> E*<sup>0</sup> , where *T* is the polarizability of the sphere. As a consequence, such dipole at *r* above the surface induces an image dipole with a dipole moment of *p*' that resides at *r* directly below the surface. The image dipole creates another dipole field that together with the incident field produces the dipole moment *p* [21]. An effective polarizability, *eff*, can then be derived by solving the resultant equation self-consistently. Accordingly, the scattered radiation of the incident wave from such tip-surface system can be considered is produced by the combination of the dipole and image dipole. Namely, *eff* of such combination is given by

$$\alpha\_{eff} = \alpha\_T \left( 1 + \mathfrak{h} \cos 2\theta\_i \right) F(r, \theta\_i) \,\,\,\,\,\tag{1}$$

where

$$F\left(r,\theta\_i\right) = \frac{1}{1 - \beta \left(\frac{\varepsilon\_T - 1}{\varepsilon\_T + 2}\right) \left(\frac{1 + \cos^2\theta\_i}{8}\right) \left(\frac{a}{a+z}\right)^3} \,\,\,\tag{2}$$

$$
\alpha\_T = 4\pi a^3 \frac{\varepsilon\_T - 1}{\varepsilon\_T + 2} \,\, ^\prime \tag{3}
$$

and

$$
\beta = \left(\varepsilon - 1\right) / \left(\varepsilon + 1\right). \tag{4}
$$

*z* is the separation between the tip apex and the sample surface and is equal to *r a* and, furthermore, and is the ratio between the dipole moments of the dipole of the tip apex and the image dipole. The scattering light field, given by

$$E\_{sca} \propto \mathbf{u}\_{eff} \times E\_{0'} \tag{5}$$

directly reflects *eff* which conveys the dielectric property of the sample and the tip-sample separation and the field *E*<sup>0</sup> that induces it. Consequently, *s*-SNOM can extract the distribution of the dielectric constant of the sample if the tip-sample separation is fixed, as well as the optical field at the surface if the sample is uniform. Figure 3 shows the calculated scattering intensity <sup>2</sup> *<sup>E</sup>*0 of a chromium sphere on the surfaces of Au, SiO2 and Si as a function of *r a* based on Eq. (5). Two facts can be extracted from this figure. First, the scattering intensity is sensitive to the dielectric constant of the sample, engendering *s*-SNOM to be a local probe of the dielectric property. Second, the scattering intensity bears a nearfield nature it decreases almost exponentially to a plateau as *r a* 1.5 . This feature thus

Figure 2 shows the geometric schematic of the interaction of a *p*-polarized incident electromagnetic wave with an electric field *E*0 that impinges onto the surface with an

i. A sphere with a radius of *a* and a dielectric constant of

SNOM. The gap between the sphere and the surface is *zra* . According to the Mie's theory of a sphere [20], the sphere illuminated by the incident light gives an induced point dipole with a dipole moment of *p* that is equal to *<sup>T</sup> E*<sup>0</sup> , where *T* is the polarizability of the sphere. As a consequence, such dipole at *r* above the surface induces an image dipole with a dipole moment of *p*' that resides at *r* directly below the surface. The image dipole creates another dipole field that together with the incident field produces the dipole

*eff* of such combination is given by

<sup>1</sup> ,

*T*

*T*

equation self-consistently. Accordingly, the scattered radiation of the incident wave from such tip-surface system can be considered is produced by the combination of the dipole and

<sup>2</sup> <sup>3</sup>

2 8

<sup>3</sup> <sup>1</sup> <sup>4</sup>

*z* is the separation between the tip apex and the sample surface and is equal to *r a* and,

separation and the field *E*0 that induces it. Consequently, *s*-SNOM can extract the distribution of the dielectric constant of the sample if the tip-sample separation is fixed, as well as the optical field at the surface if the sample is uniform. Figure 3 shows the calculated scattering intensity <sup>2</sup> *<sup>E</sup>*0 of a chromium sphere on the surfaces of Au, SiO2 and Si as a function of *r a* based on Eq. (5). Two facts can be extracted from this figure. First, the scattering intensity is sensitive to the dielectric constant of the sample, engendering *s*-SNOM to be a local probe of the dielectric property. Second, the scattering intensity bears a nearfield nature it decreases almost exponentially to a plateau as *r a* 1.5 . This feature thus

*T a* 

2 *T*

is the ratio between the dipole moments of the dipole of the tip apex and

*eff* which conveys the dielectric property of the sample and the tip-sample

*T i*

<sup>1</sup> 1 cos <sup>1</sup>

the tip apex, residing at *r* above the surface of sample that has a dielectric constant of

*eff*, can then be derived by solving the resultant

1 cos2 , *eff T ii F r* , (1)

*a a z*

1 1 . (4)

*E E sca eff* <sup>0</sup> , (5)

*<sup>T</sup>* that symbolizes

, (2)

, (3)

, in *s*-

incident angle

image dipole. Namely,

where

and

furthermore, and

directly reflects

moment *p* [21]. An effective polarizability,

*i*

*F r*

the image dipole. The scattering light field, given by

makes *s*-SNOM in theory a near-field probe. As a final note to the near-field electromagnetic interaction mechanism, although more complete models have been proposed [22] the physical nature illustrated by the simple model still remains the main results from these complicated models.

Fig. 3. Calculated scattering intensity, *Isca*, of near-field interaction between a chromium sphere and three different samples Au (red line), Si (blue line) and SiO2 (green line) *vs*. *z* based on quasi-static dipole model. *r* is the separation between the center of the sphere and the sample surface; *a* is the radius of the sphere.

For a *p*-polarized incident wave, the induced dipole at the sphere has a component normal to the surface, owing to the non-zero field component of the incident wave along the surface normal direction. The induced image dipole is also along the same direction, resulting in an effective polarizability that is larger than *<sup>T</sup>* . Furthermore, according to Eqs. (1) and (2), *eff* reaches the maximal value at i = 60º in most cases. Namely, at this incident angle, the scattered radiation is maximized. On the other hand, for an *s*-polarized incident wave, its field component is parallel to the surface, producing a point dipole that also follows the same direction. The image dipole beneath the sample surface is on the other hand along the opposite direction and thus produces a dipole field that counteracts the incident field. Effectively, it partially cancels the dipole above the surface. The resultant effective polarizability in this case is smaller than *<sup>T</sup>* . That is, the scattered radiation is much smaller than that produced in the case of the *p*-polarized wave excitation. The distinction can be thousand folds difference for a metallic tip [23].

## **3. Setup of** *s***-SNOM**

One major challenge facing the development of *s*-SNOM is how to separate the extremely weak near-field signal originated from the tip apex from the huge background signal originated from the giant scattering radiation from the shaft of the tip and the sample. This is caused by the fact that the illuminated region of the incident optical wave cannot be smaller than the one defined by the diffraction limit. This practical problem was solved by

High-Resolution Near-Field Optical Microscopy: A Sub-10

confocal setup that is used to select only the region of the tip apex.

2 cos 2

reference beam, *L* is the laser frequency, *n* is the harmonic order, and

*ref sca ref sca*

sample surface, both *sca I* and

hand, scanned while the sample is fixed.

**4. Extracting near-field images** 

Nanometer Probe for Surface Electromagnetic Field and Local Dielectric Trait 329

Figure 4 shows the optical layout of modified heterodyne *s*-SNOM that is good for multiplewavelength excitation. A CW laser which can be a HeNe laser or a diode-pumped solidstate (DPSS) laser serves as the coherent excitation light source. The laser beam is first split into two parts by a beamsplitter, BS. The transmitted part, as the excitation beam, is sent to the AFM setup in which a micro-objective lens (MO) focuses it into the tip apex with an incident angle of 60° and the field direction being in the incident plane (*p*-polarized excitation). The scattering radiation is collected backward with the same objective lens. As the AFM tip is dithering at a frequency of ~300 kHz (), the collected scattering radiation is modulating at and its harmonics. The reflected part, as the reference beam, is delivered to a frequency shifter that is an acousto-optical modulator. The diffracted beam that is shifted in frequency by is reflected backward to the frequency shifter to experience another deflection and frequency shifting and thus follows the same path of the incoming beam. With this approach, although the reference beam with a different wavelength would be diffracted at a different angle, it should return back to the same path, without altering the optical alignment. The reference beam then combines with the collected scattering radiation at the beamsplitter. The resultant beam is sent to a high-speed photodetector through a

The detected signal by the photodetector is proportional to the square of the combined field

where *sca I* is the collected scattering intensity, *ref I* is the intensity of the frequency-shifted

scattering radiation with respect to the reference beam. As the total detected signal is composed an AC signal modulated at a frequency of 2 *n* , a lock-in amplifier referenced to such frequency retrieves the AC component. With the AFM tip is scanned over the

simultaneously recorded. The system can be operated in two scanning modes: sample- and tip-scanning modes. In the sample-scanning mode, the sample is scanned by a piezo-driven *xy* stage while the tip is fixed in position. In the tip-scanning mode, the tip is, on the other

On the basis of the nonlinear behavior of the near-field interaction with respect to the tipsample separation, as shown in Eq. (1), it is necessary to place the extracted optical signals of different harmonic orders in scrutiny to verify their exponential-decay dependences on such separation (Fig. 3). Figure 5(a) shows the extracted optical signals of first to fourth harmonic orders as a function of the tip-sample separation from a gold surface with nanometer-scaled gold particles. The scattering signal drops almost exponentially with the tip-sample separation, signifying the recorded third and fourth-harmonic signals are generated in near field. A fit of the fourth-harmonic signal to an exponential decay curve gives a decay length of 10 nm, reflecting the short-range electromagnetic interaction between the tip and the

2

are thus retrieved, while the surface topology is

, (6)

is the phase of the

of the frequency-shifted reference beam and the collected scattering radiation [27]:

exp 2 exp

*I I II n t*

*I E i t E i n ti*

*tot ref L sca L*

Wickramasinghe *et al*. [10] and recently by Keilmann *et al*. [14-15]. In their approaches, an interferometric technique combining a dithering tip effectually extracts the weak near-field signal. Taking advantage of the nonlinear dependence of the scattering light field on the tipsample separation, as shown in Eq. (2), the small variation on the tip-sample separation through the tip dithering or tapping produces many harmonic modulation terms in the scattering light field. While the first harmonic term is dominated by the large background that comes from the scattering from the tip shaft and the sample, the higher harmonic terms contain only the nature of the near-field electromagnetic interaction if the mechanical anharmonicity of the tip-dithering action is put under control [24-25]. The interferometrybased technique has two extra benefits. First, both amplitude and phase can in principle be extracted simultaneously. Second, the weak scattering radiation from the near-field zone can be amplified, which will be manifested below. There are two interferometry-based schemes: homodyne [23, 26] and heterodyne [27]. In the homodyne scheme, a coherent laser beam acts as the excitation light source and the local oscillator simultaneously. As the phase information of the scattering radiation is buried within the detected DC signal, its extraction is not straightforward. In the heterodyne scheme, one part of the laser beam is frequency shifted and, accordingly, the mixed signal between it and the other part is modulating in time, greatly facilitating the phase extraction. The shortcoming is that implementing multiple-wavelength excitation is formidable. The drawbacks of the two schemes have been overcome by pseudoheterodyne [28] and modified heterodyne schemes [29], separately. These interferometric schemes have been developed to extract both the amplitude and phase of the scattering contribution in the near-field region without being interfered by the background scattering [26-31]. Taking advantage of the nonlinear dependence of the scattering light field on the tip-sample separation, as shown in Eq. (2), the small variation on the tip-sample separation through tip dithering or tapping produces many harmonic modulation terms in the scattering light field. While the first-harmonic term is dominated by the large background, the higher-harmonic terms contain only the nature of the near-field electromagnetic interaction if the mechanical anharmonicity of the tip-dithering action is under control [24-25]. Here the modified heterodyne technique is delineated. For the homodyne scheme and its improved version, the authors refer to the publications by Keilmann *et al*. [23].

Fig. 4. Optical layout of modified heterodyne *s*-SNOM. BS, beamsplitter; MO, microobjective lens; CM, curved mirror. Blue and red lines symbolize two excitation wavelengths.

Wickramasinghe *et al*. [10] and recently by Keilmann *et al*. [14-15]. In their approaches, an interferometric technique combining a dithering tip effectually extracts the weak near-field signal. Taking advantage of the nonlinear dependence of the scattering light field on the tipsample separation, as shown in Eq. (2), the small variation on the tip-sample separation through the tip dithering or tapping produces many harmonic modulation terms in the scattering light field. While the first harmonic term is dominated by the large background that comes from the scattering from the tip shaft and the sample, the higher harmonic terms contain only the nature of the near-field electromagnetic interaction if the mechanical anharmonicity of the tip-dithering action is put under control [24-25]. The interferometrybased technique has two extra benefits. First, both amplitude and phase can in principle be extracted simultaneously. Second, the weak scattering radiation from the near-field zone can be amplified, which will be manifested below. There are two interferometry-based schemes: homodyne [23, 26] and heterodyne [27]. In the homodyne scheme, a coherent laser beam acts as the excitation light source and the local oscillator simultaneously. As the phase information of the scattering radiation is buried within the detected DC signal, its extraction is not straightforward. In the heterodyne scheme, one part of the laser beam is frequency shifted and, accordingly, the mixed signal between it and the other part is modulating in time, greatly facilitating the phase extraction. The shortcoming is that implementing multiple-wavelength excitation is formidable. The drawbacks of the two schemes have been overcome by pseudoheterodyne [28] and modified heterodyne schemes [29], separately. These interferometric schemes have been developed to extract both the amplitude and phase of the scattering contribution in the near-field region without being interfered by the background scattering [26-31]. Taking advantage of the nonlinear dependence of the scattering light field on the tip-sample separation, as shown in Eq. (2), the small variation on the tip-sample separation through tip dithering or tapping produces many harmonic modulation terms in the scattering light field. While the first-harmonic term is dominated by the large background, the higher-harmonic terms contain only the nature of the near-field electromagnetic interaction if the mechanical anharmonicity of the tip-dithering action is under control [24-25]. Here the modified heterodyne technique is delineated. For the homodyne scheme and its improved

version, the authors refer to the publications by Keilmann *et al*. [23].

Fig. 4. Optical layout of modified heterodyne *s*-SNOM. BS, beamsplitter; MO, micro-

objective lens; CM, curved mirror. Blue and red lines symbolize two excitation wavelengths.

Figure 4 shows the optical layout of modified heterodyne *s*-SNOM that is good for multiplewavelength excitation. A CW laser which can be a HeNe laser or a diode-pumped solidstate (DPSS) laser serves as the coherent excitation light source. The laser beam is first split into two parts by a beamsplitter, BS. The transmitted part, as the excitation beam, is sent to the AFM setup in which a micro-objective lens (MO) focuses it into the tip apex with an incident angle of 60° and the field direction being in the incident plane (*p*-polarized excitation). The scattering radiation is collected backward with the same objective lens. As the AFM tip is dithering at a frequency of ~300 kHz (), the collected scattering radiation is modulating at and its harmonics. The reflected part, as the reference beam, is delivered to a frequency shifter that is an acousto-optical modulator. The diffracted beam that is shifted in frequency by is reflected backward to the frequency shifter to experience another deflection and frequency shifting and thus follows the same path of the incoming beam. With this approach, although the reference beam with a different wavelength would be diffracted at a different angle, it should return back to the same path, without altering the optical alignment. The reference beam then combines with the collected scattering radiation at the beamsplitter. The resultant beam is sent to a high-speed photodetector through a confocal setup that is used to select only the region of the tip apex.

The detected signal by the photodetector is proportional to the square of the combined field of the frequency-shifted reference beam and the collected scattering radiation [27]:

$$\begin{aligned} I\_{tot} & \propto \left| E\_{ref} \exp\left[ i \left( \alpha\_L - 2\Delta \right) t \right] + E\_{sca} \exp\left[ i \left( \alpha\_L + n\Omega \right) t + i\mathfrak{q} \right] \right|^2 \\ & \propto I\_{ref} + I\_{sca} + 2\sqrt{I\_{ref} I\_{sca}} \cos\left[ \left( 2\Delta + n\Omega \right) t + \mathfrak{q} \right] \end{aligned} \tag{6}$$

where *sca I* is the collected scattering intensity, *ref I* is the intensity of the frequency-shifted reference beam, *L* is the laser frequency, *n* is the harmonic order, and is the phase of the scattering radiation with respect to the reference beam. As the total detected signal is composed an AC signal modulated at a frequency of 2 *n* , a lock-in amplifier referenced to such frequency retrieves the AC component. With the AFM tip is scanned over the sample surface, both *sca I* and are thus retrieved, while the surface topology is simultaneously recorded. The system can be operated in two scanning modes: sample- and tip-scanning modes. In the sample-scanning mode, the sample is scanned by a piezo-driven *xy* stage while the tip is fixed in position. In the tip-scanning mode, the tip is, on the other hand, scanned while the sample is fixed.

#### **4. Extracting near-field images**

On the basis of the nonlinear behavior of the near-field interaction with respect to the tipsample separation, as shown in Eq. (1), it is necessary to place the extracted optical signals of different harmonic orders in scrutiny to verify their exponential-decay dependences on such separation (Fig. 3). Figure 5(a) shows the extracted optical signals of first to fourth harmonic orders as a function of the tip-sample separation from a gold surface with nanometer-scaled gold particles. The scattering signal drops almost exponentially with the tip-sample separation, signifying the recorded third and fourth-harmonic signals are generated in near field. A fit of the fourth-harmonic signal to an exponential decay curve gives a decay length of 10 nm, reflecting the short-range electromagnetic interaction between the tip and the

High-Resolution Near-Field Optical Microscopy: A Sub-10

electromagnetic resonance of the tip and the sample under scrutiny.

modified by focused-ion beam.

Nanometer Probe for Surface Electromagnetic Field and Local Dielectric Trait 331

Two more facts can be extracted from the near-field images of 3rd and 4th harmonic orders, shown in Figs. 5(d) and (e), are worthy of further discussion. Firstly, the near-field optical signal observed on large Au nanoparticles (diameter > 200 nm) is larger than that observed on small ones (diameter < 100 nm). This may be originated from the fact that the observed scattering signal from the tip-sample system can be enhanced by its plasmon resonance character [32]. As the plasmon resonance wavelength of a small Au nanoparticle is shorter than that of a large Au nanoparticle and thus is further away from the excitation wavelength of 632.8 nm [33], the corresponding effective polarizability for the small nanoparticle can be smaller than that for the large nanoparticle. Secondly, enhanced scattering signal is evident in the gap between these particles, which can be attributed to the following two causes. On the one hand, the gap mode existing between the two adjacent nanoparticles [34] induces localized strong field within and thus enhances optical scattering. The resonance wavelength of the gap mode is, on the other hand, red shifted and is closer to the excitation wavelength, thus increasing the corresponding effective polarizability and also enhancing the scattering radiation. These factors must be accounted for the interpretation of the extracted near-field images with the use of the excitation wavelength close to the

As to the geometry of the *s*-SNOM setup shown in Fig. 4, there are several advantages for such side-illumination geometry. In sum, except for the better laser excitation and signal collection efficiencies (60º incident angle and *p*-polarization excitation), the sample needs not be transparent. In contrast, for *s*-SNOM with a transmission-illumination geometry in which the excitation laser beam illuminates the tip apex through the sample and along the tip shaft, transparent samples are must and furthermore a special polarization configuration is prepared for the excitation beam to enhance the field component at the tip apex along the tip shaft [35-37]. Nevertheless, for the side-illumination geometry, the cantilever that holds the tip shaft cannot obstruct the excitation laser beam from irradiating the tip apex. Namely, the tips must protrude from the front side of the cantilever. As a consequence, this geometry entails special AFM tips allowing for side illumination (such as AdvancedTEC tips from Nanosensor, Olympus Probes, Visible Apex tips from Bucker, etc.) or conventional tips

Lastly, two differing considerations in choosing the tip material are given to the use of *s*-SNOM in probing local dielectric property and extracting local field. For the first application, the material under study is in general not near electromagnetic resonance with the incident optical wave, for which the scattering signal from the near-field interaction between the tip and the sample is often very weak. To enhance the scattering signal, the tip is preferably made by metal (silver or gold) that bears plasmon resonance with respect to the excitation laser beam. Equations (1) and (3) show that the resultant scattering signal can thus be amplified by the use of such metal tip. As the conventional AFM tips are made with the application of high precision etching process on crystalline silicon and silicon nitride, the shape of the tip apex can thus be controlled down to sub-20 nm scale. Coating of single or multiple layers of metals through thermal deposition can be applied to the tip to create a special dielectric property that is suitable for near-field applications [38]. The thickness of the coating has to be larger than the skin depth of the metal coating at the excitation wavelength to avoid the effect by the underneath tip material. However, silver and gold often tend to aggregate in tens of nanometer on the tip surface [39], creating non-continuous coating and thus bearing unstable optical response. Meticulous control in the metal coating

sample illustrated by Eq. (1) and demonstrating the near-field nature of the high harmonicorder signals. Figure 5(b) shows the topography image of rough Au coated silicon surface. The prominent features of this image show one-to-one correspondence with the images of the scattering optical signals of the second to fourth harmonic orders, as shown in Figs. 5(c) to (e). The interference-like ripples in Fig. 6(c) is an artifact that could be caused by the interference between the scattering light wave of the tip shaft and that of the sample, as similarly observed previously [23]. This assignment is because a slight nonlinear mechanical response of the tip dithering motion at a frequency of provides a certain amount of sinusoidal component at 2 that then introduces some harmonic contribution at 2 into the elastic scattering optical signal from the tip shaft. That trait is also manifested itself in its non-decay dependence on the tip-sample separation, *z*, shown in Fig. 5(a), which is a direct evidence of the non-near field scattering contribution by the tip shaft.

Fig. 5. (a) Collected *s*-SNOM signals of 1st (orange line), 2nd (red line), 3rd (green line), and 4th (blue line) harmonic orders on Au surface as a function of tip-sample separation, *z*; Scanned images of topography (b) and *s*-SNOM signal of 2nd (c), 3rd (d), and 4th (e) harmonic orders. Scale bars represent 100 nm. The black solid line is the fit to an exponential decay. The excitation wavelength is 632.8 nm.

sample illustrated by Eq. (1) and demonstrating the near-field nature of the high harmonicorder signals. Figure 5(b) shows the topography image of rough Au coated silicon surface. The prominent features of this image show one-to-one correspondence with the images of the scattering optical signals of the second to fourth harmonic orders, as shown in Figs. 5(c) to (e). The interference-like ripples in Fig. 6(c) is an artifact that could be caused by the interference between the scattering light wave of the tip shaft and that of the sample, as similarly observed previously [23]. This assignment is because a slight nonlinear mechanical response of the tip dithering motion at a frequency of provides a certain amount of sinusoidal component at 2 that then introduces some harmonic contribution at 2 into the elastic scattering optical signal from the tip shaft. That trait is also manifested itself in its non-decay dependence on the tip-sample separation, *z*, shown in Fig. 5(a), which is a direct

evidence of the non-near field scattering contribution by the tip shaft.

Fig. 5. (a) Collected *s*-SNOM signals of 1st (orange line), 2nd (red line), 3rd (green line), and 4th (blue line) harmonic orders on Au surface as a function of tip-sample separation, *z*; Scanned images of topography (b) and *s*-SNOM signal of 2nd (c), 3rd (d), and 4th (e) harmonic orders. Scale bars represent 100 nm. The black solid line is the fit to an

exponential decay. The excitation wavelength is 632.8 nm.

Two more facts can be extracted from the near-field images of 3rd and 4th harmonic orders, shown in Figs. 5(d) and (e), are worthy of further discussion. Firstly, the near-field optical signal observed on large Au nanoparticles (diameter > 200 nm) is larger than that observed on small ones (diameter < 100 nm). This may be originated from the fact that the observed scattering signal from the tip-sample system can be enhanced by its plasmon resonance character [32]. As the plasmon resonance wavelength of a small Au nanoparticle is shorter than that of a large Au nanoparticle and thus is further away from the excitation wavelength of 632.8 nm [33], the corresponding effective polarizability for the small nanoparticle can be smaller than that for the large nanoparticle. Secondly, enhanced scattering signal is evident in the gap between these particles, which can be attributed to the following two causes. On the one hand, the gap mode existing between the two adjacent nanoparticles [34] induces localized strong field within and thus enhances optical scattering. The resonance wavelength of the gap mode is, on the other hand, red shifted and is closer to the excitation wavelength, thus increasing the corresponding effective polarizability and also enhancing the scattering radiation. These factors must be accounted for the interpretation of the extracted near-field images with the use of the excitation wavelength close to the electromagnetic resonance of the tip and the sample under scrutiny.

As to the geometry of the *s*-SNOM setup shown in Fig. 4, there are several advantages for such side-illumination geometry. In sum, except for the better laser excitation and signal collection efficiencies (60º incident angle and *p*-polarization excitation), the sample needs not be transparent. In contrast, for *s*-SNOM with a transmission-illumination geometry in which the excitation laser beam illuminates the tip apex through the sample and along the tip shaft, transparent samples are must and furthermore a special polarization configuration is prepared for the excitation beam to enhance the field component at the tip apex along the tip shaft [35-37]. Nevertheless, for the side-illumination geometry, the cantilever that holds the tip shaft cannot obstruct the excitation laser beam from irradiating the tip apex. Namely, the tips must protrude from the front side of the cantilever. As a consequence, this geometry entails special AFM tips allowing for side illumination (such as AdvancedTEC tips from Nanosensor, Olympus Probes, Visible Apex tips from Bucker, etc.) or conventional tips modified by focused-ion beam.

Lastly, two differing considerations in choosing the tip material are given to the use of *s*-SNOM in probing local dielectric property and extracting local field. For the first application, the material under study is in general not near electromagnetic resonance with the incident optical wave, for which the scattering signal from the near-field interaction between the tip and the sample is often very weak. To enhance the scattering signal, the tip is preferably made by metal (silver or gold) that bears plasmon resonance with respect to the excitation laser beam. Equations (1) and (3) show that the resultant scattering signal can thus be amplified by the use of such metal tip. As the conventional AFM tips are made with the application of high precision etching process on crystalline silicon and silicon nitride, the shape of the tip apex can thus be controlled down to sub-20 nm scale. Coating of single or multiple layers of metals through thermal deposition can be applied to the tip to create a special dielectric property that is suitable for near-field applications [38]. The thickness of the coating has to be larger than the skin depth of the metal coating at the excitation wavelength to avoid the effect by the underneath tip material. However, silver and gold often tend to aggregate in tens of nanometer on the tip surface [39], creating non-continuous coating and thus bearing unstable optical response. Meticulous control in the metal coating

High-Resolution Near-Field Optical Microscopy: A Sub-10

Nanometer Probe for Surface Electromagnetic Field and Local Dielectric Trait 333

The following two examples illustrate how the field interaction and the geometric factors around the tip influence the spatial resolution of *s*-SNOM. The first sample is an array of silver nanoparticles embedded in aluminum oxide matrix. The silver nanoparticles were electrodeposited into a two-dimensional hexagonal ordered nanochannel array that was formed during anodization of smooth aluminum foil [40]. The gap between adjacent nanoparticles is about 5 nm and confirmed by electron microscopy. Figure 6 shows its topography and near-field intensity amplitude images recorded with a silicon tip with a radius of curvature of less than 10 nm. Notice that the close examination of the two images shows that a large intensity extends for ~6 nm between adjacent nanoparticles. In this observation, the nanoparticle array with a specific interparticle spacing serves as a ruler and confirms the lateral resolution of this *s*-SNOM measurement. An *s*-SNOM image of aggregated gold nanoparticles were reported previously [32] to portray the coherently oscillating nature of plasmon resonant of individual nanoparticles, expect that no confirmation of the gap by other means was provided. As an example, using a carbon nanotube attached on a silicon tip, Hillenbrand and his workers successfully recorded both amplitude and phase images of gold nanoparticles with a good spatial resolution, though no direct proof by electron microscopy was given [41]. The second example is a square array of annular trenches on a gold film of 200 nm thickness. These carved rings were made by focused ion beam. The diameters of the inner and outer circles are 250 and 330 nm, respectively; the depth is 200 nm; the spacing between adjacent rings is 600 nm. Figure 7 shows the topology and near-field amplitude scanned with sharp and blunt PtIr5-coated

Fig. 7. Topology images of annular trench array on gold film made by focused ion beam recorded with (a) sharp and (c) blunt tips and their corresponding intensity amplitude images, (b) and (d), respectively. The diameters of the inner and outer circles are 250 and 330

nm, respectively. Scale bars represent 200 nm.

process is necessity to increase its production yield. The resonance wavelength of a silver coated tip is about 450 nm while that of a gold one is about 600 nm. For such reason, the silver-coated tip is often used with the excitation wavelengths shorter than 600 nm, while the gold-coated tip is with the wavelengths longer than 600 nm. Furthermore, silver has a smaller optical loss than gold, but it can oxidize or sulfurize in ambient condition, altering its optical property in time. On the other hand, gold is rather stable in air, while it is softer than silver and thus does not endure during scanning probe operation. One has to place such factors into account while choosing tip coating for *s*-SNOM. For the applications of retrieving local field, the disturbance by the tip has to be minimized as much as possible. For such reason, the electromagnetic resonance of the tip needs to be avoided and therefore silicon or silicon nitride tips are commonly used directly. This is so because their electromagnetic resonance wavelengths are distant from the visible wavelength range. One concern has to be placed in the use of silicon tips. As silicon oxidizes in air, a thin silicon oxide coating (1-2 nm) can modify the optical response with respect to the excitation laser beam considerably, accordingly diminishing the scattering signal [38].
