We report on the implementation of metal nanoparticles as probes for scattering and apertureless near-field optical investigations in the mid-infrared (mid-IR) spectral regime. At these wavelengths, an efficient electric-field confinement is necessary and achieved here through a gold metal nanoparticle of 80 nm in diameter (Au80-MNP) acting as the optical antenna. The Au80-MNP is attached to a standard AFM cantilever used as the spatial manipulator. When approached to a sample surface while being illuminated with an infrared beam, the Au80-MNP produces a considerably improved spatial confinement of the electric field compared to an ordinary scattering AFM tip. We demonstrate here the confinement normal to the sample surface by making use of a sample-induced phonon polariton resonance in a ferroelectric lithium niobate sample. Our experimental findings are in very good agreement with the quasistatic dipole model and show improved optical resolution via well-selected antenna particles.
© 2008 Optical Society of America
Three approaches to investigate materials optically with a resolution beyond the diffraction limit can be distinguished: aperture SNOM, scattering SNOM, and STED.
Aperture scanning near-field optical microscopy (aperture SNOM, also referred to as NSOM — near-field scanning optical microscopy), which was proposed by Synge already in 1928 , achieves an improved optical resolution by restricting the illuminated or the detection area through a pinhole with a size well below the diffraction limit [2,3], for instance by using a metal-coated tapered optical fiber. The drawback of this technique is the low throughput (∼10-6), originating from the high losses experienced by light propagating in a waveguide of diameter less than ½λ. Inherently, the resolution is limited by the finite effective size of the pinhole given by the penetration depth of light into the metal coating (∼10 nm) . Also, thermal damage to the probe or sample has been reported [6,7] and implementing aperture SNOM in the mid-IR suffers from the lack of suitable waveguides .
Later, scattering scanning near-field optical microscopy (s-SNOM or apertureless SNOM) was established. Instead of an aperture, s-SNOM makes use of Babinet’s principle thus achieving the spatial confinement through light scattering from an object much smaller than the wavelength. The apex of the tip of an atomic force microscope (AFM) or a purposely attached particle can be used as the scatterer. The discrimination between the actual near-field signal scattered by the probe and background scattering is crucial to s-SNOM. Elegant solutions have been established either by modulation of the tip-sample distance [9,10] or by dark-field contrast . For visible light an optical resolution down to 1 nm has been reported .
The third technique is known as stimulated emission depletion (STED), which relies on far-field optics. Fluorescence is excited and then it is locally depleted using patterned illumination of a different wavelength, thus allowing a resolution better than 50 nm [13,14]. STED is inherently restricted to fluorescence measurements and requires synchronized pulsed laser sources as well as sophisticated beam shaping.
Among these three microscopy techniques, s-SNOM appears to be the most universal, also for the IR wavelength range. However, the practical realization of s-SNOM meets with certain obstacles, especially concerning the choice and reproducible fabrication of an efficient and confined scattering center. The use of a metal-coated AFM tip as the scatterer is well established, although not the ideal solution because the resulting signal intensity and signal-to-noise-ratio in backscattering geometry are rather low. Moreover, different AFM tips show highly different backscattering efficiencies with regard to the sample near field, and therefore the usability of a particular AFM tip typically has to be determined via trial and error.
In the present paper, we report an approach how to overcome these limitations, possibly pushing s-SNOM for applications by a broader community. We show that s-SNOM can be considerably improved by the use of metal nanoparticle (MNP) tips exhibiting well-defined scattering properties. For an AFM tip carrying a gold MNP (Au-MNP) at its apex, subwavelength s-SNOM imaging has already been demonstrated in the visible spectral regime . Here, we extend this approach to the mid-IR, where the relevant ratio between the wavelength and the MNP diameter is even higher. For the wavelength used, the near-field signal is enhanced by phonon polariton resonances of the coupled tip-sample system [16,17]. Sample-specific phonon resonances make the mid-IR a particularly attractive spectral range for s-SNOM, as they provide a fingerprint of the sample under investigation and thus constitute an efficient contrast mechanism in s-SNOM imaging. At the same time, however, s-SNOM in the mid-IR suffers from the following drawbacks: Since the wavelength λ of some tens of micrometers matches well with the tip height of some ten to twenty micrometers, the antenna behavior of an ordinary AFM tip is much more pronounced in the mid-IR than in the visible range. Such an antenna significantly increases the effective optical tip size and concurrently reduces the resolution of s-SNOM. Modeling the scattering by such a bare AFM tip requires the entire tip structure to be taken into account, which needs an enormous computational effort. Moreover the effective tip dipole stays well inside the solid AFM tip . Still, these issues are very much relaxed if a spatially well restricted scattering center, such as a MNP, properly attached to the tip apex, is used. In particular, such a configuration is well described by the popular analytical dipole model, which treats the scatterer as a point dipole .
In the following, we present experimental data showing that a gold metal nanoparticle measuring 80 nm in diameter (Au80-MNP) attached to an AFM tip is superior to a standard AFM tip for s-SNOM probing in the mid-IR. Furthermore, we demonstrate that the Au80-MNP spatially confines the near-field scattering and that the resulting scattering behavior is in accordance with the dipole model.
As an improved scattering probe, we use a platinum/iridium-coated pyramidal silicon AFM tip carrying a single Au-MNP attached to the tip apex. The cantilever type used has a nominal resonance frequency f0 = 190 kHz (PPP-NCLPt, Nanosensors). A spherical Au80-MNP from a colloidal particle solution (EM.GC80, British Biocell International) is attached to the tip apex by a method similar to that described for tapered fibers by Kalkbrenner et al. . Since colloidal particle solutions provide particles with a uniform shape and a narrow size distribution, we obtain tips having reproducible scattering properties. In addition every particle that is attached to an AFM tip is inspected optically beforehand and its backscattering spectrum is measured. The backscattering spectrum of a Au-MNP is characteristic to the size and shape of the particle. Thus particles with deviations in shape or having a different size are excluded from the picking process. A detailed description how to attach optically selected single MNPs of sizes down to 10 nm in diameter to an AFM or optical fiber tip is under preparation . Such probes can be used resonantly as well as nonresonantly with respect to their localized surface plasmon resonances. In the present paper we show the application of a Au80-MNP as a highly localized mid-IR probe.
Figure 1(a) schematically shows a bottom view of such a Au-MNP tip. Figures 1(b) and 1(c) display close-up scanning electron microscopy (SEM) images of the tip apex with the Au80-MNP attached, revealing a secondary electron (SE) and material contrast, respectively. We cut off the foremost 300 nm of the AFM tip pyramid to provide a suitable platform onto which the MNP is attached. The particle then constitutes the front part of the AFM tip, i.e., the part interacting with the sample surface. Residuals of the glue used to attach the gold particle are visible in Fig. 1(b), crawling up the sides of the AFM pyramidal tip. Figure 1(c) provides evidence that the particle on the tip indeed consist of gold, as seen from the elemental contrast provided by the backscattered-electron detector of the SEM.
To investigate the performance of these specially designed tips, we measure the dependence of the near-field signal on the tip-sample distance z for 20 wavelength steps of our IR light source within the desired wavelength region. To locate the sample surface and to control the tip-sample distance, we use an AFM based on laser beam deflection, operated in the phase-locked true noncontact mode . To avoid artifacts in the optical signal, it is indispensable to keep the oscillation amplitude constant [19,22]. This is ensured by a closed-loop amplitude controller which is integrated in the frequency-modulated (FM) AFM controller. For every wavelength, the near-field signal is recorded while the tip-sample distance is continuously reduced at constant oscillation amplitude A0. The approach is stopped when the damping signal of the tip oscillation, as measured by the oscillation amplitude controller, reaches 109% of the value measured far away from the sample surface. By this, we reliably obtain a minimum tip-sample distance of a few nanometers. If the tip is approached further, the damping increases quickly and the tip oscillation becomes unstable.
For a comparative evaluation of the optical properties of the tip, we perform the same experiment also with a standard platinum/iridium-coated silicon AFM tip as the reference tip having no platform and carrying no MNP.
As a versatile illumination source, we use the free-electron laser (FEL) in Dresden-Rossendorf offering a tunable wavelength between 4 and 200 μm, with the radiation being delivered as a continuous train of picosecond pulses at a repetition rate of 13 MHz. The FEL provides a time-averaged power as strong as 10 W in maximum.
The infrared laser beam is reflected by a beam splitter foil and subsequently focused onto the tip by a parabolic gold mirror at an angle of 20° with respect to the sample surface . The backscattered light is collimated by the same mirror, passes the beam splitter foil, and is focused by another mirror onto a liquid-nitrogen-cooled HgCdTe detector. In our experiment, an average infrared power of up to 120 mW in case of p-polarized light and 60 mW in case of s-polarized light was focused onto the tip apex with a spot diameter of about 300 μm, resulting in an average power density of up to 130 W/cm2 (p-polarized) and up to 65 W/cm2 (s-polarized).
The tip oscillation amplitude A0 measured typically 30 nm. The detector signal was demodulated during consecutive runs at the second 2fcant and third harmonics 3fcant of the actual cantilever oscillation frequency fcant by means of a lock-in amplifier, in order to be sensitive to the nonlinear contribution of the near-field in the backscattered optical signal. Thereby, far-field contributions to the scattering signal were efficiently suppressed since they are predominantly modulated at the first harmonic fcant [10,17]. We examined the wavelength range between 12.55 μm and 14.4 μm, where a sample-induced phonon resonance of the coupled system made up of the Au-MNP-tip and the ferroelectric lithium niobate (LNO) sample enhances the optical signal.
As a sample, single-domain lithium niobate (LNO) with an average rms surface roughness of less than 1 nm was chosen. Its crystallographic c-axis was oriented parallel both to the sample surface and to the plane of incidence (cf. Fig. 2). The relevant phonon resonances of LNO are situated at 15.9 μm and 17.1 μm for the electric field being oriented parallel and perpendicularly to the LNO c-direction, respectively . The resonances of the coupled tip-sample system occur when the real part of the dielectric constant of the sample ε′s takes on an appropriate value below -1 (negative 1) . This happens on the short-wavelength side of the aforementioned phonon resonances, where ε′s decreases monotonically with increasing wavelength and becomes strongly negative in the close vicinity of the resonance.
3. Derivation of the expected resonances of the coupled tip-sample system
As mentioned before, a strong confinement of the near-field interaction is expected when a particle tip as introduced in Fig. 1 is used. We expect the scattering properties to be essentially those of the particle, which intentionally has a diameter far below the wavelength and thus should fit the dipole approximation very well. Hence, the comparison of our experimental observations with predictions of the dipole model constitutes a conclusive test.
Within the dipole model, the tip is represented by a tiny spherical scatterer of radius r and dielectric constant εtip having the scalar polarizability αtip = 4π r 3(εtip -1)/[εtip +2) . The real part of the dielectric function ε′tip of the Au-MNP as well as of the platinum/iridium coating of the standard cantilever take on large negative values in the wavelength range used. They amount to ε′Au = - 6790, ε′Pt = - 1825, and ε′Ir = - 2863 for λ = 12.4 μm, and decrease with increasing λ. Also, for all three metals the imaginary part of the dielectric constant tip has a large positive value greater than 1000 in the same wavelength range. Therefore, αtip is almost constant, depending solely on the tip diameter:
The total scattering cross section Ctotal of the coupled tip-sample system is the sum of two contributions C⊥ and C∥, describing the response to the components of the exciting field (as set up by the incident light wave) perpendicular and parallel to the sample surface, respectively :
(excitation field perpendicular to the surface)
(excitation field parallel to the surface).
Here, h denotes the effective distance between the tip dipole and the sample surface, k = 2 π/λ denotes the wave vector, and β is the surface response function of the sample containing the dielectric constant of the sample εs:
In case of s-polarized incident light only C ∥ contributes, whereas in the p-polarized case the C ⊥ component dominates the scattering with a minor C ∥ addition. As LNO is optically anisotropic, we take εs = ε ½ a ε ½ c with εa, εc being the ordinary and extraordinary coefficients of the dielectric tensor [25,26]. The real part ε′s of the effective dielectric constant of LNO decreases monotonically with increasing wavelength from -1.9 at λ = 12.55 μm to -8.4 at λ = 14.4 μm (data taken from ). The resonance appears as a pole of the cross section for βαtip =16π h 3 (C ⊥) or βαtip =32π 3 (C ∥). With αtip ∼4πr 3, the resonance condition reads as β = 4(h/r)3 (C ⊥) and β = 8(h/r)3 (C ∥). As both h and r are positive, the scattering cross section becomes maximal when β reaches the corresponding positive value. If h is large compared to r, the resonance is characterized by a large positive value of β, which corresponds to ε′s being close to -1. At smaller distances the resonance occurs at a more negative value of ε′s; hence a decrease in the tip-sample distance h will shift the resonance towards larger wavelengths.
Also note the influence of the diameter of the scatterer on the spatial extension of the resonance. Because the scattering depends on h/r, a smaller effective radius r of the scatterer makes the scattering spatially more confined. Consequently, the resolution normal to the sample surface increases when a smaller scatterer is used, which is exactly the goal of our work presented here.
4. Comparison of the measurements with the corresponding calculations
Figures 3(a) and 3(b) display the relative near-field signal strength demodulated at the third harmonic 3fcant, as calculated for s- and p-polarized light from the dipole model. As discussed above, all scattering resonances shift towards larger wavelengths for decreasing tip-sample distance. The parameters used for the calculations are given in detail below. First though, we will compare the results of the calculations with our experimental findings.
Figures 3(c) to 3(f) display the measured amplitude of the third-harmonic scattering signals for s- and p-polarized incident light. The average residual signal at large distances has been subtracted from every data set. Also, all experimental data have been normalized to compensate for the variation of the incident FEL power (as monitored by a separate detector during the measurement) and for the spectral characteristics of the detector sensitivity as well as for the transmittance and reflectance characteristics of the IR beam splitters in the illumination and detection path.
In the following we will analyze the spectral features of the recorded and calculated approach data. First we will examine and compare data for both directions of polarization and then discuss the features that are predominantly concerning s-polarized or p-polarized incident light, respectively.
For both directions of polarization the dipole model predicts two signal maxima when the optical signal at the third harmonic 3fcant of the cantilever frequency fcant is recorded [see Fig. 3(a),(b)]. In our calculations as well as in the experimental data sets, a major maximum is observed at longer wavelengths and a minor maximum at shorter wavelengths, see Fig. 3(a)–(c),(e),(f). Furthermore, in the calculation, the signal maxima for s polarization lie at a shorter wavelength than for p polarization [Fig. 3(a),(b)]. This is confirmed by our experiment, both for the standard tip [Fig. 3(c),(d)] and for the Au80-MNP tip [Fig. 3(e),(f)]. Also, for both simulation and experiment the resonances are spectrally narrower for s-polarized incident light than in case of p-polarized incident light. The experimental full width at half maximum (FWHM) at the sample surface (z = 0 nm) for s-polarized light amounts to 200 nm for both tips [Fig. 3(c),(e)]. In case of p-polarized light it amounts to 300 nm FWHM for the Au80-MNP tip [Fig. 3(f)] and to 250-300 nm for the platinum/iridium-coated standard tip [Fig. 3(d)]. Hence also the spectral width of the resonances shows a good agreement with the calculation and moreover the spectral resolution is not influenced by the type of the probe tip that is used. This has been analyzed in detail and confirmed for the major and minor maxima for s-polarized light (data not shown).
In case of s-polarized light, the shift of the resonance towards longer wavelengths with decreasing tip-sample distance, as predicted by the dipole model, is clearly observed for the Au80-MNP tip, whereas it is hardly observed for the standard tip. All signal maxima shift with decreasing tip-sample distance towards larger wavelengths λ, i.e., to more negative values of ε′s and therefore lower values of β[Fig. 3(c),(e)]. Note that in accordance with the dipole model, this behavior is much more pronounced for the Au80-MNP tip, indicating a smaller effective tip size, hence providing a spatially much more confined scattering.
With p-polarized light, the difference between the Au80-MNP tip and the standard tip is even more pronounced. Approach measurements performed with the standard tip exhibit no resonance shift with increasing tip-sample distance [Fig. 3(d)]. Thus, the scattering signal does not follow the prediction of the dipole model at all. Moreover, in case of the standard tip the major maximum is broadened so much that it is no longer separated from the minor maximum [Fig. 3(d)]. As indicated above, this is most probably due to an antenna-like behavior of the AFM tip, because the rather large tip height falls within the range of the excitation wavelength and the electric field is mainly oriented along the tip axis. In contrast, for the tip with the MNP attached, the near-field interaction becomes decoupled from the tip antenna and the behavior observed is as predicted by the dipole model, i.e., a spectral shift occurs upon approach [Fig. 3(f)]. Hence, the Au80-MNP tip can be used for any polarization direction of the impinging light beam.
Besides, the optical near-field signal has totally vanished at a tip-sample distance of at most 60 nm for the Au80-MNP tip for s-polarized as well as for p-polarized light [Fig. 3(e) and 3(f)]. This implies that the platinum/iridium coating which is also present at the tip shaft of the Au80-MNP tip does not disturb the measurement, because it is separated from the surface by a particle of 80 nm in diameter.
Note that all resonances are offset in the calculation towards shorter wavelengths than observed experimentally. For both tips, the offset amounts to 0.5 μm in case of s-polarized light and to more than 0.4 μm in case of p-polarized light. The reason for that might be that the near-field properties are not correctly described by the dielectric function of LNO given in the literature , which was determined by a far-field measurement.
The findings for the third harmonic with regard to the resonance shift as a function of the tip-sample distance are confirmed by similar observations and modeling results obtained for the second harmonic (data not shown).
5. Improved spatial resolution
The comparison of Figs. 3(c) and 3(e) reveals that the Au80-MNP tip effectively confines the scattering signal to the surface. In order to illustrate this more clearly, we have analyzed the demodulated optical amplitude at the third harmonic in more detail for s-polarized light at a wavelength of λ = 13.7 μm. For both tips, the signal measured close to the sample surface is maximal at this wavelength [see Fig. 3(c) and 3(e)]. Even though the signal amplitude is 43 % larger for the standard tip in absolute numbers (data not shown), the Au80-MNP tip has the advantage that the signal is much more confined to the surface under inspection. Note that the ratio of the maximum signal to the noise is the same for both types of tips (cf. Fig. 4). This is most likely due to a reduced far-field contribution to the noise in case of the Au80-MNP tip.
The improved confinement can be derived from Fig. 4, in which the amplitudes have been plotted as a function of the tip-sample distance after normalization to the respective signal measured at the sample surface. The distance z from the surface at which the amplitude has dropped to half the value measured close to the surface (z = 0) amounts to z = 29 nm for the standard tip, but to only z = 12 nm for the Au80-MNP tip. This distance is determined by the effective tip size, which obviously has been efficiently reduced by attaching the Au-MNP. This also manifests itself as a more pronounced spectral shift of the signal maximum with tip-sample distance, as observed in Fig. 3(e) versus 3(c).
6. Parameters of the scattering-signal calculation
As stated before, in order to calculate Fig. 3(a) and 3(b) we used εs = ε ½ a ε ½ c  with the complex elements of the dielectric tensor of LNO εa (electric field perpendicular to the crystallographic c-axis) and εc (electric field parallel to the c-axis) taken from . In case of p-polarized light the incident electric field E0 was split into components perpendicular and parallel to the surface: E ⊥ = E0 cos(20°) and E ∥ = E0 sin(20°). Furthermore, the generalized Fresnel formulae for the reflectivity of an anisotropic material were used to calculate the electric field at the tip that results from the superposition of the incident light with light reflected by the sample surface . This was carried out for each wavelength and for both polarizations. The additional phase shift of the electric field due to the finite distance between the tip dipole and the sample surface was neglected. Even at a distance of 100 nm where all near-field signals have practically vanished, see Fig. 3(c-f), the phase shift amounts to only 2.6°.
As was shown by  for IR wavelengths, the probe dipole is effectively displaced from the center of the metallic sphere towards the sample for small separations z. Therefore, to account for this effect within the dipole approximation, we have to assume a minimal relative separation h/r of less than 1. In our simulation we used h/r = 0.65 as the minimal dipole-to-surface distance. For calculating the signal at higher harmonics, the tip oscillation amplitude was set to 0.25 r. The apparent spatial extension of the calculated scattering signal was matched to the experimental data by adjusting the displayed maximum distance to hmax = 1.05 r in Fig. 3(a) and 3(b).
In conclusion, we have demonstrated that a Au-MNP substantially enhances the optical characteristics of the s-SNOM tip. The resolution normal to the sample surface is improved to less than 20 nm, and the tip scattering properties can be suitably described by the dipole model. More specifically, the different tip-sample resonance lobes are clearly separable and do not merge to a single lobe as observed for ordinary (large) scatterers such as the AFM tip. This allows for an easier interpretation and simulation of experimental data, especially for light polarized parallel to the plane of incidence and thus having a strong electric field component along the tip axis. This is also favorable for Raman [27 ], scattering [28 ] and fluorescent near-field investigations [29 ].
The effective tip size also determines the lateral optical resolution. Therefore, its reduction by the Au-MNP will probably allow for an even higher lateral resolution than the resolution of λ/200 that was achieved in a previous investigation using a standard Pt/Ir-coated AFM tip in the mid-IR [30,31]. Moreover, we hope to reduce the optical far-field background by attaching the Au-MNP to an uncoated silicon AFM tip and thus improve the signal-to-noise ratio with respect to a metal-coated AFM tip. However, this is left to future research.
We gratefully acknowledge the funding of the project by the European Network of Excellence “Plasmo-Nano-Devices” and the German Science Foundation DFG (projects HE 3352/4-1 and EN 434/22-1). Furthermore, we thank Ellen Kern for the SEM micrography, the whole ELBE team for their support, and René Kullock for fruitful discussions.
References and links
1. E. H. Synge, “A Suggested Method for extending Microscopic Resolution into the Ultra-Microscopic Region,” Philos. Mag. 6, 356–362 (1928).
3. D. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984). [CrossRef]
4. B. Knoll and F. Keilmann, “Electromagnetic fields in the cutoff regime of tapered metallic waveguides,” Opt. Commun. 162, 177–181 (1999). [CrossRef]
6. R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194, 378–382 (1999). [CrossRef]
7. Y. D. Suh and R. Zenobi, “Improved Probes for Scanning Near-field Optical Microscopy,” Adv. Mater. 12, 1139–1142 (2000). [CrossRef]
8. F. Keilmann, “Vibrational-infrared near-field microscopy,” Vib. Spectrosc. 29, 109–114 (2002). [CrossRef]
11. T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202, 72–76 (2001). [CrossRef]
13. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994). [CrossRef]
17. S. Schneider, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Impact of optical in-plane anisotropy on near-field phonon polariton spectroscopy,” Appl. Phys. Lett. 90, 143101–143103 (2007). [CrossRef]
18. J. Renger, S. Grafström, L. M. Eng, and R. Hillenbrand, “Resonant light scattering by near-field-induced phonon polaritons,” Phys. Rev. B 71, 75410–1 (2005). [CrossRef]
19. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000). [CrossRef]
20. M. T. Wenzel, P. Olk, T. Härtling, and L. M. Eng, “Fabrication of highly reproducible and well characterized scattering scanning near-field (s-SNOM) probes based on colloidal gold nanoparticles,” manuscript in preparation (2008).
21. T. R. Albrecht, P. Grütter, D. Horne, and D. Rugar, “Frequency modulation detection using high-Q-cantilevers for enhanced force microscope sensitivity,” J. Appl. Phys. 69, 668–673 (1991). [CrossRef]
22. L. Billot, M. Lamy de la Chapelle, D. Barchiesi, S.-H. Chang, S. K. Gray, J. A. Rogers, A. Bouhelier, P.-M. Adam, J.-L. Bijeon, G. P. Wiederrecht, R. Bachelot, and P. Royer, “Error signal artifact in apertureless scanning near-field optical microscopy,” Appl. Phys. Lett. 89, 023105–1 (2006). [CrossRef]
23. A. S. Barker and R. Loudon, “Dielectric Properties and Optical Phonons in LiNbO3,” Phys. Rev. 158, 433–445 (1967) [CrossRef]
24. D. Lide, CRC Handbook of Chemistry and Physics 73th Edition (CRC Press Inc., Boca Rato, FL, USA, 1992) pp. 12–137.
25. I. Lindell, K. Nikoskinen, and A. Viljanen, “Electrostatic image method for the anisotropic half space,” IEE Proc. Sci. Meas. Technol. 144, 156–162 (1997). [CrossRef]
26. S. C. Schneider, S. Grafström, and L. M. Eng, “Scattering near-field optical microscopy of optically anisotropic systems,” Phys. Rev. B 71, 115418–115422 (2005). [CrossRef]
30. S. C. Schneider, “Scattering Scanning Near-Field Optical Microscopy on Anisotropic Dielectrics,” PhD thesis, Technische Universität Dresden, Germany (2007).
31. S. C. Kehr, M. Cebula, O. Mieth, T. Härtling, J. Seidel, S. Grafström, L. M. Eng, S. Winnerl, D. Stehr, and M. Helm, “Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser,” Phys. Rev. Lett. 100, 256403–1 (2008) [CrossRef]