The dependence of the near-field signal on the dielectric function of a specific material proposes scattering-type near-field optical microscopy (s-SNOM) as a viable tool for material characterization studies. Our experiment shows that specific material identification by s-SNOM is not a straightforward task as parameters involved in the detection scheme can also influence material contrast measurements. More precisely, we demonstrate that s-SNOM contrast in a pseudo-heterodyne detection configuration depends on the oscillation amplitude of the reference mirror and that for reliable measurements of the contrast between different materials this aspect needs to be taken into consideration.
© 2014 Optical Society of America
In the past decade, scanning near-field optical microscopy (SNOM) has attracted a considerable amount of interest as nano-scale research is becoming more important with each day. The scattering-SNOM (s-SNOM) variants have been shown to provide very promising high resolution imaging capabilities in more than several experiments [1–3]. The working principle of the s-SNOM technique relies on a metallic probe being brought up in the close proximity of a sample surface and scanned across it, while a laser beam is focused on the interaction region between the probe and the sample. The electric field intensity of the laser beam causes the formation of an oscillating dipole [4–9] located in the near-field region, which radiates in the far-field range. This scattered light contains information from the near-field region and its detection is exploited so as to provide the s-SNOM image.
The main drawback of this technique consists in the presence of an intense background light (reflected from outside the interaction area between the probe and the sample), which makes the detection of the near-field scattered light very difficult. Reported solutions to this problem are based on the non-linearity of the scattered light signal on the tip-sample distance: when driving the probe into oscillation close above the sample with frequency fo and amplitude Aprobe, the modulated near-field signal will contain several higher harmonics of the oscillation frequency, while the background light signal will be constrained to the DC and fundamental frequency [8,10]. Thus, demodulating the backscattered light at higher harmonics, the influence of the background light will be diminished. It has been shown however that this method is not sufficient for an efficient background light suppression and, along with higher harmonics demodulation, three interferential detection methods are widely used: homodyne [8,11–13], heterodyne [1,11,14] and pseudo-heterodyne detection [15–17]. Among these three methods, the pseudo-heterodyne detection proved to be the most efficient to suppress the background-light and to lead to a good image contrast in s-SNOM imaging [15,18]. This detection configuration consists in a Michelson interferometer with one interferometer arm focused onto the tip (which will determine the formation of the oscillating dipole) and the other one (the reference beam) reflected off a harmonic oscillating reference mirror. The reference beam interferes with the scattered light from the near-field of the sample and the interference signal will contain the near-field information at frequencies , where fo is the probe oscillation frequency, M is the mirror oscillation frequency and n, m are integers. By using a lock-in amplifier locked at the spectral harmonics, the near-field signal is straightforward collected.
Although the pseudo-heterodyne method is considered at this time to be one of the best choices for s-SNOM detection, the influence of the involved parameters on the resulting image contrast is still not completely understood. The present work contributes to this area by providing theoretical and experimental evidence that the oscillation amplitude of the reference mirror has a strong influence on s-SNOM image contrast.
2. Materials and methods
Computer simulations have been performed based on the characteristics of the calibration sample that has been used in the experimental work. This sample contains 5x5 μm2 rectangular Platinum elements deposited on a Sapphire substrate. The Platinum domains have a thickness of 5 nm. The s-SNOM contrast corresponds to different intensities of the scattered light generated by the metal (Platinum, εPlatinum = −11.275-18.722i at wavelength 635 nm ) and by the dielectric material (Sapphire, εSapphire = 3.139 at wavelength 635 nm ).
By using the MATLAB software platform, we have performed simulations that reflect the influence of the reference mirror’s oscillation amplitude on the pseudo-heterodyne s-SNOM image contrast.
The parameters involved in all calculations and simulations are based on the configuration of our experimental homemade pseudo-heterodyne s-SNOM setup : beam wavelength, λ = 635 nm; probe’s oscillation frequency, fo = 50 kHz; oscillation amplitude of the probe, Aprobe = 75 nm; probe’s tip diameter, a = 30 nm; reference mirror oscillation frequency, M = 800 Hz. The long working distance objective required by the s-SNOM system had a numerical aperture NA = 0.42. The oscillation amplitude of the reference mirror was varied between 10 – 800 nm to study its influence in the image contrast. The scanning probe has a Platinum coated tip.
In s-SNOM, the image is generated by collecting the light that is scattered from the tip – sample’s surface interaction region. The intensity of the electric field scattered from the near-field region of the sample (Enf) can be represented as [4,5,21]:
In Eq. (1), Ei is the intensity of the incident electric field, αeff is the effective polarizability and Ct is a proportional constant (considered to have the value of 1019 for a reasonable interference ). The effective polarizability is given by [4,5]:22] (with d being the minimal separation tip-sample during probe’s oscillation above the sample and t is time). Thus,, which implies that .
The reference beam (phase modulated by means of the reference mirror’s oscillation) can be written as:
Here, , λ is the wavelength of the laser beam, A is the oscillation amplitude of the mirror, M is the oscillation frequency of the mirror, and t is time.
The intensity of the background electric field (amplitude modulated by the probe’s oscillation) can be expressed as :
Because the background field has no influence on the spectral components situated at (where n,m ≠ 0) , in a first approximation we neglect the background light given by Eq. (4). Thus, in the pseudo-heterodyne scheme, the waves Enf and Eref will interfere, and the interference signal (which represents the detected near-field signal), I, will be given by:Eq. (5) only the interference term is relevant, since the other terms will be constant. Therefore, I is proportional with the cosine of phase difference between the two waves:
3.1 Magnitude of the spectral components vs. oscillation amplitude of the reference mirror
For a better understanding of the reference wave’s influence on the interference signal, the phase of the near-field scattered wave can be kept constant (which is equivalent to the situation when the probe tip is situated at a constant distance from the sample) and the cosine in Eq. (6) can be viewed as the real part of an exponential complex number. In this scenario, the interference term in Eq. (5) can be written as:
The coefficients km are given by the Jacobi – Anger expansion and Jm is the Bessel function of order m. Thus, Eq. (9) shows that each spectral component at frequencies is strongly dependent on the oscillation amplitude A of the reference mirror.
This dependency is shown graphically computing the magnitude of km from Eq. (9) as a function of the mirror’s oscillation amplitude, A, which is varied between 10 nm and 800 nm. The result is plotted in Fig. 1, with continuous curves, for m = 1 and m = 2 (the first two harmonics), corresponding to the fundamental mirror frequency and second harmonic frequency, respectively.
For a second confirmation of the s-SNOM signal’s spectral components dependency on the mirror’s oscillation amplitude we compute the Fast Fourier Transform (FFT) of the interference signal given by Eq. (5). Using the dedicated function for FFT in MATLAB, the magnitude of any spectral component of the signal can be evaluated. The result is plotted in Fig. 1, with circled curves, for m = 1 and m = 2, corresponding to the fundamental mirror frequency and second harmonic frequency, respectively.
The differences between the two types of curves (Fig. 1) are caused by the variation of near-field wave phase during probe vibration (not taken into consideration in Eq. (9)) and by the fact that the calculation of the circled curves takes into consideration the optical properties of the materials involved.
An experimental confirmation of the s-SNOM signal dependency on the mirror’s oscillation amplitude is represented in Fig. 1 with black dots for values of the amplitude A in the interval 30 – 800 nm. The experiment was conducted by varying the oscillation amplitude of the mirror with a constant step while reading the output signal magnitude of the lock-in amplifier, which was locked on fo + mM, with m = 1 for a) and m = 2 for b). The probe was maintained in a close proximity to the Platinum sample surface, oscillating with frequency fo, at a fixed x, y position.
3.2 Platinum – Sapphire contrast vs. oscillation amplitude of the reference mirror
In the following section we take into consideration the fact that an s-SNOM instrument is capable of contrast differentiation between two different materials [5,8,25]. In the case of the presented experiment, a sample containing thin Platinum domains (εPlatinum = −11.275-18.722i  at wavelength 635 nm ) deposited on a Sapphire substrate (εSapphire = 3.139 at wavelength 635 nm ) was imaged, and the s-SNOM contrast between the two materials was computationally evaluated. For this, Eq. (1)–(5) and FFT of the interference intensity, I, have been used for both materials to represent the magnitude of the signal at fo + M and fo + 2M harmonic frequencies. For each of the amplitude values of the oscillating mirror, a pair of two magnitude values corresponding to the two materials, |ki|Platinum and |ki|Sapphire is obtained. For the image contrast calculation between the two materials the Michelson contrast formula  is used:
For a more comprehensive evaluation, the contrast is computed for four different minimal separations between the tip and the sample: d = 0.1 nm (tip is nearly touching the sample), d = 10 nm, d = 20 nm and d = 30 nm.
Figure 2 contains the results representing the variation of s-SNOM contrast between Platinum and Sapphire at (a) fo + M and (b) fo + 2M harmonic frequencies with the oscillation amplitude of the reference mirror, A.
Figure 2 shows that the s-SNOM material contrast obtained in the pseudo-heterodyne configuration is highly dependent on the oscillation amplitude of the reference mirror, especially when the detection is taken on the fundamental frequency of the mirror. Also, it can be noticed that the minimal separation between tip and sample has a major influence in the image contrast, but again the highest influence is observed in the case of the fundamental frequency of the mirror.
This simulation shows that in the proximity of mirror’s oscillation amplitude values for which the magnitude of spectral components |km| is zero (Fig. 1), the material contrast is decreasing, closing in to zero (Fig. 2). At the same time, it can be observed that the amplitude domains for which this effect occurs are getting larger when the distance d is increased between 0.1 – 30 nm. This increase of distance d affects as well the mean value of the contrast, yielding smaller values for the material contrast.
Although for the case m = 2 the contrast quickly drops to a low value when distance d is increased, it is preferred to use detection on m = 2 because it is less sensitive (than m = 1) to oscillation amplitude variations and the real variations of the parameter d are extremely small as the mechanical feedback system of the AFM keeps the minimal separation d to a constant value.
3.3 Influence of the cantilever instability on the image contrast
Next we take into consideration a more realistic case when, during a scanning session, the minimal position of the cantilever relative to the sample’s surface beneath it is not constant, but varies randomly in the small interval 0.1 – 10 nm . A computational evaluation of the contrast between the two materials as a function of the reference mirror’s oscillation amplitude was performed, using as imaging support the same sample as in previous experiments. For each value of the oscillation amplitude A, the minimal separation d between the tip and the sample is randomly modified in the interval 0.1 – 10 nm and the signal magnitude values corresponding to the two materials, |ki|Platinum and |ki|Sapphire are calculated. The corresponding image contrast is presented in Fig. 3 as a function of the oscillation amplitude, along with the contrast that results in an idealistic case with a perfectly oscillating cantilever, for a constant minimal tip-sample separation d = 0.1 nm. Figure 3 contains the results for two different frequency detection, (a) fo + M and (b) fo + 2M.
The effects of a mechanical unstable system can be noticed in Fig. 3. Figure 3(a) shows that if the oscillation of the reference mirror is also unstable and oscillates with an amplitude that randomly varies between 180 nm and 190 nm, the contrast variations will be consistent (between 31.9% and 63.8%).
We have used our s-SNOM setup to experimentally confirm this effect. During a scanning session of the sample containing Platinum domains on Sapphire substrate, a small external mechanical perturbation that caused a temporary instability of the probe vibration was deliberately introduced, resulting in a severe changing of the s-SNOM image contrast, as can be observed in Fig. 4. Figure 4(b) presents also an image contrast outside the Pt square boundaries – a scanning artifact that is due to the external mechanical perturbation.
3.4 Simulated and experimental s-SNOM images
A further step towards reproducing a realistic case was placed by taking into consideration the background light given in Eq. (4). A topographic image of Platinum rectangular domains deposited on the Sapphire substrate sample was collected by Atomic Force Microscopy and was used in our simulations to define the regions where the Platinum film is deposited (Fig. 5(a)). We choose three different amplitude values around the first point where the contrast in Fig. 2(a) is zero to evidence the inversion of the image contrast in the case of fo + M frequency detection. The three reference mirror’s oscillation amplitudes are A1 = 365 nm (Contrast ≈36%), A2 = 385 nm (Contrast ≈0%) and A3 = 405 nm (Contrast ≈-5%). In the frame of the performed simulation, the topographic image was computationally “scanned” pixel-by-pixel and line-by-line taking into accounts the identified Platinum regions. If a pixel is contained in a Platinum region, the complex electric permittivity will be εPlatinum; otherwise the complex electric permittivity will have the value of εSapphire. For each image pixel Eqs. (1)–(5) are applied, but the interference signal will contain the contribution of Ebkg given by Eq. (4):
For this signal the FFT is applied and the signal magnitude at fo + M is retained. When all pixels have been “scanned”, the values of all retained magnitudes are scaled to obtain a grayscale s-SNOM image, and the simulation is complete. Figures 5(b)–5(d) present the resulting simulated pseudo-heterodyne s-SNOM image. We considered a minimal separation d = 0.1 nm between the tip and the sample during the simulated scanning session. Also for the scanning experiments the distance d was estimated to a value of 0.1 nm using the AFM scanning software. The resulting simulated images are illustrated in Fig. 5 along with experimental s-SNOM images collected while using the same parameter values.
Figures 5(b)–5(d) and 5(e)–5(g) illustrate how the contrast between the Platinum rectangular domain and the Sapphire substrate varies as a function of the oscillation amplitude of the reference mirror, in the case of f + M frequency detection. In the simulated images topographic features are visible due to small variations of the cantilever’s oscillation amplitude, deliberately introduced in the simulation for a more realistic simulation. Figure 5 shows as well that the simulation and the experimental results correspond in a consistent proportion. The contrast values between Platinum and Sapphire for the three different mirror amplitudes, for both simulated and experimental images are presented in Table 1.
Similar simulations and experiments were done for signal detection on fo + 2M frequency. In this case, the oscillation amplitudes for which the determinations were made were chosen in a region where the contrast variation with oscillation amplitude is most evident from Fig. 2(b): A4 = 480 nm, A5 = 500 nm and A6 = 520 nm.
Figures 6(b)–6(d) and 6(e)–6(g) illustrate how the contrast between Platinum and Sapphire domains varies as a function of the oscillation amplitude of the reference mirror, when signal demodulation is performed on f + 2M frequency. Figure 6 as well shows that the simulation and the experimental results correspond in a consistent proportion. The contrast values between Platinum and Sapphire for the three mirror amplitudes, for both simulated and experimental images are presented in Table 2.
Comparing the two detection modes (on frequencies f + M and f + 2M) it can be clearly stated that detection in the second harmonic frequency of the mirror is preferred to detection on the fundamental frequency, as the tip-sample separation, d, is kept constant by the mechanical system of the AFM. Furthermore, in the region where detection on the fundamental frequency of the mirror gives a contrast that is highly dependent on the oscillation amplitude (e.g. 365 – 405 nm), for detection on the second harmonic of the mirror’s oscillation frequency a constant value of the contrast (~-41%) is obtained.
Our experiment demonstrates that in a pseudo-heterodyne s-SNOM configuration the image contrast between two different materials is highly dependent on the oscillation amplitude of the reference mirror, A. The contrast may take values of opposite signs for different amplitude values, and even zero values in some cases. The performed simulations show that it is advisable to avoid the values of the mirror’s oscillation amplitudes at which |km| (given by Eq. (9) and plotted in Fig. 1) is zero due to the fact that around these points the material contrast is the lowest. For future developments of a consistent method for material-specific identification using the pseudo-heterodyne s-SNOM scheme, this influence of the reference mirror must be taken into consideration.
The results show that the contrast between two different materials has a periodical behavior when varying the mirror’s oscillation amplitude (see Fig. 2), and its period is larger for higher harmonic demodulation of the mirror’s oscillation frequency. Figure 2 also reveals that for the |k2| (m = 2) spectral component the image contrast tends to maintain a constant value for wider ranges of the mirror’s oscillation amplitude than for the |k1| (m = 1) component. This leads to the conclusion that is better to detect the near-field signal based on higher harmonics of the mirror oscillation frequency, as small variations of the oscillation amplitude of the mirror will have a lower effect on image contrast.
Our experiment shows as well that the mechanical stability of the probe above the sample during scanning plays a key role when performing s-SNOM imaging. As Figs. 2 and 3 show, the contrast is highly dependent on tip-sample minimal separation and the contrast can drastically change during a scanning session if the minimal separation varies within just a few nanometers.
This theoretical and experimental study on image contrast for pseudo-heterodyned s-SNOM configuration clearly demonstrates that the oscillation amplitude of the reference mirror has an important influence on image contrast between different materials. The image contrast has a periodical behavior when varying the oscillation amplitude of the reference mirror. For higher harmonic demodulation, its period is larger and tends to maintain a constant value for wider ranges of the mirror’s oscillation amplitude. Our experiments reveal as well that the instabilities in the probe’s vibration have a severe influence on s-SNOM image contrast.
The presented work was supported by the UEFISCDI PN-II-PT-PCCA-2011-3.2-1162 Research Grant and by the EC 7th Framework Programme under grant agreement n° 280804 (LANIR).
References and links
1. A. Bek, R. Vogelgesang, and K. Kern, “Apertureless scanning near field optical microscope with sub-10 nm resolution,” Rev. Sci. Instrum. 77(4), 043703 (2006). [CrossRef]
4. J. M. Atkin, S. Berweger, A. C. Jones, and M. B. Raschke, “Nano-optical imaging and spectroscopy of order, phases, and domains in complex solids,” Adv. Phys. 61(6), 745–842 (2012). [CrossRef]
7. R. Hillenbrand, “Towards phonon photonics: scattering-type near-field optical microscopy reveals phonon-enhanced near-field interaction,” Ultramicroscopy 100(3-4), 421–427 (2004). [CrossRef] [PubMed]
8. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000). [CrossRef]
9. M. B. Raschke and C. Lienau, “Apertureless near-field optical microscopy: tip-sample coupling in elastic light scattering,” Appl. Phys. Lett. 83(24), 5089–5091 (2003). [CrossRef]
10. R. Esteban, R. Vogelgesang, and K. Kern, “Tip-substrate interaction in optical near-field microscopy,” Phys. Rev. B 75(19), 195410 (2007). [CrossRef]
11. L. Gomez, R. Bachelot, A. Bouhelier, G. P. Wiederrecht, S. Chang, S. K. Gray, F. Hua, S. Jeon, J. A. Rogers, M. E. Castro, S. Blaize, I. Stefanon, G. Lerondel, and P. Royer, “Apertureless scanning near-field optical microscopy: a comparison between homodyne and heterodyne approaches,” J. Opt. Soc. Am. B 23(5), 823–833 (2006). [CrossRef]
12. S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmarest, P. Gadenne, V. Shubin, A. Sarychev, and V. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82(22), 4520–4523 (1999). [CrossRef]
13. M. Esslinger, J. Dorfmüller, W. Khunsin, R. Vogelgesang, and K. Kern, “Background-free imaging of plasmonic structures with cross-polarized apertureless scanning near-field optical microscopy,” Rev. Sci. Instrum. 83(3), 033704 (2012). [CrossRef] [PubMed]
14. J. E. Hall, G. P. Wiederrecht, S. K. Gray, S. H. Chang, S. Jeon, J. A. Rogers, R. Bachelot, and P. Royer, “Heterodyne apertureless near-field scanning optical microscopy on periodic gold nanowells,” Opt. Express 15(7), 4098–4105 (2007). [CrossRef] [PubMed]
15. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006). [CrossRef]
16. M. Schnell, A. García-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoantennas,” Nat. Photonics 3(5), 287–291 (2009). [CrossRef]
17. Z. Nuño, B. Hessler, J. Ochoa, Y. S. Shon, C. Bonney, and Y. Abate, “Nanoscale subsurface- and material-specific identification of single nanoparticles,” Opt. Express 19(21), 20865–20875 (2011). [CrossRef] [PubMed]
18. M. Vaez-Iravani and R. Toledo-Crow, “Pure linear polarization imaging in near field scanning optical microscopy,” Appl. Phys. Lett. 63(2), 138–140 (1993). [CrossRef]
19. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
20. G. A. Stanciu, C. Stoichita, R. Hristu, S. G. Stanciu, and D. E. Tranca, “Metallic samples investigated by using a scattering near-field optical microscope,” in Proceedings of the 14 International Conference on the Transparent Optical Networks (ICTON), M. Jaworski, M. Marciniak, eds. (IEEE Comput., New York, 2012), p. 3. [CrossRef]
21. C. C. Liao and Y. L. Lo, “Phenomenological model combining dipole-interaction signal and background effects for analyzing modulated detection in apertureless scanning near-field optical microscopy,” Prog. Electromagn. Res. 112, 415–440 (2011).
22. B. Gotsmann, C. Seidel, B. Anczykowski, and H. Fuchs, “Conservative and dissipative tip-sample interaction forces probed with dynamic AFM,” Phys. Rev. B 60(15), 11051–11061 (1999). [CrossRef]
24. L. P. Yatsenko, B. W. Shore, and K. Bergmann, “An intuitive picture of the physics underlying optical ranging using frequency shifted feedback lasers seeded by a phase-modulated field,” Opt. Commun. 282(11), 2212–2216 (2009). [CrossRef]
25. A. J. Huber, D. Kazantsev, F. Keilmann, J. Wittborn, and R. Hillenbrand, “Simultaneous IR material recognition and conductivity mapping by nanoscale near-field microscopy,” Adv. Mater. 19(17), 2209–2212 (2007). [CrossRef]
27. R. García and A. San Paulo, “Attractive and repulsive tip-sample interaction regimes in tapping-mode atomic force microscopy,” Phys. Rev. B 60(7), 4961–4967 (1999). [CrossRef]