Abstract

In order to obtain broadband near-field infrared (IR) spectra, a Fourier-transform IR spectrometer (FT-IR) and a ceramic light source were used with a scattering-type scanning near-field optical microscope (s-SNOM). To suppress the background (far-field) scattering, the distance between the scattering probe and the sample was modulated with frequency Ω by a piezo-electric actuator, and the Ω component was extracted from the signal with a lock-in detection. With Ω=30 kHz, a peak-to-peak modulation amplitude of 198 nm, and a probe with smooth surface near the tip, broadband near-field IR spectra could be obtained in the 1200-2500 cm−1.

© 2011 OSA

1. Introduction

Infrared (IR) spectroscopy is a versatile analytical method in many fields such as biological, material, and earth sciences [1]. The selection rules are different between visible/Raman and IR spectroscopy. In addition, IR spectra may provide useful information that cannot be obtained with visible/Raman spectra. However, recent increasing needs for characterization of sub-micron materials by IR spectroscopy are facing the diffraction limit of IR light, preventing a spatial resolution higher than approximately 10 µm. Near-field optics has been developed for overcoming the diffraction limit [2, 3]. In the visible range, aperture-type fiber probes and scattering-type metal tip probes have been used for the near-field studies, such as photoluminescence and Raman spectroscopies [3]. In the IR range, on the other hand, available transmitting fiber probes have low transmittance and high cost. Therefore, scattering type metal tip probes have mainly been used for IR near-field experiments. However, the enhancement of near-field signal around a metal tip is reported to be only 10 to 103 fold in the mid-IR region, which is much smaller than the 106 fold enhancement for the visible case [3]. In addition, both the incident light and the scattered signal have the same wavelength in the IR near-field study, unlike the visible photoluminescence and Raman case. These features make the detection of IR near-field signal much more difficult than the visible case. Accordingly, intense IR laser sources have been used to increase the near-field signal intensity, and a cantilever modulation system has been used to distinguish the near-field scattering from the background scattering [49]. While these studies obtained near-field IR images having a spatial resolution of higher than 30 nm [9], the spectral bandwidth was limited to approximately 300 cm−1 (approximately 800 to 1100 cm−1) due to the laser source [4]. More broadband light sources such as a ceramic light source [10] or a synchrotron light source [11] were used in an attempt to obtain broadband near-field spectra in the mid-IR.

A cantilever modulation has been used in the laser type of near-field measurement. The sample to probe distance was modulated with a frequency of Ω, and the resulting first (Ω), second (2Ω), and third (3Ω) Fourier components were extracted to reduce the background scattering [5]. The first (Ω) component has been found to consist mostly of standing wave features and they were explained by the interference between light scattered from the sample surface and that from the cantilever edge [5, 8]. The higher harmonic components nΩ (n ≥ 2) have been employed for the reduction of this interference, taking advantage of strong nonlinear sample-tip distance (Z) dependence of the near-field signal. However, the interference feature still remains in the extracted higher harmonics nΩ (n ≥ 2). The 1Ω, 2Ω and 3Ω modulated components have been considered as the cross-term between the scattering lights from the probe shaft (E0) (including the standing wave) and the electromagnetic field localized around the probe tip (Ei i = 1,2,3) [5]. The detected signals (E0 Ei cos(φ0 – φi)) were affected by the phase shifts between E0 and Ei, which persist in the higher harmonic nΩ (n ≥ 2) signals [5].

The goal of the present study is to obtain broadband near-field IR spectra by combining a Fourier-transform IR spectrometer (FTIR) with a scattering type scanning near-field optical microscope (s-SNOM). A scattering type probe made of glass fiber coated by Au was used. Here, a step originally located near the tip of the probe was eliminated by the focused ion beam milling to reduce interference of scattered signals. A ceramic light source was employed to obtain broadband IR spectra [12,13]. The background scattering component was reduced by modulating the sample-tip distance by a piezo-electric sample stage [10]. Modulated 1Ω component was extracted from the detector output to obtain broadband IR spectra containing large contribution of near-field signals in this study.

2. Experimental methods

A commercially available FTIR spectrometer (FTIR-620, JASCO Co.) with a ceramic light source (blackbody temperature = 1300 K), a Ge coated KBr beam splitter and a s-SNOM system (NFIR 300N, JASCO Co.) equipped with a liquid nitrogen cooled photoconductive MCT detector (typical sensitivity D* = 1.9*1011) were used. Detected signals were processed in the FTIR spectrometer (low pass filter with the cut-off frequency (fc) = 3120Hz, with zero filling). The IR source becomes generally stable after 2 hours and the absorbance level remains typically within +- 0.001. The signals obtained in this study by the MCT detector were weak enough and non-linearity of the detector was not expected. Figure 1 schematically shows the experimental set-up used in this study. The output beam from a commercial FT-IR equipped with a ceramic IR source was focused by a Cassegrainian mirror onto the horizontal sample surface with a beam angle of around 45°. The incident IR beam was vertically polarized by a wire grid polarizer placed in the FT-IR optics. A piezoelectric actuator was placed beneath the probe tip on the sample stage to modulate the probe-sample distance. Scattered IR signals were collected by another Cassegrainian mirror at 90° from the incident direction and detected by an MCT detector. The first (Ω) and the second harmonic (2Ω) components of the MCT output were extracted by a lock-in amplifier. A sample was placed on the actuator, which was used to modulate the probe-sample distance.

 

Fig. 1 A schematic diagram of the experimental set-up used for the present broad-band near-field IR studies. A piezoelectric actuator placed beneath the probe tip is oscillated with a frequency of Ω (6 or 30 kHz) and the Ω or 2Ω frequency component is extracted from the MCT detector output using a lock-in amplifier.

Download Full Size | PPT Slide | PDF

Two modes of operations, namely the “integral mode” and the “spectral mode”, were used with this set-up. In the integral mode, the moving mirror of the FTIR interferometer was stopped to obtain total IR energy without dispersion, which was defined here as integral IR intensity. The output of the lock-in amplifier was directly recorded while other parameters such as probe-sample distance, sample position, and modulation amplitude were varied. In this mode, the modulation frequency (Ω) and amplitude of the actuator were 6 kHz and 33-198 nm (peak to peak), respectively. The lock-in amplifier used was PerkinElmer Model 5105 [10]. In the spectral mode operation, on the other hand, IR spectra were measured while scanning a mirror of the Michelson interferometer at 1 mm/s. The modulation frequency of 30 kHz and 198 nm peak-to-peak amplitude were used. The first (Ω) component was extracted from the detector output by another lock-in amplifier (NF Corporation LI5640), and input to the FT-IR data processing program to record an interferogram of the near-field signal.

Two types of probes shown in Fig. 2 , referred to as the “Type A” and “Type B”, were used in this study. Type A probe [Fig. 2(a)] was made with chemical etching of a SiO2 glass fiber. Then, Au was coated on the surface of the probe [14]. Type B probe [Fig. 2(b)] was obtained by removing the “step” located near the tip of Type A probe, indicated by the arrow in Fig. 2(a). The removal was done with a focused ion beam milling before Au coating. The radius of the tip was 250 nm for both types of probes.

 

Fig. 2 Scanning electron microscopic images of the two types of probes used in this study. In (a), the red arrow indicates the “step”, discussed in the text. The step was removed for Type B probe.

Download Full Size | PPT Slide | PDF

These probes were oscillated at their resonant frequency of about 16 kHz. When a sample surface, mounted on the piezoelectric XYZ stage, was approached to within a few tens of nanometers from the probe tip, the oscillation amplitude was decreased as a result of ‘shear force’ interaction with the sample [15]. The probe tip was illuminated by a diode laser. Then the amplitude of the reflected laser intensity was monitored by a Si photo detector, and was used to control the height (Z) of the piezoelectric stage via a feedback circuit. By recording the Z value as the sample was raster scanned in the XY plane, a topographic map of the sample surface was constructed.

3. Results and discussion

3.1 Modulated IR intensities against the probe-sample distance under the integral mode operation

Figure 3 shows the measured integral IR intensity as a function of probe-Au mirror distance for Types A and B probes with Ω and 2Ω components. As already mentioned, the IR signal intensity scattered from the probe tip was detected by the MCT detector without scanning the Michelson interferometer, and its output was analyzed by two lock-in amplifiers so as to extract 1Ω and 2Ω components (Ω = 6 kHz) simultaneously. The modulation amplitude of the piezo-electric actuator was 130 nm peak-to-peak. Obtained 2Ω integral intensities in Fig. 3 using Type A and B probes (oscillation amplitude: 132 nm) showed similar sharp decay with distance showing the signal localization [5]. While 1Ω integral intensities of Type A probe showed wavy features and remained over several micrometers, the 1Ω component of type B probe showed rapid decrease within about 300 nm. The 1Ω integral IR intensity decreased to 50% of maximum at around z= 300 nm, and increased slightly for the 2 - 3 μm region. This difference of IR signal decrease curves between the two types of probes can be due to the presence of the step structure near the tip of type A probe (indicated by the red arrow in Fig. 2). In fact, Hillenbrand and Keilmann (2002) reported similar wavy intensity curves for the cantilever tips. Brehm et al. (2008) interpreted these wavy forms to originate from interference between the near-field IR signal from the sample surface and that from the cantilever surface. Therefore, the observed wavy curve for Type A probe might also be due to a similar interference effect.

 

Fig. 3 Integral signal intensity as a function of sample-probe distance recorded with Types A and B probes and modulation frequencies of 1Ω and 2Ω. The 1Ω component for the type B probe showed strong localization.

Download Full Size | PPT Slide | PDF

For the type B probe without a step, both the 1Ω and 2Ω components in Fig. 3 show an enhancement of IR signal within 300 nm, which is comparable to the probe tip radius. IR signal intensities for the 1Ω component are 10 times larger than those for the 2Ω component (Fig. 3). Therefore, the 1Ω component for the type B probe is considered to be useful for the near-field IR measurements. The integral intensities of the both types of probes were mostly in-phase (phase: ~5°). Small phase shifts were considered to be originated from adhesive softness.

3.2 Mapping of modulated integral IR intensity

In order to examine the spatial resolution of 1Ω integral IR signals, a mapping of the modulated integral IR intensity was recorded with a standard sample shown in Fig. 4(a) . The standard sample was fabricated with the electron beam lithography. An organic film (ZEP-520A, ZEON Co.) was coated on an Au mirror, and an electron beam was applied to a rectangular area. The electron-damaged organic area was dissolved by a solvent (pentyl acetate) to obtain rectangular area (approximately 500 µm x 500 µm) of the Au mirror inside the organic film. An area of 8 µm x 1.6 µm including the border line between the Au mirror and the organic film was selected for the mapping measurement. This area was line-scanned with a velocity of 200 [nm/sec] over an 8 µm distance across the organic/Au boarder line (X direction scanning time: 40 seconds). Seven X-line scans were conducted on a 1.6 µm width to test and ensure the reproducibility of the data. The voltage of the piezo-electric stage was taken from the A/D converter (Interface, LPC-321116) with the sampling rate of 1kHz, and divided into 400 pixels for every X-line on the topographic image. Voltage signals were averaged for each pixel to represent sample heights as shown in Fig. 4(b). The 1Ω component of the lock-in amplifier was simultaneously obtained with the same A/D converter and divided and averaged into the same pixel as shown in Fig. 4(c). Note that the data in Figs. 4(b) and 4(c) were measured simultaneously, while keeping constant distance between the tip and the sample/Au via the shear-force feedback mentioned in Section 2.

 

Fig. 4 (a) Laser scanning confocal microscopic image of the standard sample used in this work, which was fabricated by electron beam lithography. A straight border line can be seen at the center of the picture between an organic film covering on the Au mirror (left) and the Au mirror (right). (b) Topographic image showing the border line between the organic film area (0 µm ≤ X ≤ 4 µm) and Au area (4 µm ≤ X ≤ 8 µm). The height of the organic film is approximately 300 nm. (c) IR integral intensity image of the same area as in (b). A sharp jump of IR intensity is observed within hundreds of nanometers at the border line. The data in (b) and (c) were measured simultaneously, while keeping a constant tip-sample distance via the shear-force feedback

Download Full Size | PPT Slide | PDF

The topographic image in Fig. 4(b) shows a sharp step of approximately 300 nm located near X = 4 µm. This step correspond to the border between the organic film and the Au mirror. While the Au mirror is seen to be fairly flat around Z = 0 nm, the organic film surface shows a height variations of about 50 nm. The IR signal mapping for Au mirror in Fig. 4(c) also indicates a relatively flat intensity distribution. On the other hand, for the organic film area, IR signals were lower than the Au area (approximately 75± 8%). As shown in Fig. 3, the IR signal intensity decreased to about 50% at 300 nm probe-Au distance with Type B probe. However, the organic film of 300 nm thickness showed larger signals (about 75% of the Au mirror). This difference of signal intensities is probably due to near-field signals from the organic film. The IR signal intensity image in Fig. 4(c) shows a rapid change at X = 4 µm with a width of about 300 nm, indicating a much higher spatial resolution than the IR wavelength (2.5 to 10 µm). The border positions in the seven line scan images in Fig. 4(c) show small fluctuations. This might be related to the near-field enhancement at the edge of the organic film.

3.3 Modulated integral IR intensities with different modulation amplitudes

In order to examine the dependence of oscillation amplitudes of piezo-electric actuator on the integral IR intensities for the type B probe, the oscillation amplitude was changed among 33, 66, 132 and 198 nm. Larger modulation amplitudes were not applied because of the technical limits of the instruments. The result is shown in Fig. 5(a) . For all the oscillation amplitudes, the 1Ω integral intensity showed a rapid decrease within approximately 300 nm, which is close to the tip radius. These curves were fitted by the following model function:

 

Fig. 5 (a) Integral IR intensity measured as a function of the distance between the probe tip and the Au mirror. The peak-to-peak modulation amplitudes are 33 (purple curve), 66 (blue), 132 (red), 198 (black) nm. (b) Parameters A (black dots), B (red dots) and (c) C, obtained from the fitting of the data in (a) using Eq. (1), plotted as a function of the oscillation amplitude. The broken lines are guide to the eye.

Download Full Size | PPT Slide | PDF

f(z)=A+Bez/C.

Here, z is the tip-Au distance, and the fitting parameters A, B, and C are expected to represent a offset component including z-independent background scattering, the magnitude and the spatial localization of the near-field signal, respectively. The results of the fitting are shown in Figs. 5(b) and 5(c). It is seen that the near-field component (parameter B) increases linearly with the amplitude. Therefore, the largest amplitude of 198 nm was employed for the following spectral mode experiments. The background parameter A also showed a linear increase with amplitude, and the localization parameter C showed a slight increase with amplitude. The origin for these results is unclear.

3.4 Broad-band IR spectra with 1Ω modulated component

The results of spectral mode measurements are described in this section. In obtaining broadband IR spectra, Ω was set to 30 kHz, which was well separated from the probe oscillation frequency of 16 kHz. As shown in Fig. 1, the in-phase 1Ω component from the lock-in amplifier was input to the FTIR processing unit to obtain an interferogram. Both type A and type B probes were used, and placed with the closest distance to Au mirror. Figure 6 shows the obtained IR spectra based on the 1Ω component of the scattered signal. In addition to the 1Ω spectra, a “reference spectrum” showing the intrinsic spectral distribution was also recorded without using the actuator and lock-in amplifier. Both of the reference spectrum and 1Ω spectra were obtained with 150 accumulations (measurement time ~4 min) and a spectral resolution of 16 cm−1. In Fig. 6, the reference spectrum is scaled down to approximately match the 1Ω spectra. The absorptions seen around 1600, 2330, and 3600 cm−1 are due to CO2 and H2O in the air. The spectrum measured with type A probe [(c) in Fig. 6] shows wavy features of about 1000 cm−1 periodicity. These features can be related to a standing wave of scattered light between the probe edge and the sample surface with 10 μm optical path difference, because only the probe step was removed while keeping all the other measurement parameters unchanged. Such an interference effect has been already suggested by several studies [5]. The spectrum measured with type B [(b) in Fig. 6] probe does not show wavy features. This can be understood by the absence of a step near the tip for the type B probe. In addition, the spectrum of type B probe clearly shows absorption features around 2330 cm−1 and 3600 cm−1 due to CO2 and H2O. These results indicate that the 1Ω component measured with the type B probe has potential to be used for obtaining broadband IR spectra in the 6000 to 800 cm−1 range.

 

Fig. 6 1Ω spectra measured with the type A probe (c: green) and the type B probe (b: blue) together with the reference IR spectrum (a: red) obtained without using actuator and lock-in amplifier.

Download Full Size | PPT Slide | PDF

3.5 Dependence of 1Ω spectra on the probe-Au distance

Figure 7 shows 1Ω spectra measured with type B probe at probe-Au distances z=0, 100 and 200 nm. For all the cases, the signal intensity decreased with increasing z. Note that the intensity in the lower wavenumber range (below ~ 2500 cm−1) decreased more significantly than that in the higher wave number range. For instance, the signal intensity at 2000 cm−1 decreased to approximately 1/4 from z=0 to 200 nm. Significant decrease of lower wave number components within 200 nm indicates that the low wave number component has a large contribution from the near-field region within the probe tip radius (250 nm). To our knowledge, this is the first demonstration of broadband near-field spectra in the mid-IR range with the ceramic light source.

 

Fig. 7 Modulated IR spectra with the type B probe with increasing probe - Au mirror distance from closest (a: blue) to 100 nm (b: green) and 200 nm (c: red).

Download Full Size | PPT Slide | PDF

In order to estimate the wave number dependence of near-field component, the spectrum at z=200 nm in Fig. 7 was subtracted from that at z=0 nm, and then the resulting spectrum was normalized by the reference spectrum in Fig. 6. The result is shown in Fig. 8 . The IR spectra measured at z > 200 nm are considered to contain large background contribution, as demonstrated in Fig. 5. Therefore, the spectrum resulting from this subtraction is expected to contain mostly near-field component. The spectrum in Fig. 8 shows an increasing trend from 2500 to 1200 cm−1. This result suggests larger near-field IR signals for lower wavenumber regions.

 

Fig. 8 Estimated near-field contribution in the 1Ω spectrum, given by the spectrum measured at z=0 nm [Fig. 7(a)] minus that at z=200 nm [Fig. 7(c)], normalized by the reference spectrum [Fig. 6(a)].

Download Full Size | PPT Slide | PDF

3.6 Computer simulations for the wave number dependence of near-field IR signal

In order to theoretically analyze the wave number dependence of near-field IR signals around the Au coated probe tip, computer simulations of electromagnetic field (|E|) compared with incident field (|E0|) at different wave numbers were performed using a free program Cassandra [16]. The 3D boundary element method was used to solve Maxwell’s equations for this configuration. First, an incident IR wavelength of 11 µm was applied around the Au coated probe tip with the tip radius of 250 nm [Fig. 9(a) ]. The relative electromagnetic field (|E|/|E0|) showed a strong localization within 250 nm distance from the probe tip [Fig. 9(a)]. The enhancement of electromagnetic field for the wavelength of 11 µm becomes larger for smaller probe tip radius [Fig. 9(b)]. The strong enhancement can be explained by the lightning-rod effect.

 

Fig. 9 Results of numerical calculations for the spatial and spectral distributions of near-field electric field around a metal probe tip. (a) The distribution of relative electromagnetic field (|E|/|E0|) in the XZ plane. The tip radius is 250 nm with an incident IR radiation of 11 µm wavelength. (b) Profile of |E|/|E0| as a function of distance from the probe tip for various probe tip radii (color: tip radius) = (black: 250 nm), (red: 500 nm) and (blue: 1000 nm). (c) The relative electromagnetic field at a distance of 50 nm from the probe tip as a function of wave number. The probe tip radii are 250, 500 and 1000 nm.

Download Full Size | PPT Slide | PDF

Second, the electromagnetic field at a distance of 50 nm from the Au probe tip (X, Z = 0 nm, - (radius + 50) nm) were plotted against the wavenumber (Fig. 9(c)). For the probe tip radius of 250 nm, the electromagnetic field increases significantly for smaller wave number (longer wavelength) below about 1500 cm−1 (Fig. 9(c)). The present computer simulations with different wavelengths show clearly the wavenumber dependence of near-field enhancement in the mid-IR region, which can be explained by the lightning-rod effect [17]. In the results of Fig. 9(c), with a larger probe tip radius, less enhancement of the electromagnetic field is seen. This is in agreement with the decay curves in Fig. 9(b). In addition, with a larger radius, the wave number region with large electromagnetic field enhancement becomes narrower. Therefore, a smaller probe tip radius would increase the width of wave number region for near-field measurement. These results of computer simulation support the wave number dependence of near-filed enhancement in our experimental studies, namely a larger enhancement of near-field signals for lower wave number region.

4. Conclusions

In order to obtain broadband near-field IR spectra, a piezo-electric actuator was placed on the sample stage of FT-IR with a ceramic light source combined with a s-SNOM. The following results were obtained by this modulation measurement:

  • (1) For type B probe without a step near the tip, both the 1Ω and 2Ω integral intensities rapidly decreased with tip-sample distance below 300 nm, which was comparable to the tip radius. This result indicates that a near-field signal was in fact obtained by our set-up based on a ceramic source. The integral intensity for the 1Ω component was 10 times higher than that for the 2Ω component.
  • (2) A mapping of the integral IR intensity was obtained on the surface of a standard sample fabricated by the electron beam lithography. The obtained mapping showed a rapid change of intensity within about 300 nm across the border between an organic film and an Au mirror. This corresponds to a much higher spatial resolution than the IR wavelength (2.5 to 10 µm), which further indicates the near-field nature of the obtained signal.
  • (3) To estimate the wavenumber dependence of the near-field signal, the 1Ω IR spectrum obtained with the type B probe at a distance of 200 nm from the Au mirror was subtracted from that at the closest distance, and the resulting spectrum was divided by the reference (unmodulated) spectrum. The obtained spectrum showed a broad distribution of intensity over at least 1200 to 2500 cm−1.

These results indicate that broadband near-field IR spectra with a wavenumber resolution of 16 cm−1 at least in the 1200 - 2500 cm−1 range could be obtained for the first time with the ceramic light source by using the modulation technique. Although the present result shows a great potential of our apparatus, further improvements are necessary in order to establish practical broadband near-field IR spectroscopy. In particular, IR absorption bands of some standard materials should be measured with our apparatus. For obtaining a higher signal-to-noise ratio, a brighter broadband IR source such as synchrotron radiation might be useful [11].

Acknowledgements

Fabrication of standard samples with the electron beam lithography was supported by Professor Hirokazu Tada and Dr. Masato Ara through Osaka University Trans-disciplinary Graduate and Refresher Programs for Education, Research and Training in the Fields of Nanoscience and Nanotechnology (OU-NANOPROGRAM). M. I. is supported by research assistantship of the Graduate School of Science, Osaka University and JASRI research studentship.

References and links

1. J. M. Hollas, Modern Spectroscopy, 3rd ed. (John Wiley and Sons, Chichester, 1996).

2. M. Ohtsu, (Ed.), Near-Field Nano/Atom Optics and Technology (Springer-Verlag, Tokyo, 1998).

3. S. Kawata, (Ed.), Near-Field Optics and Surface Plasmon Polaritons (Springer-Verlag, Berlin, 2001).

4. S. Amarie, T. Ganz, and F. Keilmann, “Mid-infrared near-field spectroscopy,” Opt. Express 17(24), 21794–21801 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-24-21794. [CrossRef]   [PubMed]  

5. 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]  

6. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000). [CrossRef]   [PubMed]  

7. H. G. von Ribbeck, M. Brehm, D. W. van der Weide, S. Winnerl, O. Drachenko, M. Helm, and F. Keilmann, “Spectroscopic THz near-field microscope,” Opt. Express 16(5), 3430–3438 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-5-3430. [CrossRef]   [PubMed]  

8. M. Brehm, A. Schliesser, F. Cajko, I. Tsukerman, and F. Keilmann, “Antenna-mediated back-scattering efficiency in infrared near-field microscopy,” Opt. Express 16(15), 11203–11215 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-11203. [CrossRef]   [PubMed]  

9. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999). [CrossRef]  

10. M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011). [CrossRef]  

11. Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011). [CrossRef]  

12. Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010). [CrossRef]  

13. N. Kuya, S. Nakashima, S. Okumura, M. Nakauchi, S. Kimura, and Y. Narita, “Near-field infrared microspectroscopy on the distribution of water and organics in submicron area,” in Physicochemistry of Water in Geological and Biological Systems E.D. S. Nakashima ed. (Universal Academy Press, Inc., Tokyo, 2004)

14. S. Mononobe and M. Ohtsu, “Fabrication of a Pencil-Shaped Fiber Probe for Near-Field Optics by Selective Chemical Etching,” J. Lightwave Technol. 14(10), 2231–2235 (1996). [CrossRef]  

15. E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992). [CrossRef]   [PubMed]  

16. Jan Fostier, “Open FMM” http://openfmm.sourceforge.net/index.php?id=0.

17. K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. J. M. Hollas, Modern Spectroscopy, 3rd ed. (John Wiley and Sons, Chichester, 1996).
  2. M. Ohtsu, (Ed.), Near-Field Nano/Atom Optics and Technology (Springer-Verlag, Tokyo, 1998).
  3. S. Kawata, (Ed.), Near-Field Optics and Surface Plasmon Polaritons (Springer-Verlag, Berlin, 2001).
  4. S. Amarie, T. Ganz, and F. Keilmann, “Mid-infrared near-field spectroscopy,” Opt. Express 17(24), 21794–21801 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-24-21794 .
    [Crossref] [PubMed]
  5. 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]
  6. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
    [Crossref] [PubMed]
  7. H. G. von Ribbeck, M. Brehm, D. W. van der Weide, S. Winnerl, O. Drachenko, M. Helm, and F. Keilmann, “Spectroscopic THz near-field microscope,” Opt. Express 16(5), 3430–3438 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-5-3430 .
    [Crossref] [PubMed]
  8. M. Brehm, A. Schliesser, F. Cajko, I. Tsukerman, and F. Keilmann, “Antenna-mediated back-scattering efficiency in infrared near-field microscopy,” Opt. Express 16(15), 11203–11215 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-11203 .
    [Crossref] [PubMed]
  9. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
    [Crossref]
  10. M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
    [Crossref]
  11. Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
    [Crossref]
  12. Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
    [Crossref]
  13. N. Kuya, S. Nakashima, S. Okumura, M. Nakauchi, S. Kimura, and Y. Narita, “Near-field infrared microspectroscopy on the distribution of water and organics in submicron area,” in Physicochemistry of Water in Geological and Biological Systems E.D. S. Nakashima ed. (Universal Academy Press, Inc., Tokyo, 2004)
  14. S. Mononobe and M. Ohtsu, “Fabrication of a Pencil-Shaped Fiber Probe for Near-Field Optics by Selective Chemical Etching,” J. Lightwave Technol. 14(10), 2231–2235 (1996).
    [Crossref]
  15. E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992).
    [Crossref] [PubMed]
  16. Jan Fostier, “Open FMM” http://openfmm.sourceforge.net/index.php?id=0 .
  17. K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003).
    [Crossref]

2011 (2)

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

2010 (1)

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

2009 (1)

2008 (2)

2003 (1)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003).
[Crossref]

2000 (2)

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]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

1999 (1)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
[Crossref]

1996 (1)

S. Mononobe and M. Ohtsu, “Fabrication of a Pencil-Shaped Fiber Probe for Near-Field Optics by Selective Chemical Etching,” J. Lightwave Technol. 14(10), 2231–2235 (1996).
[Crossref]

1992 (1)

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992).
[Crossref] [PubMed]

Aizawa, K.

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

Amarie, S.

Betzig, E.

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992).
[Crossref] [PubMed]

Brehm, M.

Cajko, F.

Crozier, K. B.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003).
[Crossref]

Drachenko, O.

Ganz, T.

Helm, M.

Hillenbrand, R.

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

Ikemoto, Y.

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

Inoue, T.

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

Ishikawa, M.

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

Katsura, M.

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Kebukawa, Y.

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

Keilmann, F.

Kino, G. S.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003).
[Crossref]

Kinoshita, T.

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

Knoll, B.

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]

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
[Crossref]

Mononobe, S.

S. Mononobe and M. Ohtsu, “Fabrication of a Pencil-Shaped Fiber Probe for Near-Field Optics by Selective Chemical Etching,” J. Lightwave Technol. 14(10), 2231–2235 (1996).
[Crossref]

Moriwaki, T.

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

Nakamura-Messenger, K.

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

Nakashima, S.

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

Ohtsu, M.

S. Mononobe and M. Ohtsu, “Fabrication of a Pencil-Shaped Fiber Probe for Near-Field Optics by Selective Chemical Etching,” J. Lightwave Technol. 14(10), 2231–2235 (1996).
[Crossref]

Okamura, H.

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Quate, C. F.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003).
[Crossref]

Schliesser, A.

Sundaramurthy, A.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003).
[Crossref]

Trautman, J. K.

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992).
[Crossref] [PubMed]

Tsukerman, I.

van der Weide, D. W.

von Ribbeck, H. G.

Winnerl, S.

Zolensky, M. E.

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

e-J. Surf. Sci. Nanotech. (1)

Y. Ikemoto, T. Moriwaki, T. Kinoshita, M. Ishikawa, S. Nakashima, and H. Okamura, “Near-Field Spectroscopy with Infrared Synchrotron Radiation Source,” e-J. Surf. Sci. Nanotech. 9, 63–66 (2011).
[Crossref]

J. Appl. Phys. (1)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003).
[Crossref]

J. Lightwave Technol. (1)

S. Mononobe and M. Ohtsu, “Fabrication of a Pencil-Shaped Fiber Probe for Near-Field Optics by Selective Chemical Etching,” J. Lightwave Technol. 14(10), 2231–2235 (1996).
[Crossref]

Meteorit. Planet. Sci. (1)

Y. Kebukawa, S. Nakashima, M. Ishikawa, K. Aizawa, T. Inoue, K. Nakamura-Messenger, and M. E. Zolensky, “Spatial distribution of organic matter in the Bells CM2 chondrite using near-field infrared microspectroscopy,” Meteorit. Planet. Sci. 45(3), 394–405 (2010).
[Crossref]

Nature (1)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999).
[Crossref]

Opt. Commun. (1)

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]

Opt. Express (3)

Phys. Rev. Lett. (1)

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

Science (1)

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992).
[Crossref] [PubMed]

Surf. Sci. Nanotech. (1)

M. Ishikawa, M. Katsura, S. Nakashima, K. Aizawa, T. Inoue, Y. Ikemoto, and H. Okamura, “Application of a Modulating Technique to Detect Near-Field Signals Using a Conventional IR Spectrometer with a Ceramic Light Source,” Surf. Sci. Nanotech. 9, 40–45 (2011).
[Crossref]

Other (5)

N. Kuya, S. Nakashima, S. Okumura, M. Nakauchi, S. Kimura, and Y. Narita, “Near-field infrared microspectroscopy on the distribution of water and organics in submicron area,” in Physicochemistry of Water in Geological and Biological Systems E.D. S. Nakashima ed. (Universal Academy Press, Inc., Tokyo, 2004)

J. M. Hollas, Modern Spectroscopy, 3rd ed. (John Wiley and Sons, Chichester, 1996).

M. Ohtsu, (Ed.), Near-Field Nano/Atom Optics and Technology (Springer-Verlag, Tokyo, 1998).

S. Kawata, (Ed.), Near-Field Optics and Surface Plasmon Polaritons (Springer-Verlag, Berlin, 2001).

Jan Fostier, “Open FMM” http://openfmm.sourceforge.net/index.php?id=0 .

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

A schematic diagram of the experimental set-up used for the present broad-band near-field IR studies. A piezoelectric actuator placed beneath the probe tip is oscillated with a frequency of Ω (6 or 30 kHz) and the Ω or 2Ω frequency component is extracted from the MCT detector output using a lock-in amplifier.

Fig. 2
Fig. 2

Scanning electron microscopic images of the two types of probes used in this study. In (a), the red arrow indicates the “step”, discussed in the text. The step was removed for Type B probe.

Fig. 3
Fig. 3

Integral signal intensity as a function of sample-probe distance recorded with Types A and B probes and modulation frequencies of 1Ω and 2Ω. The 1Ω component for the type B probe showed strong localization.

Fig. 4
Fig. 4

(a) Laser scanning confocal microscopic image of the standard sample used in this work, which was fabricated by electron beam lithography. A straight border line can be seen at the center of the picture between an organic film covering on the Au mirror (left) and the Au mirror (right). (b) Topographic image showing the border line between the organic film area (0 µm ≤ X ≤ 4 µm) and Au area (4 µm ≤ X ≤ 8 µm). The height of the organic film is approximately 300 nm. (c) IR integral intensity image of the same area as in (b). A sharp jump of IR intensity is observed within hundreds of nanometers at the border line. The data in (b) and (c) were measured simultaneously, while keeping a constant tip-sample distance via the shear-force feedback

Fig. 5
Fig. 5

(a) Integral IR intensity measured as a function of the distance between the probe tip and the Au mirror. The peak-to-peak modulation amplitudes are 33 (purple curve), 66 (blue), 132 (red), 198 (black) nm. (b) Parameters A (black dots), B (red dots) and (c) C, obtained from the fitting of the data in (a) using Eq. (1), plotted as a function of the oscillation amplitude. The broken lines are guide to the eye.

Fig. 6
Fig. 6

1Ω spectra measured with the type A probe (c: green) and the type B probe (b: blue) together with the reference IR spectrum (a: red) obtained without using actuator and lock-in amplifier.

Fig. 7
Fig. 7

Modulated IR spectra with the type B probe with increasing probe - Au mirror distance from closest (a: blue) to 100 nm (b: green) and 200 nm (c: red).

Fig. 8
Fig. 8

Estimated near-field contribution in the 1Ω spectrum, given by the spectrum measured at z=0 nm [Fig. 7(a)] minus that at z=200 nm [Fig. 7(c)], normalized by the reference spectrum [Fig. 6(a)].

Fig. 9
Fig. 9

Results of numerical calculations for the spatial and spectral distributions of near-field electric field around a metal probe tip. (a) The distribution of relative electromagnetic field (|E|/|E0|) in the XZ plane. The tip radius is 250 nm with an incident IR radiation of 11 µm wavelength. (b) Profile of |E|/|E0| as a function of distance from the probe tip for various probe tip radii (color: tip radius) = (black: 250 nm), (red: 500 nm) and (blue: 1000 nm). (c) The relative electromagnetic field at a distance of 50 nm from the probe tip as a function of wave number. The probe tip radii are 250, 500 and 1000 nm.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

f ( z ) = A + B e z / C .

Metrics