- Email: [email protected]
THz near-field imaging
1 May 1998
Optics Communications 150 Ž1998. 22–26
THz near-field imaging S. Hunsche a
a,)
, M. Koch b, I. Brener c , M.C. Nuss
a
Bell Laboratories – Lucent Technologies, 101 Crawfords Corner Rd., Holmdel, NJ 07733, USA b Sektion Physik, Ludwig-Maximilians UniÕersitat, Germany ¨ 80799 Munchen, ¨ c Bell Laboratories, Lucent Technologies, 600 Mountain AÕe, Murray Hill, NJ 07974, USA Received 13 August 1997; revised 29 December 1997; accepted 20 January 1998
Abstract We present first results of near-field imaging with ultrashort, broadband far-infrared pulses. By focusing the radiation into a tapered metal tip with a small exit aperture and scanning a sample in the near field of this aperture, sub-wavelength spatial resolution better than lr4 is demonstrated. q 1998 Published by Elsevier Science B.V. All rights reserved. PACS: 07.57.–c; 42.65.Re; 07.79.–v Keywords: THz imaging; Far-infrared microscopy; Near-field microscopy; Ultrafast technology
High-resolution imaging beyond the diffraction limit of conventional optical systems is rather commonly achieved in scanning near-field optical microscopy w1–3x. This technique is based on the fact that the distribution of light intensity immediately behind a small aperture, such as the end of a tapered, metal-coated optical fiber, is determined by the size of the aperture rather than diffraction or the wavelength of the radiation. Scanning a sample at a subwavelength distance to the aperture and measuring the transmitted light intensity can result in a spatial resolution of a few nanometers. Similarly, sub-wavelength resolution even down to lr10 6 w4x has been demonstrated with radio to microwave radiation, which can be efficiently confined using bipolar transmission lines, such as coaxial cables, terminated by a sharp conducting tip w4–7x or resonant antennas coupled to millimeter wave guides w8–10x. In both optical w11,12x and microwave w4x near-field imaging great care has to be taken to avoid topography-related artifacts induced by any kind of tip–sample distance regulation. In the THz or far-infrared region of the electromagnetic spectrum, near-field imaging was apparently hindered by
)
E-mail: [email protected]
the large losses of existing transmission lines and the low sensitivity of traditional FIR sources and detectors. To our knowledge there has been only one previous demonstration of FIR near-field probing to study the local properties of a semiconductor structure with a spatial resolution of approximately lr2 w13x. On the other hand, the THz region is of considerable interest for obtaining spectroscopic information about a large variety of physical systems. This has become particularly evident after the development of time-domain Terahertz spectroscopy ŽTHz-TDS., which is based on optoelectronic generation and detection of sub-picosecond electrical with ultrashort laser pulses and provides numerous advantages over more traditional FIR techniques w14x. Recently, we have developed a scanning FIR imaging system, based on THz-TDS, that is capable of producing ‘‘chemical contrast’’ images showing, e.g., the water content of biological samples or the doping profile of semiconductor wafers w15,16x. For a first demonstration of THz near-field imaging, we follow the most basic approach, similar to Ref. w13x, and insert a small aperture in the focus of the imaging system described in Ref. w15x. The experimental set-up is schematically depicted in Fig. 1. The THz emitter is a biased gold stripline on a semi-insulating GaAs substrate and the receiver a dipole antenna formed on low-temperature grown GaAs. The collimating and focusing optics for the THz
0030-4018r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 0 4 4 - 3
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
23
Fig. 1. Experimental set-up.
radiation consists of metal-coated off-axis paraboloid mirrors. In order to improve the transmission through the aperture, we use a tapered metal tube, analogous to the tapered fibers used in near-field scanning optical microscopes. This tube is formed by electro-plating a small conical aluminum tip with a CrrNi alloy. The full taper angle is 338, approximately matched to the f-number of the focusing optics. After removal of the aluminum cone and polishing of the CrrNi tip small, nearly circular apertures of d tip F 100 mm – corresponding to lr3 for a typical radiation frequency of 1 THz – can be easily obtained. The outer diameter of the polished tip is 2 mm and this area is brought in flat mechanical contact with the sample surfaces for most of the experiments presented below. Two tips were used, one with a circular aperture of 100 mm diameter and one with a slightly elliptical aperture of 50 = 80 mm. Fig. 2a shows THz time-domain data of reference pulses propagated through the set-up without aperture, and pulses transmitted through the elliptical aperture oriented parallel to the polarization of the THz pulses. The data shown are averaged over 500 single-scan waveforms using a fast scanning delay line at 20 Hz. According to the maximum peak-to-peak amplitude of the time-resolved data, the amplitude transmission coefficient of the aperture is approximately 1r130. Fourier transforms of the timedomain data indicate that this factor is strongly frequency dependent, as can be expected from the existence of a cut-off wavelength, which is lc s 1.71d for circular wave guides with diameter d w13x. The resulting high-pass filtering of the signal also accounts for the changes of the THz waveform from a well-defined single-cycle pulse towards a more oscillating structure. Although there is no sharp cut-off, probably due to the tapered geometry, the transmitted signal extends to lower frequencies for larger aperture sizes. This is shown in Fig. 2b, which depicts Fourier spectra of THz pulses transmitted through both apertures used. Trace Ža. and Žb. correspond to the 50 = 80 mm elliptical aperture and polarization of the THz pulses along the long Ža. and short Žb. axis, respectively, and trace Žc. is taken with the 100 mm diameter circular aperture. Below 0.25 THz, these spectra
are dominated by noise. Clearly, the low-frequency edge of the transmission spectra varies with the aperture size and additionally with polarization for the elliptical aperture. Qualitatively, the latter may be understood from the
Fig. 2. a.: THz waveforms transmitted through the tip with 50=80 mm elliptical aperture, oriented parallel to the polarization of the THz field Žsolid line., and reference waveforms, taken without aperture Ždashed line.. b.: Normalized Fourier spectra of THz pulses transmitted through the near-field tips used. Ža. 50=80 mm elliptical aperture, oriented parallel to the THz polarization; Žb. same aperture, oriented perpendicular to the polarization; Žc. 100 mm diameter circular aperture. Dash-dotted line: reference spectrum, without aperture.
24
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
Fig. 3. THz line-scans over a sharp metal edge. Ža. 50=80 mm elliptical aperture aligned parallel to the edge; sample: gold film on sapphire substrate. Žb. 100 mm circular aperture; sample: razor blade. Žc. Razor blade scan through free space focus without aperture.
transmission properties of an infinite slit with sub-wavelength width, which have been shown to be strongly polarization dependent w17,18x. Since no cut-off exists for polarization perpendicular to an infinite slit, it can be expected that the transmission through the elliptical aperture is mainly determined by the extension perpendicular to the polarization axis, in reasonable agreement with the experimental data. We note that it was not possible to determine the transmission coefficient through the aperture quantitatiÕely, since both the larger focal diameter in front of the aperture and the larger diffraction losses after passing it lead to additional losses for the low-frequency components of the THz pulses. In all cases however, there is significant signal amplitude for frequencies below 1.25 THz, i.e., wavelengths larger than twice the aperture size. To test the potential aperture-size defined spatial resolution, we scanned a sharp metal edge across the near field tips and measured the drop of the THz amplitude as a function of the edge position. In Fig. 3, these data are compared for the elliptical aperture oriented parallel to the edge Žcurve a. and the 100 mm aperture Žcurve b. with equivalent data taken with the ‘‘standard’’ THz imaging set-up, i.e., without aperture Žcurve c.. The sample used was the edge of a thin Ž250 nm. layer of gold evaporated on a sapphire substrate and scanned in mechanical contact with the near field tip for curve Ža. and a razor blade for Žb. and Žc.. The plotted signal is obtained by integration over a small frequency range after real-time Fourier transforming of the time-domain THz waveforms. The frequency ranges were chosen such that the averaged wavelength was 225 mm for all curves. Clearly, the near-field tips lead to a drastic improvement in resolution over the free-space focused imaging system. From the distance between the 90% and the 10% of maximum signal level,
we can quantify the spatial resolution for the near-field measurements as 140 mm for curve Žb. and 55 mm for curve Ža.. The latter almost perfectly matches the aperture diameter along the scan axis and corresponds to a spatial resolution of better than lr4, clearly indicating that the enhancement of resolution by the aperture is a near-field effect. The lower Žrelative. resolution obtained with the 100 mm aperture is probably a result of the wedge shape of the razor blade used, which resulted in a finite distance between the aperture and the scanning edge of approximately 20 mm. For this case the resolution is expected to be approximately the sum of aperture size and tip–sample distance, in reasonable agreement with the data. Since this strong dependence of the spatial resolution on the tip–sample distance may be regarded as a characteristic feature of near-field imaging we have performed scans over a line-pattern sample at different tip–sample distances, using the elliptical aperture oriented parallel with the line pattern. These data are shown in Fig. 4. The sample is part of a USAF-1951 resolution test pattern consisting of gold lines Ž250 nm thickness. on a high-resistivity silicon substrate Ž250 mm thickness., which is almost completely transparent to the THz radiation. The structures seen in Fig. 4 have linewidths of 198, 177, 157 and 140 mm, respectively. The THz signal in this measurement is the field amplitude at a fixed time delay, corresponding to the pulse maximum at a large distance from any sample structure, taken with a lock-in amplifier for better signal-to noise ratio. This signal is sensitive to both amplitude and phase changes, which leads to a stronger ‘‘overshoot’’ of the signal near an edge Žas compared with Fig. 3. and apparently to the triangular structure of the scanned signal
Fig. 4. THz scans over a line-pattern sample at various sample–tip separations. The sample structure is schematically shown at the bottom, where black bars correspond to gold covered areas. The curves are offset for clarity; ds 0 corresponds to mechanical contact between tip and sample.
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
instead of the expected ‘‘flat bottom’’ shape, quite similar to the data in Ref. w7x. We note however, that a periodic structure will generally cause a periodic modulation of the near-field signal, and that a decrease of modulation depth by a factor of two may be taken as a definition of the spatial resolution w3x. The fact that the scan at d s 0, corresponding to mechanical contact between tip and sample, shows no variation of modulation depth for the different line widths therefore indicates that the resolution is indeed much better than the smallest feature size of the sample. In contrast, at a sample–tip separation of 100 mm we observe an overall reduction of the signal level, which may be tentatively attributed to a near-field enhancement of the signal at d s 0, and more important a distinct reduction of the modulation depth between the 198 mm lines and the 140 mm lines by approximately a factor of two. We conclude that the spatial resolution in our experiments closely matches the common estimate in near-field imaging, namely the sum of aperture size and tip–sample distance. At larger separation however, the decay of spatial resolution appears to be slower, so that some residual structure of the 198 mm lines can still be distinguished at a separation of 400 mm. A detailed understanding of the signal in this regime would clearly require a precise modeling of the tip emission, diffraction by the sample structure and the imaging properties of the THz detection optics. To illustrate the imaging properties of the near-field aperture, Fig. 5 shows a two-dimensional scan over group 2 and 3 Žsmallest line widths 70 mm and 35 mm, respectively. of the resolution test target. None of the features in
25
this area can be resolved using the diffraction-limited imaging set-up without near-field tip. The data was taken with both the elliptical aperture and the polarization oriented along the y-axis of the figure. The gray scales depict the amplitude of the THz signal integrated in frequency domain from 0.6–2.3 THz. The corresponding average wavelength is 220 mm. Each point of the Ž90 = 100.-pixel image corresponds to an average of only two THz waveforms taken at a rate of 20 Hz, i.e. the total acquisition time for this image was only 15 minutes. The smallest resolvable features in this image are the vertical lines of group 3, element 3, which have a line width and separation of 50 mm. This agrees exactly with the horizontal diameter of the elliptical aperture used and with the resolution estimated from the data in Fig. 3. Based on the average wavelength of 220 mm, the resolution in the x-direction of the image is therefore lr4.4. Even for the upper boundary of the integration interval in frequency domain Žwhere only very little signal is present, according to Fig. 2b. the observed resolution is significantly better than lr2. Improvements in signal-to noise ratio and data acquisition rate should allow a restriction of the integration range to smaller frequencies, e.g., below 1 THz, which would result in a further improvement of the relative spatial resolution. Obviously, the best resolution is obtained only in the x-direction of Fig. 5, while the horizontal line patterns appear rather blurred, i.e., both resolution and contrast in the y-direction are worse than in the horizontal. One obvious reason for the reduced resolution is the larger extension of the elliptical aperture in y-direction. In addi-
Fig. 5. Near-field image of a resolution test pattern, taken with the 50 = 80 mm elliptical aperture aligned along y and the sample in contact with the focusing tip.
26
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
tion, the sample was continuously scanned along this axis using a dc motor, while THz transients are detected and analyzed at a rate of 20 Hz. However, the lower contrast of the horizontal lines and the apparent contrast reversal seen in the lines in the lower right corner might indicate a polarization dependence of the near-field signal. A polarization dependence of resolution and contrast has been predicted, e.g., in Ref. w17x. This question will be subject of further investigations. From a practical point of view, a complete high-resolution image with identical resolution along both axes of the sample might be obtained by combining two scans with orthogonal orientation of the sample. Finally, we would like to point out that the near-field imaging technique presented here does not require any sophisticated sample preparation and is not restricted to certain types of highly artificial samples. Furthermore, it seems possible to maintain all modes to obtain image contrast that have been previously demonstrated for freespace THz imaging w15x. In conclusion, we present a first demonstration of near-field imaging with broadband ultrashort THz pulses. We use a tapered metal tip with sub-wavelength exit aperture to confine the THz radiation and demonstrate far-infrared imaging with a spatial resolution of lr4 that is completely determined by the size of the aperture.
Acknowledgements We gratefully acknowledge valuable contributions by F. Beisser, J. Fromm, D.M. Mittleman, and R. Jacobsen as well as useful discussions with J. Stark and J. Feldmann. S.H. acknowledges funding by the Alexander von Humboldt Foundation.
References w1x D.W. Pohl, Scanning near-field optical microscopy, in: Advances in Optical and Electron Microscopy, Academic Press, 1991. w2x E. Betzig, J.K. Trautmann, Science 257 Ž1992. 189, and references therein. w3x M.A. Paesler, P.J. Moyer, Near-Field Optics, Wiley, New York, 1996. w4x B. Knoll, F. Keilmann, A. Kramer, R. Guckenberger, Appl. Phys. Lett. 70 Ž1997. 2667. w5x M. Fee, S. Chu, T.W. Hansch, Optics Comm. 69 Ž1989. 219. ¨ w6x F. Keilmann, D.W. van der Weide, T. Eickelkamp, R. Merz, D. Stockle, Optics Comm. 129 Ž1996. 15. ¨ w7x D.W. van der Weide, Appl. Phys. Lett. 70 Ž1997. 677. w8x M. Golosovsky, D. Davidov, Appl. Phys. Lett. 68 Ž1996. 1579. w9x T. Wei, X.-D. Xiang, W.G. Wallace-Freedman, P.G. Schulz, Appl. Phys. Lett. 68 Ž1996. 3506. w10x R.D. Grober, R.J. Schoelkopf, D.E. Prober, Appl. Phys. Lett. 70 Ž1997. 1354. w11x B. Hecht, H. Bielefeldt, Y. Inouye, D.W. Pohl, J. Appl. Phys. 81 Ž1997. 2492. w12x V. Sandoghdar, S. Wegschneider, G. Krausch, J. Mlynek, J. Appl. Phys. 81 Ž1997. 2499. w13x F. Keilmann, Infrared Phys. Technol. 36 Ž1995. 217. w14x M.C. Nuss, J. Orenstein, Terahertz time-domain spectroscopy, in: G. Gruener ŽEd.., Millimeter-Wave Spectroscopy of Solids, Springer Topics in Applied Physics, Vol. 74, Springer, Berlin, 1998. w15x B.B. Hu, M.C. Nuss, Optics Lett. 20 Ž1995. 1716. w16x D.M. Mittleman, R.H. Jacobsen, M.C. Nuss, IEEE J. Selected Top. Quantum Electron. 2 Ž1996. 679. w17x L. Novotny, D.W. Pohl, P. Regli, J. Opt. Soc. Am. A 11 Ž1994. 1768. w18x A. Nahata, T.F. Heinz, IEEE J. Selected Top. Quantum Electron. 2 Ž1996. 701.
Optics Communications 150 Ž1998. 22–26
THz near-field imaging S. Hunsche a
a,)
, M. Koch b, I. Brener c , M.C. Nuss
a
Bell Laboratories – Lucent Technologies, 101 Crawfords Corner Rd., Holmdel, NJ 07733, USA b Sektion Physik, Ludwig-Maximilians UniÕersitat, Germany ¨ 80799 Munchen, ¨ c Bell Laboratories, Lucent Technologies, 600 Mountain AÕe, Murray Hill, NJ 07974, USA Received 13 August 1997; revised 29 December 1997; accepted 20 January 1998
Abstract We present first results of near-field imaging with ultrashort, broadband far-infrared pulses. By focusing the radiation into a tapered metal tip with a small exit aperture and scanning a sample in the near field of this aperture, sub-wavelength spatial resolution better than lr4 is demonstrated. q 1998 Published by Elsevier Science B.V. All rights reserved. PACS: 07.57.–c; 42.65.Re; 07.79.–v Keywords: THz imaging; Far-infrared microscopy; Near-field microscopy; Ultrafast technology
High-resolution imaging beyond the diffraction limit of conventional optical systems is rather commonly achieved in scanning near-field optical microscopy w1–3x. This technique is based on the fact that the distribution of light intensity immediately behind a small aperture, such as the end of a tapered, metal-coated optical fiber, is determined by the size of the aperture rather than diffraction or the wavelength of the radiation. Scanning a sample at a subwavelength distance to the aperture and measuring the transmitted light intensity can result in a spatial resolution of a few nanometers. Similarly, sub-wavelength resolution even down to lr10 6 w4x has been demonstrated with radio to microwave radiation, which can be efficiently confined using bipolar transmission lines, such as coaxial cables, terminated by a sharp conducting tip w4–7x or resonant antennas coupled to millimeter wave guides w8–10x. In both optical w11,12x and microwave w4x near-field imaging great care has to be taken to avoid topography-related artifacts induced by any kind of tip–sample distance regulation. In the THz or far-infrared region of the electromagnetic spectrum, near-field imaging was apparently hindered by
)
E-mail: [email protected]
the large losses of existing transmission lines and the low sensitivity of traditional FIR sources and detectors. To our knowledge there has been only one previous demonstration of FIR near-field probing to study the local properties of a semiconductor structure with a spatial resolution of approximately lr2 w13x. On the other hand, the THz region is of considerable interest for obtaining spectroscopic information about a large variety of physical systems. This has become particularly evident after the development of time-domain Terahertz spectroscopy ŽTHz-TDS., which is based on optoelectronic generation and detection of sub-picosecond electrical with ultrashort laser pulses and provides numerous advantages over more traditional FIR techniques w14x. Recently, we have developed a scanning FIR imaging system, based on THz-TDS, that is capable of producing ‘‘chemical contrast’’ images showing, e.g., the water content of biological samples or the doping profile of semiconductor wafers w15,16x. For a first demonstration of THz near-field imaging, we follow the most basic approach, similar to Ref. w13x, and insert a small aperture in the focus of the imaging system described in Ref. w15x. The experimental set-up is schematically depicted in Fig. 1. The THz emitter is a biased gold stripline on a semi-insulating GaAs substrate and the receiver a dipole antenna formed on low-temperature grown GaAs. The collimating and focusing optics for the THz
0030-4018r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 0 3 0 - 4 0 1 8 Ž 9 8 . 0 0 0 4 4 - 3
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
23
Fig. 1. Experimental set-up.
radiation consists of metal-coated off-axis paraboloid mirrors. In order to improve the transmission through the aperture, we use a tapered metal tube, analogous to the tapered fibers used in near-field scanning optical microscopes. This tube is formed by electro-plating a small conical aluminum tip with a CrrNi alloy. The full taper angle is 338, approximately matched to the f-number of the focusing optics. After removal of the aluminum cone and polishing of the CrrNi tip small, nearly circular apertures of d tip F 100 mm – corresponding to lr3 for a typical radiation frequency of 1 THz – can be easily obtained. The outer diameter of the polished tip is 2 mm and this area is brought in flat mechanical contact with the sample surfaces for most of the experiments presented below. Two tips were used, one with a circular aperture of 100 mm diameter and one with a slightly elliptical aperture of 50 = 80 mm. Fig. 2a shows THz time-domain data of reference pulses propagated through the set-up without aperture, and pulses transmitted through the elliptical aperture oriented parallel to the polarization of the THz pulses. The data shown are averaged over 500 single-scan waveforms using a fast scanning delay line at 20 Hz. According to the maximum peak-to-peak amplitude of the time-resolved data, the amplitude transmission coefficient of the aperture is approximately 1r130. Fourier transforms of the timedomain data indicate that this factor is strongly frequency dependent, as can be expected from the existence of a cut-off wavelength, which is lc s 1.71d for circular wave guides with diameter d w13x. The resulting high-pass filtering of the signal also accounts for the changes of the THz waveform from a well-defined single-cycle pulse towards a more oscillating structure. Although there is no sharp cut-off, probably due to the tapered geometry, the transmitted signal extends to lower frequencies for larger aperture sizes. This is shown in Fig. 2b, which depicts Fourier spectra of THz pulses transmitted through both apertures used. Trace Ža. and Žb. correspond to the 50 = 80 mm elliptical aperture and polarization of the THz pulses along the long Ža. and short Žb. axis, respectively, and trace Žc. is taken with the 100 mm diameter circular aperture. Below 0.25 THz, these spectra
are dominated by noise. Clearly, the low-frequency edge of the transmission spectra varies with the aperture size and additionally with polarization for the elliptical aperture. Qualitatively, the latter may be understood from the
Fig. 2. a.: THz waveforms transmitted through the tip with 50=80 mm elliptical aperture, oriented parallel to the polarization of the THz field Žsolid line., and reference waveforms, taken without aperture Ždashed line.. b.: Normalized Fourier spectra of THz pulses transmitted through the near-field tips used. Ža. 50=80 mm elliptical aperture, oriented parallel to the THz polarization; Žb. same aperture, oriented perpendicular to the polarization; Žc. 100 mm diameter circular aperture. Dash-dotted line: reference spectrum, without aperture.
24
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
Fig. 3. THz line-scans over a sharp metal edge. Ža. 50=80 mm elliptical aperture aligned parallel to the edge; sample: gold film on sapphire substrate. Žb. 100 mm circular aperture; sample: razor blade. Žc. Razor blade scan through free space focus without aperture.
transmission properties of an infinite slit with sub-wavelength width, which have been shown to be strongly polarization dependent w17,18x. Since no cut-off exists for polarization perpendicular to an infinite slit, it can be expected that the transmission through the elliptical aperture is mainly determined by the extension perpendicular to the polarization axis, in reasonable agreement with the experimental data. We note that it was not possible to determine the transmission coefficient through the aperture quantitatiÕely, since both the larger focal diameter in front of the aperture and the larger diffraction losses after passing it lead to additional losses for the low-frequency components of the THz pulses. In all cases however, there is significant signal amplitude for frequencies below 1.25 THz, i.e., wavelengths larger than twice the aperture size. To test the potential aperture-size defined spatial resolution, we scanned a sharp metal edge across the near field tips and measured the drop of the THz amplitude as a function of the edge position. In Fig. 3, these data are compared for the elliptical aperture oriented parallel to the edge Žcurve a. and the 100 mm aperture Žcurve b. with equivalent data taken with the ‘‘standard’’ THz imaging set-up, i.e., without aperture Žcurve c.. The sample used was the edge of a thin Ž250 nm. layer of gold evaporated on a sapphire substrate and scanned in mechanical contact with the near field tip for curve Ža. and a razor blade for Žb. and Žc.. The plotted signal is obtained by integration over a small frequency range after real-time Fourier transforming of the time-domain THz waveforms. The frequency ranges were chosen such that the averaged wavelength was 225 mm for all curves. Clearly, the near-field tips lead to a drastic improvement in resolution over the free-space focused imaging system. From the distance between the 90% and the 10% of maximum signal level,
we can quantify the spatial resolution for the near-field measurements as 140 mm for curve Žb. and 55 mm for curve Ža.. The latter almost perfectly matches the aperture diameter along the scan axis and corresponds to a spatial resolution of better than lr4, clearly indicating that the enhancement of resolution by the aperture is a near-field effect. The lower Žrelative. resolution obtained with the 100 mm aperture is probably a result of the wedge shape of the razor blade used, which resulted in a finite distance between the aperture and the scanning edge of approximately 20 mm. For this case the resolution is expected to be approximately the sum of aperture size and tip–sample distance, in reasonable agreement with the data. Since this strong dependence of the spatial resolution on the tip–sample distance may be regarded as a characteristic feature of near-field imaging we have performed scans over a line-pattern sample at different tip–sample distances, using the elliptical aperture oriented parallel with the line pattern. These data are shown in Fig. 4. The sample is part of a USAF-1951 resolution test pattern consisting of gold lines Ž250 nm thickness. on a high-resistivity silicon substrate Ž250 mm thickness., which is almost completely transparent to the THz radiation. The structures seen in Fig. 4 have linewidths of 198, 177, 157 and 140 mm, respectively. The THz signal in this measurement is the field amplitude at a fixed time delay, corresponding to the pulse maximum at a large distance from any sample structure, taken with a lock-in amplifier for better signal-to noise ratio. This signal is sensitive to both amplitude and phase changes, which leads to a stronger ‘‘overshoot’’ of the signal near an edge Žas compared with Fig. 3. and apparently to the triangular structure of the scanned signal
Fig. 4. THz scans over a line-pattern sample at various sample–tip separations. The sample structure is schematically shown at the bottom, where black bars correspond to gold covered areas. The curves are offset for clarity; ds 0 corresponds to mechanical contact between tip and sample.
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
instead of the expected ‘‘flat bottom’’ shape, quite similar to the data in Ref. w7x. We note however, that a periodic structure will generally cause a periodic modulation of the near-field signal, and that a decrease of modulation depth by a factor of two may be taken as a definition of the spatial resolution w3x. The fact that the scan at d s 0, corresponding to mechanical contact between tip and sample, shows no variation of modulation depth for the different line widths therefore indicates that the resolution is indeed much better than the smallest feature size of the sample. In contrast, at a sample–tip separation of 100 mm we observe an overall reduction of the signal level, which may be tentatively attributed to a near-field enhancement of the signal at d s 0, and more important a distinct reduction of the modulation depth between the 198 mm lines and the 140 mm lines by approximately a factor of two. We conclude that the spatial resolution in our experiments closely matches the common estimate in near-field imaging, namely the sum of aperture size and tip–sample distance. At larger separation however, the decay of spatial resolution appears to be slower, so that some residual structure of the 198 mm lines can still be distinguished at a separation of 400 mm. A detailed understanding of the signal in this regime would clearly require a precise modeling of the tip emission, diffraction by the sample structure and the imaging properties of the THz detection optics. To illustrate the imaging properties of the near-field aperture, Fig. 5 shows a two-dimensional scan over group 2 and 3 Žsmallest line widths 70 mm and 35 mm, respectively. of the resolution test target. None of the features in
25
this area can be resolved using the diffraction-limited imaging set-up without near-field tip. The data was taken with both the elliptical aperture and the polarization oriented along the y-axis of the figure. The gray scales depict the amplitude of the THz signal integrated in frequency domain from 0.6–2.3 THz. The corresponding average wavelength is 220 mm. Each point of the Ž90 = 100.-pixel image corresponds to an average of only two THz waveforms taken at a rate of 20 Hz, i.e. the total acquisition time for this image was only 15 minutes. The smallest resolvable features in this image are the vertical lines of group 3, element 3, which have a line width and separation of 50 mm. This agrees exactly with the horizontal diameter of the elliptical aperture used and with the resolution estimated from the data in Fig. 3. Based on the average wavelength of 220 mm, the resolution in the x-direction of the image is therefore lr4.4. Even for the upper boundary of the integration interval in frequency domain Žwhere only very little signal is present, according to Fig. 2b. the observed resolution is significantly better than lr2. Improvements in signal-to noise ratio and data acquisition rate should allow a restriction of the integration range to smaller frequencies, e.g., below 1 THz, which would result in a further improvement of the relative spatial resolution. Obviously, the best resolution is obtained only in the x-direction of Fig. 5, while the horizontal line patterns appear rather blurred, i.e., both resolution and contrast in the y-direction are worse than in the horizontal. One obvious reason for the reduced resolution is the larger extension of the elliptical aperture in y-direction. In addi-
Fig. 5. Near-field image of a resolution test pattern, taken with the 50 = 80 mm elliptical aperture aligned along y and the sample in contact with the focusing tip.
26
S. Hunsche et al.r Optics Communications 150 (1998) 22–26
tion, the sample was continuously scanned along this axis using a dc motor, while THz transients are detected and analyzed at a rate of 20 Hz. However, the lower contrast of the horizontal lines and the apparent contrast reversal seen in the lines in the lower right corner might indicate a polarization dependence of the near-field signal. A polarization dependence of resolution and contrast has been predicted, e.g., in Ref. w17x. This question will be subject of further investigations. From a practical point of view, a complete high-resolution image with identical resolution along both axes of the sample might be obtained by combining two scans with orthogonal orientation of the sample. Finally, we would like to point out that the near-field imaging technique presented here does not require any sophisticated sample preparation and is not restricted to certain types of highly artificial samples. Furthermore, it seems possible to maintain all modes to obtain image contrast that have been previously demonstrated for freespace THz imaging w15x. In conclusion, we present a first demonstration of near-field imaging with broadband ultrashort THz pulses. We use a tapered metal tip with sub-wavelength exit aperture to confine the THz radiation and demonstrate far-infrared imaging with a spatial resolution of lr4 that is completely determined by the size of the aperture.
Acknowledgements We gratefully acknowledge valuable contributions by F. Beisser, J. Fromm, D.M. Mittleman, and R. Jacobsen as well as useful discussions with J. Stark and J. Feldmann. S.H. acknowledges funding by the Alexander von Humboldt Foundation.
References w1x D.W. Pohl, Scanning near-field optical microscopy, in: Advances in Optical and Electron Microscopy, Academic Press, 1991. w2x E. Betzig, J.K. Trautmann, Science 257 Ž1992. 189, and references therein. w3x M.A. Paesler, P.J. Moyer, Near-Field Optics, Wiley, New York, 1996. w4x B. Knoll, F. Keilmann, A. Kramer, R. Guckenberger, Appl. Phys. Lett. 70 Ž1997. 2667. w5x M. Fee, S. Chu, T.W. Hansch, Optics Comm. 69 Ž1989. 219. ¨ w6x F. Keilmann, D.W. van der Weide, T. Eickelkamp, R. Merz, D. Stockle, Optics Comm. 129 Ž1996. 15. ¨ w7x D.W. van der Weide, Appl. Phys. Lett. 70 Ž1997. 677. w8x M. Golosovsky, D. Davidov, Appl. Phys. Lett. 68 Ž1996. 1579. w9x T. Wei, X.-D. Xiang, W.G. Wallace-Freedman, P.G. Schulz, Appl. Phys. Lett. 68 Ž1996. 3506. w10x R.D. Grober, R.J. Schoelkopf, D.E. Prober, Appl. Phys. Lett. 70 Ž1997. 1354. w11x B. Hecht, H. Bielefeldt, Y. Inouye, D.W. Pohl, J. Appl. Phys. 81 Ž1997. 2492. w12x V. Sandoghdar, S. Wegschneider, G. Krausch, J. Mlynek, J. Appl. Phys. 81 Ž1997. 2499. w13x F. Keilmann, Infrared Phys. Technol. 36 Ž1995. 217. w14x M.C. Nuss, J. Orenstein, Terahertz time-domain spectroscopy, in: G. Gruener ŽEd.., Millimeter-Wave Spectroscopy of Solids, Springer Topics in Applied Physics, Vol. 74, Springer, Berlin, 1998. w15x B.B. Hu, M.C. Nuss, Optics Lett. 20 Ž1995. 1716. w16x D.M. Mittleman, R.H. Jacobsen, M.C. Nuss, IEEE J. Selected Top. Quantum Electron. 2 Ž1996. 679. w17x L. Novotny, D.W. Pohl, P. Regli, J. Opt. Soc. Am. A 11 Ž1994. 1768. w18x A. Nahata, T.F. Heinz, IEEE J. Selected Top. Quantum Electron. 2 Ž1996. 701.