Spectroscopic near-field microscopy using frequency combs in the mid-infrared

We introduce a new concept of spectroscopic near-field optical microscopy that records broad infrared spectra at each pixel during scanning. Two coherent beams with harmonic frequency-comb spectra are employed, one for illuminating the scanning tip, the other as reference for multi-heterodyne detection of the scattered light. Our implementation yields 200 cm-1 wide amplitude and phase spectra centered at 950 cm-1 (this band can be tuned between 700 and 1400 cm -1). We introduce a new technique of background suppression enabled by the short, 10 μs ”snapshot” acquisition of infrared spectra which allows time-resolving the tapping motion. Thus we demonstrate broad-band mid-infrared near-field imaging that is essentially free of background artefacts. © 2006 Optical Society of America OCIS codes: (180.5810) Scanning microscopy; (240.6490) Spectroscopy, surface; (290.1350) Backscattering; (290.5870) Scattering, Rayleigh; (300.6300) Spectroscopy, Fourier transforms; (300.6310) Spectroscopy, heterodyne; (300.6340) Spectroscopy, infrared References and links 1. J. Wessel, “Surface-enhanced optical microscopy,” J. Opt. Soc. Am. B 2, 1538–1540 (1985). 2. F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 Angstrom resolution,” Science 269, 1083–1085 (1995). 3. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000). 4. A. Lahrech, R. Bachelot, P. Gleyzes, and A. C. Boccara, “Infrared-reflection-mode near-field microscopy using an apertureless probe with a resolution of λ /600,” Opt. 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Introduction
Light scattering from a scanning-probe tip is the basis of the apertureless optical near-field microscope (SNOM) [1][2][3] that offers unprecedented spatial resolution < 20 nm even with long-wavelength illumination in the mid-infrared [4][5][6][7][8][9].If realized as a general, truely spectroscopic SNOM this instrument could enable chemical recognition at the nanoscale, which is highly desirable for the nanosciences.One possible mode of probing the material-characteristic vibrational "fingerprint" features is to illuminate the tip in the near-visible and detect the Raman-scattered spectrum.However, the Raman scattering is basically very weak even with the strong efficiency enhancement that is inducible by the tip (tip-enhanced Raman scattering, TERS) [1,10,11].Alternatively, interaction with the molecular-vibrational "fingerprints" can be realized by illuminating the tip in the mid-infrared and detecting the elastic (Rayleigh) scattering.Such scattering SNOM (s-SNOM) offers astounding sensitivity as we demonstrated by the infrared near-field spectra of the phonon resonance of dielectrics [7], the molecular-vibrational resonance of polymers [8], and recently, with single-virus amide-I vibrational mapping [12].The latter gave a strong spectral contrast with only 10 zl = (22 nm) 3 of material volume.It appears feasible that the s-SNOM could determine and analyze the infrared spectrum of even a single macromolecule of (2nm) 3 .
Unfortunately only monochromatic s-SNOMs have been available up to now.Spectroscopic contrasts could thus only be explored by comparing many repeated images of the same scene, with sequentially altered infrared frequency.This procedure is very time-consuming, and furthermore, the subsequent evaluation of all recorded images to assign a spectrum to each pixel is prone to systematic errors.The sample generally drifts, and the imaging conditions do not remain stable, especially when the beam alignment and the tapping motion change, or when the tip erodes or becomes contaminated.A spectrally-parallel operation of s-SNOM, on the other hand, would fully overcome these drawbacks.The key challenges are to find a well-focusable infrared illumination that delivers all frequencies of interest simultaneously, and a fast spectrometer that can assess and assign the scattered light spectrum.As an aside we remark that a hot sample has recently been observed to generate rudimentary near-field signals, in a novel emission mode of s-SNOM operation [13].

Broadband infrared spectrometry
The traditional broadband source for infrared spectroscopy has been the thermal emitter.At a temperature of 1000 K its emission power per cm 2 surface area into half space is maximally 0.24 W when integrated over a 10% wide band centered at 10 μm wavelength.The spectral analysis of thermal radiation historically started with the time-consuming sequential spectroscopy of rotating a diffraction grating.A large step forward came with computers that enabled parallel spectroscopy (Fellget advantage) based on the Fourier transform of an interferometric record of infrared power (FTIR spectroscopy).For this, thermal radiation passes through an interferometer, often of Michelson type, and an interferogram is recorded by mechanically scanning the retardation between two partial beams.State-of-the-art FTIR spectrometers serve as ubiquiteous analytical instruments in chemistry, biology and physics.
Since here we are interested in highly localized scattering it is essential to calculate the power available for illuminating a probing tip.Thermal radiation is incoherent and can not be focused to a higher intensity than present at the emitting surface, after a fundamental law of thermodynamics.With the source parameters above, this limit is 0.24 W/cm 2 = 0.24 μW/(10 μm) 2 , but only a fraction of this value will be attainable with a realistic lens or mirror arrangement.Monochromatic s-SNOM in the mid-infrared, however, operates with about 5 orders of magnitude higher intensity.Optimally a 10 mW coherent beam is focused to a diffraction-limited spot of about 10 μm diameter, so that a 128x128 pixel image can be recorded in about 10 min [14].
Higher power is not advisable because it causes unwanted heating of the cantilever and the sample.Lower power can be tolerated, but at the expense of lengthened recording time.Clearly for this reason broadband thermal illumination of s-SNOM has not yet been realized.Still it may become possible with future improvements of s-SNOM technology such as significantly better detectors, collection optics, or near-field antenna efficiencies (the latter we define as the combined efficiencies of the scattering tip to convert the free-space beam into a near-field spot at its apex, and back into a free-space beam).
Coherent broadband infrared radiation is available from synchrotron sources or from spectral conversion of pulsed laser beams [15].In both cases the beam can in principle be focused to a diffraction-limited spot size, and the spectral analysis can be done by interferometry.Our present study explores the latter source, employing a nonlinear-optic process for converting a repetitively pulsed near-visible laser beam.The ultrahigh stability [16] of the resulting midinfrared beam's repetition rate has recently enabled a novel concept of infrared interferometry and spectroscopy based on frequency-comb heterodyning (comb-FTIR) [17,18].This concept employs time-domain retardation without any mechanically moving stage.It is related to asynchronous optical sampling (ASOPS) [19] that has recently also enabled self-scanned THz spectroscopy [20,21].Comb-FTIR has a demonstrated potential of rapid spectral acquisition [22,23] and this is why we explore its capability of powering s-SNOM here.

Frequency-comb infrared near-field microscope
Coherent frequency comb beams contain a large number of evenly spaced spectral lines and propagate as laser-like, diffraction-limited beams [16].Two such beams are required to form a frequency-comb spectrometer [17,18,23] which we couple here with s-SNOM.As schematically outlined in Fig. 1 two separate lasers emit near-infrared pulse trains which generate, by difference-frequency conversion in nonlinear crystals, two beams of mid-infrared pulse trains.These contain a broad band of frequencies that can range at least up to f max ≈ τ −1 where τ is the duration of the near-infrared pump pulses.With commercially available Ti:sapphire lasers τ can be as short as 10 fs so that mid-infrared frequencies as high as 100 THz, equivalent to 3 μm wavelength, can be and have been realized [24].Both mid-infrared beams have spectra with exactly harmonic comb structure, that means sharp lines with frequencies exactly equal to multiples of the pulse repetition frequency f r [18,25].Note that the carrier envelope frequency offset which is present (and possibly fluctuating) in the near-infrared pulse trains emitted by the Ti:sapphire lasers cancels in the process of difference frequency generation [18].It is this property that has enabled the principle of heterodyne detection to be applied to all lines at once [17].For this the two mid-infrared beams are aligned to interfere on a power detector, and their repetition frequencies f r and f r + Δ are set slightly different such that each line at n f r of one beam has just one partner line at n( f r + Δ) in the other beam with which it can generate just one beat frequency nΔ below a low-pass filter limit.By superposition of all lines, the resulting detector signal becomes a radio-frequency pulse train with repetition rate Δ.This can be Fourier-transformed to reveal a harmonic radiowave comb of beat oscillations nΔ that encode one-by-one the infrared spectrum in amplitude and phase [18,23].
Coupling with the s-SNOM tip is achieved by the diffraction-limited sharp focus of a paraboloid mirror (Fig. 1).Although not required we choose collecting the scattered radiation with the same mirror, and thus detect direct back-scattering.This geometry was introduced by us with monochromatic s-SNOM earlier, since it makes the beam alignment particularly simple [3].The optical path differs principally from former comb spectrometers [18,23,26] where the sample is placed after the beam combiner; here we expose the sample to one of the beams only.The tip-scattered beam is superimposed with the second mid-infrared beam which serves as reference.The advantage of this optical layout-reminiscent of "asymmetric " FTIR-is .Schematic optical path of spectroscopic mid-infrared near-field microscope, combining a coherent frequency-comb infrared spectrometer (comb-FTIR) with a scatteringtype scanning near-field optical microscope (s-SNOM).Two Ti:sapphire oscillators emit 10 fs near-infrared pulses (green beam paths) at slightly different repetition frequencies f r and f r + Δ whose coincidence is detected by a cross-correlation detector (CC).Two GaSe crystals generate broadband infrared beams (red beam paths) one of which is focused to and back-scattered from a cantilevered AFM tip, then superimposed with the other beam using a ZnSe beam combiner (BC).The infrared detector (DET) continuously records radiowave pulses that repeat at frequency Δ, each of them encoding a backscattered spectrum.The sample is raster-scanned.
that we detect interferometrically and thus record both amplitude and phase of scattering.This is essential for s-SNOM for three different reasons.The first is that only the complementarity of amplitude and phase contrasts constitutes a complete characterization of the sample's local optical response [3].Secondly, interferometric detection is needed to suppress the unwanted artefact caused by "background" scattering [3,[28][29][30].A third, instrumental reason is that the signal gain coming with interferometric detection greatly alleviates S/N problems connected with weak near-field scattering, irrespective of whether the detection is of homodyne [30], heterodyne [3], pseudo-heterodyne [29], or multi-heterodyne type as in our frequency-comb s-SNOM here which simultaneously handles a huge number of pairs of signal and reference frequencies [18,23].
Our experimental implementation uses two commercial Ti:sapphire lasers (FemtoSource Compact Pro, Femtolasers) emitting 10 fs pulses with a 100 nm wide spectrum (FWHM) centered at 800 nm wavelength, at 500 mW quasi-c.w.power [23].The second laser contains a piezotranslatable mirror to finely set the repetition rate.Mid-infrared beams are obtained by focusing onto 200 μm thick GaSe plates [31,32] with f = 50 mm parabolic mirrors used 90 • off-axis.The output is collimated with similar mirrors and resembles a fundamental-mode Gaussian beam with diameter of about 12 mm, and a power of about 15 μW.Sharper focusing of the near-infrared beam is not likely to further significantly boost the mid-infrared power, because already with the present focusing two-photon absorption in GaSe [33] causes a power loss of 25%, as extrapolated from measurements with attenuators.The mid-infrared spectrum taken with a commercial FTIR spectrometer (Fig. 2(a)) is seen to be movable over the region 700 to 1400 cm -1 by orienting the GaSe plates; our detector becomes insensitive below 700 cm -1 [34], but emission at least down to 100 cm -1 has been reported [32].For the present study we use 55 • incidence to center the spectrum at 950 cm -1 (in order to observe the near-field resonance of SiC [7]), and an in-plane orientation optimized for vertical mid-infrared polarization.Red light transmitted through the GaSe plates helps aligning the mid-infrared beams.The collimating mirror is at first set to maximize a mid-infrared detector signal in large distance (10 m), and subsequently translated 70 μm towards the GaSe plate for optimum collimation.To combine the mid-infrared beams we use a 3 mm thick, uncoated, plane-parallel ZnSe plate at s-polarized incidence 23 • from the plate normal (BC in Fig. 1).With a refractive index of 2.4 its reflectivity is nominally 21% per surface, and its direct transmissivity 62%.For alignment and calibration we place at first a plane retroreflecting mirror before the s-SNOM's focusing mirror.The detector (DET) then receives 13% and 62%, respectiveley, of beam 1 and beam 2 power.An f = 25 mm a.r.-coatedGe lens is used for focusing.The detector is a 200 μm diameter, photovoltaic HgCdTe element (Kolmar KMPV11, with internal amplifier) with 74 V/mW nominal responsivity.The individual beams yield signals of about 70 and 20 mV, respectively.When they interfere we observe regular, transient interferograms as reported earlier [18,23] with amplitudes up to 30 mV, a value that affirms a high degree of coherence and matching of the beam directions, divergences and polarizations.Laser 1 freely runs at repetition frequency f r = 125.117MHz, as measured with a fast detector (MenloSystems APD210) of light reflected from the GaSe plate.Hence the infrared frequency of 1000 cm -1 , for example, is the 239,610th harmonic of f r .We set laser 2 by piezoelectric mirror translation to a slightly higher repetition rate of f r + Δ.The choice of Δ assigns 239,610 Δ to be the radio frequency which carries phase and amplitude information on the infrared frequency of 1000 cm -1 .We set Δ to 83.47 Hz so 1000 cm -1 is encoded at 20 MHz, a frequency well accepted in the detector's operating band of 0.001 to 30 MHz.This choice of a relatively high radio frequency allows very short "snapshot" recording times: the length of an interferogram need not be longer than 10 μs to determine the infrared spectrum with 5 cm -1 resolution.Note this value considerably exceeds the separation of adjacent comb elements, f r = 125 MHz = 0.004 cm -1 , thus each spectral point averages over ≈ 1250 adjacent comb elements.An example calculated from a single recording is shown in Fig. 2b, whereby the oscilloscope (LeCroy wavesurfer 422) was triggered off the signal.Fourier transform of the 10 μs transient yields the radiowave spectrum which equals the product of the amplitude spectra of both interfering infrared comb beams [18,23].We note an overall agreement in shape and position with the single infrared beam's power spectrum in Fig. 2.
For assessing the relatively weak tip-scattering spectra in s-SNOM we have to average consecutive multi-heterodyne radiowave transients captured in Δ = 83.47Hz sequence.Such a noise reduction technique-reported here for the first time with frequency-comb spectrometry-could in principle be impaired by pulse jitter of the lasers, and by fluctuations of our several meters of optical path length.For a trigger we use a cross correlation receiver (CC in Fig. 1) that accomodates two sample beams (thin green lines in Fig. 1) reflected off the near-infrared beams from ZnSe Brewster plates.We use mirrors to delay beam 1 by twice the distance between beam combiner (BC) and tip, to ensure that near-infrared pulses from both lasers coincide on the CC receiver at the same times when the mid-infrared pulses coincide on the DET detector.CC has an f = 10 mm glass lens to focus both beams travelling in parallel at a separation of about 4 mm, onto a BBO crystal for non-collinear sum-frequency generation.With the undeviated, transmitted beams (fundamental and second harmonic) blocked, the generated blue sum-frequency beam passes through a high-pass optical filter to a photomultiplier (Hamamatsu 5783).The output signal is low-pass-filtered at 5 MHz and consists of 270 ns (FWHM) pulses at repetition rate Δ = 83.47Hz, representing a self-scanned cross correlation trace with a time-scale magnification of f r /Δ = 1,500,000.Apart from providing a trigger this signal can conveniently serve for actively stabilizing Δ (we apply this signal to a lock-in amplifier with 83.47 Hz external reference, and feed the X output directly to the piezotranslator of laser 2 to correct for slow thermal drifts).
The optical system is designed for both a possibly sharp focus and high collection efficiency, to make up for the fact that the input power of about 15 μW is three orders of magnitude weaker than ideal for s-SNOM.With an f = 10 mm focal-length paraboloid the converging beam subtends 55 • vertically (from 5 • to 60 • elevation), and about 55 • horizontally.With this we estimate a focus diameter (FWHM) of about λ .As much as 12% of the scattered radiation should be collected into the backward beam when we assume isotropic scattering into the halfspace above a fully reflecting sample.To adjust the focus we first align the input beam from laser 1 to be parallel to the paraboloid axis, by observing its visible part, then translate the paraboloid while inspecting the tip's diffraction pattern on a white sample.Afterwards we insert a pair of roughened NaCl windows at Brewster's angle (incidence plane vertical) before the beam splitter (BC) to strongly attenuate the near-visible light that would heat the tip, while passing >96% of the mid-infrared power.Next the tapping motion of the tip is activated at the cantilever resonance frequency Ω/2π = 20 kHz, and an Au sample is approached.The HgCdTe detector signal, lock-in amplified at 2Ω reference, then serves to optimize the paraboloid alignment; this nΩ signal (with n ≥ 2) is well established in monochromatic s-SNOM for containing near-field information nearly free of background-scattering artefacts [3,5,27].Thus it can serve the same role of alignment optimization also in any broadband, spectrally-integrating s-SNOM.Good practice of s-SNOM calls for taking approach curves to ascertain the tapping amplitude, the set point, and the achievement of near-field interaction [3,14,27].In principle these tests are as easily performed with the broadband spectrally-integrating s-SNOM.
In Fig. 3 we show comparative s-SNOM images based on the 2Ω signal for broadband and monochromatic mid-infrared illumination, respectively (free tapping amplitude 2 Δz = 29 nm pp , set point 90%).Note this detection is of self-homodyne type, i.e. the near-field scattered light interferes with the background-scattered light so it does not allow the distinction of amplitude and phase contrasts [27].In this situation contrasts can become distorted or even inversed depending on the background phase which can be manipulated by the alignment of the focus with respect to the tip [27].Both infrared images show characteristic contrasts between three materials, with the dust particles darkest because their low refractive index leads to a comparably very weak near-field interaction [35].In the monochromatic image the border line between Au and SiC comes out sharper because of a shorter time constant of lock-in amplification; the high The infrared images are obtained at 2Ω demodulation of the detector signal with illumination either by monochromatic CO 2 laser at 932 cm -1 , or spectrally-integrated broadband beam 1 spanning 800-1100 cm -1 .The arrow depicts the direction of the incident beam (for explanation of dashed line and color series see Fig. 5).
signal level of SiC is due to the phonon-resonant near-field interaction that peaks near the frequency used [7].In the broadband, spectrally-integrated image Au appears brighter than SiC, possibly because we routinely adjust the mid-infrared focus by maximizing the broadband 2Ω signal when the tip contacts an Au sample.

Near-field-contrast imaging in frequency-comb s-SNOM
With the CC signal as trigger the transient infrared interferograms of tip-scattering can be averaged to emerge well above noise (Fig. 4).This confirms that the timing jitter is small enough not to impair the coherent summation of the beat waveform which contains frequencies between 16 and 22 MHz.Thus comb-FTIR is adequately combinable with s-SNOM, even with the presently weak mid-infrared source, and clear amplitude and phase spectra of tip-scattering result.Note this capability alone enables convenient spectroscopic studies of total backscattering from the tip-sample system.This will be the topic of a forthcoming article.We focus here on the near-field information contained in the scattering signal.Its extraction requires a new method to suppress background scattering.Unfortunately the standardly used method mentioned above, of harmonic demodulation of the detector signal is not compatible with the multi-heterodyne spectral analysis of comb-FTIR.The reason is that the tapping frequency is lower than the suitable radiowave beat frequencies.Therefore we conceive here another procedure for background suppression that is likewise based on the fact that nearfield scattering is much more distance-dependent than background scattering.We make use of the short recording time of frequency-comb spectra, which happens in 10 μs snapshots that are shorter than the tapping period 2π/Ω = 50 μs.Together with each interferogram we store the cantilever deflection signal which is proportional to the momentary tip-sample distance z.Typically 5,000 spectra are recorded in 60 s at a given pixel.Derived spectra with reduced background can then be computed from sorted spectra σ (z) = s(z)e iϕ (z) .While the most plausible ansatz would be a Taylor series σ (z) = σ 0 + σ 1 z + σ 2 z 2 + ..., we choose to mimick the harmonic-demodulation method in order to attain comparability of our results with those of standard monochromatic s-SNOM.Therefore we arrange the sorted spectra to a virtual time sequence according to z(t) = Δz(1 + sin Ωt) with 2Δz = 26 nm, and compute a Fourier series σ (t) = σ 0 + σ 1 e iΩt + σ 2 e i2Ωt + ... for each frequency.As a result we obtain the direct scattering spectrum σ 0 as well as the "demodulated" scattering spectra σ 1 , σ 2 ,.... Fig. 5. Results of an infrared-spectroscopic s-SNOM line scan taken in 20 min, along the 4 μm long dashed line in Fig. 3. Three complex (amplitude and phase) spectra are evaluated and colour coded as marked in Fig. 3, for each of 20 sequential tip positions separated by 200 nm.The upper panel shows the direct scattering spectrum σ 0 which transforms gradually from the initial position on Au (green) to the final on SiC (yellow).The middle and lower panels, respectively, show demodulated spectra of first and second order, σ 1 and σ 2 that change abruptly at the material boundary, and are dominated by the near-field interaction between tip and sample material.
Figure 5 displays the resulting direct and demodulated spectra, in amplitude and phase, along a 4 μm line scan which was taken along the dashed line in Fig. 3.We see that the direct spectra σ 0 are clearly visible while the second-order demodulated spectra σ 2 are barely above noise.The overall, parabolic form of the phase spectra is an instrumental baseline, due to chirp induced by NaCl crystals in the path of beam 1.It is remarkable that there are much stronger differences between the σ 0 and σ 1 spectra than between the σ 1 and σ 2 spectra, in regard of their shapes as well as their changeablility along the scan.Only the σ 1 and σ 2 spectra show an abrupt change at the material boundary, i.e. from a featureless shape on Au to a structured one on SiC that exhibits an enhanced amplitude as well as a characteristic phase change at frequencies below about 950 cm -1 .We recognize this as the well-documented behaviour expected from phonon-resonant near-field scattering on SiC [7,9,36,37].Therefore we tentatively assign our spectra σ 1 and σ 2 to be dominated by the near-field interaction.The σ 0 spectra, on the other hand, are dominated by background scattering because they exhibit a rather gradual change along the scan with no abrupt change at the material boundary, and do not show the SiC nearfield resonance.Fig. 6.S-SNOM amplitude spectra (slightly smoothed) vs approach of SiC sample, with tip-sample distances z indicated in the inset.The near-field resonance in s 1 appears only at tip-sample distances z < 100 nm, as to be expected for the limited reach of near-field interaction.
An independent test is performed by inspecting spectroscopic approach curves.For this we take direct and demodulated s-SNOM spectra, with 2Δz = 29 nm tapping amplitude and 90% set point, at a position on SiC which is 1 μm away from the material boundary in Fig. 3. Spectra are recorded with the sample retracted in 25 nm steps.Figure 6 shows that the s 0 amplitude spectra change gradually during approach, by up to about 30% between z = 0 and z = 200 nm.This is not unexpected from earlier observations with monochromatic s-SNOM, and mainly due to interference between different illumination/emission paths [3,5,27,28,38].The s 1 amplitude spectra, in contrast, exhibit the characteristic near-field resonance peak in the region 900 -930 cm -1 when the tip is in contact, as in Fig. 5.The peak remains when the tip is off contact, but its height becomes reduced in the region z = 75 nm, and it disappears for distances z > 100 nm.This reduction is as expected from monochromatic s-SNOM, the observed range of the near-field interaction agrees with former work.The range of 50 to 75 nm should be of the order of the curvature radius of the tip, which is specified as 30 nm but increases during use by abrasion.Thus the approach dependence fully supports that the σ 1 spectra are dominated by near-field information.
Furthermore, we note that the σ 0 , σ 1 and σ 2 spectra in Fig. 5 are quantitatively related since they are all from a single data set.We thus obtain the amplitude ratio s 1 /s 0 ≈ 0.05 on average over all wavelengths and tip positions, and s 2 /s 1 ≈ 0.3.We compare these experimental values with a predicted reduction of the background signal with increasing demodulation order, as has recently been derived in detail [28].With our parameters 2Δz = 26 nm and λ = 10.5μm,eq. ( 9) of ref. [28] predicts the background amplitude be reduced by 55 in the first order, and by 10,000 in the second order.With this our s 2 spectra should be pure near-field spectra (plus noise).Our s 1 spectra, however, should still contain a discernible background contribution.Yet this seems not the case in Fig. 5.If the s 1 spectra had some background contribution, any spectral features of the background s 0 would induce (possibly modified) features in s 1 .In case of a dispersionless sample like Au where the near-field interaction is likewise dispersionless [3], any s 0 feature would even be directly replicated in s 1 .The Au background spectra (greenblue) exhibit an indeed full modulation feature in the s 0 spectrum, but a close inspection of the correspondingly averaged s 1 spectrum (not shown) sets an upper limit of 20% of spectral modulation corresponding to s 0 .This lets us conclude that background expressed in the s 0 amplitude becomes reduced at least 100-fold in the first order.
Our measurement thus yields a broad spectral coverage of the near-field response at the SiC resonance, extending the limited tuning range and filling the gaps of monochromatic s-SNOM [7,9,36,37].For further noise reduction we compute the (complex) average over seven σ 1 spectra on SiC in Fig. 5, and normalize the result by the (complex) average over seven others on Au (omitting six spectra close to the boundary).The resulting normalized amplitude spectrum (Fig. 7) shows that a transition occurs near 940 cm -1 , from enhancement to suppression with respect to Au.The relative phase increases due to phonon resonance to about 180 • near 940 cm -1 .Both observations seem in accord with monochromatic s-SNOM observation.A direct comparison is, however, not indicated because published data are from second and third order demodulation only.A spectrum of s 2 from another undoped SiC crystal has a narrower resonance at slightly higher frequency and the maximum amplitude about five times larger than the value in our spectrum, 2.5 ± 0.5 [37].Part of the discrepancy might be technical, due to the general increase of s-SNOM contrast with increasing demodulation order [3,27], but also unsuppressed background might contribute.

Conclusions and outlook
We have successfully combined time-domain coherent infrared spectroscopy, based on multiheterodyning two infrared frequency-comb beams, with scattering-type scanning infrared nearfield microscopy.At each pixel, spectra of amplitude and phase contrast are obtained simultaneously and together with topography.The frequency range covered is from 850 to 1050 cm -1 , but could be moved within the limits of 700 to 1400 cm -1 by reorienting the nonlinear-optical crystals.Line images taken on a partly Au-covered SiC sample reveal nearly background-free near-field spectra.
A routine operation of spectroscopic s-SNOM with infrared frequency combs has however not yet been achieved, because with the given weak source the detector noise requires 60 s of integration time per pixel.The needed improvement of the signal-to-noise ratio could be along different paths, first of all better detectors such as superconducting bolometers [39,40] or electro-optic sampling [24].Another possibility is to increase the rate of recording spectra, beyond the present 83.47 Hz, by a triggered manipulation of the laser's length [22].We have already demonstrated up to 1000 spectra/s [23].With a realistic rate of 3000 spectra/s we can expect a reduction of the required integration time to 2 s/pixel.A different, more effective improvement could be exploring stronger infrared frequency-comb beams.If the present power of 15 μW could be boosted towards the optimal power of 10 mW, even with collecting only 83.47 spectra/s a full spectral acquisition could be attained in only 60 ms per pixel.This then would indeed constitute a conveniently fast scanned spectroscopic s-SNOM.The frequency coverage could also be extended beyond the 200 cm -1 width presently used.A coverage of all the range from 3 to 4000 cm -1 has already been achieved using thinner nonlinear crystals, together with electrooptic detection [24,32,41].This ultrabroadband range completely covers the mid and far infrared in one setup!Apart from the molecular-vibrational resonances mentioned in the introduction, this very broad range houses molecular rotation and libration resonances which could be exploited for their specific contrasts, phonon resonances of polar crystals (as in the SiC example above), and furthermore a series of conduction phenomena such as the Drude response contrast which could yield carrier density [6] and mobility, but also more exotic types of conductivity such as in superconductors and two-dimensional electron systems.

Fig. 1
Fig.1.Schematic optical path of spectroscopic mid-infrared near-field microscope, combining a coherent frequency-comb infrared spectrometer (comb-FTIR) with a scatteringtype scanning near-field optical microscope (s-SNOM).Two Ti:sapphire oscillators emit 10 fs near-infrared pulses (green beam paths) at slightly different repetition frequencies f r and f r + Δ whose coincidence is detected by a cross-correlation detector (CC).Two GaSe crystals generate broadband infrared beams (red beam paths) one of which is focused to and back-scattered from a cantilevered AFM tip, then superimposed with the other beam using a ZnSe beam combiner (BC).The infrared detector (DET) continuously records radiowave pulses that repeat at frequency Δ, each of them encoding a backscattered spectrum.The sample is raster-scanned.

Fig. 2 .
Fig.2.(a) Normalized spectra of mid-infrared frequency-comb beam, determined with a classical FTIR spectrometer, for four different near-infrared beam incidence angles on a GaSe crystal oriented for type-I phase-matching; the total power decreases when tuning the spectra towards higher frequencies.(b) Comb-FTIR "input" spectrum for illuminating the near-field microscope, measured with a flat mirror inserted between BC and s-SNOM in Fig.1, by recording a single radiowave transient interferogram and subsequent Fourier transformation.

Fig. 3 .
Fig. 3. Infrared s-SNOM images (4x3.5 μm 2 , recorded in 2 min.) of partly Au-covered SiC.The topography shows the 20 nm Au film on the left side, and some dust particles.The infrared images are obtained at 2Ω demodulation of the detector signal with illumination either by monochromatic CO 2 laser at 932 cm -1 , or spectrally-integrated broadband beam 1 spanning 800-1100 cm -1 .The arrow depicts the direction of the incident beam (for explanation of dashed line and color series see Fig.5).

Fig. 7 .
Fig.7.Normalized scattering contrast spectrum, in amplitude and phase (full curves, smoothed), of σ 1 response of SiC relative to Au, obtained as average (data points) over σ 1 spectra in Fig.5.As Au is dispersionless in the mid infrared, this relative spectrum largely depicts the near-field phonon-resonant interaction between tip and SiC.