Toward Far-field Vibrational Spectroscopy of Single Molecules at

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Toward Far-field Vibrational Spectroscopy of Single Molecules at Room Temperature M. J. Winterhalder,† A. Zumbusch,† M. Lippitz,‡ and M. Orrit*,§ †

Department of Chemistry, University of Konstanz, D-78457 Konstanz, Germany 4th Physics Institute, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany and Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany § MoNOS, Huygens Laboratory, P.O. Box 9504, 2300 RA Leiden University, Netherlands ‡

ABSTRACT: We propose a new scheme for the extraction of chemically sensitive vibrational information from a single fluorescent molecule at room temperature. Our approach is based on a three-photon fluorescence excitation scheme, with selectivity in the production of a vibrational population of the ground state. We estimate the expected signal in perturbation theory for a standard dye molecule, compare its magnitude qualitatively to noise and various background sources, and discuss the experimental realization of this scheme.

1. INTRODUCTION Vibrational spectroscopy by infrared absorption and Raman scattering is an indispensable tool in analytical chemistry and material science. Is it possible to apply fluorescence techniques, which routinely achieve single-molecule sensitivity, to obtain vibrationally resolved information at the single-molecule level and at nanometer scales? Following the frequency of a single molecule’s vibration with cm-1 resolution would give information on the structure and dynamics of its environment, for example, by revealing mechanical strain or couplings to its surroundings. Similar chemical information is contained in the widths, splittings, and intensities of vibrational bands.1 Rigid molecules at low temperatures often show well-resolved fluorescence spectra, from which vibrational information is readily obtained. Although fluorescence spectroscopy has been one of the first techniques demonstrated at the single-molecule level,2 it only applies at cryogenic temperatures because of the formidable broadening of the optical lines of molecules at ambient conditions. During the long fluorescence lifetime (nanoseconds), a molecule’s environment explores many configurations in room-temperature systems, and moreover, electronic levels are homogeneously broadened by fast dynamics. As a consequence, the vibrational selectivity of low-temperature spectra is lost in fluorescence spectra at room temperature, which result from the superposition of many overlapping broad vibrational bands. Apart from optical excitation, vibrational spectra of individual organic molecules can also be obtained by inelastic electron tunnelling spectroscopy with a scanning tunnelling microscope r 2011 American Chemical Society

(STM).3 Here, conductance changes at electron energies resonant with molecular vibrations lead to vibrational spectra. The same approach can also be used to electronically excite the fluorescence of individual chromophores.4 Provided that these are separated from the metal substrate, vibrationally resolved emission spectra can be recorded in this manner. While vibrational spectroscopy with an STM has the important advantage of offering topological as well as spectroscopical information, its limitations resemble those of optical single-molecule fluorescence excitation at cryogenic temperatures. Vibrationally resolved STM data of individual molecules can therefore only be acquired under ultrahigh vacuum conditions at cryogenic temperatures. One way to perform vibrational spectroscopy at room temperature with very high sensitivity is by surface-enhanced Raman scattering (SERS5), which, to a large extent, relies on the enhancement of optical fields in the vicinity of metallic structures. However, the proximity of metal surfaces can strongly perturb the systems under study, for example, proteins, which often undergo denaturation when interacting with surfaces. Therefore, an urgent need remains for molecular analysis far from any metal surface and in well-controlled and natural environments. The scheme we propose herein for vibrational analysis of a single molecule at room temperature is a variation of the Special Issue: Shaul Mukamel Festschrift Received: October 8, 2010 Revised: December 20, 2010 Published: March 07, 2011 5425

dx.doi.org/10.1021/jp109652s | J. Phys. Chem. B 2011, 115, 5425–5430

The Journal of Physical Chemistry B

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Figure 2. Two resonant diagrams contributing to the two-photonexcited vibrational coherence. The intermediate state can be the purely excited state e or its associated vibronic state w.

Figure 1. Level scheme and principle of the intended experiment.

fluorescence excitation spectrum where the excitation results from interaction with three laser pulses. Two pump pulses with two different colors are used. The beating of their two frequencies excites a molecular vibration by the difference frequency, as in the first step of coherent anti-Stokes Raman scattering (CARS) microscopy.6 In a second step, a third pulse selectively transfers the created vibrational population into a population of the fluorescent state. Emission of a fluorescence photon can then be detected spectrally resolved from the excitation. Because it relies on fluorescence, the technique has the potential to reach singlemolecule sensitivity.7 Moreover, tuning the frequency of one of the pump pulses yields a fluorescence excitation spectrum which maps out the spectrum of active molecular vibrations. A related approach consisting in infrared excitation of vibrational states and subsequent fluorescence excitation has been employed for timeresolved vibrational spectroscopy of bulk samples.8 In comparison, our approach has the advantage that it addresses vibrational modes which strongly couple to the electronic transitions. This, however, is a prerequisite for reaching the single-molecule sensitivity level. In this manuscript, we explore the conditions requested for this experiment. We estimate the expected signal quantitatively and discuss background sources qualitatively.

2. THEORY The three-photon excitation scheme discussed here is shown in Figure 1. Two simultaneous pump beams at frequencies ω1 and ω2 prepare a coherence between the ground state g and a vibrational state v, by absorption of a photon at ω1 and stimulated emission of a photon at ω2. A similar process is involved in CARS, where this coherence then mixes with a third photon at frequency ω3 to produce a coherent field at ωCARS = ω1 - ω2 þ ω3. Here, however, we are interested in single-molecule signals only, so that no coherent addition of the fields of many molecules can occur.9 The standard methods of detecting coherent optical signals obviously cannot be applied to observe the weak field produced by a single molecule. Instead, we propose to use the vibrational population to create a hot band in the fluorescence spectrum excited by a frequency ω3. This population of the vibrational state is produced by the continuous driving of the coherence between the ground and vibrational states via the

electric dipoles involving optically allowed transitions. In the second step of the process (see Figure 1), one detects the vibrational population by exciting with a probe pulse at ω3, which converts the vibrational population into a population of the fluorescent state. The resulting anti-Stokes fluorescence is blue-shifted with respect to ω3 by one vibrational quantum Ωv. It is therefore possible to separate it from the ω3 photons with high efficiency with suitable spectral filters. Because the intensity of this hot band fluorescence depends on the amount of vibrational population, it is itself a function of the frequency difference ω1 ω2, and it resonates when ω1 - ω2 ≈ Ωv. By tuning one of the pump frequencies, for example ω2, one obtains spectroscopic information (position, width, intensity) about the vibrational state of the fluorescent molecule. This approach, however, primarily addresses those vibrational modes which are strongly coupled to the optical transition, i.e., the modes which are active in fluorescence. 2.1. Two-Photon Excitation of a Vibrational Population. We first consider a hypothetical three-level molecule with ground state g, one vibrational state v, and one excited state e. The perturbation expansion of the density matrix (see, for example, refs 10 and 11) gives the vibrational coherence of the three-level system due to laser fields EB1 and EB2. This perturbation expression should be summed over all possible virtual levels contributing to the vibrational population. However, we expect the first excited electronic state e to give the leading contribution in the sum and therefore retain only the particular term involving this level as the intermediate state. The two corresponding resonant diagrams are shown in Figure 2. The expression of (g,v) coherence follows F

ð2Þ

vg

" # W1 W2 1 1 þ ¼ pg ~ vg Þ ðω1 - ω ~ eg Þ ð - ω2 - ω ~ eg Þ ðω1 - ω2 - ω ð1aÞ

where ω ~eg and ω ~vg are the Bohr frequencies of the respective coherences including phase relaxation rates. pg is the population of the ground state g, and we have neglected the initial thermal population of the vibrational state v. W1 = |μBeg 3 EB1|/p and W2 = |μBev 3 EB2|/p are the Rabi frequencies corresponding to the first and second fields, respectively, and the associated transition dipole moments μBeg for the field EB1 at frequency ω1 and μBev for 5426

dx.doi.org/10.1021/jp109652s |J. Phys. Chem. B 2011, 115, 5425–5430


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the field EB2 at frequency ω2. The fields are amplitudes corresponding to positive frequency components only. Note that, for the usual case of a weak electron-vibration coupling, the second transition has the reduced oscillator strength of the efv vibronic transition. The second term in eq 1a is smaller than the first one because it requires the stimulated emission of photon 2 to occur before the absorption of photon 1. In the following, we shall neglect this process and reduce (eq 1a) to its first term only Fð2Þ vg ¼ pg

W1 W2 1 ~ vg Þ ðω1 - ω ~ eg Þ ðω1 - ω2 - ω

ð1bÞ

2.2. Case of Four Levels. Molecules are not three-level systems. Even in a simplified model where just one vibrational quantum of only one vibrational mode is considered, we have to take the two vibrational components, g and v, of the ground state and the two vibronic components, e and w, of the excited state into account. We then have a four-level system. The contributions of the two sets of states (g,e) and (v,w) cancel to a large extent, but a small difference in their resonant denominators gives rise to a net signal. Hereafter, for simplicity, we assume a purely linear coupling between electron and vibration. In the crude Born-Oppenheimer approximation, the matrix element of the dipole moment operator between the ground state with n vibrational quanta and the excited state with m quanta of the same vibration is given by ! mæ Æg; njμje; mæ ¼ ! μeg Ænj~

where μBeg is the electronic transition dipole vector, and the Æn|m~æ coefficients are overlaps between vibrational wave functions in the ground and excited states called Franck-Condon amplitudes. For the four states considered here, |gæ |g;0æ, |væ |g;1æ, |eæ |e;0æ, and |wæ |e;1æ, and in the linear coupling approximation, the Franck-Condon amplitudes between states are given by 2 ~ Æ0j0æ ¼ e-ξ =2 1 2 ~ Æ1j1æ ¼ e-ξ =2 ð1 - ξ2 Þ 1 2 ~ ~ Æ0j1æ ¼ - Æ1j0æ ¼ ξe-ξ =2 ξ

where ξ is a small dimensionless parameter characterizing the displacement of the vibration coordinate upon electronic excitation. Introducing these values of the dipole moments in (eq 1b), we obtain " # ^2 W1 W ξ ξ ð2Þ F vg pg ~ vg ω1 - ω ~ eg ω1 - ω ~ wg ω1 - ω2 - ω ¼ pg

Weff ~ vg ω1 - ω2 - ω

with an effective Rabi frequency for the two-photon interaction Weff

^ 2ξ -Ωv W1 W ~ eg Þðω1 - ω ~ wg Þ ðω1 - ω

^ 2, with W ^2 = Ωv is the vibration frequency and W2 = ξW |μBeg 3 EB2|/p. The two contributions from gfefv and gfwfv

paths therefore almost cancel each other, except for a small difference due to their different energy denominators. 2.3. Vibrational Population. The two pump pulses at frequencies ω1 and ω2 create a (g,v) coherence, which can interact with the third field at frequency ω3 and create a coherent (e,g) polarization. The field created by this polarization in a single molecule is too weak to be measured. There is no coherent amplification mechanism by which the fields of many molecules interfere constructively to create a detectable macroscopic field.9 However, the vibrational coherence itself gives rise to a population pv of the vibrational state v, which can be detected at the single molecule level by an induced fluorescence photon. We hereafter calculate the vibrational population created by the two pump pulses. (i) Let us first consider pulses much longer than the coherence lifetime (τ . T2(v)), and neglect the population decay. From the equation of motion of the (g,v) coherence F expressed in the rotating frame F ipF_ ¼ Weff pg - ip T2 ðvÞ we deduce the steady state value F = -iWeffT2(v) of the coherence. Using the equation of motion of the population pv, we obtain, after a pulse of duration τ pv ¼ 2Weff 2 T2 ðvÞτ (ii) For pulses shorter than T2(v), the population grows quadratically in pulse duration. A similar calculation leads to pv ¼ ðWeff τÞ2 In both cases, the resulting population of the vibrational state will give rise to an anti-Stokes transition (hot band) in the fluorescence excited by the third pulse. Provided the probe pulse at frequency ω3 arrives within the population decay time T1(v) from the pump pulses, we may neglect population relaxation, and the additional fluorescence signal due to the created vibrational population will be given by F ¼ σ v p v I3 τ 3 φ where σv is the cross-section of the hot band; I3 and τ3 are the intensity (in number of photons per unit time and area) and duration of the reading pulse; and φ is the fluorescence quantum yield.

3. EXPERIMENTAL IMPLEMENTATION, EXPECTED SIGNAL, AND BACKGROUND SOURCES Hereafter, we estimate the order of magnitude of the threephoton excited fluorescence intensity for reasonable pulse characteristics and for a typical fluorophore. To observe the threephoton-excited fluorescence, one excites the vibrational hot band generated by the pump pulses with a reading pulse. This third pulse, which is red-shifted with respect to the energy of the fluorescent state, for example, by a quantum of a C-C stretching vibration about 1500 cm-1, will give rise to fluorescence light at the frequency of the purely electronic (0-0) emission. For a rigid aromatic molecule, this emission is nearly resonant with the (0-0) absorption and can be spectrally filtered from the reading pulse. A first obvious source of background is the thermal population of the vibrational state v (Figure 3a), typically 10-3 at room temperature for a C-C stretch. The thermal population 5427



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Figure 3. Various processes causing background signals.

of all other coupled modes which can be brought to the fluorescent state by the third pulse will contribute to the background as well. Fluorescence may also be excited by the absorption of two pump photons (Figure 3b), either from the wave with frequency ω1 or from that with frequency ω2, or from their combination. By contrast, the intensity of the probe beam with frequency ω3 can be chosen to be much below that of the other two beams since it serves for a linear, electronically resonant excitation. Background due to nonlinear excitations involving the probe beam can therefore be neglected. The background processes can be measured independently by blocking one or two of the three beams, and a real-time background subtraction can be performed with modulation and lock-in techniques.12,13 In this way, only the change of intensity due to the desired excitation scheme can be isolated. If the fast decay of the vibration population imposes (partially) overlapping the probing pulse with frequency ω3 with the pump pulses, an additional background source will be the nonresonant CARS signal at ωCARS = ω1 - ω2 þ ω3 from the matrix material. Use of a backscattering detection geometry eventually in combination with time gating can be employed to completely remove this background signal. A second way of subtracting background signals is to monitor the total fluorescence while scanning one of the pump frequencies, say, ω2. This generates a spectrum with a resonance when the frequency ω2 of the respective pump beam resonates with the difference ω1 - Ωv. Processes with no vibrational resonance components will give rise to a nearly constant background. Let us now estimate the expected fluorescence count rate. We assume 10 mW pump beams with a repetition rate of 100 MHz (100 pJ per pulse) and a pulse duration of 1 ps. These parameters are reasonable for many commercial laser systems. Focusing such pulses on a diffraction-limited spot does not lead to damage of the substrates. We assume a spot diameter of about d = 1000 nm because the pump pulses can be in the near-infrared and because objective aberrations and transmission are less favorable in this range. The peak laser intensity of the pump waves is of the order of I = (P/d2) = (10-10 J)/(10-12 s 10-12 m2) = 1014 W/m2. This corresponds to a laser field amplitude (positive frequency only) of E = (1/2)[(2I)/(ε0c)]1/2 = [(1014)/(10-11 6 108)]1/2 V/m = 108 V/m, which we take equal for both pump waves. A typical value for the transition dipole moment of a good fluorophore can be deduced from its radiative lifetime, 4 ns: μeg = 4 10-29 Cm. The associated Rabi frequency is therefore

Figure 4. Numerical simulation of the proposed excitation scheme. (a) Vibrational states of several frequencies are pumped by pulses 1 and 2 and probed by transferring the population to the excited state e. (b) The thermal population of all vibrational states combined with the spectral width of the probe pulse and the broadening of the excited electronic state make the population of many states contribute to a background signal. Only part of it is modified by the pump pulses. (c) The two strongest peaks in the vibrational spectrum can be found in the fluorescence signal, assuming in total 106 detected photons.

W = (μegE)/(p) = (4 10-29 108)/(10-34) rad/s ≈ 4 1013 rad/s. To calculate the effective Rabi frequency, we need the detun~eg|. Assuming ω1 = 1.9 ing of the first pump wave, δω = |ω1 - ω ~2 = 10 000 cm-1) and ω ~eg = 3.8 1015 rad/s (υ ~2 1015 rad/s (υ = 20 000 cm-1), we get δω ≈ 2 1015 rad/s. The effective Rabi frequency for the two-photon transition involves the FranckCondon amplitude. We assume a vibronic intensity of 0.04, a conservative value for the C-C stretch intensity in a typical dye, which corresponds to an amplitude of ξ ≈ 0.2. With a vibrational frequency of Ωv = 1500 cm-1, we obtain Weff ¼

W1 2 ξΩv 2 1010 rad=s δω2

For a dephasing rate γv = [1/(T2(v)] = 1012 s-1 of the (g,v) transition, the probability of two-photon excited vibrational population per pulse is pv = 2Weff2(τ/γv) = 2 4 1020 10-24 ≈ 8 10-4, which leads to 8 104 vibrational excitations per second. For an intensity of the reading wave close to saturation of the hot band, i.e., some MW/cm2 (1 mW), we expect a signal of the order of a thousand counts per second. To estimate whether this additional signal is detectable against the thermal background, we simulated the vibrational spectrum obtainable from a single molecule with the proposed method (Figure 4). The starting point is the vibrational mode spectrum (Figure 4a) which has characteristic modes in the fingerprint 5428


The Journal of Physical Chemistry B region. We assume that the spectrum is given by the spectral mode density and neglect for simplicity all variations in the coupling efficiency to the pump or probe pulses. The population of all vibrational modes can be transferred to the excited state e with equal efficiency, as long as the probe pulse with frequency ω3 is resonant with the transition. The width of that resonance is given by the spectral width of the probe pulse and, more importantly, by the broadening of the excited state. It is indicated by the blue Gaussian peak in Figure 4a. All vibrational states covered by the probe pulse with frequency ω3 will be probed. The pump pulses with frequencies ω1 and ω2 together change the population of one state or a small range of states, indicated by the green Gaussian peak in Figure 4a. Taking into account the thermal population of the states at room temperature, several modes contribute to a background signal in the detected fluorescence, which is also present when no pump-induced additional population is created (Figure 4b). The pump pulses then increase the population in one of these states (red line in Figure 4b). When the difference frequency between the pump pulses is scanned over the vibrational resonances, we find the resonances back in the fluorescence signal of the molecule. For the trace in Figure 4c we assumed a total number of 106 detected photons, which is reasonable for good single-molecule fluorophores. We find that the two strongest peaks of the assumed vibrational spectrum are clearly visible in the fluorescence trace, broadened by the finite spectral width of the pump process.

4. CONCLUSION AND OUTLOOK A number of different methods suited for highly sensitive vibrational microscopy have recently been developed.6,12 How does our scheme compare with alternative approaches for the acquisition of single-molecule vibrational spectra at room temperature? Recently, Freudiger et al. demonstrated stimulated Raman scattering microscopy on a low number of molecules.12 In this approach, two laser beams delivering pump and Stokes pulses are employed, and a modulation on the intensity of one transmitted beam is detected while the other beam is actively intensity modulated. Whenever a molecule is successfully transferred into the vibrational state, the Stokes pulse gains a photon, whereas the pump pulse looses one. Both gain and loss can be used for detection. The lowest reported concentration detected is 50 μM, which corresponds to about 3000 molecules per focal volume. Compared to this technique, the advantage of our scheme of transferring the vibrational population into the electronic excited state is comparable to the advantage of single-molecule fluorescence spectroscopy over absorption spectroscopy. Fluorescence happens on a dark, low noise background, while absorption has to be visible on the shot noise of the transmitted beam. While the vibrational fluorescence signal detected with the scheme proposed here is not detected against a zero background, as the thermal populated states give a background, the background and the shot noise on it are much smaller than the shot noise on the strong Stokes beam employed in stimulated Raman scattering microscopy. The situation changes when working directly on the electronic transition, as the electronic absorption cross section of a molecule is about 15 orders of magnitude larger than its Raman cross section. Under these conditions, the stimulated emission from about five molecules in the focus of a microscope has been reported.14 As before, the modulation transfer from a pump to a probe beam was monitored, but now a much weaker probe with less shot

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noise could be used. However, this experiment does not give any vibrational information. While the aforementioned experiments mainly are aimed at imaging applications, also purely spectroscopic approaches based on the population of vibrational states of individual molecules have recently been published.15 In these experiments, two ultrashort laser beams are used to first launch a wavepacket in an excited electronic state and then to probe dynamics of this wavepacket. Provided that the spectral width is sufficiently large, the first laser pulse creates a coherent superposition of several vibrational states of the first electronic excited state. Depending on the relative phase and temporal delay of the second laser pulse, the fluorescence is enhanced or reduced, as the second pulse can either increase or decrease the probability that the molecule ends up in the excited state, from where it can emit. The appealing aspect here is that both pulses do not need to saturate the molecule, and many photons can be collected until photobleaching. From the temporal evolution of the signal, it is in principle possible to derive information of the spectral position of the vibrations involved in the superposition via a Fourier transformation. This, however, requires long intensity trajectories, which are difficult to obtain. In conclusion, we present a novel approach to perfoming vibrational spectroscopy on single molecules at room temperature. The method is based on the coherent population of vibrational states and the subsequent population transfer to an electronically excited state. The latter is then monitored via its fluorescence emission. Using this scheme, vibrational spectra are obtainable by tuning the frequency difference of the pump lasers involved in the coherent excitation step. In addition, timeresolved vibrational data can be obtained by delaying the probing pulse. Simulations confirm the suitability of this approach for the detection of single-molecule spectra.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT M.W. and A.Z. gratefully acknowledge financial support by the SFB767. ’ REFERENCES (1) Carey, P. R. Raman crystallography and other biochemical applications of Raman Microscopy. Annu. Rev. Phys. Chem. 2006, 57, 527–554. (2) Tchenio, P.; Myers, A. B.; Moerner, W. E. Dispersed fluorescence spectra of single molecules of pentacene in p-terphenyl. J. Phys. Chem. 1993, 97, 2491–2493. (3) Liu, N.; Silien, C.; Ho, W.; Maddox, J. B.; Mukamel, S.; Liu, B.; Bazan, G. C. Chemical imaging of single 4,7,12,15-tetrakis[2.2]paracyclophane by spatially resolved vibrational spectroscopy. J. Chem. Phys. 2007, 127, 244711. (4) Qiu, X. H.; Nazin, G. V.; Ho, W. Vibrationally Resolved Fluorescence Excited with Submolecular Precision. Science 2003, 299, 542–546. (5) Kneipp, K.; Kneipp, H.; Itzkan, I.; Dasari, R. R.; Feld, M. S. Ultrasensitive Chemical Analysis by Raman Spectroscopy. Chem. Rev. 1999, 99, 2957–2975. 5429



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(6) Zumbusch, A.; Holtom, G. R.; Xie, X. S. Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering. Phys. Rev. Lett. 1999, 82, 4142–4145. (7) Moerner, W. E.; Orrit, M. Illuminating single molecules in condensed matter. Science 1999, 283, 1670–1676. (8) Laubereau, A.; Seilmeier, A.; Kaiser, W. A new technique to measure ultrashort vibrational relaxation times in liquid samples. Chem. Phys. Lett. 1975, 36, 232–237. (9) Marx, C. A.; Harbola, U.; Mukamel, S. Nonlinear optical spectroscopy of single, few, and many molecules. Phys. Rev. A 2008, 77, 022110. (10) Shen, Y. R. The principles of nonlinear optics; Wiley: New York, 1984; p 13. (11) Mukamel, S. Principles of nonlinear optical spectroscopy; Oxford University Press: Oxford, 1995; p 154. (12) Freudiger, C. W.; Min, W.; Saar, B. G.; Holtom, G. R.; He, C. W.; Tsai, J. C.; Kang, J. X.; Xie, X. S. Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy. Science 2008, 322, 1857–1861. (13) Braun, D.; Libchaber, W. Computer-based photon-counting lock-in for phase detection at the shot-noise limit. Opt. Lett. 2002, 27, 1418–1420. (14) Min, W.; Lu, S. J.; Chong, S. S.; Roy, R.; Holtom, G. R.; Xie, X. S. Imaging chromophores with undetectable fluorescence by stimulated emission microscopy. Nature 2009, 461, 1105. (15) Brinks, D.; Stefani, F. D.; Kulzer, F.; Hildner, R.; Taminiau, T. H.; Avlasevich, Y.; M€ullen, K.; van Hulst, N. F. Visualizing and controlling vibrational wave packets of single molecules. Nature 2010, 465, 905–908.

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Toward Far-field Vibrational Spectroscopy of Single Molecules at

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