NANO LETTERS
Band Gap Photobleaching in Isolated Single-Walled Carbon Nanotubes
2003 Vol. 3, No. 11 1549-1554
Michael S. Arnold,† Jay E. Sharping,‡ Samuel I. Stupp,†,§,| Prem Kumar,‡,⊥ and Mark C. Hersam*,† Department of Materials Science and Engineering, Department of Electrical and Computer Engineering, Department of Chemistry, Feinberg School of Medicine, Department of Physics and Astronomy, Northwestern UniVersity, EVanston, Illinois 60208-3108 Received August 31, 2003; Revised Manuscript Received September 19, 2003
ABSTRACT Using pump−probe characterization, band gap photobleaching has been observed from semiconducting single-walled carbon nanotubes (SWNTs) isolated in aqueous suspensions in an effort to evaluate SWNTs as a near-infrared optical material. The measured photobleaching was optimized for co-polarization of pump and probe lasers in resonance with the second and first van Hove transitions, respectively. A saturation of photobleaching intensity was observed for large pump intensities greater than ∼1 kW cm-2 and for probe intensities approaching ∼500 W cm-2. The observed photobleaching is attributed to the relaxation of excited electron−hole pairs to the band edges, resulting in decreased absorption and increased stimulated emission.
Semiconducting single-walled carbon nanotubes (SWNTs) are an intriguing direct band gap material (Eg ∼ 1 eV) in the near-infrared1,2 - a technologically important portion of the optical spectrum for fiber-optic communications3,4 and medical imaging.5,6 One-dimensional materials such as carbon nanotubes and semiconductor nanowires have recently received substantial attention as potential components for optical and optoelectronic devices because of several key advantages over bulk materials.7-20 By controlling the size of one-dimensional materials, the energy band gap and optical emission range of these materials can be tailored due to quantum confinement effects.8-10,20 Furthermore, because one-dimensional materials exhibit large peaks in their electronic density of states (van Hove singularities1,2), the excitation power necessary for net optical gain in these materials is reduced.14,21 In pump-probe spectroscopic studies of films of aggregated SWNTs, transient photobleaching has been observed on the 1 ps time scale.17-19 Such films have been used as saturable absorbers in passively mode-locked fiber lasers, taking advantage of the ultrafast carrier dynamics in aggregated nanotubes.18 However, two major differences between aggregated and isolated nanotubes have recently been highlighted.7,8,10 First, the observation of spontaneous * Corresponding author. E-mail:
[email protected]. † Department of Materials Science and Engineering. ‡ Department of Electrical and Computer Engineering. § Department of Chemistry. | Feinberg School of Medicine. ⊥ Department of Physics and Astronomy. 10.1021/nl034726f CCC: $25.00 Published on Web 10/04/2003
© 2003 American Chemical Society
emission from optically pumped SWNTs isolated in aqueous suspensions7 and from ambipolar SWNT field-effect transistors9,11 has demonstrated that the quantum efficiency for radiative emission in isolated SWNTs is substantially larger than in aggregated SWNTs. The radiative efficiency of aggregated SWNTs is expected to be drastically reduced by fast nonradiative recombination of electron-hole pairs in the metallic components of SWNT bundles.7,22 Second, compared with aggregated SWNTs, the optical absorbance and emission cross-sections of isolated SWNTs are larger and spectrally sharper.7 Consequently, the magnitude of optical absorption and emission due to specific nanotube chiralities is enhanced in solutions of isolated SWNTs with respect to the background absorption. The finer absorption and emission spectra of isolated SWNTs suggest that these nanomaterials may possess additional enhanced optical properties compared to aggregated SWNTs. Consequently, in this paper, we focus on isolated SWNTs. Using optical pump-probe characterization, we delineate the dependence of photobleaching on aggregation, pH, pump and probe wavelength, polarization, and intensity. The results demonstrate stronger photobleaching in isolated SWNTs, a photobleaching polarization dependence, and spectral dependencies and provide information concerning carrier dynamics. Solutions of isolated SWNTs for pump-probe characterization were prepared by mixing 0.005 wt % raw highpressure carbon monoxide (HiPCO) grown single-walled carbon nanotube material (Carbon Nanotechnologies, Inc.) consisting of upward of 30% iron catalyst particles and
Figure 1. Normalized absorbance spectrum of SWNTs as a function of centrifugation time. The absorbance cross-sections of isolated SWNTs are sharper and more significant with respect to the background absorbance. The ‘*’ and ‘#’ symbols mark the E22 and E11 transitions, respectively, of the nanotube chirality under study.
amorphous carbon impurities and 1.0 wt % sodium dodecyl sulfate (SDS, Fisher Scientific, >99%) in 10-18 mL heavy water (deuterium oxide, D2O, Cambridge Isotopes, 99%) by bath ultrasonication (Bransonics 3510) for 20-25 min. Aggregations of nanotubes were then disrupted by horn ultrasonication (Fisher Scientific, Sonic Dismembrator 550) for 10-15 min using a tapered microtip extension coupled to a 1/2 in. horn. Remaining aggregations and isolated nanotubes were then separated by ultracentrifugation (48
krpm, 75 min, Beckman-Coulter TLA100.3 rotor). This procedure for isolating SWNTs in aqueous solutions of surfactant is based on one recently developed by O’Connell and co-workers.7 Figure 1 depicts the progression of the absorbance spectrum of a SWNT solution as aggregates are removed by ultracentrifugation. Control solutions of aggregated nanotubes were prepared for comparison with isolated nanotubes by heating solutions of isolated SWNTs or by lyophilization and resuspension. In the heating treatment, slight aggregation was induced by heating samples to 99 °C for 93 min. In the lyophilization treatment, overnight lyophilization was followed by nanotube resuspension at the original concentration. Both control solutions appeared visibly homogeneous. To optically excite SWNTs, a 76 MHz pulsed mode-locked Ti:sapphire laser (Coherent, Inc.) tunable from 700 to 1000 nm (spectral full-width at half-maximum of 1.6 nm and temporal full-width at half-maximum of 0.3 ps at 740 nm) was used (Figure 2), and photobleaching was monitored with one of three continuous wave (CW) probe laser wavelengths (1047, 1053, or 1064 nm). A local maximum in photobleaching intensity was observed near a probe wavelength of 1053 nm (corresponding to the E11 transition) and for a pump wavelength of 740 nm (corresponding to the E22 transition). In previous absorption and spontaneous emission measurements, this pair of transitions has been assigned to either (10, 2) or (11, 0) chirality nanotubes.8,10 Both the pump and probe beams were collinearly polarized, separately focused, and combined using a dichroic beam splitter. The pump and probe beams were aligned in a collinear geometry to pass through a square 10.00 mm path-length quartz cuvette at the probe beam waist (Figure 2a, d). The probe beam measured 80-254 µm in diameter at the cuvette depending on the focusing optic, and the probe beam was always characterized by a confocal length that was greater than the
Figure 2. Measurement of band gap photobleaching. (A) Illustration of pump-probe technique. The pump beam excites SWNTs solubilized by SDS in D2O at a driving frequency of 76 MHz, and the intensity of a collinear probe beam is modulated at the driving frequency. (An angle between pump and probe is depicted for clarity.) (B) Schematic of band structure depicting optical absorption. (C) Schematic of band structure depicting stimulated emission. A pulsed pump tuned to the E22 transition excites electron-hole pairs, which relax to the band edges, decreasing optical absorption and contributing to coherent stimulated emission in the presence of a probe beam. (D) Experimental setup. Both the pump and probe beams are spatially overlapped and collinearly pass through the sample. The modulated probe beam is incident to an InGaAs photodiode. 1550
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cuvette path length. To maintain constant excitation throughout the sample for aggregation, pH, spectral, and polarization experiments, the pump beam was collimated at a diameter of ∼2 mm throughout the cuvette. To approach saturationregime pump intensities for intensity dependence studies, the pump beam was focused down to a radius of 16 µm at the beam waist in the solution. For this case, the specified average pump intensities are average pump powers divided by the beam area at the waist. To detect photobleaching, the pump beam was filtered from the transmitted probe by using either Schott glass RG830 optical filters or a diffraction grating followed by an iris. In both filtering schemes, the modulated, transmitted probe beam was focused onto an InGaAs PIN photodiode (Epitaxx, ETX-100), and the output photocurrent signal at 76 MHz was amplified (Miteq M/N AU-4A-0110), measured using an electrical spectrum analyzer (Agilent, 54624A, 1 kHz bandwidth), and averaged 100 times to account for fluctuations in the pump and probe intensities. Before amplifying, the photocurrent signal was passed through a 30 MHz high-pass filter and an 80 MHz low-pass filter to avoid saturation of the electronic amplifier. The background electronic noise over a 100 kHz span around 76 MHz was averaged and subtracted from the measured data. To measure the sign of the probe modulation, a digital oscilloscope (Agilent, Infiniium 54825A) was used. In this work, we quantify the magnitude of photobleaching intensity by measurement of the probe modulation intensity, which we have defined as the 76 MHz Fourier component of the output probe power divided by the area of the probe beam in the SWNT solution. Since the resolution of pulse-widths shorter than 2 ns was limited by the bandwidth of our photodetector and amplifier, our reported probe modulation intensity is reduced by roughly the response time of our detector and amplifier divided by the relaxation time of the SWNTs. Thus, we cannot report on the relative magnitude of the SWNT photobleaching intensity compared to the background absorption, and future time-resolved studies of SWNT photobleaching will be necessary to shed light on this subject. Figures 2a-c schematically depict band gap absorption and stimulated emission from SWNTs. Electron-hole pairs are generated via absorption of the pump beam tuned to the E22 van Hove transition, and some of the excess electrons and holes rapidly relax from the second to the first subbands of the conduction and valence bands respectively via nonradiative processes creating a nonequilibrium free carrier population.7 When the probe beam is tuned to the E11 van Hove transition, photobleaching is observed for two reasons. First, the nonequilibrium free carrier inversion results in a decreased rate of optical absorption, and, second, electronhole pair recombination is induced leading to coherent stimulated emission. In an effort to verify the apparent observation of band gap photobleaching, multiple control experiments were performed. The observation of photobleaching required the presence of both the pump and the probe beams, eliminating spontaneous emission and pump leakage as sources for the apparent probe modulation. Spontaneous emission was Nano Lett., Vol. 3, No. 11, 2003
Figure 3. Detection of probe modulation. When the pump beam is off, the probe beam is not modulated by SWNT band gap photobleaching (red trace). When the probe beam is off, spontaneous emission from SWNTs excited by the pump beam is detected (blue trace). When both the pump and probe beams are on, a large probe modulation signal is detected due to SWNT photobleaching (black). Note that when the probe beam is on, the background noise is larger due to shot noise from the CW probe.
observed at the photodetector, but because of the large distances between the sample and the detector in the experimental setup, it was several orders of magnitude weaker than the probe modulation (Figure 3). In addition, the transmitted probe intensity was measured to increase in response to the excitation pump, ruling out modulation due to thermally induced optical limiting effects that have been observed in SWNT dispersions.23,24 Other control experiments confirmed that isolated SWNTs served as the optical media for the observed photobleaching. In particular, probe modulation was not observed for solutions of D2O or 1.0% SDS in D2O. Furthermore, the intensity of probe modulation in solutions of isolated SWNTs decreased with decreasing SWNT concentration. The presence of photobleaching was also dependent on the degree of SWNT aggregation and the solution pH level (Figure 4). For example, the photobleaching intensity from intentionally aggregated nanotube solutions was reduced by a factor of 2 in heated nanotube solutions and by a factor of 120 in lyophilized nanotube solutions. Fast, nonradiative recombination in aggregated SWNTs likely contributes to reduced nonequilibrium carrier distributions and reduced photobleaching. In addition, by decreasing the solution pH, the photobleaching intensity decreased to immeasurable levels due to protonation of nanotube sidewalls7,25 but was reversibly restored by neutralizing the pH. SWNT protonation is thought to trap the highest lying valence electrons, preventing their contribution to band gap absorption and spontaneous emission.25 Such a mechanism would also contribute to reduced photobleaching. Thus, the pH dependence strongly suggests that the observed photobleaching is due to SWNTs in solution rather than impurities such as amorphous carbon and metal catalyst particles. More detailed experiments were performed to characterize the properties of band gap photobleaching. By fixing the probe wavelength at 1053 nm, we measured the intensity of probe modulation as a function of pump wavelength and mapped the joint density of states for the corresponding E22 1551
Figure 4. Control solutions. Probe modulation intensity versus average pump intensity for isolated, heated, and lyophilized nanotube solutions. The probe modulation intensity from the lyophilized nanotubes is reduced by a factor of 120 due to aggregation effects. Input probe intensity measured 65 W cm-2. (Inset) Probe modulation intensity vs average pump intensity for isolated nanotube solutions at neutral and acidic pH. Changes in probe modulation intensity with pH are reversible. Axes and units of the main figure and the insert are the same.
transition (Figure 5a). A sharp peak in probe modulation intensity was observed for excitation at 740 nm (1.67 eV). A peak in optical absorption was also observed near this energy (Figure 1). The top half of the photobleaching lineshape has been fit to a Lorentzian with a full-width at halfmaximum of 65 meV as shown in Figure 5. Broadening of spectral features is expected due to short free carrier lifetimes in SWNTs as a result of fast electron-electron scattering on the 100 fs time-scale.22 Another broader peak in the emission spectra is observed at longer wavelengths (Figure 5a) and is consistent with G-band stimulated resonance Stokes Raman scattering since the measured difference in pump and probe wavenumbers is approximately 1600 cm-1 (refs 26,27). In a similar fashion, the E11 transition can be mapped by fixing the pump wavelength at the center of the E22 transition peak and monitoring the magnitude of probe modulation at different probe wavelengths (Figure 5b). As expected, photobleaching occurs most efficiently when the probe is tuned near the direct band gap energy. The mean intensity of probe modulation at 1064 nm was 75% of that at 1053 nm and the mean intensity at 1047 nm was 29% of that at 1053 nm.28 Assuming a Lorentzian line-shape, the center of the photobleaching intensity is red-shifted 5.6 ( 1.8 meV from the measured absorbance spectrum (centered at 1053 nm - Figure 1), with a full-width at half-maximum of less than 18 meV.28 The apparent red-shift between absorbance and photobleaching is consistent with the shift observed for spontaneous emission,7 and the narrower width of the E11 transition when compared with the E22 transition is also consistent with slower relaxation across the band gap. It should be noted that the probe modulation is positive for 1552
Figure 5. Spectral dependencies. (A) Dependence of probe modulation intensity on pump photon energy for a fixed probe wavelength (λ) at 1053 nm. A least-squares fit of the E22 transition to a Lorentzian centered at 1.67 eV with a full-width at halfmaximum of 65 meV is shown. The peak observed in the probe modulation intensity for pump energies near 1.4 eV is consistent with stimulated resonance Raman scattering. (B) Dependence of probe modulation intensity as a function of average pump intensity for three different probe wavelengths for a pump tuned to the center of the E22 transition and an average probe intensity of 3.6 W cm-2.
energies both larger and smaller than the center of the E11 transition, indicating that the observed probe modulation is not due to a shift in the transition induced by perturbation from the excitation pump. The effects of pump and probe polarizations were also studied to characterize the one-dimensional character of SWNTs. Measurements indicate that the probe modulation intensity is maximized for collinear polarization of pump and probe beams, while this intensity is reduced by about a factor of 2 for cross-linear polarizations (Figure 6). In a Nano Lett., Vol. 3, No. 11, 2003
Figure 6. Polarization dependence. Photobleaching is roughly twice as efficient for copolarization of pump and probe beams. Input probe intensity measured 20 W cm-2.
solution of randomly oriented nanotubes, a select subset of nanotubes oriented parallel to the excitation polarization will be most efficiently pumped.9,11,13 As a result of this anisotropic excitation, a probe that is copolarized with the pump will then interact most efficiently with this excited subset of nanotubes, thus maximizing the probe modulation intensity. Accordingly, we anticipate that photobleaching would be optimized for spatially aligned SWNTs. Carrier dynamics and saturation effects in SWNTs can be characterized by analysis of the dependence of photobleaching intensity on pump and probe intensities. As expected in a dilute solution, the intensity of photobleaching increases linearly with pump intensity at low pump intensities (as pump-generated electron-hole pairs rapidly relax to the band edges increasing the charge carrier inversion in a linear fashion) and sub-linearly at large intensities (Figure 7a). This sublinear behavior is consistent with a semiconductor approaching complete inversion, in which the band gap transitions saturate due to filling and depletion of the finite number of energy levels in the conduction and valence bands, respectively. This nonlinearity is also consistent with increased nonradiative multiparticle recombination at increased nonequilibrium free carrier densities. To analyze nonlinearities and SWNT saturation effects, linear response of detector and amplifier was ensured, and solution stirring was implemented to reduce thermally refractive effects, which were characterized by profiling pump and probe beam geometries. It should be noted that solution stirring was not implemented for aggregation, pH, spectral, and polarization studies, creating the observed nonlinearities toward the high end of the pump-intensity range in these figures. For various pump intensities the probe modulation intensity is noted to increase with increasing probe intensity (Figure 7b). In the small probe intensity regime, the probe modulation intensity increases linearly with probe intensity, Nano Lett., Vol. 3, No. 11, 2003
Figure 7. Pump and probe intensity dependencies. (A) Saturation of probe modulation intensity at high average pump intensities, independent of probe intensity. At low average pump intensities, the observed probe modulation intensity varies linearly with the pump intensity. (B) Probe modulation intensity versus input probe intensity and respective fits to the saturation model x/(1+x/xS). An increase in the fit probe saturation intensity with pump intensity is consistent with enhanced nonradiative recombination at large free carrier densities.
while sub-linear behavior is observed for large probe intensities. This sub-linearity is consistent with a probe intensity saturation model in which the nanotube effective interband recombination lifetime decreases as a result of stimulated recombination and emission for large probe intensities. For low solution concentrations, photobleaching is expected to follow the form x/(1+x/xS) where x is the incident probe intensity and xS is a free parameter representing the probe saturation intensity.29,30 In this model, at the 1553
saturation intensity, the rate of stimulated recombination is equal to the intrinsic rate of recombination in the absence of a stimulating probe. Therefore, for probe intensities much larger than the saturation intensity, the effective interband recombination lifetime will be dominated by stimulated recombination, inducing a reduction in the inverted carrier population and saturation. The probe saturation intensity determined by least-squares fitting in Figure 7b increases with pump intensity. This behavior is again consistent with increased multiparticle recombination at large nonequilibrium free carrier densities such as nonradiative Auger recombination that has been observed in other zero and one-dimensional materials.20,21 In this saturation model, the fit probe saturation intensity characterizes an upper limit for possible SWNT optical amplifier performance. In summary, we have observed near-infrared band gap photobleaching in isolated semiconducting single-walled carbon nanotubes. This photobleaching was 2 orders of magnitude more intense in solutions of isolated SWNTs than in control solutions of aggregated SWNTs and was optimized for pump and probe lasers in resonance with the second and first van Hove transitions, respectively. A saturation of photobleaching intensity was observed for large pump intensities greater than ∼1 kW cm-2 and for probe intensities approaching ∼500 W cm-2. These results suggest design constraints for potential SWNT optical devices. For example, the fit probe saturation intensity constrains maximum possible SWNT optical amplifier performance. Furthermore, the polarization dependence of photobleaching suggests that controlled alignment of SWNTs in optical materials will be a key factor in maximizing infrared SWNT device performance and exploiting the one-dimensional nature of SWNTs. In conclusion, from analysis of aggregation, pH, spectral, polarization, and intensity dependencies, we attribute the observed photobleaching to the relaxation of excited electronhole pairs to the band edges, which results in a decrease in the rate of optical absorption and an increase in the rate of stimulated emission in isolated SWNTs. Acknowledgment. Support from a Beckman Young Investigator Award (M.C.H.), a National Defense Science and Engineering Graduate Fellowship (M.S.A.), and a Department of Defense Multidisciplinary University Research Initiative Fellowship (J.E.S.) are gratefully acknowledged. This work was also partially supported by the National Science Foundation under NSF award numbers DMR0134706 and EEC-0118025 and the Department of Energy under award number DE-FG02-00ER45810/A001. We thank L. Edelman for sample preparation, J. Huang for AFM imaging, and S. Dugan for preliminary optical characterization. References (1) Charlier, J.-C.; Issi, J.-P. Appl. Phys. A 1998, 67, 79-87. (2) Saito, R., Kataura, H.; Eds. Top. Appl. Phys. 2001, 80, 213-247. (3) Suematsu, Y.; Arai, S. IEEE J. Sel. Top. Quantum Electron. 2000, 6, 1436-1449.
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(4) Harris, J. S. IEEE J. Sel. Top. Quantum Electronics 2000, 6, 11451160. (5) Raghavachiari, R. Near-Infrared Applications in Biotechnology; Marcel Dekker: New York, 2001. (6) Weissleder, R.; Tung, C.-H.; Mahmood, U.; Bogdanov Jr., A. Nature Biotechnol. 1999, 117, 375-378. (7) O’Connell, M. J.; Bachilo, S. M.; Huffman, C. B.; Moore, V. C.; Strano, M. S.; Haroz, E. H.; Rialon, K. L.; Boul, P. J.; Noon, W. H.; Kittrell, C.; Ma, J.; Hauge, R. H.; Weisman, R. B.; Smalley, R. E. Science 2002, 297, 593-596. (8) Bachilo, S. M.; Strano, M. S.; Kittrell, C.; Hauge, R. H.; Smalley, R. E.; Weisman, R. B. Science 2002, 298, 2361-2366. (9) Misewich, J. A.; Martel, R.; Avouris, Ph.; Tsang, J. C.; Heinze, S.; Tersoff, J. Science 2003, 300, 783-786. (10) Hagen, A.; Hertel, T. Nano Lett. 2003, 3, 383-388. (11) Freitag, M.; Martin, Y.; Misewich, J. A.; Martel, R.; Avouris, Ph. Nano Lett. 2003, 3, 1067-1071. (12) Duan, X.; Huang, Y.; Agarwal, R.; Lieber, C. M. Nature 2003, 421, 241-245. (13) Wang, J.; Gudiksen, M. S.; Duan, X.; Cui, Y.; Lieber, C. M. Science 2001, 293, 1455-1457. (14) Huang, M. H.; Mao, S.; Feick, H.; Yan, H.; Wu, Y.; Kind, H.; Weber, E.; Russo, R.; Yang P. Science 2001, 292, 1897-1899. (15) Johnson, J. C.; Choi, H.-J.; Knutsen, K. P.; Schaller, R. D.; Yang, P.; Saykally, R. J. Nature Mater. 2002, 1, 106-110. (16) Bjo¨rk, M. T.; Ohlsson, B. J.; Sass, T.; Persson, A. I.; Therlander, C.; Magnusson, M. H.; Deppert, K.; Wallenberg, L. R.; Samuelson, L. Appl. Phys. Lett. 2002, 80, 1058-1060. (17) Lauret, J.-S.; Voisin, C.; Cassabois, G.; Delalande, C.; Roussignol, Ph.; Jost, O.; Capes L. Phys. ReV. Lett. 2003, 90, 057404. (18) Set, S. Y.; Yaguchi, H.; Tanaka, Y.; Jablonski, M.; Sakakibara, Y.; Rozhin, A.; Tokumoto, M.; Kataura, H.; Achiba, Y.; Kikuchi, K. Mode-locked fiber lasers based on a saturable absorber incorporating carbon nanotubes, post-deadline paper 16D44-1 presented at the Optical Fiber Communications Conference sponsored by the Optical Society of America, Atlanta, Georgia, 23-28 March 2003. (19) Ichida, M.; Hamanaka, Y.; Kataura, H.; Achiba, Y.; Nakamura, A. Physica B 2002, 323, 237. (20) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H.-J.; Bawendi, M. G. Science 2002, 290, 314-317. (21) Handbook of Semiconductor Lasers and Photonic Integrated Circuits; Suematsu, Y., Adams, A. R., Eds.; Chapman and Hall: London, UK, 1994, 96-260. (22) Hertel, T.; Fasel, R.; Moos, G. Appl. Phys. A 2002, 75, 449-465. (23) Riggs, J. E.; Walker, D. B.; Carroll, D. L.; Sun Y.-P J. Phys. Chem. B 2000, 104, 7071-7076. (24) Vivien, L.; Riehl, D.; Delouis, J.-F.; Delaire, J. A.; Hache, F.; Anglaret, E. J. Opt. Soc. Am. B 2002, 19, 208-214. (25) Strano, M. S.; Huffman, C. B.; Moore, V. C.; O’Connell, M. J.; Haroz, E. H.; Hubbard, J.; Miller, M.; Rialon, K.; Kittrell, C.; Ramesh, S.; Hauge, R. H.; Smalley, R. E. J. Phys. Chem. B 2003, 107, 69796985. (26) Dresselhaus, M. S.; Dresselhaus, G.; Jorio, A.; Souza Filho, A. G.; Saito, R. Carbon 2002, 40, 2043-2061. (27) Rafailov, P. M.; Jantoljak, H.; Thomsen, C. Phys. ReV. B 2000, 61, 16179. (28) The Lorentzian fit was determined by least-squares fitting of the relative probe modulation measured at the three different probe energies for pump intensities between 2 and 5 W cm-2. Errors in the two reported fit parameters (the spectral shift and the spectral full-width at half-maximum) were determined by analyzing the extremes of all possible Lorentzian curves passing less than two standard deviations from the mean (in both dimensions) for each probe energy. (29) Verdeyen, J. T. Laser Electronics; Holonyak, N., Jr., Ed.; Prentice Hall Series in Solid State Physical Electronics; Prentice Hall: Englewood Cliffs, NJ, 2001. (30) Saleh, B. E. A.; Teich, M. C. Fundamentals of Photonics; Goodman, J. W.; Ed.; Wiley Series in Pure and Applied Optics; Wiley: New York, NY, 1991.
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