Using pre-designed trains of femtosecond optical pulses, we have selectively excited coherent phonons of the radial breathing mode of specific-chirality single-walled carbon nanotubes within an ensemble sample. By analyzing the initial phase of the phonon oscillations, we prove that the tube diameter initially increases in response to ultrafast photoexcitation. Furthermore, from excitation profiles, we demonstrate that an excitonic absorption peak of carbon nanotubes periodically oscillates as a function of time when the tube diameter undergoes radial breathing mode oscillations.PACS numbers: 78.67. Ch,71.35.Ji, Single-walled carbon nanotubes (SWNTs), hollow onedimensional nanostructures with unique electronic, mechanical, and optical properties, come in a variety of species, or chiralities. Some of them are metallic and others semiconducting, depending on their chiral indices (n,m) [1,2,3]. This diversity, while making them such unusual nanomaterials, often makes it challenging to extract reliable parameters on chirality-dependent properties from experimental results on ensemble samples. Currently, there are world-wide efforts on SWNT purification, separation, and enrichment, producing promising results [4,5,6,7,8]. However, a standard for fabrication of these samples has yet to be established.Here, we present a novel method that allows us to study single-chirality nanotubes even though the sample contains nanotubes of many different chiralities. Specifically, we have utilized the techniques of femtosecond pulse shaping [9,10,11] in ultrafast pump-probe spectroscopy of SWNTs to selectively excite the coherent lattice vibrations [12,13] of the radial breathing mode (RBM) of specific chiralities. The excitation spectra of such coherent phonons (CPs) provide chirality-specific information on the processes of light absorption, phonon generation, and phonon-induced band structure modulations in unprecedented detail. In particular, the excitation-energy-dependence of the phase of the CP oscillations provides direct, time-domain evidence that band gap oscillations follow the diameter oscillations in the RBM coherent phonon mode.The sample studied was a micelle-suspended SWNT solution, where the SWNTs (HiPco batch HPR 104) were suspended as individuals with sodium cholate [14]. The optical setup was that of standard degenerate pumpprobe spectroscopy, but chirality selectivity was achieved by using multiple pulse trains, with a pulse-to-pulse interval corresponding to the period of a specific RBM mode. Among different species of nanotubes, those having RBM frequencies that are matched to the repetition rate of multiple pulse trains will generate large amplitude coherent oscillations with increasing oscillatory response to each pulse, while others will have diminished coherent responses [15,16,17]. The tailoring of multiple pulse trains from femtosecond pulses was achieved using the pulse-shaping technique described elsewhere [10]. Pulse trains are incident on an ensemble of nanotubes as a pump beam, and coherent RBM osc...

Using femtosecond pump-probe spectroscopy with pulse shaping techniques, one can generate and detect coherent phonons in chirality-specific semiconducting single-walled carbon nanotubes. The signals are resonantly enhanced when the pump photon energy coincides with an interband exciton resonance, and analysis of such data provides a wealth of information on the chirality-dependence of light absorption, phonon generation, and phonon-induced band structure modulations. To explain our experimental results, we have developed a microscopic theory for the generation and detection of coherent phonons in single-walled carbon nanotubes using a tight-binding model for the electronic states and a valence force field model for the phonons. We find that the coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on photoexcited carrier density. We compared our theoretical results with experimental results on mod 2 nanotubes and found that our model provides satisfactory overall trends in the relative strengths of the coherent phonon signal both within and between different mod 2 families. We also find that the coherent phonon intensities are considerably weaker in mod 1 nanotubes in comparison with mod 2 nanotubes, which is also in excellent agreement with experiment.

We have investigated the polarization dependence of the generation and detection of radial breathing mode (RBM) coherent phonons (CP) in highly-aligned single-walled carbon nanotubes. Using polarization-dependent pump-probe differential-transmission spectroscopy, we measured RBM CPs as a function of angle for two different geometries. In Type I geometry, the pump and probe polarizations were fixed, and the sample orientation was rotated, whereas, in Type II geometry, the probe polarization and sample orientation were fixed, and the pump polarization was rotated. In both geometries, we observed an almost complete quenching of the RBM CPs when the pump polarization was perpendicular to the nanotubes. For both Type I and II geometries, we have developed a microscopic theoretical model to simulate CP generation and detection as a function of polarization angle and found that the CP signal decreases as the angle goes from 0• (parallel to the tube) to 90• (perpendicular to the tube). We compare theory with experiment in detail for RBM CPs created by pumping at the E44 optical transition in an ensemble of single-walled carbon nanotubes with a diameter distribution centered around 3 nm, taking into account realistic band structure and imperfect nanotube alignment in the sample. We theoretically determined a cos 8 (θ) dependence for Type I CP spectroscopy experiments and a cos 4 (φ) polarization dependence for Type II CP spectroscopy experiments, and after including misalignment effects to our fitting, we determined the nematic order parameter of our sample to be 0.81.

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