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...

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