Polarization dependence of coherent phonon generation and detection in highly-aligned single-walled carbon nanotubes

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We have investigated the polarization dependence of the generation and detection of radial breathing mode (RBM) coherent phonons (CPs) 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${}^{ˆ}$ (parallel to the tube) to 90${}^{ˆ}$ (perpendicular to the tube). We compare theory with experiment in detail for RBM CPs created by pumping at the ${E}_{44}$ 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 $\mathrm{cos}{}^{8}(\ensuremath{\theta})$ dependence for Type I CP spectroscopy experiments and a $\mathrm{cos}{}^{4}(\ensuremath{\phi})$ 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.