Polarization-dependent coherent phonon spectroscopy of single-walled carbon nanotubes*

To extend our previous studies\footnote{Nano Lett.~{\bf 6}, 2696 (2006); Phys.~Rev.~Lett.~{\bf 102}, 037402 (2009); Phys.~Rev.~B {\bf 79}, 205434 (2009).} of coherent phonon (CP) dymaincs in single-walled carbon nanotubes (SWNTs), we investigate the polarization anisotropy of the radial breathing mode (RBM) in highly-aligned SWNTs. We measure RBM CPs as a function of both the angle between the tube axis and the pump polarization ($\theta_1$) and the angle between the pump and probe polarizations ($\theta_2$), observing complete quenching of the RBM when $\theta_1$ = 90$^\circ$. We simulate CP dynamics varying both $\theta_1$ and $\theta_2$ and find that the CP signal decreases as $\theta_1$ goes from 0$^\circ$ (parallel to the tube) to 90$^\circ$. We compare theory with experiment for RBM CPs created by pumping at the $E_{44}$ optical transition in an ensemble of SWNTs with a diameter distribution centered around 3~nm.