  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 a very nearly 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 degrees (parallel to the tube) to
90 degrees (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.
