Cross-polarized optical absorption of single-walled nanotubes by polarized photoluminescence excitation spectroscopy

Cross-polarized absorption peaks of isolated single-walled carbon nanotubes (SWNTs) were observed by polarized photoluminescence excitation (PLE) spectroscopy. Using a simple theory for PL anisotropy, the observed PLE spectra are decomposed into ``pure'' components of the photoexcitation for incident light polarized parallel and perpendicular to the SWNT axis. For several $(n,m)$ SWNTs, distinct peaks corresponding to perpendicular excitation were observed. The measured transition energies for perpendicular excitations were blueshifted compared to the qualitative values predicted within a single-particle theory. The results indicate a smaller exciton binding energy for perpendicular excitations than for parallel excitations.