Optically excited single-walled carbon nanotube exciton dynamics are predicted using a stochastic model including
linear and nonlinear decay pathways. Results are fitted to the photoluminescence behavior of a single 4-μm long airsuspended
(9,8) single-walled carbon nanotube. Hard photoluminescence saturation is observed even with only a few
excitons are present in the single-walled carbon nanotube. The absorption coefficient is estimated to be 0.01 - 0.04, and
photoluminescence quantum efficiency is 13%. Femtosecond excitation correlation spectroscopy dynamics are consistent
with linear and nonlinear (exciton-exciton annihilation) lifetimes of 80 ps and 0.8 ps respectively.