  Luminescence properties of carbon nanotubes are strongly affected by exciton
diffusion, which plays an important role in various nonradiative decay
processes. Here we perform photoluminescence microscopy on hundreds of
individual air-suspended carbon nanotubes to elucidate the interplay between
exciton diffusion, end quenching, and exciton-exciton annihilation processes. A
model derived from random-walk theory as well as Monte Carlo simulations are
utilized to analyze nanotube length dependence and excitation power dependence
of emission intensity. We have obtained the values of exciton diffusion length
and absorption cross section for different chiralities, and diameter-dependent
photoluminescence quantum yield have been observed. The simulations have also
revealed the nature of a one-dimensional coalescence process, and an analytical
expression for the power dependence of emission intensity is given.
