  Highly efficient exciton-exciton annihilation process unique to
one-dimensional systems is utilized for super-resolution imaging of
air-suspended carbon nanotubes. Through the comparison of fluorescence signals
in linear and sublinear regimes at different excitation powers, we extract the
efficiency of the annihilation processes using conventional confocal
microscopy. Spatial images of the annihilation rate of the excitons have
resolution beyond the diffraction limit. We investigate excitation power
dependence of the annihilation processes by experiment and Monte Carlo
simulation, and the resolution improvement of the annihilation images can be
quantitatively explained by the superlinearity of the annihilation process. We
have also developed another method in which the cubic dependence of the
annihilation rate on exciton density is utilized to achieve further sharpening
of single nanotube images.
