  An analytical expression is obtained for the biexciton binding energy as a
function of the inter-exciton distance and binding energy of constituent
quasi-one-dimensional excitons in carbon nanotubes. This allows one to trace
biexciton energy variation and relevant non-linear absorption under external
conditions whereby the exciton binding energy varies. The non-linear absorption
lineshapes calculated exhibit characteristic asymmetric (Rabi) splitting as the
exciton energy is tuned to the nearest interband plasmon resonance. These
results are useful for tunable optoelectronic device applications of optically
excited semiconducting carbon nanotubes, including the strong excitation regime
with optical non-linearities.
