  Exciton effects on conjugated polymers and the resulting optical
nonlinearities are investigated in soliton lattice states. We use the
Su-Schrieffer-Heeger model with long-range Coulomb interactions for electrons.
The third-harmonic generation (THG) at off-resonant frequencies is calculated
as functions of the soliton concentration and the chain length of the polymer.
The magnitude of the THG with 10 percent doping increases by the factor of
about 10^2 from that of the neutral system. The large increase of the order two
is common for several Coulomb interaction strengths, and is seen in open
systems as well as in periodic systems.
