  Exciton effects on conjugated polymers are investigated in the soliton
lattice system. We use the Su-Schrieffer-Heeger model with long-range Coulomb
interactions treated by the single-excitation configuration-interaction method.
The soliton band is present in the Peierls gap of the doped system. There
appears a new kind of the exciton where an electron-hole pair is excited
between the soliton band and the continuum states. We find that the oscillator
strengths accumulate rapidly at this exciton as the soliton concentration
increases. The contribution from the lowest exciton is more than 90% at the 10%
doping. The third-harmonic generation (THG) at off-resonance frequencies is
calculated as functions of the soliton concentration and the chain length of
the polymer. The optical nonlinearity by the THG at the 10% doping increases by
the factor about 10^2 from that of the neutral system.
