Nonlinear optical response of conjugated polymers: Electron-hole anharmonic-oscillator picture

A nonlinear optical response of conjugated polymers is calculated using an electron-hole (exciton) representation. Equations of motion are derived which map the calculation of ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ onto the dynamics of N(2N-1) nonlocal coupled anharmonic oscillators representing electrons and holes, N being the number of double bonds. The scaling of the static ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ with size and Coulomb interactions is shown to be directly correlated with the exciton coherence size associated with the relative electron-hole motion.