Four-level `essential states' model of an optical nonlinearity in π-conjugated polymers

It is shown that the theoretical description of optical nonlinearity in π-conjugated polymers must necessarily include both the on-site and intersite electron correlations. In spite of the infinite number of states that, in principle, contribute to the third-order optical nonlinearity in long chains, it is shown that only three dominant nonlinear optical channels, involving four `essential states', determine the bulk of the optical nonlinearity. A universality in one dimension is pointed out. The relative locations and natures of these four essential states are practically independent of the Coulomb interactions. In ideal isolated strands, third-harmonic generation experiments should find two three-photon resonances, and not merely one, as has been generally assumed. In systems with strong interchain interactions, band formation can lead to overlaps between the long wavelength three-photon resonance and a two-photon resonance. Two-photon resonances other than the one due to the essential two-photon excited state will have vanishingly weak intensities due to cancellations between nonlinear optical channels with opposite signs.