Soliton-antisoliton configurations and the linear and nonlinear optical response of degenerate-ground-state conjugated polymers

The contributions of soliton-antisoliton (SS{}) configurations to the linear and third-order nonlinear optical response are investigated for conjugated polymers having a degenerate ground state. We treat the direct photoproduction of charged solitons as a nonlinear Franck-Condon problem and obtain analytical expressions for the linear optical susceptibility χ⁽¹⁾({ω}). With the help of the oscillator strength sum rule, we decompose the {π}-π* oscillator strength into two parts; a contribution where the final states are charged SS{} pairs and a contribution where the final states are free electron-hole pairs (as in the noninteracting rigid lattice). The linear optical coefficients calculated from χ⁽¹⁾({ω}) are in general agreement with optical data obtained from trans-polyacetylene. The results imply that approxiamtely 25% of the integrated oscillator strength of trans-polyacetylene arises from the direct photoproduction of solitons.A parallel treatment of the generalized third-order nonlinear optical susceptibility χ⁽³⁾(ω_σ) is presented, demonstrating that, for any third-order process, contributions arising from neutral SS{} pair configurations as intermediate states are one to two orders of magnitude larger than the corresponding rigid-lattice contribution. This mechanism for χ⁽³⁾ is enabled by nonlinear zero-point motion which provides a finite Franck-Condon overlap between the ground and SS{} excited state lattice wave functions. The large contribution to χ⁽³⁾ from the SS{} intermediate states results from the large transition dipole moment between the free electron-hole pair excited states of Bᵤ symmetry and the Ag symmetric neutral SS{} excited state. This enhanced transition dipole moment is a consequence of the large virtual shifts of oscillator strength associated with the localized SS{} electron-lattice configuration. The third-harmonic conversion efficiency χ⁽³⁾(3{ω}) is further enhanced by a condition unique to degenerate-ground-state systems, simultaneous two- and three-photon resonance.