Nonlinear optics of conjugated polymers: A coupled exciton-phonon-gas approach

Conjugated polymers are modeled as a system of one-dimensional pi electrons interacting via a short-range Coulomb interaction and coupled to an underlying harmonic lattice, i.e., as an extended Peierls-Hubbard model. A perturbative bosonization procedure is employed to map the original Hamiltonian onto an effective one describing a coupled, one-dimensional exciton-phonon gas (EPG), which should be especially useful in discussing nonlinear optics. This approach treats excitons as ideal Bose (quasi)particles subject to effective interactions, which in turn are the microscopic origin of the nonlinear optics response of the material. In particular, we derive effective interaction vertices for (i) exciton-exciton scattering, (ii) exciton-phonon coupling, and (iii) (nonlinear) exciton-light coupling within a semiclassical approximation. As an application of the EPG model to nonlinear optics of conjugated polymers, we study, in the collisionless regime, the steady state response of a coherently pumped EPG with respect to a spectrally broad test laser. The EPG approach discusses this particular four-wave-mixing experiment in terms of an externally driven, interacting two-component Bose gas. It explains optical Stark effects and inverse Raman scattering as due to composite excitations whose electronic and phononic degrees of freedom depend upon pump frequency and pump intensity.