Multiple-photon absorption and saturation in Frenkel-exciton chains

Numerical and analytical nonperturbative approaches to calculating the steady-state nonlinear optical response of small Frenkel-exciton chains are developed. In the strong-field limit the nonlinear response is due largely to the multiexciton states, which are directly obtained for a generally disordered Frenkel chain using the fermion transformation. A nonperturbative calculation of multiphoton saturation near the exciton band edge using a basis set which includes n-exciton (or n-fermion) states up to and including n=5 is presented. In the limit of pure radiative damping, the saturation intensity for n-photon absorption is found to scale as (N+1${)}^{6/\mathit{n}\mathrm{-}5}$, where N is the number of two-level molecules in the chain. In the perturbative limit the rate at which photons are absorbed scales as (N+1${)}^{5\left(\mathit{n}\mathrm{-}1\right)}$. This remarkably strong size dependence for n>1 is caused by both cooperative and resonance effects.