Nonlinear susceptibilities of molecular aggregates: Enhancement ofχ(3)by size

We investigate the third-order nonlinear-optical susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ in molecular aggregates and its scaling with aggregate size. The aggregate is modeled as a collection of N-interacting, homogeneously broadened two-level systems, where the interaction includes both the static dipole-dipole coupling and superradiant coupling. Our expression for ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$, derived using Liouville-space Green-function techniques, contains contributions from excitons as well as biexcitons. The scaling of ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ with aggregate size and its dependence on the laser detuning and homogeneous and inhomogeneous dephasing rates are analyzed. ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ contains terms that scale as ∼$N^2$ and ∼N(N-1). However, under off-resonant conditions these terms interfere destructively, resulting in a linear ∼N scaling, which is precisely what is expected for N monomers. Detailed calculations of phase-conjugate degenerate four-wave mixing and pump-probe spectroscopy are performed. In the first case we predict the existence of a narrow dephasing-induced resonance superposed on the broader superradiant exciton line shape. Pump-probe spectroscopy shows a series of biexciton absorption lines, some of which are superradiantly broadened.