Scaling of Fluorescence Stokes Shift and Superradiance Coherence Size in Disordered Molecular Aggregates

Fluorescence line shapes and cooperative spontaneous emission in disordered one-dimensional molecular aggregates are calculated using closed expressions derived by applying the method of optimal fluctuation. A simple scaling relation L s ∼ ω s -1/2 is established between the low temperature disorder-induced Stokes shift ω s and the superradiance enhancement factor L s . Scaling of the Stokes shift with aggregate size, and the time-dependent Stokes shift are discussed as well. Excellent agreement is obtained with numerical simulations.