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Using a density matrix formalism we derive a general expression for the resonant response of an ensemble of molecular aggregates to two optical pulses. The aggregates, which can be of arbitrary geometry, are described by a Frenkel exciton Hamiltonian including exciton–exciton interactions. A hierarchy of resonant coherent transient signals is generated having wave vectors sk1+(1-s)k2, where ki is the wave vector of the ith pulse and s is an integer. General expressions for the differential pump–probe absorption spectrum D(ω;tD) (s=0) and the photon echo Iecho(tD) (s=-1) are presented for arbitrary pulse intensities. Applications are made to a linear chain of interacting Frenkel excitons with nearest neighbor exciton–exciton interaction A and exciton transfer J. Analytical expressions for D(ω;tD) and Iecho(tD) are obtained which are valid to third order in the aggregate-field interaction. The influence of the optically active red (blue) biexciton which detaches from the bottom (top) of the two-exciton band when A<-2|J| (A>=2|J|) is investigated. Biexcitons appear as extra peaks in D(ω;tD) and as oscillations in Iecho(tD). Finite size effects are responsible for quantum beat oscillations in D(ω;tD) and long time oscillations in the echo decay. Quantum beats arise predominantly from the difference between the lowest one-exciton frequencies. Our theory successfully describes the salient spectral features in the pump–probe spectra of J-aggregates. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Studies spontaneous emission and absorption in an aggregate of pi-conjugated oligomers. Aggregate Hamiltonian; Aggregate-field interaction Hamiltonian; Evaluation of absorption spectra for aggregates; Radiative emission; Radiative decay in an isolated oligomer; Radiative decay in aggregates.