Using numerical simulations, we investigate to what extent the pump-probe spectrum can be used as a tool to determine the exciton delocalization length in disordered molecular (J) aggregates. We compare the delocalization length obtained through heuristic arguments from the spectral separation between the bleaching and the one-to two-exciton induced absorption features in this spectrum to the delocalization length obtained from the participation ratio at the J band center. We find that up to a certain saturation length these two delocalization lengths are indeed proportional. In the case of long-pulse two-color pump-probe spectra, the slope of this linear scaling is insensitive to the pump frequency; it is sensitive to the width of the probe pulse. Beyond the saturation length, which is determined by the homogeneous line width of the exciton transitions, both the two-color and the short-pulse pump-probe spectra saturate and no longer can be used as a measure for the delocalization length. The latter applies to the B850 ring of bacterial antenna complexes.

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We study the properties of one-dimensional exciton systems in which the commonly made Heitler-London approximation ͑HLA͒ is relaxed. The nonresonant interaction terms which then exist, mix the multi-exciton bands of the HLA. Our approach is based on the exact diagonalization of the Hamiltonian, which is possible using the Jordan-Wigner and Bogoliubov transformations. Exact expressions for transition dipoles between multi-particle states are given. Results of our exact theory for the ground state and one-particle energies, the superradiant enhancement, the pump-probe spectrum, and the linear absorption to multi-particle states are compared quantitatively to the HLA, to the Bose approximation ͑where the excitons are treated as bosons͒, and to perturbation theory. In this comparative study, we use parameter values that are relevant to much studied quasi-one-dimensional J aggregates, such as PIC and TDBC. We find that for these systems the strongest effects of the HLA occur in the oscillator strengths of the various optical transitions. In particular, the exciton delocalization length derived from the experimentally observed superradiant enhancement is overestimated by roughly 10% due to the HLA. Also, the transition between the ground state and three-particle states, which is strictly forbidden in the HLA, does obtain a finite oscillator strength due to the non-resonant interactions.

Using the coherent potential approximation ͑CPA͒, we study the absorption spectra of two-dimensional molecular aggregates formed from binary random molecular mixtures. In addition to the substitutional randomness, we include Gaussian randomness in the transition frequencies within each of the two classes of molecules. The latter is motivated by the considerable disorder that is typical for two-dimensional aggregates. By comparing to exact diagonalization results for small clusters, we show that the CPA gives an excellent description of the spectra for this kind of disorder, both in the cases of amalgamation and persistence type mixing. Taking into account long-range excitation transfer interactions mediated by the extended molecular transition dipoles, we analyze experimental spectra of amalgamation-type mixed cyanine aggregates adsorbed on AgBr ͕100͖surfaces that are also reported here. We find good agreement between theory and experiment for the position, the width, and the general shape of the absorption line as a function of the mixing ratio. The analysis also allows us to estimate the slip angle characterizing the structure of these aggregates.

We study the absorption line shape caused by Frenkel excitons in one-dimensional ring-shaped molecular aggregates, such as circular light-harvesting systems, subjected to dynamic disorder with a finite correlation time. We focus on dichotomic noise and show that for arbitrary orientations of the molecular transition dipoles relative to the ring, the absorption spectrum may be calculated exactly by solving two very similar sets of 2N coupled linear equations of motion, where N is the number of molecules in the ring. These sets are a factor of N smaller than in methods developed previously, which allows us to evaluate the exact line shapes for N up to 12 and study size dependence of the spectra. Previous exact calculations were limited to hexamers (N=6). Moreover, in contrast to earlier work, we take into account long-range dipolar transfer interactions between all molecules in the ring. We find that the dipole orientation and the long-range interactions strongly affect the dependence of the spectrum on the ring size. This holds true particularly for the exchange narrowing of the linewidths in the fast-fluctuation regime.