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Journal of Luminescence

Optical absorption of molecular aggregates with colored noise

Martijn Wubs, Jasper Knoester

Published Feb 1, 1998• 12 citations
Publisher

Abstract

We study the optical absorption line shape for molecular aggregates in which the effect of the environment is modeled by a stochastic fluctuation of the molecular transition frequencies. We argue that exchange narrowing of this disorder is not only possible in the static limit, but also in the fast-fluctuation limit. The latter is further investigated using numerical calculations for dichotomic noise.

DOI
10.1016/s0022-2313(97)00156-7

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We study the optical absorption line shape for molecular aggregates in which the effect of the environment is modeled by a stochastic fluctuation of the molecular transition frequencies. We argue that exchange narrowing of this disorder is not only possible in the static limit, but also in the fast-fluctuation limit. The latter is further investigated using numerical calculations for dichotomic noise.
We investigate the third-order nonlinear-optical susceptibility ${\ensuremath{\chi}}^{(3)}$ 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 ${\ensuremath{\chi}}^{(3)}$, derived using Liouville-space Green-function techniques, contains contributions from excitons as well as biexcitons. The scaling of ${\ensuremath{\chi}}^{(3)}$ with aggregate size and its dependence on the laser detuning and homogeneous and inhomogeneous dephasing rates are analyzed. ${\ensuremath{\chi}}^{(3)}$ contains terms that scale as \ensuremath{\sim}N2{N}^{2}N2 and \ensuremath{\sim}N(N-1). However, under off-resonant conditions these terms interfere destructively, resulting in a linear \ensuremath{\sim}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.
The performance of approximate theories for the collective nonlinear optical response of assemblies of interacting molecules is investigated by comparing their predictions to exact calculations. To this end, the nonlinear absorption coefficient of linear molecular aggregates with energetic disorder is studied with the aid of Monte Carlo simulations. It is shown that the well-known local-field approximation (LFA) cannot describe the near-resonance nonlinear absorption spectrum for disorder values up to the nearest-neighbor intermolecular interactions; surprisingly, it is found that the validity of the LFA does not at all improve with growing disorder. By contrast, the ``excitonic two-level system'' approximation, in which each collective one-photon transition (Frenkel exciton) of the assembly is treated as an independent two-level system, turns out to describe the collective nonlinear response of the aggregates in a much better way and, moreover, rapidly improves for growing disorder values. It is shown that both models correctly describe the linear optical response and that, within the framework of the LFA, a close connection exists between the rotating-wave approximation and the Heitler-London approximation.
Signatures of chemical exchange and spectral diffusion in 2D photon-echo line shapes of molecular aggregates are studied using model calculations for a dimer whose Hamiltonian parameters are stochastically modulated. Cross peaks induced by chemical exchange and by exciton transport have different dynamics and distinguish two models which have the same absorption spectrum (a two-state jump bath modulation model of a dimer and a four-state jump bath model of a single chromophore). Slow Gaussian-Markovian spectral diffusion of a symmetric dimer induces new peaks which are damped as the dipole moment is equilibrated. These effects require an explicit treatment of the bath and may not be described by lower-level theories such as the Redfield equations, which eliminate the bath.
Using a reduced equation of motion for the density matrix which accounts for spontaneous emission and superradiance, we analyze the fluorescence and transient grating (TG) decays from a dilute, optically thin distribution of molecular aggregates. We find that the fluorescence is a limited form of superradiance, where cooperativity is restricted to the number N of two level systems which make up the aggregate. The dependence of the linear aggregate decay rate on the amount of inhomogeneous broadening, which is randomly distributed according to Gaussian line shape of width (1/e)2σ, is calculated. It is shown that σ must be comparable in magnitude to the nearest neighbor dipole–dipole coupling V and not the superradiant decay rate, in order to quench the superradiance.
The line shapes of saturation spectroscopy in optically thick two-level media are calculated for atomic and molecular transitions. Line narrowing and distortion effects due to propagation are presented. For Doppler-broadened media it is shown that, due to multiphoton processes, the natural linewidth limits the ultimate narrowing that can be reached. Thus, up to ${\ensuremath{\alpha}}_{0}L=20,$ only when the rate-equation approximation is valid subhomogeneous linewidths are expected.