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Optics and Spectroscopy

Modulation instability of homogeneous resonant excitation regimes of molecular J aggregates

Nikolay A. Veretenov, Leonid A. Nesterov, Nikolay N. Rosanov, Sergey V. Fedorov

Published Aug 1, 2014• 1 citation
Publisher

Abstract

We have performed a linear analysis of the stability of stationary states of homogeneous resonant excitation regimes of molecular J aggregates with coherent sustaining radiation. In the analysis, we have taken into account not only two-particle but also three-particle interactions of molecules, which are related to the exciton-exciton annihilation mechanism. Our detailed investigation of the stability of stationary states has allowed us to determine stability and instability regions and correlate them with the existence of bistability boundaries.

DOI
10.1134/s0030400x14080256

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We have performed a linear analysis of the stability of stationary states of homogeneous resonant excitation regimes of molecular J aggregates with coherent sustaining radiation. In the analysis, we have taken into account not only two-particle but also three-particle interactions of molecules, which are related to the exciton-exciton annihilation mechanism. Our detailed investigation of the stability of stationary states has allowed us to determine stability and instability regions and correlate them with the existence of bistability boundaries.
The paper deals with generalization of investigation materials performed by the authors in recent years and analysis of obtained results. The subject of the paper is accounting of many-particle interactions in molecular J-aggregates at their resonance excitation by laser radiation. In this case, not only twin interactions are taken into considerations, but also the interactions of a given particle with three and more particles simultaneously. Three basic directions can be denoted among carried out investigations. The first direction is connected with derivation (from the first principles) of motion equations for molecular of J-aggregates in view of many-particle interactions, and also twin correlations between particles. The derivation of equations from the first principles leads in general to the system of coupled equations for the means of products of n operators relating to n different molecules. Since n increases in every following equation, the problems arise, connected with uncoupling of this system and also factorization of the means with the highest n. The most difficult and complicated problem in this process is correct calculation of relaxed terms, arising due to exciton-exciton annihilation. The first direction is connected concretely with solution of all above mentioned problems. Within the second direction the study of bistability has been carried out on the basis of obtained equations, in view of three-particle interactions. Meanwhile primary attention has been concentrated on analysis of homogeneous regimes in J-aggregates. It has been shown, in particular, that accounting of many-particle contributions leads to the shift of bistability boundary into region of smaller constants of exciton-exciton annihilation. And, at last, the third direction of investigations is connected with analysis of modulation instability for stationary states of J-aggregates considered earlier at bistability study. The study of stability region boundaries and their correlation with boundaries of bistability regions has been carried out. Obtained results give the possibility to determine more rigorously the parameters region, where nonlinear effects can be observed. They can be used for development of optical logic devices and, in particular, molecular memory circuits.
Using a model of a homogeneous chain of molecules, we have analyzed bistability in resonantly excited J aggregates taking into account three-particle contributions to the exciton-exciton annihilation. These contributions, which have an interference nature, have previously been calculated in a work by B.N. Levinsky, L.A. Nesterov, B.D. Fainberg, and N.N. Rosanov (Opt. Spectrosc. 115 (3), 406 (2013)) in the course of derivation of equations of motion for J aggregates from first principles. Factorization of expectation values that correspond to these contributions leads to a closed system of equations in which not only pair, but also triple, interactions between molecules of the chain are taken into account. Numerical calculations have been performed, and their results have been compared with those obtained in calculations without taking into account three-particle contributions. We have shown that, on the whole, the inclusion of three-particle interference contributions in equations of motion leads to a restriction of the domain of existence of hysteresis. This, in turn, makes it possible to more reliably single out a real range of parameters in which nonlinear optical effects can considerably manifest themselves.
The interaction of laser radiation with single J aggregates of cyanine dyes is theoretically analyzed and numerically simulated. The quantum-mechanical calculations of the equilibrium geometry and the energies and intensities of the lowest singlet electronic transitions in pseudoisocyanine chloride and its linear (chain) oligomers are fulfilled. The data of these calculations can serve as parameters of the analyzed model of interaction of J aggregates with radiation in the one-particle density matrix approximation. This model takes into account relaxation processes, the annihilation of excitations at neighboring molecules, and inhomogeneous broadening. Assuming that the inhomogeneous broadening is absent, calculations demonstrate the existence of spatial bistability, molecular switching waves, and dissipative solitons. The effect of the inhomogeneous broadening and the radiation intensity on the effective coherence length in linear (chain) J aggregates is analyzed.
A theory of resonant interaction with radiation of J aggregates based on chains of two-level molecules coupled by the retarded dipole‒dipole interaction has been developed. The effect of pair correlations between the chain molecules on the bistable response of this system under the influence of external resonant radiation has been investigated within the homogeneous chain model. Traditionally, these systems have been described using single-particle density matrices corresponding to each molecule. In this description, twoparticle interactions are represented in the factorized form and do not include correlations between the interacting molecules. In this study, the correlation corrections have been estimated taking into account the influence of only the nearest neighbors, while their values have found to be of the same order of magnitude as the factorized two-particle expectation values for which these corrections have been calculated. As a result, the dipole‒dipole interaction of a particular molecule with the nearest neighbors is so strong that the description of this interaction in the factorized form becomes inappropriate and can be used only for a qualitative analysis of the response of the chain. In order to obtain correct quantitative characteristics, it is necessary to abandon the factorization of the two-particle expectation values, at least for nearest neighbors.
We generalize our recent work on the optical bistability of thin films of molecular aggregates [J. A. Klugkist et al., J. Chem. Phys. 127, 164705 (2007)] by accounting for the optical transitions from the one-exciton manifold to the two-exciton manifold as well as the exciton-exciton annihilation of the two-exciton states via a high-lying molecular vibronic term. We also include the relaxation from the vibronic level back to both the one-exciton manifold and the ground state. By selecting the dominant optical transitions between the ground state, the one-exciton manifold, and the two-exciton manifold, we reduce the problem to four levels, enabling us to describe the nonlinear optical response of the film. The one- and two-exciton states are obtained by diagonalizing a Frenkel Hamiltonian with an uncorrelated on-site (diagonal) disorder. The optical dynamics is described by means of the density matrix equations coupled to the electromagnetic field in the film. We show that the one- to two-exciton transitions followed by a fast exciton-exciton annihilation promote the occurrence of bistability and reduce the switching intensity. We provide estimates of pertinent parameters for actual materials and conclude that the effect can be realized.