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Physical Review A

Mirrorless optical bistability of linear molecular aggregates

Victor A Malyshev, Pablo Moreno

Published Jan 1, 1996• 71 citations
Publisher

Abstract

The bistable response of linear molecular aggregates modeled as linear chains of two-level systems is shown. We carry out analytical and numerical calculations of the aggregate population by means of the system of coupled nonlinear equations for the density matrices of individual molecules. Our conclusion is that bistable behavior of the population results from the dependence of resonance frequency of the aggregate on the number of excited molecules. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.416

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arXiv:0712.2354•The Journal of Chemical Physics•Feb 27, 2008•10 citations
The bistable response of linear molecular aggregates modeled as linear chains of two-level systems is shown. We carry out analytical and numerical calculations of the aggregate population by means of the system of coupled nonlinear equations for the density matrices of individual molecules. Our conclusion is that bistable behavior of the population results from the dependence of resonance frequency of the aggregate on the number of excited molecules. \textcopyright{} 1996 The American Physical Society.
Abstract The possibility of mirrorless optical bistability in molecular aggregates with dipole–dipole interaction was studied theoretically. Dimers and ordered layers of the Langmuir–Blodgett type or J‐aggregates consisting of identical polyatomic fluorescent molecules were chosen as molecular aggregate models. The investigation was carried out on the basis of the Bogolubov equation chain for the density matrix of molecular aggregates and its components. It is shown that the fluorescence intensity and absorption ability are described by bistable and hysteresislike behaviour when the parameters of the molecular aggregate and pumping radiation are chosen suitably. An analysis of the bistability mechanism in such aggregates is given. Possibilities of controlling one light beam by another and switching polychromatic light flow by using a bistable device based on molecular aggregates are discussed.
A numerical study of the optical bistable response of an open linear Frenkel chain of three-level molecules is carried out, making use of the one-molecule density-matrix approach. We analyze the joint effect of the presence of boundaries and of the exciton-exciton annihilation on the bistable behavior of a chain. The former is going to destroy such behavior due to the spatial inhomogeneity of the population growing with time. The latter resists a preferable creation of the population at a certain segment of the chain stabilizing the system and, thus, provides the conditions for bistability to be realized.
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.
A theoretical study of transmittivity of an ultrathin film (of thickness smaller than an optical wavelength) consisting of oriented linear aggregates is carried out. We show that within a certain domain of the incident field amplitude, optical transitions of a single disordered aggregate, the eigenstates of which are represented by the Frenkel exciton states, can be treated in the framework of a two-level approximation. This allows us to claim that an ensemble of linear aggregates is analogous to that comprised of inhomogeneously broadened two-level systems. Based on this analogy, we show that the transmittivity of the film can manifest a bistable behavior originating from the coupling of the aggregates via the emission (far-zone) field. This mechanism of bistability differs from that occurring in a single perfect aggregate. In the latter case, bistability results from the population-dependent resonance frequency shift of an individual aggregate, originating from the coupling of the molecules via the dipole–dipole (near-zone) field. Estimates of the driving parameters show that real candidates, to realize the type of behavior we found, are such well-studied objects as J-aggregates of polymethine dyes or thin films of thiophene oligomers.
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.