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Physical Review A

Optical bistable response of an open linear Frenkel chain: Exciton-exciton annihilation and boundary effects

Victor A Malyshev, H. Glaeske, K.‐H. Feller

Published Jul 1, 1998• 25 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.58.670

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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.
We theoretically analyze the optical response from an ultrathin film built up of oriented molecular aggregates, the operating states of which are represented by Frenkel exciton states. A four-level model, involving transitions between the ground, one-exciton and two-exciton states, exciton-exciton annihilation from the two-exciton state as well as relaxation from the annihilation level back to the one-exciton and ground states, is used for describing the film optical response. It is proved that the exciton-exciton annihilation may act not as a destructive but, on the contrary, as a constructive factor tending towards the occurrence of bistability. In particular, the effect of inhomogeneous broadening of the exciton optical transition, preventing the bistable behavior, may be suppressed considerably due to a fast exciton-exciton annihilation.
We perform a theoretical study of the nonlinear optical response of an ultrathin film consisting of oriented linear aggregates. A single aggregate is described by a Frenkel exciton Hamiltonian with uncorrelated on-site disorder. The exciton wave functions and energies are found exactly by numerically diagonalizing the Hamiltonian. The principal restriction we impose is that only the optical transitions between the ground state and optically dominant states of the one-exciton manifold are considered, whereas transitions to other states, including those of higher exciton manifolds, are neglected. The optical dynamics of the system is treated within the framework of truncated optical Maxwell-Bloch equations, in which the electric polarization is calculated by using a joint distribution of the transition frequency and the transition dipole moment of the optically dominant states. This function contains all the statistical information about these two quantities that govern the optical response and is obtained numerically by sampling many disorder realizations. We derive a steady-state equation that establishes a relationship between the output and input intensities of the electric field and show that within a certain range of the parameter space this equation exhibits a three-valued solution for the output field. A time-domain analysis is employed to investigate the stability of different branches of the three-valued solutions and to get insight into switching times. We discuss the possibility to experimentally verify the bistable behavior.
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.
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.
A numerical study of reflectivity and transmittivity of an ensemble of short oriented linear Frenkel chains, which forms a thin film with a thickness of the order of an optical wavelength, is carried out. The eigenstates of a single chain are considered to be of a collective (excitonic) origin. A distribution of chains over lengths resulting in inhomogeneous broadening of the exciton optical transition is taken into account. We report a bistable behavior of both reflectivity and transmittivity of the film in a spectral domain close to the exciton resonance, caused by saturation of the nonlinear refraction index. Estimates of driving parameters show that thin films of oriented J-aggregates of polymethine dyes deposited on a dielectric substrate seem to be a suitable object for observation of the predicted behavior.