  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.
