  We study the excitonic coupling and homogeneous spectral line width of brick
layer J-aggregate films. We begin by analysing the structural information
revealed by the two-exciton states probed in two-dimensional spectra. Our first
main result is that the relation between the excitonic couplings and the
spectral shift in a two-dimensional structure is different (larger shift for
the same nearest neighbour coupling) from that in a one-dimensional structure,
which leads to an estimation of dipolar coupling in two-dimensional lattices.
We next investigate the mechanisms of homogeneous broadening - population
relaxation and pure dephasing - and evaluate their relative importance in
linear and two-dimensional aggregates. Our second main result is that pure
dephasing dominates the line width in two-dimensional systems up to a crossover
temperature, which explains the linear temperature dependence of the
homogeneous line width. This is directly related to the decreased density of
states at the band edge when compared with linear aggregates, thus reducing the
contribution of population relaxation to dephasing. Pump-probe experiments are
suggested to directly measure the lifetime of the bright state and can
therefore support the proposed model.
