  Any ultrafast optical spectroscopy experiment is usually accompanied by the
necessary routine of ultrashort-pulse characterisation. The majority of pulse
characterisation approaches solve either a one-dimensional (e.g. via
interferometry) or a two-dimensional (e.g. via frequency-resolved measurements)
problem. Solution of the two-dimensional pulse-retrieval problem is generally
more consistent due to problem's over-determined nature. In contrast, the
one-dimensional pulse-retrieval problem is impossible to solve unambiguously as
ultimately imposed by the fundamental theorem of algebra. In cases where
additional constraints are involved, the one-dimensional problem may be
possible to solve, however, existing iterative algorithms lack generality, and
often stagnate for complicated pulse shapes. Here we use a deep neural network
to unambiguously solve a constrained one-dimensional pulse-retrieval problem
and show the potential of fast, reliable, and complete pulse characterisation
using interferometric cross-correlation time traces (determined by the pulses
with partial spectral overlap).
