  Characterizing ultrashort optical pulses has always been a critical but
difficult task, which has a broad range of applications. We propose and
demonstrate a self-referenced method of characterizing ultrafast pulses with a
multimode fiber. The linear and nonlinear speckle patterns formed at the distal
end of a multimode fiber are used to recover the spectral amplitude and phase
of an unknown pulse. We deploy a deep learning algorithm for phase recovery.
The diversity of spatial and spectral modes in a multimode fiber removes any
ambiguity in the sign of the recovered spectral phase. Our technique allows for
single-shot pulse characterization in a simple experimental setup. This work
reveals the potential of multimode fibers as a versatile and multi-functional
platform for optical sensing.
