  As a new degree of freedom for optical manipulation, recently spatiotemporal
optical vortices (STOVs) carrying transverse orbital angular momentums have
been experimentally demonstrated with pulse shapers. Here a spatiotemporal
differentiator is proposed to generate STOVs with transverse orbital angular
momentum. In order to create phase singularity in the spatiotemporal domain,
the spatiotemporal differentiator is designed by breaking spatial mirror
symmetry. In contrast to pulse shapers, the device proposed here is a simple
one-dimensional periodic nanostructure and thus it is much more compact. For a
normal incident pulse, the differentiator generates a transmitted STOV pulse
with transverse orbital angular momentum. Furthermore, the interference of the
generated STOVs can be used to detect the sharp changes of pulse envelopes, in
both spatial and temporal dimensions.
