  Spatiotemporal control over the intensity of a laser pulse has the potential
to enable or revolutionize a wide range of laser-based applications that
currently suffer from the poor flexibility offered by conventional optics.
Specifically, these optics limit the region of high intensity to the Rayleigh
range and provide little to no control over the trajectory of the peak
intensity. Here, we introduce a nonlinear technique for spatiotemporal control,
the "self-flying focus," that produces an arbitrary trajectory intensity peak
that can be sustained for distances comparable to the focal length. The
technique combines temporal pulse shaping and the inherent nonlinearity of a
medium to customize the time and location at which each temporal slice within
the pulse comes to its focus. As an example of its utility, simulations show
that the self-flying focus can form a highly uniform, meter-scale plasma
suitable for advanced plasma-based accelerators.
