  An optical pulse asymptotically reaching zero group velocity in tapered
waveguides can ultimately stop at a certain position in the taper accompanied
by a strong spatial compression. This phenomenon can be also observed in
spatio-temporal systems where the pulse velocity asymptotically reaches the
velocity of a tapered front. The first system is well known from tapered
plasmonic waveguides where adiabatic nano-focusing of light is observed. Its
counterpart in the spatio-temporal system is the optical push broom effect
where a nonlinear front collects and compresses the signal. Here, we use the
slowly-varying envelope approximation to describe such systems. We demonstrate
an analytical solution for the linear taper and the piecewise linear dispersion
and show that the solution in this case resembles that of an optical lens in
paraxial approximation. In particular, the spatial distribution of the focused
light represents the Fourier transform of the signal at the input.
