One can see that, as is explained in the PRL article, the phase shift is not a complete polarity reversal (the lowest frequencies are not reversed.)
The field shown is the E-field component normal to the viewing plane, in a central cross-section of a 3D simulation. The mirror (on the right) is simply the discretized approximation of a rotationally symmetric parabolic shape. Its shape can clearly be seen at the moment the signal is reflected.
The simulation was done on an FDTD grid with size:
space*time = 80*80*80 * 200. Absorbing boundaries
are present (Berenger's technique) consisting of the
outermost 10 cells. The code that computed it is in
the following files:
After that, the freeware tool
was used, with the command:
gifsicle -l -d 25 ?.gif ??.gif ???.gif > gouy.gif
to combine the separate pictures into a movie.
For more FDTD results see Half-wave dipole