Figure 5

Normalized cross-Wigner real part (\(\text {Re}[{\mathscr{C}}{\mathscr{W}}]_{\Psi ,\psi _0}\)) as a function of x and k for \(t=50\) ms, \(\tau =50\) ms and \(\gamma = 0\) in (a,b), while for (c,d) we used \(\gamma = -1\). In (a,c), we consider the Gouy phase difference, and in (b,)c), we do not consider it. As for the free propagation context, the Gouy phase is crucial for providing a precise and accurate description of the cross-Wigner. We change the value of \(\gamma\) to -1, in this plot, since the phase effect is more noticeable than for the case where \(\gamma =0\) (See methods subsection Gouy phase behavior with correlation parameter bellow). We have similar results for the imaginary component.