Electron diffraction through an aperture in a potential wall

We study the diffraction of a two-dimensional Gaussian wavepacket through a rectangular aperture in a finite potential wall (one slit experiment). For wavepacket with incident wavevector k₀ satisfying the diffraction condition, k₀ = 2π/w, w being the slit width, the near field (Fresnel-like) diffraction pattern behind the slit can be clearly seen for small time duration (<0.2ps). At later time steps, the diffracted beam is fragmented into lobes (perpendicular to the direction of incidence of the wavepacket) as a result of the multiple reflections of the wavepacket inside the slit (assumed to be of finite thickness). At later time, no far-field Fraunhoffer diffraction pattern is observed in our numerical simulations.