Self-reconstruction of wave packets due to spatio-temporal couplings

The spatio-temporal self-reconstruction of the wave function fulfilling the wale equation is examined. The effect is based on the sampling of the spatial spectrum of the wave function in the cylindrical coordinates and on its coupling to the temporal frequency spectrum. The predetermined spatiotemporal profile of the wave function is approximately reconstructed at the periodic spatial intervals along the propagation direction for the continuous temporal spectrum. The periodicity appearing in both the spatial and temporal evolutions are examined for wavefields with the discrete temporal spectrum. The reconstructed field then simultaneously exhibits propagation properties known as the self-imaging and the mode-locking.