Abstract:

We introduce two-dimensional (2D) linear and nonlinear Talbot eects. They are produced by propagating periodic 2D diraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot eect originates from 2D rogue waves and forms in a bulk 3D nonlinear
medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a  phase shift; no other recurrences are observed. Dierent from the nonlinear Talbot eect, the linear eect displays the usual fractional Talbot images as well. We also
nd that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the eect. We also nd that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot eect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot eect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue wave initial condition is sucient but not necessary for the observation of the eect. It may also be observed from other periodic inputs, provided they are set on a nite background. The 2D eect may nd utility in the production of 3D photonic crystals.