Two-dimensional linear and nonlinear Talbot effect from rogue waves

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, th...

Nonlinear Talbot effect.

We propose and experimentally demonstrate the nonlinear Talbot effect from nonlinear photonic crystals. The nonlinear Talbot effect results from self-imaging of the generated periodic intensity pattern at the output surface of the crystal. To illustrate the effect, we experimentally observed second-harmonic Talbot self-imaging from 1D and 2D periodically poled LiTaO(3) crystals. Both integer an...

Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability

The Talbot Effect for two-dimensional massless Dirac fermions

A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theor...

Theory of nonlinear Talbot effect

The nonlinear Talbot effect, in which self-images are formed by generated parametric light from the nonlinear optical process, is presented in this paper. The comparison is made between the conventional Talbot effect and the newly observed nonlinear case. The essence of such nonlinear self-images is provided and future work on this effect is also discussed. The conceptional extension achieved h...