The Talbot Effect Of The Periodically Modulated Wave Field

It has been developed rapidly since the concept of Talbot effect comes to people's minds.The simplicity and beauty of Talbot self-imaging have attracted the interest of many researchers because of it's widely applications in the imaging technology.In the optics,if an optical grating or a periodic structure is illuminated by a coherent light,the self-imaging of the optical grating or the periodic structure periodically replicates at certain imaging planes,which is called the Talbot effect.In this paper,we consider nonlinear Schrodinger equation as theoretical research model.Firstly,analytical calculation was used to obtain the soliton solution of the nonlinear Schrodinger equation.We present the three soliton solutions on background for the nonlinear Schrodinger equation and discuss their respective localization.Based on the Akhmediev breathers,we demonstrate the Talbot effect from propagating the maximally compressed pulse train in a nonlinear media and a linear media.The results show that the periodic incident wave exactly reappears at certain distances and its half a period shifted image appears at the distances halfway in between.Secondly,based on the maximally compressed pulse train,we consider a linearly modulated continuous wave as the initial state to demonstrate the Talbot effect.The results show that the recurrence patterns of the Talbot effect can be drawn by suitably choosing the frequency modulation factor.Finally,we consider coupled nonlinear Schrodinger equation as theoretical model,numerical simulation was used to demonstrate the Talbot recurrence in PT-symmetric coupled waveguide.The results show that the PT-Symmetric Talbot revivals can also occur in the presence of nonlinearity,which is different from the Talbot effect in the linear PT-Symmetric photonic lattices.