Interaction of Airy-Gaussian beams in photonic lattices with defects

We investigate numerically the interaction between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss that the beams with different intensities and phases launch into the different lattice structures but accelerate in opposite directions. During interactions, the interference fringe, breathers, and soliton pairs are observed. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift and the beam interval. For a certain lattice period, the periodic interference fringe can form. A constructive or destructive interference can vary with the defect depth and phase shift. While the nonlinearity is introduced, the breathers is generated. Especially in the self-defocusing media, the appropriate AiG beam amplitude and lattice depth may lead to the formation of soliton pairs, On the contrary, the interaction of two Gaussian beams is diffraction.