Propagation of an Airy-Gaussian beam in defected photonic lattices

We investigate numerically that a finite Airy-Gaussian (AiG) beam varies its trajectory and shape in defected photonic lattices. Propagation properties and beam self-bending are controlled with modulation depth and period of photonic lattices, positive and negative defects, beam distribution factor and nonlinearities. For positive defects, the pseudo-period oscillation and localization of the AiG beam may form under a certain condition, while the beam diffuses in negative defects. Moreover, the solitons may appear during the propagation when the self-focusing nonlinearity is introduced.