Trajectory variations of optical Bloch oscillations for Airy beams in transversely and longitudinally modulated photonic lattices

We consider four types of modulated photonic lattices and numerically study the optical Bloch oscillations of Airy beams in these periodic structures. Our results demonstrate that in transversely modulated photonic lattices, the oscillation period increases and the amplitude reduces as the separation variation index increases. However, the increasing of the width variation index could lead to a consistent reduction of oscillation period and amplitude. On the other hand, in three kinds of longitudinally bent photonic lattices, the optical Bloch oscillation trajectories of Airy beams follow the waveguide shape perfectly within the whole propagation length. For another three kinds of refractive index longitudinally varied lattices, the optical Bloch oscillation period and amplitude are limited with the increasing of refractive index, contributing to the presentation of dramatically different Airy propagation trajectories. Our study proposes a new view to manipulate the Airy trajectory in periodic structures.