Trajectory engineering of Airy–Talbot effect via dynamic linear potential

Abstract

We demonstrate, both theoretically and numerically, the efficient trajectory manipulation of the Airy–Talbot effect in dynamic linear potentials. Exact solutions of this accelerating self-imaging phenomenon, designed by adding shifted copies of the fundamental accelerating beam with arbitrary coefficients, are derived. It is shown that the Airy–Talbot effect can follow a predefined trajectory by engineering the index gradient, while its Talbot length is the same as that in free space. The generalization to a higher dimension is also discussed.