Propagations of Airy beams with quadratic phase modulation, and their interaction in paraxial optical systems

Abstract

We, both theoretically and numerically, investigate dynamic evolutions of Airy beams with quadratic phase modulation (QPM) and their interaction in paraxial optical systems, including free space, dynamic linear potential, and parabolic potential. In free space case, the beam with negative QPM will undergo deceleration and then acceleration, while positive QPM beam only accelerates. The presence of dynamic linear index potentials leads to single beam propagating along predefined trajectory and counterpropagating beams following asymmetric trajectories. The intersection points and their range are only dependent on QPM parameter. For parabolic index potentials, the beam exhibits periodic inversion of profile and periodic self-Fourier transformation. QPM causes the trajectory modulated and the energy distribution distorted, and considerably influences the intersection points. We extend our results to circular Airy beams with QPM. Beside the shape and trajectory modified, the autofocusing effect can be strengthened or weakened in negative or positive QPM case.