Interaction between spatiotemporal collinear self-decelerating Airy elegant-Laguerre-Gaussian wave packets in free space

Based on the (3+1)-dimensional free-space Schrödinger equation, the analytical solutions to the equation for the propagating properties of two three-dimensional collinear self-decelerating Airy-elegant-Laguerre-Gaussian(AELG) light beams in free space are investigated. The different mode numbers, the mode index for each of the collinear beams, weight factor of combined beam, and initial phase difference will affect the profiles of the wave packets, and thus giving the method to control the spatiotemporal profiles during propagation. The spatiotemporal profiles will rotate if none of the mode parameters are equal to zero, and there are vortices in the center of the phase distribution curve. If the mode parameters are positive numbers, the profiles of the beams will rotate in a helical clockwise direction. Otherwise, if the mode parameters are negative numbers,they will rotate in a helical anticlockwise direction during propagation. The wave packets will also rotate when the relative phase is varied. However, the rotation principles of these two rotation characteristics are completely different. The spatiotemporal hollow self-decelerating AELG wave packets can be attained if the mode numbers of the collinear AiELG wave packets are the same. Multi-ring structure evolves into single-ring structure along radial direction with their propagation distance increasing during propagation, which makes the hollow part expand continuously.